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| 1 | +<prover> |
| 2 | + <k> |
| 3 | + .CoqSentences |
| 4 | + </k> |
| 5 | + <exit-code> |
| 6 | + 1 |
| 7 | + </exit-code> |
| 8 | + <goals> |
| 9 | + .GoalCellSet |
| 10 | + </goals> |
| 11 | + <declarations> |
| 12 | + <declaration> |
| 13 | + axiom \equals ( AndComm , \lambda { A { Term } , B { Term } , H { Term } , .Patterns } \or ( \exists { H0 , H1 , .Patterns } \and ( \equals ( H , conj ( H0 , H1 , .Patterns ) ) , conj ( H1 , H0 , .Patterns ) , .Patterns ) , .Patterns ) ) |
| 14 | + </declaration> <declaration> |
| 15 | + axiom \equals ( IF_then_else , or ( and , P , Q , .Patterns ) ( and , not , P , R , .Patterns ) ) |
| 16 | + </declaration> <declaration> |
| 17 | + axiom \equals ( iff , and ( \forall { x { Term } , .Patterns } B , .Patterns ) ( \forall { y { Term } , .Patterns } A , .Patterns ) ) |
| 18 | + </declaration> <declaration> |
| 19 | + axiom \equals ( not , \lambda { A { Term } , .Patterns } \forall { x { Term } , .Patterns } False ) |
| 20 | + </declaration> <declaration> |
| 21 | + axiom \type ( I ( .Patterns ) , True ) |
| 22 | + </declaration> <declaration> |
| 23 | + axiom \type ( S ( .Patterns ) , nat ( - , > , nat , .Patterns ) ) |
| 24 | + </declaration> <declaration> |
| 25 | + axiom \type ( Z ( .Patterns ) , nat ) |
| 26 | + </declaration> <declaration> |
| 27 | + axiom \type ( conj ( .Patterns ) , \forall { x { Term } , .Patterns } \forall { y { Term } , .Patterns } ( and ( A , B , .Patterns ) ) ) |
| 28 | + </declaration> <declaration> |
| 29 | + axiom \type ( ex_intro1 ( .Patterns ) , \forall { x { Term } , .Patterns } \forall { y { Term } , .Patterns } ( ex1 ( A , P , .Patterns ) ) ) |
| 30 | + </declaration> <declaration> |
| 31 | + axiom \type ( ex_intro2 ( .Patterns ) , \forall { x { Term } , .Patterns } \forall { y { Term } , .Patterns } ( ex2 ( P , .Patterns ) ) ) |
| 32 | + </declaration> <declaration> |
| 33 | + axiom \type ( ex_intro4 ( .Patterns ) , \forall { x { Term } , .Patterns } \forall { y { Term } , .Patterns } ( ex4 ( A , .Patterns ) ( P , .Patterns ) ) ) |
| 34 | + </declaration> <declaration> |
| 35 | + axiom \type ( or_introl ( .Patterns ) , \forall { x { Term } , .Patterns } ( or ( A , B , .Patterns ) ) ) |
| 36 | + </declaration> <declaration> |
| 37 | + axiom \type ( or_intror ( .Patterns ) , \forall { y { Term } , .Patterns } ( or ( A , B , .Patterns ) ) ) |
| 38 | + </declaration> <declaration> |
| 39 | + sort Term |
| 40 | + </declaration> <declaration> |
| 41 | + symbol AndComm ( .Sorts ) : Term |
| 42 | + </declaration> <declaration> |
| 43 | + symbol False ( .Sorts ) : Term |
| 44 | + </declaration> <declaration> |
| 45 | + symbol I ( .Sorts ) : Term |
| 46 | + </declaration> <declaration> |
| 47 | + symbol IF_then_else ( .Sorts ) : Term |
| 48 | + </declaration> <declaration> |
| 49 | + symbol S ( .Sorts ) : Term |
| 50 | + </declaration> <declaration> |
| 51 | + symbol True ( .Sorts ) : Term |
| 52 | + </declaration> <declaration> |
| 53 | + symbol Z ( .Sorts ) : Term |
| 54 | + </declaration> <declaration> |
| 55 | + symbol and ( .Sorts ) : Term |
| 56 | + </declaration> <declaration> |
| 57 | + symbol conj ( .Sorts ) : Term |
| 58 | + </declaration> <declaration> |
| 59 | + symbol ex1 ( .Sorts ) : Term |
| 60 | + </declaration> <declaration> |
| 61 | + symbol ex2 ( .Sorts ) : Term |
| 62 | + </declaration> <declaration> |
| 63 | + symbol ex4 ( .Sorts ) : Term |
| 64 | + </declaration> <declaration> |
| 65 | + symbol ex_intro1 ( .Sorts ) : Term |
| 66 | + </declaration> <declaration> |
| 67 | + symbol ex_intro2 ( .Sorts ) : Term |
| 68 | + </declaration> <declaration> |
| 69 | + symbol ex_intro4 ( .Sorts ) : Term |
| 70 | + </declaration> <declaration> |
| 71 | + symbol iff ( .Sorts ) : Term |
| 72 | + </declaration> <declaration> |
| 73 | + symbol nat ( .Sorts ) : Term |
| 74 | + </declaration> <declaration> |
| 75 | + symbol not ( .Sorts ) : Term |
| 76 | + </declaration> <declaration> |
| 77 | + symbol or ( .Sorts ) : Term |
| 78 | + </declaration> <declaration> |
| 79 | + symbol or_introl ( .Sorts ) : Term |
| 80 | + </declaration> <declaration> |
| 81 | + symbol or_intror ( .Sorts ) : Term |
| 82 | + </declaration> |
| 83 | + </declarations> |
| 84 | +</prover> |
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