%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP090-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 10:09:14 AM UTC 2026
% Result : Unsatisfiable 0.22s 0.59s
% Output : Proof 1.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP090-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n004.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 09:18:36 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.59 Command-line arguments: --no-flatten-goal
% 0.22/0.59
% 0.22/0.59 % SZS status Unsatisfiable
% 0.22/0.59
% 1.19/0.63 % SZS output start Proof
% 1.19/0.63 Axiom 1 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 1.19/0.63 Axiom 2 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 1.19/0.63 Axiom 3 (single_axiom): divide(divide(X, divide(Y, Z)), divide(X, Y)) = Z.
% 1.19/0.63
% 1.19/0.63 Lemma 4: multiply(X, Y) = divide(X, inverse(Y)).
% 1.19/0.63 Proof:
% 1.19/0.63 multiply(X, Y)
% 1.19/0.63 = { by axiom 2 (multiply) }
% 1.19/0.63 divide(X, divide(divide(Z, Z), Y))
% 1.19/0.63 = { by axiom 1 (inverse) R->L }
% 1.19/0.63 divide(X, inverse(Y))
% 1.19/0.63
% 1.19/0.63 Lemma 5: inverse(divide(divide(X, Y), X)) = Y.
% 1.19/0.63 Proof:
% 1.19/0.63 inverse(divide(divide(X, Y), X))
% 1.19/0.63 = { by axiom 1 (inverse) }
% 1.19/0.63 divide(divide(divide(X, Y), divide(X, Y)), divide(divide(X, Y), X))
% 1.19/0.63 = { by axiom 3 (single_axiom) }
% 1.19/0.63 Y
% 1.19/0.63
% 1.19/0.63 Lemma 6: inverse(inverse(X)) = X.
% 1.19/0.63 Proof:
% 1.19/0.63 inverse(inverse(X))
% 1.19/0.63 = { by axiom 1 (inverse) }
% 1.19/0.63 inverse(divide(divide(X, X), X))
% 1.19/0.63 = { by lemma 5 }
% 1.19/0.63 X
% 1.19/0.63
% 1.19/0.63 Lemma 7: divide(inverse(divide(X, Y)), inverse(X)) = Y.
% 1.19/0.63 Proof:
% 1.19/0.63 divide(inverse(divide(X, Y)), inverse(X))
% 1.19/0.63 = { by axiom 1 (inverse) }
% 1.19/0.63 divide(inverse(divide(X, Y)), divide(divide(Z, Z), X))
% 1.19/0.63 = { by axiom 1 (inverse) }
% 1.19/0.63 divide(divide(divide(Z, Z), divide(X, Y)), divide(divide(Z, Z), X))
% 1.19/0.63 = { by axiom 3 (single_axiom) }
% 1.19/0.63 Y
% 1.19/0.63
% 1.19/0.63 Lemma 8: divide(X, divide(Y, Y)) = X.
% 1.19/0.63 Proof:
% 1.19/0.63 divide(X, divide(Y, Y))
% 1.19/0.63 = { by lemma 6 R->L }
% 1.19/0.63 divide(X, inverse(inverse(divide(Y, Y))))
% 1.19/0.63 = { by lemma 6 R->L }
% 1.19/0.63 divide(inverse(inverse(X)), inverse(inverse(divide(Y, Y))))
% 1.19/0.63 = { by axiom 1 (inverse) }
% 1.19/0.63 divide(inverse(divide(divide(divide(Y, Y), divide(Y, Y)), X)), inverse(inverse(divide(Y, Y))))
% 1.19/0.63 = { by axiom 1 (inverse) R->L }
% 1.19/0.63 divide(inverse(divide(inverse(divide(Y, Y)), X)), inverse(inverse(divide(Y, Y))))
% 1.19/0.63 = { by lemma 7 }
% 1.19/0.63 X
% 1.19/0.63
% 1.19/0.63 Lemma 9: inverse(divide(X, Y)) = divide(Y, X).
% 1.19/0.63 Proof:
% 1.19/0.63 inverse(divide(X, Y))
% 1.19/0.63 = { by axiom 3 (single_axiom) R->L }
% 1.19/0.63 inverse(divide(divide(divide(Y, divide(Y, X)), divide(Y, Y)), Y))
% 1.19/0.63 = { by lemma 8 }
% 1.19/0.63 inverse(divide(divide(Y, divide(Y, X)), Y))
% 1.19/0.63 = { by lemma 5 }
% 1.19/0.63 divide(Y, X)
% 1.19/0.63
% 1.19/0.63 Lemma 10: divide(inverse(X), divide(Y, X)) = inverse(Y).
% 1.19/0.63 Proof:
% 1.19/0.63 divide(inverse(X), divide(Y, X))
% 1.19/0.63 = { by lemma 6 R->L }
% 1.19/0.63 divide(inverse(X), inverse(inverse(divide(Y, X))))
% 1.19/0.63 = { by lemma 7 R->L }
% 1.19/0.63 divide(inverse(divide(inverse(divide(Y, X)), inverse(Y))), inverse(inverse(divide(Y, X))))
% 1.19/0.63 = { by lemma 7 }
% 1.19/0.63 inverse(Y)
% 1.19/0.63
% 1.19/0.63 Lemma 11: divide(inverse(Y), inverse(X)) = divide(X, Y).
% 1.19/0.63 Proof:
% 1.19/0.63 divide(inverse(Y), inverse(X))
% 1.19/0.63 = { by lemma 9 R->L }
% 1.19/0.63 inverse(divide(inverse(X), inverse(Y)))
% 1.19/0.63 = { by lemma 10 R->L }
% 1.19/0.63 inverse(divide(divide(inverse(Y), divide(X, Y)), inverse(Y)))
% 1.19/0.63 = { by lemma 5 }
% 1.19/0.63 divide(X, Y)
% 1.19/0.63
% 1.19/0.63 Lemma 12: divide(divide(X, Y), X) = inverse(Y).
% 1.19/0.63 Proof:
% 1.19/0.63 divide(divide(X, Y), X)
% 1.19/0.63 = { by lemma 6 R->L }
% 1.19/0.63 inverse(inverse(divide(divide(X, Y), X)))
% 1.19/0.63 = { by lemma 5 }
% 1.19/0.63 inverse(Y)
% 1.19/0.63
% 1.19/0.63 Lemma 13: divide(Y, inverse(X)) = divide(X, inverse(Y)).
% 1.19/0.63 Proof:
% 1.19/0.63 divide(Y, inverse(X))
% 1.19/0.63 = { by lemma 5 R->L }
% 1.19/0.63 divide(inverse(divide(divide(Z, Y), Z)), inverse(X))
% 1.19/0.63 = { by lemma 11 }
% 1.19/0.63 divide(X, divide(divide(Z, Y), Z))
% 1.19/0.63 = { by lemma 12 }
% 1.19/0.63 divide(X, inverse(Y))
% 1.19/0.63
% 1.19/0.63 Lemma 14: divide(inverse(Y), X) = divide(inverse(X), Y).
% 1.19/0.63 Proof:
% 1.19/0.63 divide(inverse(Y), X)
% 1.19/0.63 = { by lemma 5 R->L }
% 1.19/0.63 divide(inverse(Y), inverse(divide(divide(Z, X), Z)))
% 1.19/0.63 = { by lemma 11 }
% 1.19/0.63 divide(divide(divide(Z, X), Z), Y)
% 1.19/0.63 = { by lemma 12 }
% 1.19/0.63 divide(inverse(X), Y)
% 1.19/0.63
% 1.19/0.63 Lemma 15: divide(divide(X, Y), Z) = divide(inverse(Y), divide(Z, X)).
% 1.19/0.63 Proof:
% 1.19/0.63 divide(divide(X, Y), Z)
% 1.19/0.63 = { by lemma 9 R->L }
% 1.19/0.63 inverse(divide(Z, divide(X, Y)))
% 1.19/0.63 = { by lemma 10 R->L }
% 1.19/0.63 divide(inverse(divide(Z, X)), divide(divide(Z, divide(X, Y)), divide(Z, X)))
% 1.19/0.63 = { by axiom 3 (single_axiom) }
% 1.19/0.63 divide(inverse(divide(Z, X)), Y)
% 1.19/0.63 = { by lemma 9 }
% 1.19/0.63 divide(divide(X, Z), Y)
% 1.19/0.63 = { by lemma 11 R->L }
% 1.19/0.63 divide(inverse(Y), inverse(divide(X, Z)))
% 1.19/0.63 = { by lemma 9 }
% 1.19/0.63 divide(inverse(Y), divide(Z, X))
% 1.19/0.63
% 1.19/0.63 Lemma 16: divide(Z, divide(Y, X)) = divide(X, divide(Y, Z)).
% 1.19/0.63 Proof:
% 1.19/0.63 divide(Z, divide(Y, X))
% 1.19/0.63 = { by lemma 6 R->L }
% 1.19/0.63 divide(inverse(inverse(Z)), divide(Y, X))
% 1.19/0.63 = { by lemma 15 R->L }
% 1.19/0.63 divide(divide(X, inverse(Z)), Y)
% 1.19/0.63 = { by lemma 13 }
% 1.19/0.63 divide(divide(Z, inverse(X)), Y)
% 1.19/0.63 = { by lemma 15 }
% 1.19/0.63 divide(inverse(inverse(X)), divide(Y, Z))
% 1.19/0.63 = { by lemma 6 }
% 1.19/0.63 divide(X, divide(Y, Z))
% 1.19/0.63
% 1.19/0.63 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)).
% 1.19/0.64 Proof:
% 1.19/0.64 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 1.19/0.64 = { by lemma 4 }
% 1.19/0.64 tuple(multiply(divide(inverse(b2), inverse(b2)), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 1.19/0.64 = { by lemma 4 }
% 1.19/0.64 tuple(divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 1.19/0.64 = { by axiom 1 (inverse) R->L }
% 1.19/0.64 tuple(inverse(inverse(a2)), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 1.19/0.64 = { by lemma 4 }
% 1.19/0.64 tuple(inverse(inverse(a2)), multiply(divide(a3, inverse(b3)), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 1.19/0.64 = { by lemma 4 }
% 1.19/0.64 tuple(inverse(inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)), multiply(inverse(a1), a1), multiply(a4, b4))
% 1.19/0.64 = { by lemma 4 }
% 1.19/0.64 tuple(inverse(inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)), divide(inverse(a1), inverse(a1)), multiply(a4, b4))
% 1.19/0.64 = { by lemma 4 }
% 1.19/0.64 tuple(inverse(inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 1.19/0.64 = { by lemma 6 }
% 1.19/0.64 tuple(a2, divide(divide(a3, inverse(b3)), inverse(c3)), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 1.19/0.64 = { by lemma 11 R->L }
% 1.19/0.64 tuple(a2, divide(inverse(inverse(c3)), inverse(divide(a3, inverse(b3)))), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 1.19/0.64 = { by lemma 6 }
% 1.19/0.64 tuple(a2, divide(c3, inverse(divide(a3, inverse(b3)))), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 1.19/0.64 = { by lemma 9 }
% 1.19/0.64 tuple(a2, divide(c3, divide(inverse(b3), a3)), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 1.19/0.64 = { by lemma 11 R->L }
% 1.19/0.64 tuple(a2, divide(c3, divide(inverse(a3), inverse(inverse(b3)))), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 1.19/0.64 = { by lemma 6 }
% 1.19/0.64 tuple(a2, divide(c3, divide(inverse(a3), b3)), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 1.19/0.64 = { by lemma 16 R->L }
% 1.19/0.64 tuple(a2, divide(b3, divide(inverse(a3), c3)), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 1.19/0.64 = { by lemma 14 }
% 1.19/0.64 tuple(a2, divide(b3, divide(inverse(c3), a3)), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 1.19/0.64 = { by lemma 16 R->L }
% 1.19/0.64 tuple(a2, divide(a3, divide(inverse(c3), b3)), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 1.19/0.64 = { by lemma 14 R->L }
% 1.19/0.64 tuple(a2, divide(a3, divide(inverse(b3), c3)), divide(inverse(a1), inverse(a1)), divide(a4, inverse(b4)))
% 1.19/0.64 = { by lemma 13 }
% 1.19/0.64 tuple(a2, divide(a3, divide(inverse(b3), c3)), divide(inverse(a1), inverse(a1)), divide(b4, inverse(a4)))
% 1.19/0.64 = { by lemma 6 R->L }
% 1.19/0.64 tuple(a2, divide(a3, divide(inverse(b3), inverse(inverse(c3)))), divide(inverse(a1), inverse(a1)), divide(b4, inverse(a4)))
% 1.19/0.64 = { by lemma 11 }
% 1.19/0.64 tuple(a2, divide(a3, divide(inverse(c3), b3)), divide(inverse(a1), inverse(a1)), divide(b4, inverse(a4)))
% 1.19/0.64 = { by lemma 9 R->L }
% 1.19/0.64 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(inverse(a1), inverse(a1)), divide(b4, inverse(a4)))
% 1.19/0.64 = { by lemma 8 R->L }
% 1.19/0.64 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(divide(inverse(a1), inverse(a1)), divide(X, X)), divide(b4, inverse(a4)))
% 1.19/0.64 = { by axiom 1 (inverse) R->L }
% 1.19/0.64 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), inverse(divide(X, X)), divide(b4, inverse(a4)))
% 1.19/0.64 = { by axiom 1 (inverse) }
% 1.19/0.64 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(divide(inverse(b1), inverse(b1)), divide(X, X)), divide(b4, inverse(a4)))
% 1.19/0.64 = { by lemma 8 }
% 1.19/0.64 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(inverse(b1), inverse(b1)), divide(b4, inverse(a4)))
% 1.19/0.64 = { by lemma 4 R->L }
% 1.19/0.64 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(inverse(b1), inverse(b1)), multiply(b4, a4))
% 1.19/0.64 = { by lemma 4 R->L }
% 1.19/0.64 tuple(a2, divide(a3, inverse(divide(b3, inverse(c3)))), multiply(inverse(b1), b1), multiply(b4, a4))
% 1.19/0.64 = { by lemma 4 R->L }
% 1.19/0.64 tuple(a2, multiply(a3, divide(b3, inverse(c3))), multiply(inverse(b1), b1), multiply(b4, a4))
% 1.19/0.64 = { by lemma 4 R->L }
% 1.19/0.64 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 1.19/0.64 % SZS output end Proof
% 1.19/0.64
% 1.19/0.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------