%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP095-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 10:09:15 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP095-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:18:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.47 Command-line arguments: --no-flatten-goal
% 0.19/0.47
% 0.19/0.47 % SZS status Unsatisfiable
% 0.19/0.47
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 Axiom 1 (identity): identity = divide(X, X).
% 0.19/0.48 Axiom 2 (inverse): inverse(X) = divide(identity, X).
% 0.19/0.48 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(identity, Y)).
% 0.19/0.48 Axiom 4 (single_axiom): divide(divide(identity, X), divide(divide(divide(Y, X), Z), Y)) = Z.
% 0.19/0.48
% 0.19/0.48 Lemma 5: inverse(identity) = identity.
% 0.19/0.48 Proof:
% 0.19/0.48 inverse(identity)
% 0.19/0.48 = { by axiom 2 (inverse) }
% 0.19/0.48 divide(identity, identity)
% 0.19/0.48 = { by axiom 1 (identity) R->L }
% 0.19/0.48 identity
% 0.19/0.48
% 0.19/0.48 Lemma 6: divide(inverse(X), divide(divide(divide(Y, X), Z), Y)) = Z.
% 0.19/0.48 Proof:
% 0.19/0.48 divide(inverse(X), divide(divide(divide(Y, X), Z), Y))
% 0.19/0.48 = { by axiom 2 (inverse) }
% 0.19/0.48 divide(divide(identity, X), divide(divide(divide(Y, X), Z), Y))
% 0.19/0.48 = { by axiom 4 (single_axiom) }
% 0.19/0.48 Z
% 0.19/0.48
% 0.19/0.48 Lemma 7: divide(inverse(Y), inverse(X)) = divide(X, Y).
% 0.19/0.48 Proof:
% 0.19/0.48 divide(inverse(Y), inverse(X))
% 0.19/0.48 = { by axiom 2 (inverse) }
% 0.19/0.48 divide(inverse(Y), divide(identity, X))
% 0.19/0.48 = { by axiom 1 (identity) }
% 0.19/0.48 divide(inverse(Y), divide(divide(divide(X, Y), divide(X, Y)), X))
% 0.19/0.48 = { by lemma 6 }
% 0.19/0.48 divide(X, Y)
% 0.19/0.48
% 0.19/0.48 Lemma 8: divide(X, identity) = inverse(inverse(X)).
% 0.19/0.48 Proof:
% 0.19/0.48 divide(X, identity)
% 0.19/0.48 = { by lemma 7 R->L }
% 0.19/0.48 divide(inverse(identity), inverse(X))
% 0.19/0.48 = { by lemma 5 }
% 0.19/0.48 divide(identity, inverse(X))
% 0.19/0.48 = { by axiom 2 (inverse) R->L }
% 0.19/0.48 inverse(inverse(X))
% 0.19/0.48
% 0.19/0.48 Lemma 9: multiply(X, Y) = divide(X, inverse(Y)).
% 0.19/0.48 Proof:
% 0.19/0.48 multiply(X, Y)
% 0.19/0.48 = { by axiom 3 (multiply) }
% 0.19/0.48 divide(X, divide(identity, Y))
% 0.19/0.48 = { by axiom 2 (inverse) R->L }
% 0.19/0.48 divide(X, inverse(Y))
% 0.19/0.48
% 0.19/0.48 Lemma 10: inverse(inverse(inverse(X))) = inverse(X).
% 0.19/0.48 Proof:
% 0.19/0.48 inverse(inverse(inverse(X)))
% 0.19/0.48 = { by lemma 8 R->L }
% 0.19/0.48 divide(inverse(X), identity)
% 0.19/0.48 = { by lemma 5 R->L }
% 0.19/0.48 divide(inverse(X), inverse(identity))
% 0.19/0.48 = { by lemma 7 }
% 0.19/0.48 divide(identity, X)
% 0.19/0.48 = { by axiom 2 (inverse) R->L }
% 0.19/0.48 inverse(X)
% 0.19/0.48
% 0.19/0.48 Lemma 11: divide(inverse(X), divide(inverse(X), inverse(inverse(Y)))) = Y.
% 0.19/0.48 Proof:
% 0.19/0.48 divide(inverse(X), divide(inverse(X), inverse(inverse(Y))))
% 0.19/0.48 = { by lemma 7 }
% 0.19/0.48 divide(inverse(X), divide(inverse(Y), X))
% 0.19/0.48 = { by axiom 2 (inverse) }
% 0.19/0.48 divide(inverse(X), divide(divide(identity, Y), X))
% 0.19/0.48 = { by axiom 1 (identity) }
% 0.19/0.48 divide(inverse(X), divide(divide(divide(X, X), Y), X))
% 0.19/0.48 = { by lemma 6 }
% 0.19/0.48 Y
% 0.19/0.48
% 0.19/0.48 Lemma 12: inverse(inverse(X)) = X.
% 0.19/0.48 Proof:
% 0.19/0.48 inverse(inverse(X))
% 0.19/0.48 = { by lemma 10 R->L }
% 0.19/0.48 inverse(inverse(inverse(inverse(X))))
% 0.19/0.48 = { by lemma 8 R->L }
% 0.19/0.48 divide(inverse(inverse(X)), identity)
% 0.19/0.48 = { by axiom 1 (identity) }
% 0.19/0.48 divide(inverse(inverse(X)), divide(inverse(inverse(X)), inverse(inverse(X))))
% 0.19/0.48 = { by lemma 11 }
% 0.19/0.48 X
% 0.19/0.48
% 0.19/0.48 Lemma 13: divide(X, inverse(Y)) = divide(Y, inverse(X)).
% 0.19/0.48 Proof:
% 0.19/0.48 divide(X, inverse(Y))
% 0.19/0.48 = { by lemma 7 R->L }
% 0.19/0.48 divide(inverse(inverse(Y)), inverse(X))
% 0.19/0.48 = { by lemma 12 }
% 0.19/0.48 divide(Y, inverse(X))
% 0.19/0.48
% 0.19/0.48 Lemma 14: divide(inverse(X), Y) = divide(inverse(Y), X).
% 0.19/0.48 Proof:
% 0.19/0.48 divide(inverse(X), Y)
% 0.19/0.48 = { by lemma 7 R->L }
% 0.19/0.48 divide(inverse(Y), inverse(inverse(X)))
% 0.19/0.48 = { by lemma 12 }
% 0.19/0.48 divide(inverse(Y), X)
% 0.19/0.48
% 0.19/0.48 Lemma 15: divide(inverse(Z), divide(X, Y)) = divide(inverse(X), inverse(divide(Y, Z))).
% 0.19/0.48 Proof:
% 0.19/0.48 divide(inverse(Z), divide(X, Y))
% 0.19/0.48 = { by lemma 11 R->L }
% 0.19/0.48 divide(inverse(Z), divide(divide(inverse(inverse(divide(Y, Z))), divide(inverse(inverse(divide(Y, Z))), inverse(inverse(X)))), Y))
% 0.19/0.48 = { by lemma 12 }
% 0.19/0.48 divide(inverse(Z), divide(divide(divide(Y, Z), divide(inverse(inverse(divide(Y, Z))), inverse(inverse(X)))), Y))
% 0.19/0.48 = { by lemma 12 }
% 0.19/0.48 divide(inverse(Z), divide(divide(divide(Y, Z), divide(divide(Y, Z), inverse(inverse(X)))), Y))
% 0.19/0.48 = { by lemma 12 }
% 0.19/0.48 divide(inverse(Z), divide(divide(divide(Y, Z), divide(divide(Y, Z), X)), Y))
% 0.19/0.48 = { by lemma 6 }
% 0.19/0.48 divide(divide(Y, Z), X)
% 0.19/0.48 = { by lemma 7 R->L }
% 0.19/0.48 divide(inverse(X), inverse(divide(Y, Z)))
% 0.19/0.48
% 0.19/0.48 Lemma 16: inverse(divide(X, Y)) = divide(Y, X).
% 0.19/0.48 Proof:
% 0.19/0.48 inverse(divide(X, Y))
% 0.19/0.48 = { by axiom 2 (inverse) }
% 0.19/0.48 divide(identity, divide(X, Y))
% 0.19/0.48 = { by lemma 5 R->L }
% 0.19/0.48 divide(inverse(identity), divide(X, Y))
% 0.19/0.48 = { by lemma 15 }
% 0.19/0.48 divide(inverse(X), inverse(divide(Y, identity)))
% 0.19/0.48 = { by lemma 8 }
% 0.19/0.48 divide(inverse(X), inverse(inverse(inverse(Y))))
% 0.19/0.48 = { by lemma 10 }
% 0.19/0.48 divide(inverse(X), inverse(Y))
% 0.19/0.48 = { by lemma 7 }
% 0.19/0.48 divide(Y, X)
% 0.19/0.48
% 0.19/0.48 Lemma 17: divide(divide(X, Y), Z) = divide(inverse(Y), divide(Z, X)).
% 0.19/0.48 Proof:
% 0.19/0.48 divide(divide(X, Y), Z)
% 0.19/0.48 = { by lemma 12 R->L }
% 0.19/0.48 divide(divide(X, Y), inverse(inverse(Z)))
% 0.19/0.48 = { by lemma 12 R->L }
% 0.19/0.48 divide(inverse(inverse(divide(X, Y))), inverse(inverse(Z)))
% 0.19/0.48 = { by lemma 7 }
% 0.19/0.48 divide(inverse(Z), inverse(divide(X, Y)))
% 0.19/0.48 = { by lemma 15 R->L }
% 0.19/0.48 divide(inverse(Y), divide(Z, X))
% 0.19/0.48
% 0.19/0.48 Lemma 18: divide(Z, divide(Y, X)) = divide(X, divide(Y, Z)).
% 0.19/0.48 Proof:
% 0.19/0.48 divide(Z, divide(Y, X))
% 0.19/0.48 = { by lemma 12 R->L }
% 0.19/0.48 divide(inverse(inverse(Z)), divide(Y, X))
% 0.19/0.48 = { by lemma 17 R->L }
% 0.19/0.48 divide(divide(X, inverse(Z)), Y)
% 0.19/0.48 = { by lemma 13 R->L }
% 0.19/0.48 divide(divide(Z, inverse(X)), Y)
% 0.19/0.48 = { by lemma 17 }
% 0.19/0.48 divide(inverse(inverse(X)), divide(Y, Z))
% 0.19/0.48 = { by lemma 12 }
% 0.19/0.48 divide(X, divide(Y, Z))
% 0.19/0.48
% 0.19/0.48 Goal 1 (prove_these_axioms): tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4)) = tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4)).
% 0.19/0.48 Proof:
% 0.19/0.48 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.19/0.48 = { by lemma 9 }
% 0.19/0.48 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), divide(inverse(a1), inverse(a1)), multiply(a4, b4))
% 0.19/0.48 = { by axiom 1 (identity) R->L }
% 0.19/0.48 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), identity, multiply(a4, b4))
% 0.19/0.48 = { by lemma 9 }
% 0.19/0.48 tuple(multiply(divide(inverse(b2), inverse(b2)), a2), multiply(multiply(a3, b3), c3), identity, multiply(a4, b4))
% 0.19/0.48 = { by axiom 1 (identity) R->L }
% 0.19/0.48 tuple(multiply(identity, a2), multiply(multiply(a3, b3), c3), identity, multiply(a4, b4))
% 0.19/0.48 = { by lemma 9 }
% 0.19/0.48 tuple(divide(identity, inverse(a2)), multiply(multiply(a3, b3), c3), identity, multiply(a4, b4))
% 0.19/0.48 = { by axiom 2 (inverse) R->L }
% 0.19/0.48 tuple(inverse(inverse(a2)), multiply(multiply(a3, b3), c3), identity, multiply(a4, b4))
% 0.19/0.48 = { by lemma 9 }
% 0.19/0.48 tuple(inverse(inverse(a2)), multiply(divide(a3, inverse(b3)), c3), identity, multiply(a4, b4))
% 0.19/0.48 = { by lemma 9 }
% 0.19/0.48 tuple(inverse(inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)), identity, multiply(a4, b4))
% 0.19/0.48 = { by lemma 9 }
% 0.19/0.48 tuple(inverse(inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)), identity, divide(a4, inverse(b4)))
% 0.19/0.48 = { by lemma 7 R->L }
% 0.19/0.48 tuple(inverse(inverse(a2)), divide(inverse(inverse(c3)), inverse(divide(a3, inverse(b3)))), identity, divide(a4, inverse(b4)))
% 0.19/0.48 = { by lemma 12 }
% 0.19/0.48 tuple(a2, divide(inverse(inverse(c3)), inverse(divide(a3, inverse(b3)))), identity, divide(a4, inverse(b4)))
% 0.19/0.48 = { by lemma 12 }
% 0.19/0.48 tuple(a2, divide(c3, inverse(divide(a3, inverse(b3)))), identity, divide(a4, inverse(b4)))
% 0.19/0.48 = { by lemma 16 }
% 0.19/0.48 tuple(a2, divide(c3, divide(inverse(b3), a3)), identity, divide(a4, inverse(b4)))
% 0.19/0.48 = { by lemma 14 }
% 0.19/0.48 tuple(a2, divide(c3, divide(inverse(a3), b3)), identity, divide(a4, inverse(b4)))
% 0.19/0.48 = { by lemma 18 R->L }
% 0.19/0.48 tuple(a2, divide(b3, divide(inverse(a3), c3)), identity, divide(a4, inverse(b4)))
% 0.19/0.48 = { by lemma 14 R->L }
% 0.19/0.48 tuple(a2, divide(b3, divide(inverse(c3), a3)), identity, divide(a4, inverse(b4)))
% 0.19/0.48 = { by lemma 18 R->L }
% 0.19/0.48 tuple(a2, divide(a3, divide(inverse(c3), b3)), identity, divide(a4, inverse(b4)))
% 0.19/0.48 = { by lemma 16 R->L }
% 0.19/0.48 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), identity, divide(a4, inverse(b4)))
% 0.19/0.48 = { by lemma 13 R->L }
% 0.19/0.48 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), identity, divide(b4, inverse(a4)))
% 0.19/0.49 = { by lemma 9 R->L }
% 0.19/0.49 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), identity, multiply(b4, a4))
% 0.19/0.49 = { by lemma 9 R->L }
% 0.19/0.49 tuple(a2, multiply(a3, divide(b3, inverse(c3))), identity, multiply(b4, a4))
% 0.19/0.49 = { by lemma 9 R->L }
% 0.19/0.49 tuple(a2, multiply(a3, multiply(b3, c3)), identity, multiply(b4, a4))
% 0.19/0.49 = { by axiom 1 (identity) }
% 0.19/0.49 tuple(a2, multiply(a3, multiply(b3, c3)), divide(inverse(b1), inverse(b1)), multiply(b4, a4))
% 0.19/0.49 = { by lemma 9 R->L }
% 0.19/0.49 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.19/0.49 % SZS output end Proof
% 0.19/0.49
% 0.19/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------