%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP088-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 10:09:14 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.46s
% Output : Proof 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP088-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % 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 09:20:25 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.46 Command-line arguments: --no-flatten-goal
% 0.09/0.46
% 0.09/0.46 % SZS status Unsatisfiable
% 0.09/0.46
% 0.09/0.49 % SZS output start Proof
% 0.09/0.49 Axiom 1 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.09/0.49 Axiom 2 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.09/0.49 Axiom 3 (single_axiom): divide(X, divide(Y, divide(Z, divide(X, Y)))) = Z.
% 0.09/0.49
% 0.09/0.49 Lemma 4: inverse(divide(X, divide(Y, inverse(X)))) = Y.
% 0.09/0.49 Proof:
% 0.09/0.49 inverse(divide(X, divide(Y, inverse(X))))
% 0.09/0.49 = { by axiom 1 (inverse) }
% 0.09/0.49 inverse(divide(X, divide(Y, divide(divide(Z, Z), X))))
% 0.09/0.49 = { by axiom 1 (inverse) }
% 0.09/0.49 divide(divide(Z, Z), divide(X, divide(Y, divide(divide(Z, Z), X))))
% 0.09/0.49 = { by axiom 3 (single_axiom) }
% 0.09/0.49 Y
% 0.09/0.49
% 0.09/0.49 Lemma 5: divide(Y, Y) = divide(X, X).
% 0.09/0.49 Proof:
% 0.09/0.49 divide(Y, Y)
% 0.09/0.49 = { by lemma 4 R->L }
% 0.09/0.49 inverse(divide(Z, divide(divide(Y, Y), inverse(Z))))
% 0.09/0.49 = { by axiom 1 (inverse) R->L }
% 0.09/0.49 inverse(divide(Z, inverse(inverse(Z))))
% 0.54/0.49 = { by axiom 1 (inverse) }
% 0.54/0.49 inverse(divide(Z, divide(divide(X, X), inverse(Z))))
% 0.54/0.49 = { by lemma 4 }
% 0.54/0.50 divide(X, X)
% 0.54/0.50
% 0.54/0.50 Lemma 6: multiply(X, Y) = divide(X, inverse(Y)).
% 0.54/0.50 Proof:
% 0.54/0.50 multiply(X, Y)
% 0.54/0.50 = { by axiom 2 (multiply) }
% 0.54/0.50 divide(X, divide(divide(Z, Z), Y))
% 0.54/0.50 = { by axiom 1 (inverse) R->L }
% 0.54/0.50 divide(X, inverse(Y))
% 0.54/0.50
% 0.54/0.50 Lemma 7: inverse(divide(X, divide(Y, Y))) = inverse(X).
% 0.54/0.50 Proof:
% 0.54/0.50 inverse(divide(X, divide(Y, Y)))
% 0.54/0.50 = { by lemma 5 }
% 0.54/0.50 inverse(divide(X, divide(inverse(X), inverse(X))))
% 0.54/0.50 = { by lemma 4 }
% 0.54/0.50 inverse(X)
% 0.54/0.50
% 0.54/0.50 Lemma 8: divide(X, divide(Y, inverse(divide(X, Y)))) = divide(Z, Z).
% 0.54/0.50 Proof:
% 0.54/0.50 divide(X, divide(Y, inverse(divide(X, Y))))
% 0.54/0.50 = { by axiom 1 (inverse) }
% 0.54/0.50 divide(X, divide(Y, divide(divide(Z, Z), divide(X, Y))))
% 0.54/0.50 = { by axiom 3 (single_axiom) }
% 0.54/0.50 divide(Z, Z)
% 0.54/0.50
% 0.54/0.50 Lemma 9: inverse(inverse(X)) = X.
% 0.54/0.50 Proof:
% 0.54/0.50 inverse(inverse(X))
% 0.54/0.50 = { by lemma 7 R->L }
% 0.54/0.50 inverse(divide(inverse(X), divide(Y, Y)))
% 0.54/0.50 = { by lemma 8 R->L }
% 0.54/0.50 inverse(divide(inverse(X), divide(X, divide(divide(Z, Z), inverse(divide(X, divide(Z, Z)))))))
% 0.54/0.50 = { by axiom 1 (inverse) R->L }
% 0.54/0.50 inverse(divide(inverse(X), divide(X, inverse(inverse(divide(X, divide(Z, Z)))))))
% 0.54/0.50 = { by lemma 7 }
% 0.54/0.50 inverse(divide(inverse(X), divide(X, inverse(inverse(X)))))
% 0.54/0.50 = { by lemma 4 }
% 0.54/0.50 X
% 0.54/0.50
% 0.54/0.50 Lemma 10: divide(X, divide(Y, inverse(X))) = inverse(Y).
% 0.54/0.50 Proof:
% 0.54/0.50 divide(X, divide(Y, inverse(X)))
% 0.54/0.50 = { by lemma 9 R->L }
% 0.54/0.50 inverse(inverse(divide(X, divide(Y, inverse(X)))))
% 0.54/0.50 = { by lemma 4 }
% 0.54/0.50 inverse(Y)
% 0.54/0.50
% 0.54/0.50 Lemma 11: divide(divide(X, Y), X) = inverse(Y).
% 0.54/0.50 Proof:
% 0.54/0.50 divide(divide(X, Y), X)
% 0.54/0.50 = { by axiom 3 (single_axiom) R->L }
% 0.54/0.50 divide(divide(X, Y), divide(Y, divide(divide(divide(divide(Z, Z), divide(Z, Z)), divide(divide(Z, Z), divide(Z, Z))), divide(X, divide(Y, divide(divide(divide(Z, Z), divide(Z, Z)), divide(divide(Z, Z), divide(Z, Z))))))))
% 0.54/0.50 = { by lemma 8 R->L }
% 0.54/0.50 divide(divide(X, Y), divide(Y, divide(divide(divide(divide(Z, Z), divide(Z, Z)), divide(divide(Z, Z), divide(Z, Z))), divide(X, divide(Y, divide(divide(divide(Z, Z), divide(Z, Z)), divide(Y, divide(inverse(divide(Z, Z)), inverse(divide(Y, inverse(divide(Z, Z))))))))))))
% 0.54/0.50 = { by axiom 1 (inverse) }
% 0.54/0.50 divide(divide(X, Y), divide(Y, divide(divide(divide(divide(Z, Z), divide(Z, Z)), divide(divide(Z, Z), divide(Z, Z))), divide(X, divide(Y, divide(divide(divide(Z, Z), divide(Z, Z)), divide(Y, divide(divide(divide(Z, Z), divide(Z, Z)), inverse(divide(Y, inverse(divide(Z, Z))))))))))))
% 0.54/0.50 = { by axiom 1 (inverse) R->L }
% 0.54/0.50 divide(divide(X, Y), divide(Y, divide(divide(divide(divide(Z, Z), divide(Z, Z)), divide(divide(Z, Z), divide(Z, Z))), divide(X, divide(Y, divide(divide(divide(Z, Z), divide(Z, Z)), divide(Y, inverse(inverse(divide(Y, inverse(divide(Z, Z))))))))))))
% 0.54/0.50 = { by lemma 9 }
% 0.54/0.50 divide(divide(X, Y), divide(Y, divide(divide(divide(divide(Z, Z), divide(Z, Z)), divide(divide(Z, Z), divide(Z, Z))), divide(X, divide(Y, divide(divide(divide(Z, Z), divide(Z, Z)), divide(Y, divide(Y, inverse(divide(Z, Z))))))))))
% 0.54/0.50 = { by axiom 1 (inverse) }
% 0.54/0.50 divide(divide(X, Y), divide(Y, divide(divide(divide(divide(Z, Z), divide(Z, Z)), divide(divide(Z, Z), divide(Z, Z))), divide(X, divide(Y, divide(divide(divide(Z, Z), divide(Z, Z)), divide(Y, divide(Y, divide(divide(Z, Z), divide(Z, Z))))))))))
% 0.54/0.50 = { by axiom 3 (single_axiom) }
% 0.54/0.50 divide(divide(X, Y), divide(Y, divide(divide(divide(divide(Z, Z), divide(Z, Z)), divide(divide(Z, Z), divide(Z, Z))), divide(X, Y))))
% 0.54/0.50 = { by axiom 1 (inverse) R->L }
% 0.54/0.50 divide(divide(X, Y), divide(Y, inverse(divide(X, Y))))
% 0.54/0.50 = { by lemma 10 }
% 0.54/0.50 inverse(Y)
% 0.54/0.50
% 0.54/0.50 Lemma 12: divide(divide(X, Y), Z) = divide(X, divide(Y, inverse(Z))).
% 0.54/0.50 Proof:
% 0.54/0.50 divide(divide(X, Y), Z)
% 0.54/0.50 = { by axiom 3 (single_axiom) R->L }
% 0.54/0.50 divide(X, divide(Y, divide(divide(divide(X, Y), Z), divide(X, Y))))
% 0.54/0.50 = { by lemma 11 }
% 0.54/0.50 divide(X, divide(Y, inverse(Z)))
% 0.54/0.50
% 0.54/0.50 Lemma 13: inverse(divide(X, inverse(Y))) = divide(inverse(X), Y).
% 0.54/0.50 Proof:
% 0.54/0.50 inverse(divide(X, inverse(Y)))
% 0.54/0.50 = { by lemma 11 R->L }
% 0.54/0.50 inverse(divide(X, divide(divide(inverse(X), Y), inverse(X))))
% 0.54/0.50 = { by lemma 4 }
% 0.54/0.50 divide(inverse(X), Y)
% 0.54/0.50
% 0.54/0.50 Lemma 14: inverse(divide(inverse(X), Y)) = divide(X, inverse(Y)).
% 0.54/0.50 Proof:
% 0.54/0.50 inverse(divide(inverse(X), Y))
% 0.54/0.50 = { by lemma 10 R->L }
% 0.54/0.50 divide(X, divide(divide(inverse(X), Y), inverse(X)))
% 0.54/0.50 = { by lemma 11 }
% 0.54/0.50 divide(X, inverse(Y))
% 0.54/0.50
% 0.54/0.50 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)).
% 0.54/0.50 Proof:
% 0.54/0.50 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.54/0.50 = { by lemma 6 }
% 0.54/0.50 tuple(multiply(divide(inverse(b2), inverse(b2)), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.54/0.50 = { by lemma 6 }
% 0.54/0.50 tuple(divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.54/0.50 = { by axiom 1 (inverse) R->L }
% 0.54/0.50 tuple(inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.54/0.50 = { by lemma 6 }
% 0.54/0.50 tuple(inverse(inverse(a2)), multiply(divide(a3, inverse(b3)), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.54/0.50 = { by lemma 6 }
% 0.54/0.50 tuple(inverse(inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.54/0.50 = { by lemma 6 }
% 0.54/0.50 tuple(inverse(inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)), divide(inverse(a1), inverse(a1)), multiply(a4, b4))
% 0.54/0.50 = { by lemma 6 }
% 0.54/0.50 tuple(inverse(inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 0.54/0.50 = { by lemma 9 }
% 0.54/0.50 tuple(a2, divide(divide(a3, inverse(b3)), inverse(c3)), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 0.54/0.50 = { by lemma 12 }
% 0.54/0.50 tuple(a2, divide(a3, divide(inverse(b3), inverse(inverse(c3)))), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 0.54/0.50 = { by lemma 9 }
% 0.54/0.50 tuple(a2, divide(a3, divide(inverse(b3), c3)), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 0.54/0.50 = { by lemma 14 R->L }
% 0.54/0.50 tuple(a2, divide(a3, divide(inverse(b3), c3)), divide(inverse(a1), inverse(a1)), inverse(divide(inverse(a4), b4)))
% 0.54/0.50 = { by axiom 1 (inverse) }
% 0.54/0.50 tuple(a2, divide(a3, divide(inverse(b3), c3)), divide(inverse(a1), inverse(a1)), inverse(divide(divide(divide(b4, b4), a4), b4)))
% 0.54/0.50 = { by lemma 12 }
% 0.54/0.50 tuple(a2, divide(a3, divide(inverse(b3), c3)), divide(inverse(a1), inverse(a1)), inverse(divide(divide(b4, divide(b4, inverse(a4))), b4)))
% 0.54/0.50 = { by lemma 11 }
% 0.54/0.50 tuple(a2, divide(a3, divide(inverse(b3), c3)), divide(inverse(a1), inverse(a1)), inverse(inverse(divide(b4, inverse(a4)))))
% 0.54/0.50 = { by lemma 13 }
% 0.54/0.50 tuple(a2, divide(a3, divide(inverse(b3), c3)), divide(inverse(a1), inverse(a1)), inverse(divide(inverse(b4), a4)))
% 0.54/0.50 = { by lemma 14 }
% 0.54/0.50 tuple(a2, divide(a3, divide(inverse(b3), c3)), divide(inverse(a1), inverse(a1)), divide(b4, inverse(a4)))
% 0.54/0.50 = { by lemma 13 R->L }
% 0.54/0.50 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(inverse(a1), inverse(a1)), divide(b4, inverse(a4)))
% 0.54/0.50 = { by lemma 5 }
% 0.54/0.50 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(inverse(b1), inverse(b1)), divide(b4, inverse(a4)))
% 0.54/0.50 = { by lemma 6 R->L }
% 0.54/0.50 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(inverse(b1), inverse(b1)), multiply(b4, a4))
% 0.54/0.50 = { by lemma 6 R->L }
% 0.54/0.50 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.54/0.50 = { by lemma 6 R->L }
% 0.54/0.50 tuple(a2, multiply(a3, divide(b3, inverse(c3))), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.54/0.50 = { by lemma 6 R->L }
% 0.54/0.50 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.54/0.50 % SZS output end Proof
% 0.54/0.50
% 0.54/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------