%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP097-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.07s 0.38s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP097-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sun Sep 27 09:18:34 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.38 Command-line arguments: --no-flatten-goal
% 0.07/0.38
% 0.07/0.38 % SZS status Unsatisfiable
% 0.07/0.38
% 0.07/0.39 % SZS output start Proof
% 0.07/0.39 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.07/0.40 Axiom 2 (single_axiom): divide(X, inverse(divide(divide(Y, Z), divide(X, Z)))) = Y.
% 0.07/0.40
% 0.07/0.40 Lemma 3: divide(X, inverse(divide(Y, divide(X, inverse(divide(divide(Y, Z), divide(W, Z))))))) = W.
% 0.07/0.40 Proof:
% 0.07/0.40 divide(X, inverse(divide(Y, divide(X, inverse(divide(divide(Y, Z), divide(W, Z)))))))
% 0.07/0.40 = { by axiom 2 (single_axiom) R->L }
% 0.07/0.40 divide(X, inverse(divide(divide(W, inverse(divide(divide(Y, Z), divide(W, Z)))), divide(X, inverse(divide(divide(Y, Z), divide(W, Z)))))))
% 0.07/0.40 = { by axiom 2 (single_axiom) }
% 0.07/0.40 W
% 0.07/0.40
% 0.07/0.40 Lemma 4: divide(X, inverse(divide(Y, Y))) = X.
% 0.07/0.40 Proof:
% 0.07/0.40 divide(X, inverse(divide(Y, Y)))
% 0.07/0.40 = { by axiom 2 (single_axiom) R->L }
% 0.07/0.40 divide(X, inverse(divide(Y, divide(X, inverse(divide(divide(Y, Z), divide(X, Z)))))))
% 0.07/0.40 = { by lemma 3 }
% 0.07/0.40 X
% 0.07/0.40
% 0.07/0.40 Lemma 5: divide(X, inverse(divide(Y, X))) = Y.
% 0.07/0.40 Proof:
% 0.07/0.40 divide(X, inverse(divide(Y, X)))
% 0.07/0.40 = { by lemma 4 R->L }
% 0.07/0.40 divide(X, inverse(divide(Y, divide(X, inverse(divide(Z, Z))))))
% 0.07/0.40 = { by lemma 4 R->L }
% 0.07/0.40 divide(X, inverse(divide(divide(Y, inverse(divide(Z, Z))), divide(X, inverse(divide(Z, Z))))))
% 0.07/0.40 = { by axiom 2 (single_axiom) }
% 0.07/0.40 Y
% 0.07/0.40
% 0.07/0.40 Lemma 6: divide(inverse(divide(X, X)), inverse(Y)) = Y.
% 0.07/0.40 Proof:
% 0.07/0.40 divide(inverse(divide(X, X)), inverse(Y))
% 0.07/0.40 = { by lemma 4 R->L }
% 0.07/0.40 divide(inverse(divide(X, X)), inverse(divide(Y, inverse(divide(X, X)))))
% 0.07/0.40 = { by lemma 5 }
% 0.07/0.40 Y
% 0.07/0.40
% 0.07/0.40 Lemma 7: divide(divide(X, inverse(Y)), Y) = X.
% 0.07/0.40 Proof:
% 0.07/0.40 divide(divide(X, inverse(Y)), Y)
% 0.07/0.40 = { by lemma 6 R->L }
% 0.07/0.40 divide(inverse(divide(Z, Z)), inverse(divide(divide(X, inverse(Y)), Y)))
% 0.07/0.40 = { by lemma 6 R->L }
% 0.07/0.40 divide(inverse(divide(Z, Z)), inverse(divide(divide(X, inverse(Y)), divide(inverse(divide(Z, Z)), inverse(Y)))))
% 0.07/0.40 = { by axiom 2 (single_axiom) }
% 0.07/0.40 X
% 0.07/0.40
% 0.07/0.40 Lemma 8: divide(X, inverse(Y)) = divide(Y, inverse(X)).
% 0.07/0.40 Proof:
% 0.07/0.40 divide(X, inverse(Y))
% 0.07/0.40 = { by lemma 5 R->L }
% 0.07/0.40 divide(Y, inverse(divide(divide(X, inverse(Y)), Y)))
% 0.07/0.40 = { by lemma 7 }
% 0.07/0.40 divide(Y, inverse(X))
% 0.07/0.40
% 0.07/0.40 Lemma 9: inverse(divide(X, X)) = divide(Y, Y).
% 0.07/0.40 Proof:
% 0.07/0.40 inverse(divide(X, X))
% 0.07/0.40 = { by lemma 4 R->L }
% 0.07/0.40 divide(inverse(divide(X, X)), inverse(divide(Y, Y)))
% 0.07/0.40 = { by lemma 6 }
% 0.07/0.40 divide(Y, Y)
% 0.07/0.40
% 0.07/0.40 Lemma 10: inverse(inverse(X)) = X.
% 0.07/0.40 Proof:
% 0.07/0.40 inverse(inverse(X))
% 0.07/0.40 = { by lemma 7 R->L }
% 0.07/0.40 divide(divide(inverse(inverse(X)), inverse(inverse(X))), inverse(X))
% 0.07/0.40 = { by lemma 8 }
% 0.07/0.40 divide(X, inverse(divide(inverse(inverse(X)), inverse(inverse(X)))))
% 0.07/0.40 = { by lemma 9 }
% 0.07/0.40 divide(X, divide(Y, Y))
% 0.07/0.40 = { by lemma 9 R->L }
% 0.07/0.40 divide(X, inverse(divide(divide(X, Z), divide(X, Z))))
% 0.07/0.40 = { by axiom 2 (single_axiom) }
% 0.07/0.40 X
% 0.07/0.40
% 0.07/0.40 Lemma 11: divide(X, divide(X, Y)) = Y.
% 0.07/0.40 Proof:
% 0.07/0.40 divide(X, divide(X, Y))
% 0.07/0.40 = { by lemma 5 R->L }
% 0.07/0.40 divide(divide(Y, inverse(divide(X, Y))), divide(X, Y))
% 0.07/0.40 = { by lemma 7 }
% 0.07/0.40 Y
% 0.07/0.40
% 0.07/0.40 Lemma 12: inverse(divide(X, Y)) = divide(Y, X).
% 0.07/0.40 Proof:
% 0.07/0.40 inverse(divide(X, Y))
% 0.07/0.40 = { by lemma 11 R->L }
% 0.07/0.40 divide(Y, divide(Y, inverse(divide(X, Y))))
% 0.07/0.40 = { by lemma 5 }
% 0.07/0.40 divide(Y, X)
% 0.07/0.40
% 0.07/0.40 Lemma 13: divide(inverse(X), Y) = divide(inverse(Y), X).
% 0.07/0.40 Proof:
% 0.07/0.40 divide(inverse(X), Y)
% 0.07/0.40 = { by lemma 12 R->L }
% 0.07/0.40 inverse(divide(Y, inverse(X)))
% 0.07/0.40 = { by lemma 8 }
% 0.07/0.40 inverse(divide(X, inverse(Y)))
% 0.07/0.40 = { by lemma 12 }
% 0.07/0.40 divide(inverse(Y), X)
% 0.07/0.40
% 0.07/0.40 Lemma 14: divide(inverse(X), inverse(Y)) = divide(Y, X).
% 0.07/0.40 Proof:
% 0.07/0.40 divide(inverse(X), inverse(Y))
% 0.07/0.40 = { by lemma 8 R->L }
% 0.07/0.40 divide(Y, inverse(inverse(X)))
% 0.07/0.40 = { by lemma 10 }
% 0.07/0.40 divide(Y, X)
% 0.07/0.40
% 0.07/0.40 Lemma 15: divide(X, divide(divide(X, Y), divide(Z, Y))) = Z.
% 0.07/0.40 Proof:
% 0.07/0.40 divide(X, divide(divide(X, Y), divide(Z, Y)))
% 0.07/0.40 = { by lemma 6 R->L }
% 0.07/0.40 divide(X, divide(inverse(divide(W, W)), inverse(divide(divide(X, Y), divide(Z, Y)))))
% 0.07/0.40 = { by lemma 6 R->L }
% 0.07/0.40 divide(inverse(divide(W, W)), inverse(divide(X, divide(inverse(divide(W, W)), inverse(divide(divide(X, Y), divide(Z, Y)))))))
% 0.07/0.40 = { by lemma 3 }
% 0.07/0.40 Z
% 0.07/0.40
% 0.07/0.40 Lemma 16: divide(inverse(Y), divide(inverse(X), Z)) = divide(X, divide(Y, Z)).
% 0.07/0.40 Proof:
% 0.07/0.40 divide(inverse(Y), divide(inverse(X), Z))
% 0.07/0.40 = { by lemma 12 R->L }
% 0.07/0.40 divide(inverse(Y), inverse(divide(Z, inverse(X))))
% 0.07/0.40 = { by lemma 14 }
% 0.07/0.40 divide(divide(Z, inverse(X)), Y)
% 0.07/0.40 = { by lemma 12 R->L }
% 0.07/0.40 divide(inverse(divide(inverse(X), Z)), Y)
% 0.07/0.40 = { by lemma 15 R->L }
% 0.07/0.40 divide(inverse(divide(inverse(X), Z)), divide(inverse(X), divide(divide(inverse(X), Z), divide(Y, Z))))
% 0.07/0.40 = { by lemma 12 R->L }
% 0.07/0.40 divide(inverse(divide(inverse(X), Z)), divide(inverse(X), inverse(divide(divide(Y, Z), divide(inverse(X), Z)))))
% 0.07/0.40 = { by lemma 14 }
% 0.07/0.40 divide(inverse(divide(inverse(X), Z)), divide(divide(divide(Y, Z), divide(inverse(X), Z)), X))
% 0.07/0.40 = { by lemma 12 R->L }
% 0.07/0.40 divide(inverse(divide(inverse(X), Z)), inverse(divide(X, divide(divide(Y, Z), divide(inverse(X), Z)))))
% 0.07/0.40 = { by lemma 14 }
% 0.07/0.40 divide(divide(X, divide(divide(Y, Z), divide(inverse(X), Z))), divide(inverse(X), Z))
% 0.07/0.40 = { by lemma 15 R->L }
% 0.07/0.40 divide(X, divide(divide(X, divide(divide(Y, Z), divide(inverse(X), Z))), divide(divide(divide(X, divide(divide(Y, Z), divide(inverse(X), Z))), divide(inverse(X), Z)), divide(divide(Y, Z), divide(inverse(X), Z)))))
% 0.07/0.40 = { by lemma 15 }
% 0.07/0.40 divide(X, divide(Y, Z))
% 0.07/0.40
% 0.07/0.40 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4)).
% 0.07/0.40 Proof:
% 0.07/0.40 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.07/0.40 = { by axiom 1 (multiply) }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.07/0.40 = { by axiom 1 (multiply) }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), multiply(divide(inverse(b2), inverse(b2)), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.07/0.40 = { by axiom 1 (multiply) }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.07/0.40 = { by axiom 1 (multiply) }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(divide(a3, inverse(b3)), c3), multiply(a4, b4))
% 0.07/0.40 = { by axiom 1 (multiply) }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)), multiply(a4, b4))
% 0.07/0.40 = { by axiom 1 (multiply) }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 8 }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), divide(a2, inverse(divide(inverse(b2), inverse(b2)))), divide(divide(a3, inverse(b3)), inverse(c3)), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 4 }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, inverse(b3)), inverse(c3)), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 8 }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(c3, inverse(divide(a3, inverse(b3)))), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 12 }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(c3, divide(inverse(b3), a3)), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 13 }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(c3, divide(inverse(a3), b3)), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 11 R->L }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(b3, divide(b3, divide(c3, divide(inverse(a3), b3)))), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 16 R->L }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(b3, divide(inverse(c3), divide(inverse(b3), divide(inverse(a3), b3)))), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 13 R->L }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(b3, divide(inverse(c3), divide(inverse(divide(inverse(a3), b3)), b3))), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 16 }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(b3, divide(divide(inverse(a3), b3), divide(c3, b3))), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 11 R->L }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(b3, divide(inverse(a3), divide(inverse(a3), divide(divide(inverse(a3), b3), divide(c3, b3))))), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 15 }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(b3, divide(inverse(a3), c3)), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 16 R->L }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(inverse(inverse(a3)), divide(inverse(b3), c3)), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 10 }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(b3), c3)), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 13 R->L }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), b3)), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 12 R->L }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(a4, inverse(b4)))
% 0.07/0.40 = { by lemma 8 R->L }
% 0.07/0.40 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(b4, inverse(a4)))
% 0.07/0.40 = { by lemma 6 R->L }
% 0.07/0.40 tuple(divide(inverse(divide(X, X)), inverse(divide(inverse(a1), inverse(a1)))), a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(b4, inverse(a4)))
% 0.07/0.40 = { by lemma 4 }
% 0.07/0.40 tuple(inverse(divide(X, X)), a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(b4, inverse(a4)))
% 0.07/0.40 = { by lemma 4 R->L }
% 0.07/0.40 tuple(divide(inverse(divide(X, X)), inverse(divide(inverse(b1), inverse(b1)))), a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(b4, inverse(a4)))
% 0.07/0.40 = { by lemma 6 }
% 0.07/0.40 tuple(divide(inverse(b1), inverse(b1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(b4, inverse(a4)))
% 0.07/0.40 = { by axiom 1 (multiply) R->L }
% 0.07/0.40 tuple(divide(inverse(b1), inverse(b1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))), multiply(b4, a4))
% 0.07/0.40 = { by axiom 1 (multiply) R->L }
% 0.07/0.40 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, divide(b3, inverse(c3))), multiply(b4, a4))
% 0.07/0.40 = { by axiom 1 (multiply) R->L }
% 0.07/0.40 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.07/0.40 = { by axiom 1 (multiply) R->L }
% 0.07/0.40 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.07/0.40 % SZS output end Proof
% 0.07/0.40
% 0.07/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------