%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP063-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 10:09:11 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.52s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP063-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n005.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 09:17:31 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.52 Command-line arguments: --no-flatten-goal
% 0.15/0.52
% 0.15/0.52 % SZS status Unsatisfiable
% 0.15/0.52
% 0.22/0.55 % SZS output start Proof
% 0.22/0.55 Axiom 1 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.22/0.55 Axiom 2 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.22/0.55 Axiom 3 (single_axiom): divide(X, divide(divide(divide(divide(X, X), Y), Z), divide(divide(divide(X, X), X), Z))) = Y.
% 0.22/0.55
% 0.22/0.55 Lemma 4: divide(X, inverse(Y)) = multiply(X, Y).
% 0.22/0.55 Proof:
% 0.22/0.55 divide(X, inverse(Y))
% 0.22/0.55 = { by axiom 1 (inverse) }
% 0.22/0.55 divide(X, divide(divide(Z, Z), Y))
% 0.22/0.55 = { by axiom 2 (multiply) R->L }
% 0.22/0.55 multiply(X, Y)
% 0.22/0.55
% 0.22/0.55 Lemma 5: divide(X, divide(divide(inverse(Y), Z), divide(inverse(X), Z))) = Y.
% 0.22/0.55 Proof:
% 0.22/0.55 divide(X, divide(divide(inverse(Y), Z), divide(inverse(X), Z)))
% 0.22/0.55 = { by axiom 1 (inverse) }
% 0.22/0.55 divide(X, divide(divide(inverse(Y), Z), divide(divide(divide(X, X), X), Z)))
% 0.22/0.55 = { by axiom 1 (inverse) }
% 0.22/0.55 divide(X, divide(divide(divide(divide(X, X), Y), Z), divide(divide(divide(X, X), X), Z)))
% 0.22/0.55 = { by axiom 3 (single_axiom) }
% 0.22/0.55 Y
% 0.22/0.55
% 0.22/0.55 Lemma 6: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.22/0.55 Proof:
% 0.22/0.55 multiply(X, multiply(inverse(X), Y))
% 0.22/0.55 = { by lemma 4 R->L }
% 0.22/0.55 multiply(X, divide(inverse(X), inverse(Y)))
% 0.22/0.55 = { by lemma 4 R->L }
% 0.22/0.55 divide(X, inverse(divide(inverse(X), inverse(Y))))
% 0.22/0.55 = { by axiom 1 (inverse) }
% 0.22/0.55 divide(X, divide(divide(inverse(Y), inverse(Y)), divide(inverse(X), inverse(Y))))
% 0.22/0.55 = { by lemma 5 }
% 0.22/0.55 Y
% 0.22/0.55
% 0.22/0.55 Lemma 7: divide(inverse(divide(X, X)), Y) = inverse(Y).
% 0.22/0.55 Proof:
% 0.22/0.55 divide(inverse(divide(X, X)), Y)
% 0.22/0.55 = { by axiom 1 (inverse) }
% 0.22/0.55 divide(divide(divide(X, X), divide(X, X)), Y)
% 0.22/0.55 = { by axiom 1 (inverse) R->L }
% 0.22/0.55 inverse(Y)
% 0.22/0.55
% 0.22/0.55 Lemma 8: inverse(multiply(divide(inverse(X), Y), Y)) = X.
% 0.22/0.55 Proof:
% 0.22/0.55 inverse(multiply(divide(inverse(X), Y), Y))
% 0.22/0.55 = { by lemma 4 R->L }
% 0.22/0.55 inverse(divide(divide(inverse(X), Y), inverse(Y)))
% 0.22/0.55 = { by axiom 1 (inverse) }
% 0.22/0.55 divide(divide(Z, Z), divide(divide(inverse(X), Y), inverse(Y)))
% 0.22/0.56 = { by lemma 7 R->L }
% 0.22/0.56 divide(divide(Z, Z), divide(divide(inverse(X), Y), divide(inverse(divide(Z, Z)), Y)))
% 0.22/0.56 = { by lemma 5 }
% 0.22/0.56 X
% 0.22/0.56
% 0.22/0.56 Lemma 9: inverse(multiply(inverse(X), X)) = divide(Y, Y).
% 0.22/0.56 Proof:
% 0.22/0.56 inverse(multiply(inverse(X), X))
% 0.22/0.56 = { by lemma 7 R->L }
% 0.22/0.56 inverse(multiply(divide(inverse(divide(Y, Y)), X), X))
% 0.22/0.56 = { by lemma 8 }
% 0.22/0.56 divide(Y, Y)
% 0.22/0.56
% 0.22/0.56 Lemma 10: divide(X, multiply(inverse(Y), Y)) = X.
% 0.22/0.56 Proof:
% 0.22/0.56 divide(X, multiply(inverse(Y), Y))
% 0.22/0.56 = { by lemma 8 R->L }
% 0.22/0.56 divide(X, inverse(multiply(divide(inverse(multiply(inverse(Y), Y)), Z), Z)))
% 0.22/0.56 = { by lemma 9 }
% 0.22/0.56 divide(X, inverse(multiply(divide(divide(W, W), Z), Z)))
% 0.22/0.56 = { by axiom 1 (inverse) R->L }
% 0.22/0.56 divide(X, inverse(multiply(inverse(Z), Z)))
% 0.22/0.56 = { by lemma 9 }
% 0.22/0.56 divide(X, divide(divide(inverse(X), V), divide(inverse(X), V)))
% 0.22/0.56 = { by lemma 5 }
% 0.22/0.56 X
% 0.22/0.56
% 0.22/0.56 Lemma 11: divide(X, multiply(inverse(Y), X)) = Y.
% 0.22/0.56 Proof:
% 0.22/0.56 divide(X, multiply(inverse(Y), X))
% 0.22/0.56 = { by lemma 4 R->L }
% 0.22/0.56 divide(X, divide(inverse(Y), inverse(X)))
% 0.22/0.56 = { by lemma 10 R->L }
% 0.22/0.56 divide(X, divide(inverse(Y), divide(inverse(X), multiply(inverse(Z), Z))))
% 0.22/0.56 = { by lemma 10 R->L }
% 0.22/0.56 divide(X, divide(divide(inverse(Y), multiply(inverse(Z), Z)), divide(inverse(X), multiply(inverse(Z), Z))))
% 0.22/0.56 = { by lemma 5 }
% 0.22/0.56 Y
% 0.22/0.56
% 0.22/0.56 Lemma 12: inverse(inverse(X)) = X.
% 0.22/0.56 Proof:
% 0.22/0.56 inverse(inverse(X))
% 0.22/0.56 = { by lemma 6 R->L }
% 0.22/0.56 inverse(multiply(Y, multiply(inverse(Y), inverse(X))))
% 0.22/0.56 = { by lemma 11 R->L }
% 0.22/0.56 inverse(multiply(divide(inverse(X), multiply(inverse(Y), inverse(X))), multiply(inverse(Y), inverse(X))))
% 0.22/0.56 = { by lemma 8 }
% 0.22/0.56 X
% 0.22/0.56
% 0.22/0.56 Lemma 13: divide(X, Y) = multiply(X, inverse(Y)).
% 0.22/0.56 Proof:
% 0.22/0.56 divide(X, Y)
% 0.22/0.56 = { by lemma 12 R->L }
% 0.22/0.56 divide(X, inverse(inverse(Y)))
% 0.22/0.56 = { by lemma 4 }
% 0.22/0.56 multiply(X, inverse(Y))
% 0.22/0.56
% 0.22/0.56 Lemma 14: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
% 0.22/0.56 Proof:
% 0.22/0.56 multiply(inverse(inverse(X)), Y)
% 0.22/0.56 = { by lemma 6 R->L }
% 0.22/0.56 multiply(X, multiply(inverse(X), multiply(inverse(inverse(X)), Y)))
% 0.22/0.56 = { by lemma 6 }
% 0.22/0.56 multiply(X, Y)
% 0.22/0.56
% 0.22/0.56 Lemma 15: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.22/0.56 Proof:
% 0.22/0.56 multiply(inverse(X), X)
% 0.22/0.56 = { by lemma 8 R->L }
% 0.22/0.56 inverse(multiply(divide(inverse(multiply(inverse(X), X)), Z), Z))
% 0.22/0.56 = { by lemma 9 }
% 0.22/0.56 inverse(multiply(divide(divide(W, W), Z), Z))
% 0.22/0.56 = { by lemma 9 R->L }
% 0.22/0.56 inverse(multiply(divide(inverse(multiply(inverse(inverse(Y)), inverse(Y))), Z), Z))
% 0.22/0.56 = { by lemma 8 }
% 0.22/0.56 multiply(inverse(inverse(Y)), inverse(Y))
% 0.22/0.56 = { by lemma 14 }
% 0.22/0.56 multiply(Y, inverse(Y))
% 0.22/0.56
% 0.22/0.56 Lemma 16: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 0.22/0.56 Proof:
% 0.22/0.56 multiply(X, inverse(multiply(Y, X)))
% 0.22/0.56 = { by lemma 13 R->L }
% 0.22/0.56 divide(X, multiply(Y, X))
% 0.22/0.56 = { by lemma 14 R->L }
% 0.22/0.56 divide(X, multiply(inverse(inverse(Y)), X))
% 0.22/0.56 = { by lemma 11 }
% 0.22/0.56 inverse(Y)
% 0.22/0.56
% 0.22/0.56 Goal 1 (prove_these_axioms): tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1)) = tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1)).
% 0.22/0.56 Proof:
% 0.22/0.56 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.22/0.56 = { by lemma 4 R->L }
% 0.22/0.56 tuple(multiply(divide(inverse(b2), inverse(b2)), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.22/0.56 = { by lemma 4 R->L }
% 0.22/0.56 tuple(divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.22/0.56 = { by axiom 1 (inverse) R->L }
% 0.22/0.56 tuple(inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 0.22/0.56 = { by lemma 15 }
% 0.22/0.56 tuple(inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 0.22/0.56 = { by lemma 12 }
% 0.22/0.57 tuple(a2, multiply(multiply(a3, b3), c3), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 6 R->L }
% 0.22/0.57 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(b3), multiply(inverse(inverse(b3)), c3))), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 14 R->L }
% 0.22/0.57 tuple(a2, multiply(multiply(inverse(inverse(a3)), b3), multiply(inverse(b3), multiply(inverse(inverse(b3)), c3))), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 6 R->L }
% 0.22/0.57 tuple(a2, multiply(a3, multiply(inverse(a3), multiply(multiply(inverse(inverse(a3)), b3), multiply(inverse(b3), multiply(inverse(inverse(b3)), c3))))), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 12 R->L }
% 0.22/0.57 tuple(a2, multiply(a3, multiply(inverse(a3), multiply(multiply(inverse(inverse(a3)), b3), multiply(inverse(b3), inverse(inverse(multiply(inverse(inverse(b3)), c3))))))), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 16 R->L }
% 0.22/0.57 tuple(a2, multiply(a3, multiply(inverse(a3), multiply(multiply(inverse(inverse(a3)), b3), multiply(inverse(b3), multiply(b3, inverse(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3))))))), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 14 R->L }
% 0.22/0.57 tuple(a2, multiply(a3, multiply(inverse(a3), multiply(multiply(inverse(inverse(a3)), b3), multiply(inverse(b3), multiply(inverse(inverse(b3)), inverse(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3))))))), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 6 }
% 0.22/0.57 tuple(a2, multiply(a3, multiply(inverse(a3), multiply(multiply(inverse(inverse(a3)), b3), inverse(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3))))), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 4 R->L }
% 0.22/0.57 tuple(a2, multiply(a3, multiply(inverse(a3), multiply(divide(inverse(inverse(a3)), inverse(b3)), inverse(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3))))), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 16 R->L }
% 0.22/0.57 tuple(a2, multiply(a3, multiply(inverse(a3), multiply(divide(inverse(inverse(a3)), inverse(b3)), multiply(inverse(divide(inverse(inverse(a3)), inverse(b3))), inverse(multiply(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3), inverse(divide(inverse(inverse(a3)), inverse(b3))))))))), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 6 }
% 0.22/0.57 tuple(a2, multiply(a3, multiply(inverse(a3), inverse(multiply(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3), inverse(divide(inverse(inverse(a3)), inverse(b3))))))), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 13 R->L }
% 0.22/0.57 tuple(a2, multiply(a3, multiply(inverse(a3), inverse(divide(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3), divide(inverse(inverse(a3)), inverse(b3)))))), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 13 R->L }
% 0.22/0.57 tuple(a2, multiply(a3, divide(inverse(a3), divide(multiply(inverse(multiply(inverse(inverse(b3)), c3)), b3), divide(inverse(inverse(a3)), inverse(b3))))), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 4 R->L }
% 0.22/0.57 tuple(a2, multiply(a3, divide(inverse(a3), divide(divide(inverse(multiply(inverse(inverse(b3)), c3)), inverse(b3)), divide(inverse(inverse(a3)), inverse(b3))))), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 5 }
% 0.22/0.57 tuple(a2, multiply(a3, multiply(inverse(inverse(b3)), c3)), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 14 }
% 0.22/0.57 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(X)))
% 0.22/0.57 = { by lemma 15 R->L }
% 0.22/0.57 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 0.22/0.57 % SZS output end Proof
% 0.22/0.57
% 0.22/0.57 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------