%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP067-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:12 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.43s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP067-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n007.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:15:54 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.43 Command-line arguments: --no-flatten-goal
% 0.13/0.43
% 0.13/0.43 % SZS status Unsatisfiable
% 0.13/0.43
% 0.13/0.45 % SZS output start Proof
% 0.13/0.45 Axiom 1 (identity): identity = divide(X, X).
% 0.13/0.45 Axiom 2 (inverse): inverse(X) = divide(identity, X).
% 0.13/0.45 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(identity, Y)).
% 0.13/0.45 Axiom 4 (single_axiom): divide(divide(divide(X, X), divide(X, divide(Y, divide(divide(identity, X), Z)))), Z) = Y.
% 0.13/0.45
% 0.13/0.45 Lemma 5: inverse(identity) = identity.
% 0.13/0.45 Proof:
% 0.13/0.45 inverse(identity)
% 0.13/0.45 = { by axiom 2 (inverse) }
% 0.13/0.45 divide(identity, identity)
% 0.13/0.45 = { by axiom 1 (identity) R->L }
% 0.13/0.45 identity
% 0.13/0.45
% 0.13/0.45 Lemma 6: divide(X, inverse(Y)) = multiply(X, Y).
% 0.13/0.45 Proof:
% 0.13/0.45 divide(X, inverse(Y))
% 0.13/0.45 = { by axiom 2 (inverse) }
% 0.13/0.45 divide(X, divide(identity, Y))
% 0.13/0.45 = { by axiom 3 (multiply) R->L }
% 0.13/0.45 multiply(X, Y)
% 0.13/0.45
% 0.13/0.45 Lemma 7: divide(inverse(divide(X, divide(Y, divide(inverse(X), Z)))), Z) = Y.
% 0.13/0.45 Proof:
% 0.13/0.45 divide(inverse(divide(X, divide(Y, divide(inverse(X), Z)))), Z)
% 0.13/0.45 = { by axiom 2 (inverse) }
% 0.13/0.45 divide(inverse(divide(X, divide(Y, divide(divide(identity, X), Z)))), Z)
% 0.13/0.45 = { by axiom 2 (inverse) }
% 0.13/0.45 divide(divide(identity, divide(X, divide(Y, divide(divide(identity, X), Z)))), Z)
% 0.13/0.45 = { by axiom 1 (identity) }
% 0.13/0.45 divide(divide(divide(X, X), divide(X, divide(Y, divide(divide(identity, X), Z)))), Z)
% 0.13/0.45 = { by axiom 4 (single_axiom) }
% 0.13/0.45 Y
% 0.13/0.45
% 0.13/0.45 Lemma 8: divide(inverse(inverse(multiply(X, Y))), Y) = X.
% 0.13/0.45 Proof:
% 0.13/0.45 divide(inverse(inverse(multiply(X, Y))), Y)
% 0.13/0.45 = { by lemma 6 R->L }
% 0.13/0.45 divide(inverse(inverse(divide(X, inverse(Y)))), Y)
% 0.13/0.45 = { by axiom 2 (inverse) }
% 0.13/0.45 divide(inverse(inverse(divide(X, divide(identity, Y)))), Y)
% 0.13/0.45 = { by axiom 2 (inverse) }
% 0.13/0.45 divide(inverse(divide(identity, divide(X, divide(identity, Y)))), Y)
% 0.13/0.45 = { by lemma 5 R->L }
% 0.13/0.45 divide(inverse(divide(identity, divide(X, divide(inverse(identity), Y)))), Y)
% 0.13/0.45 = { by lemma 7 }
% 0.13/0.45 X
% 0.13/0.45
% 0.13/0.45 Lemma 9: divide(X, identity) = multiply(X, identity).
% 0.13/0.45 Proof:
% 0.13/0.45 divide(X, identity)
% 0.13/0.45 = { by lemma 5 R->L }
% 0.13/0.45 divide(X, inverse(identity))
% 0.13/0.45 = { by lemma 6 }
% 0.13/0.45 multiply(X, identity)
% 0.13/0.45
% 0.13/0.45 Lemma 10: inverse(multiply(X, identity)) = inverse(X).
% 0.13/0.45 Proof:
% 0.13/0.45 inverse(multiply(X, identity))
% 0.13/0.45 = { by lemma 7 R->L }
% 0.13/0.45 divide(inverse(divide(Y, divide(inverse(multiply(X, identity)), divide(inverse(Y), Z)))), Z)
% 0.13/0.45 = { by lemma 9 R->L }
% 0.13/0.45 divide(inverse(divide(Y, divide(inverse(divide(X, identity)), divide(inverse(Y), Z)))), Z)
% 0.13/0.45 = { by axiom 1 (identity) }
% 0.13/0.45 divide(inverse(divide(Y, divide(inverse(divide(X, divide(divide(inverse(X), divide(inverse(Y), Z)), divide(inverse(X), divide(inverse(Y), Z))))), divide(inverse(Y), Z)))), Z)
% 0.13/0.45 = { by lemma 7 }
% 0.13/0.45 divide(inverse(divide(Y, divide(inverse(X), divide(inverse(Y), Z)))), Z)
% 0.13/0.45 = { by lemma 7 }
% 0.13/0.45 inverse(X)
% 0.13/0.45
% 0.13/0.45 Lemma 11: multiply(inverse(inverse(X)), identity) = X.
% 0.13/0.45 Proof:
% 0.13/0.45 multiply(inverse(inverse(X)), identity)
% 0.13/0.45 = { by lemma 10 R->L }
% 0.13/0.45 multiply(inverse(inverse(multiply(X, identity))), identity)
% 0.13/0.45 = { by lemma 9 R->L }
% 0.13/0.45 divide(inverse(inverse(multiply(X, identity))), identity)
% 0.13/0.45 = { by lemma 8 }
% 0.13/0.45 X
% 0.13/0.45
% 0.13/0.45 Lemma 12: inverse(inverse(X)) = X.
% 0.13/0.45 Proof:
% 0.13/0.45 inverse(inverse(X))
% 0.13/0.45 = { by lemma 8 R->L }
% 0.13/0.45 divide(inverse(inverse(multiply(inverse(inverse(X)), identity))), identity)
% 0.13/0.45 = { by lemma 11 }
% 0.13/0.45 divide(inverse(inverse(X)), identity)
% 0.13/0.45 = { by lemma 9 }
% 0.13/0.45 multiply(inverse(inverse(X)), identity)
% 0.13/0.45 = { by lemma 11 }
% 0.13/0.45 X
% 0.13/0.45
% 0.13/0.45 Lemma 13: divide(X, Y) = multiply(X, inverse(Y)).
% 0.13/0.45 Proof:
% 0.13/0.45 divide(X, Y)
% 0.13/0.45 = { by lemma 12 R->L }
% 0.13/0.45 divide(X, inverse(inverse(Y)))
% 0.13/0.45 = { by lemma 6 }
% 0.13/0.45 multiply(X, inverse(Y))
% 0.13/0.45
% 0.13/0.45 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3)) = tuple(identity, a2, multiply(a3, multiply(b3, c3))).
% 0.13/0.45 Proof:
% 0.13/0.45 tuple(multiply(inverse(a1), a1), multiply(identity, a2), multiply(multiply(a3, b3), c3))
% 0.13/0.45 = { by lemma 6 R->L }
% 0.13/0.45 tuple(multiply(inverse(a1), a1), divide(identity, inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.13/0.45 = { by axiom 2 (inverse) R->L }
% 0.13/0.45 tuple(multiply(inverse(a1), a1), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.13/0.45 = { by lemma 6 R->L }
% 0.13/0.45 tuple(divide(inverse(a1), inverse(a1)), inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.13/0.45 = { by axiom 1 (identity) R->L }
% 0.13/0.45 tuple(identity, inverse(inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.13/0.45 = { by lemma 12 }
% 0.13/0.45 tuple(identity, a2, multiply(multiply(a3, b3), c3))
% 0.13/0.45 = { by lemma 12 R->L }
% 0.13/0.45 tuple(identity, a2, multiply(multiply(a3, b3), inverse(inverse(c3))))
% 0.13/0.45 = { by lemma 12 R->L }
% 0.13/0.45 tuple(identity, a2, multiply(multiply(a3, inverse(inverse(b3))), inverse(inverse(c3))))
% 0.13/0.45 = { by lemma 12 R->L }
% 0.13/0.45 tuple(identity, a2, multiply(multiply(inverse(inverse(a3)), inverse(inverse(b3))), inverse(inverse(c3))))
% 0.13/0.45 = { by lemma 13 R->L }
% 0.13/0.45 tuple(identity, a2, multiply(divide(inverse(inverse(a3)), inverse(b3)), inverse(inverse(c3))))
% 0.13/0.45 = { by lemma 7 R->L }
% 0.13/0.45 tuple(identity, a2, multiply(divide(inverse(inverse(divide(inverse(divide(inverse(b3), divide(a3, divide(inverse(inverse(b3)), inverse(inverse(b3)))))), inverse(inverse(b3))))), inverse(b3)), inverse(inverse(c3))))
% 0.13/0.45 = { by axiom 1 (identity) R->L }
% 0.13/0.45 tuple(identity, a2, multiply(divide(inverse(inverse(divide(inverse(divide(inverse(b3), divide(a3, identity))), inverse(inverse(b3))))), inverse(b3)), inverse(inverse(c3))))
% 0.13/0.45 = { by lemma 6 }
% 0.13/0.45 tuple(identity, a2, multiply(divide(inverse(inverse(multiply(inverse(divide(inverse(b3), divide(a3, identity))), inverse(b3)))), inverse(b3)), inverse(inverse(c3))))
% 0.13/0.45 = { by lemma 13 }
% 0.13/0.45 tuple(identity, a2, multiply(divide(inverse(inverse(multiply(inverse(multiply(inverse(b3), inverse(divide(a3, identity)))), inverse(b3)))), inverse(b3)), inverse(inverse(c3))))
% 0.13/0.45 = { by lemma 9 }
% 0.13/0.45 tuple(identity, a2, multiply(divide(inverse(inverse(multiply(inverse(multiply(inverse(b3), inverse(multiply(a3, identity)))), inverse(b3)))), inverse(b3)), inverse(inverse(c3))))
% 0.13/0.45 = { by lemma 10 }
% 0.13/0.45 tuple(identity, a2, multiply(divide(inverse(inverse(multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(b3)))), inverse(b3)), inverse(inverse(c3))))
% 0.13/0.45 = { by lemma 8 }
% 0.13/0.45 tuple(identity, a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), inverse(inverse(c3))))
% 0.13/0.45 = { by lemma 13 R->L }
% 0.13/0.45 tuple(identity, a2, multiply(inverse(divide(inverse(b3), a3)), inverse(inverse(c3))))
% 0.13/0.45 = { by lemma 13 R->L }
% 0.13/0.45 tuple(identity, a2, divide(inverse(divide(inverse(b3), a3)), inverse(c3)))
% 0.13/0.45 = { by lemma 8 R->L }
% 0.13/0.45 tuple(identity, a2, divide(inverse(divide(inverse(b3), divide(inverse(inverse(multiply(a3, divide(inverse(inverse(b3)), inverse(c3))))), divide(inverse(inverse(b3)), inverse(c3))))), inverse(c3)))
% 0.13/0.45 = { by lemma 7 }
% 0.13/0.45 tuple(identity, a2, inverse(inverse(multiply(a3, divide(inverse(inverse(b3)), inverse(c3))))))
% 0.13/0.45 = { by lemma 12 }
% 0.13/0.45 tuple(identity, a2, multiply(a3, divide(inverse(inverse(b3)), inverse(c3))))
% 0.13/0.45 = { by lemma 13 }
% 0.13/0.45 tuple(identity, a2, multiply(a3, multiply(inverse(inverse(b3)), inverse(inverse(c3)))))
% 0.13/0.45 = { by lemma 12 }
% 0.13/0.45 tuple(identity, a2, multiply(a3, multiply(b3, inverse(inverse(c3)))))
% 0.13/0.45 = { by lemma 12 }
% 0.13/0.45 tuple(identity, a2, multiply(a3, multiply(b3, c3)))
% 0.13/0.45 % SZS output end Proof
% 0.13/0.45
% 0.13/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------