%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP094-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 0.35s 0.51s
% Output : Proof 0.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP094-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.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 09:21:56 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/0.51 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.35/0.51
% 0.35/0.51 % SZS status Unsatisfiable
% 0.35/0.51
% 0.35/0.52 % SZS output start Proof
% 0.35/0.52 Axiom 1 (identity): identity = divide(X, X).
% 0.35/0.52 Axiom 2 (inverse): inverse(X) = divide(identity, X).
% 0.35/0.52 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(identity, Y)).
% 0.35/0.52 Axiom 4 (single_axiom): divide(divide(identity, divide(X, Y)), divide(divide(Y, Z), X)) = Z.
% 0.35/0.52
% 0.35/0.52 Lemma 5: inverse(identity) = identity.
% 0.35/0.52 Proof:
% 0.35/0.52 inverse(identity)
% 0.35/0.52 = { by axiom 2 (inverse) }
% 0.35/0.52 divide(identity, identity)
% 0.35/0.52 = { by axiom 1 (identity) R->L }
% 0.35/0.52 identity
% 0.35/0.52
% 0.35/0.52 Lemma 6: divide(X, inverse(Y)) = multiply(X, Y).
% 0.35/0.52 Proof:
% 0.35/0.52 divide(X, inverse(Y))
% 0.35/0.52 = { by axiom 2 (inverse) }
% 0.35/0.52 divide(X, divide(identity, Y))
% 0.35/0.52 = { by axiom 3 (multiply) R->L }
% 0.35/0.52 multiply(X, Y)
% 0.35/0.52
% 0.35/0.52 Lemma 7: multiply(identity, X) = inverse(inverse(X)).
% 0.35/0.52 Proof:
% 0.35/0.52 multiply(identity, X)
% 0.35/0.52 = { by lemma 6 R->L }
% 0.35/0.52 divide(identity, inverse(X))
% 0.35/0.52 = { by axiom 2 (inverse) R->L }
% 0.35/0.52 inverse(inverse(X))
% 0.35/0.52
% 0.35/0.52 Lemma 8: divide(inverse(divide(X, Y)), divide(divide(Y, Z), X)) = Z.
% 0.35/0.52 Proof:
% 0.35/0.52 divide(inverse(divide(X, Y)), divide(divide(Y, Z), X))
% 0.35/0.52 = { by axiom 2 (inverse) }
% 0.35/0.52 divide(divide(identity, divide(X, Y)), divide(divide(Y, Z), X))
% 0.35/0.52 = { by axiom 4 (single_axiom) }
% 0.35/0.52 Z
% 0.35/0.52
% 0.35/0.52 Lemma 9: multiply(inverse(divide(X, Y)), X) = Y.
% 0.35/0.52 Proof:
% 0.35/0.52 multiply(inverse(divide(X, Y)), X)
% 0.35/0.52 = { by lemma 6 R->L }
% 0.35/0.52 divide(inverse(divide(X, Y)), inverse(X))
% 0.35/0.52 = { by axiom 2 (inverse) }
% 0.35/0.52 divide(inverse(divide(X, Y)), divide(identity, X))
% 0.35/0.52 = { by axiom 1 (identity) }
% 0.35/0.52 divide(inverse(divide(X, Y)), divide(divide(Y, Y), X))
% 0.35/0.52 = { by lemma 8 }
% 0.35/0.52 Y
% 0.35/0.52
% 0.35/0.52 Lemma 10: inverse(inverse(X)) = X.
% 0.35/0.52 Proof:
% 0.35/0.52 inverse(inverse(X))
% 0.35/0.52 = { by lemma 7 R->L }
% 0.35/0.52 multiply(identity, X)
% 0.35/0.52 = { by lemma 5 R->L }
% 0.35/0.52 multiply(inverse(identity), X)
% 0.35/0.52 = { by axiom 1 (identity) }
% 0.35/0.52 multiply(inverse(divide(X, X)), X)
% 0.35/0.52 = { by lemma 9 }
% 0.35/0.52 X
% 0.35/0.52
% 0.35/0.52 Lemma 11: divide(X, Y) = multiply(X, inverse(Y)).
% 0.35/0.52 Proof:
% 0.35/0.52 divide(X, Y)
% 0.35/0.52 = { by lemma 10 R->L }
% 0.35/0.52 divide(X, inverse(inverse(Y)))
% 0.35/0.52 = { by lemma 6 }
% 0.35/0.52 multiply(X, inverse(Y))
% 0.35/0.52
% 0.35/0.52 Lemma 12: multiply(X, identity) = X.
% 0.35/0.52 Proof:
% 0.35/0.52 multiply(X, identity)
% 0.35/0.52 = { by lemma 10 R->L }
% 0.35/0.52 multiply(inverse(inverse(X)), identity)
% 0.35/0.52 = { by axiom 2 (inverse) }
% 0.35/0.52 multiply(inverse(divide(identity, X)), identity)
% 0.35/0.52 = { by lemma 9 }
% 0.35/0.52 X
% 0.35/0.52
% 0.35/0.52 Lemma 13: multiply(inverse(X), X) = identity.
% 0.35/0.52 Proof:
% 0.35/0.52 multiply(inverse(X), X)
% 0.35/0.52 = { by lemma 6 R->L }
% 0.35/0.52 divide(inverse(X), inverse(X))
% 0.35/0.52 = { by axiom 1 (identity) R->L }
% 0.35/0.52 identity
% 0.35/0.52
% 0.35/0.52 Lemma 14: multiply(multiply(X, inverse(Y)), inverse(Z)) = multiply(inverse(Y), inverse(multiply(Z, inverse(X)))).
% 0.35/0.52 Proof:
% 0.35/0.52 multiply(multiply(X, inverse(Y)), inverse(Z))
% 0.35/0.52 = { by lemma 11 R->L }
% 0.35/0.52 multiply(divide(X, Y), inverse(Z))
% 0.35/0.52 = { by lemma 11 R->L }
% 0.35/0.52 divide(divide(X, Y), Z)
% 0.35/0.52 = { by lemma 9 R->L }
% 0.35/0.52 multiply(inverse(divide(inverse(divide(Z, X)), divide(divide(X, Y), Z))), inverse(divide(Z, X)))
% 0.35/0.52 = { by lemma 8 }
% 0.35/0.52 multiply(inverse(Y), inverse(divide(Z, X)))
% 0.35/0.52 = { by lemma 11 }
% 0.35/0.52 multiply(inverse(Y), inverse(multiply(Z, inverse(X))))
% 0.35/0.52
% 0.35/0.52 Lemma 15: multiply(inverse(X), Y) = multiply(Y, inverse(X)).
% 0.35/0.52 Proof:
% 0.35/0.52 multiply(inverse(X), Y)
% 0.35/0.52 = { by lemma 10 R->L }
% 0.35/0.52 multiply(inverse(X), inverse(inverse(Y)))
% 0.35/0.52 = { by lemma 10 R->L }
% 0.35/0.52 multiply(inverse(X), inverse(inverse(inverse(inverse(Y)))))
% 0.35/0.52 = { by lemma 7 R->L }
% 0.35/0.52 multiply(inverse(X), inverse(multiply(identity, inverse(Y))))
% 0.35/0.52 = { by lemma 14 R->L }
% 0.35/0.52 multiply(multiply(Y, inverse(X)), inverse(identity))
% 0.35/0.52 = { by lemma 5 }
% 0.35/0.52 multiply(multiply(Y, inverse(X)), identity)
% 0.35/0.52 = { by lemma 12 }
% 0.35/0.52 multiply(Y, inverse(X))
% 0.35/0.52
% 0.35/0.52 Lemma 16: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
% 0.35/0.52 Proof:
% 0.35/0.52 inverse(multiply(X, inverse(Y)))
% 0.35/0.52 = { by lemma 10 R->L }
% 0.35/0.52 inverse(inverse(inverse(multiply(X, inverse(Y)))))
% 0.35/0.52 = { by lemma 7 R->L }
% 0.35/0.52 multiply(identity, inverse(multiply(X, inverse(Y))))
% 0.35/0.52 = { by lemma 5 R->L }
% 0.35/0.52 multiply(inverse(identity), inverse(multiply(X, inverse(Y))))
% 0.35/0.52 = { by lemma 14 R->L }
% 0.35/0.52 multiply(multiply(Y, inverse(identity)), inverse(X))
% 0.35/0.52 = { by lemma 5 }
% 0.35/0.52 multiply(multiply(Y, identity), inverse(X))
% 0.35/0.52 = { by lemma 12 }
% 0.35/0.52 multiply(Y, inverse(X))
% 0.35/0.52
% 0.35/0.52 Lemma 17: multiply(inverse(multiply(X, Y)), X) = inverse(Y).
% 0.35/0.52 Proof:
% 0.35/0.52 multiply(inverse(multiply(X, Y)), X)
% 0.35/0.52 = { by lemma 6 R->L }
% 0.35/0.52 multiply(inverse(divide(X, inverse(Y))), X)
% 0.35/0.52 = { by lemma 9 }
% 0.35/0.52 inverse(Y)
% 0.35/0.52
% 0.35/0.52 Lemma 18: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 0.35/0.52 Proof:
% 0.35/0.52 multiply(X, inverse(multiply(Y, X)))
% 0.35/0.52 = { by lemma 10 R->L }
% 0.35/0.52 multiply(inverse(inverse(X)), inverse(multiply(Y, X)))
% 0.35/0.52 = { by lemma 17 R->L }
% 0.35/0.52 multiply(inverse(multiply(inverse(multiply(Y, X)), Y)), inverse(multiply(Y, X)))
% 0.35/0.52 = { by lemma 17 }
% 0.35/0.52 inverse(Y)
% 0.35/0.52
% 0.35/0.52 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)).
% 0.35/0.52 Proof:
% 0.35/0.52 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.35/0.52 = { by lemma 13 }
% 0.35/0.52 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), identity, multiply(a4, b4))
% 0.35/0.52 = { by lemma 13 }
% 0.35/0.52 tuple(multiply(identity, a2), multiply(multiply(a3, b3), c3), identity, multiply(a4, b4))
% 0.35/0.52 = { by lemma 7 }
% 0.35/0.52 tuple(inverse(inverse(a2)), multiply(multiply(a3, b3), c3), identity, multiply(a4, b4))
% 0.35/0.52 = { by lemma 10 }
% 0.35/0.52 tuple(a2, multiply(multiply(a3, b3), c3), identity, multiply(a4, b4))
% 0.35/0.52 = { by lemma 10 R->L }
% 0.35/0.52 tuple(a2, multiply(multiply(a3, b3), c3), identity, multiply(inverse(inverse(a4)), b4))
% 0.35/0.52 = { by lemma 15 }
% 0.35/0.52 tuple(a2, multiply(multiply(a3, b3), c3), identity, multiply(b4, inverse(inverse(a4))))
% 0.35/0.52 = { by lemma 10 }
% 0.35/0.52 tuple(a2, multiply(multiply(a3, b3), c3), identity, multiply(b4, a4))
% 0.35/0.52 = { by lemma 13 R->L }
% 0.35/0.52 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 10 R->L }
% 0.35/0.52 tuple(a2, inverse(inverse(multiply(multiply(a3, b3), c3))), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 17 R->L }
% 0.35/0.52 tuple(a2, multiply(inverse(multiply(multiply(b3, c3), inverse(multiply(multiply(a3, b3), c3)))), multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 15 R->L }
% 0.35/0.52 tuple(a2, multiply(inverse(multiply(inverse(multiply(multiply(a3, b3), c3)), multiply(b3, c3))), multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 10 R->L }
% 0.35/0.52 tuple(a2, multiply(inverse(multiply(inverse(inverse(inverse(multiply(multiply(a3, b3), c3)))), multiply(b3, c3))), multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 10 R->L }
% 0.35/0.52 tuple(a2, multiply(inverse(multiply(inverse(inverse(inverse(multiply(multiply(a3, b3), c3)))), multiply(b3, inverse(inverse(c3))))), multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 16 R->L }
% 0.35/0.52 tuple(a2, multiply(inverse(multiply(inverse(inverse(inverse(multiply(multiply(a3, b3), c3)))), inverse(multiply(inverse(c3), inverse(b3))))), multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 14 R->L }
% 0.35/0.52 tuple(a2, multiply(inverse(multiply(multiply(b3, inverse(inverse(inverse(multiply(multiply(a3, b3), c3))))), inverse(inverse(c3)))), multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 16 R->L }
% 0.35/0.52 tuple(a2, multiply(inverse(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(inverse(inverse(multiply(multiply(a3, b3), c3))))))))), multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 14 R->L }
% 0.35/0.52 tuple(a2, multiply(inverse(inverse(multiply(multiply(inverse(inverse(multiply(multiply(a3, b3), c3))), inverse(c3)), inverse(b3)))), multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 16 }
% 0.35/0.52 tuple(a2, multiply(inverse(multiply(b3, inverse(multiply(inverse(inverse(multiply(multiply(a3, b3), c3))), inverse(c3))))), multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 16 }
% 0.35/0.52 tuple(a2, multiply(inverse(multiply(b3, multiply(c3, inverse(inverse(inverse(multiply(multiply(a3, b3), c3))))))), multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 10 }
% 0.35/0.52 tuple(a2, multiply(inverse(multiply(b3, multiply(c3, inverse(multiply(multiply(a3, b3), c3))))), multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 18 }
% 0.35/0.52 tuple(a2, multiply(inverse(multiply(b3, inverse(multiply(a3, b3)))), multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 18 }
% 0.35/0.52 tuple(a2, multiply(inverse(inverse(a3)), multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 = { by lemma 10 }
% 0.35/0.52 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.35/0.52 % SZS output end Proof
% 0.35/0.52
% 0.35/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------