%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP074-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 10:09:12 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.51s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP074-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 09:17:36 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.51 Command-line arguments: --no-flatten-goal
% 0.21/0.51
% 0.21/0.51 % SZS status Unsatisfiable
% 0.21/0.51
% 0.21/0.53 % SZS output start Proof
% 0.21/0.53 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.21/0.53 Axiom 2 (single_axiom): divide(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, W)))), W) = Z.
% 0.21/0.53
% 0.21/0.53 Lemma 3: inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, divide(W, V))))) = divide(inverse(divide(divide(divide(U, U), W), Z)), V).
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, divide(W, V)))))
% 0.21/0.53 = { by axiom 2 (single_axiom) R->L }
% 0.21/0.53 divide(inverse(divide(divide(divide(U, U), W), divide(inverse(divide(divide(divide(X, X), Y), divide(Z, divide(Y, divide(W, V))))), divide(W, V)))), V)
% 0.21/0.53 = { by axiom 2 (single_axiom) }
% 0.21/0.53 divide(inverse(divide(divide(divide(U, U), W), Z)), V)
% 0.21/0.53
% 0.21/0.53 Lemma 4: divide(divide(inverse(divide(divide(divide(X, X), Y), Z)), W), divide(Y, W)) = Z.
% 0.21/0.53 Proof:
% 0.21/0.53 divide(divide(inverse(divide(divide(divide(X, X), Y), Z)), W), divide(Y, W))
% 0.21/0.53 = { by lemma 3 R->L }
% 0.21/0.53 divide(inverse(divide(divide(divide(V, V), U), divide(Z, divide(U, divide(Y, W))))), divide(Y, W))
% 0.21/0.53 = { by axiom 2 (single_axiom) }
% 0.21/0.53 Z
% 0.21/0.53
% 0.21/0.53 Lemma 5: inverse(divide(divide(divide(W, W), Y), Z)) = inverse(divide(divide(divide(X, X), Y), Z)).
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(divide(divide(divide(W, W), Y), Z))
% 0.21/0.53 = { by axiom 2 (single_axiom) R->L }
% 0.21/0.53 inverse(divide(divide(divide(W, W), Y), divide(inverse(divide(divide(divide(V, V), U), divide(Z, divide(U, divide(Y, divide(T, S)))))), divide(Y, divide(T, S)))))
% 0.21/0.53 = { by lemma 3 }
% 0.21/0.53 divide(inverse(divide(divide(divide(X2, X2), T), inverse(divide(divide(divide(V, V), U), divide(Z, divide(U, divide(Y, divide(T, S)))))))), S)
% 0.21/0.53 = { by lemma 3 R->L }
% 0.21/0.53 inverse(divide(divide(divide(X, X), Y), divide(inverse(divide(divide(divide(V, V), U), divide(Z, divide(U, divide(Y, divide(T, S)))))), divide(Y, divide(T, S)))))
% 0.21/0.53 = { by axiom 2 (single_axiom) }
% 0.21/0.53 inverse(divide(divide(divide(X, X), Y), Z))
% 0.21/0.53
% 0.21/0.53 Lemma 6: divide(divide(divide(inverse(divide(divide(divide(X, X), Y), Z)), W), V), divide(U, V)) = divide(Z, divide(U, divide(Y, W))).
% 0.21/0.53 Proof:
% 0.21/0.53 divide(divide(divide(inverse(divide(divide(divide(X, X), Y), Z)), W), V), divide(U, V))
% 0.21/0.53 = { by lemma 3 R->L }
% 0.21/0.53 divide(divide(inverse(divide(divide(divide(T, T), U), divide(Z, divide(U, divide(Y, W))))), V), divide(U, V))
% 0.21/0.53 = { by lemma 4 }
% 0.21/0.53 divide(Z, divide(U, divide(Y, W)))
% 0.21/0.53
% 0.21/0.53 Lemma 7: divide(inverse(divide(divide(divide(X, X), Y), divide(Z, Y))), inverse(divide(W, W))) = Z.
% 0.21/0.53 Proof:
% 0.21/0.53 divide(inverse(divide(divide(divide(X, X), Y), divide(Z, Y))), inverse(divide(W, W)))
% 0.21/0.53 = { by lemma 4 R->L }
% 0.21/0.53 divide(inverse(divide(divide(divide(X, X), Y), divide(Z, Y))), inverse(divide(divide(divide(inverse(divide(divide(divide(V, V), U), W)), inverse(divide(divide(divide(V, V), U), W))), divide(U, inverse(divide(divide(divide(V, V), U), W)))), W)))
% 0.21/0.53 = { by lemma 5 }
% 0.21/0.53 divide(inverse(divide(divide(divide(inverse(divide(divide(divide(inverse(divide(divide(divide(V, V), U), W)), inverse(divide(divide(divide(V, V), U), W))), divide(U, inverse(divide(divide(divide(V, V), U), W)))), W)), inverse(divide(divide(divide(inverse(divide(divide(divide(V, V), U), W)), inverse(divide(divide(divide(V, V), U), W))), divide(U, inverse(divide(divide(divide(V, V), U), W)))), W))), Y), divide(Z, Y))), inverse(divide(divide(divide(inverse(divide(divide(divide(V, V), U), W)), inverse(divide(divide(divide(V, V), U), W))), divide(U, inverse(divide(divide(divide(V, V), U), W)))), W)))
% 0.21/0.53 = { by lemma 6 }
% 0.21/0.53 divide(inverse(divide(W, divide(Z, divide(divide(U, inverse(divide(divide(divide(V, V), U), W))), inverse(divide(divide(divide(inverse(divide(divide(divide(V, V), U), W)), inverse(divide(divide(divide(V, V), U), W))), divide(U, inverse(divide(divide(divide(V, V), U), W)))), W)))))), inverse(divide(divide(divide(inverse(divide(divide(divide(V, V), U), W)), inverse(divide(divide(divide(V, V), U), W))), divide(U, inverse(divide(divide(divide(V, V), U), W)))), W)))
% 0.21/0.53 = { by lemma 4 R->L }
% 0.21/0.53 divide(inverse(divide(divide(divide(inverse(divide(divide(divide(V, V), U), W)), inverse(divide(divide(divide(V, V), U), W))), divide(U, inverse(divide(divide(divide(V, V), U), W)))), divide(Z, divide(divide(U, inverse(divide(divide(divide(V, V), U), W))), inverse(divide(divide(divide(inverse(divide(divide(divide(V, V), U), W)), inverse(divide(divide(divide(V, V), U), W))), divide(U, inverse(divide(divide(divide(V, V), U), W)))), W)))))), inverse(divide(divide(divide(inverse(divide(divide(divide(V, V), U), W)), inverse(divide(divide(divide(V, V), U), W))), divide(U, inverse(divide(divide(divide(V, V), U), W)))), W)))
% 0.21/0.53 = { by axiom 2 (single_axiom) }
% 0.21/0.53 Z
% 0.21/0.53
% 0.21/0.53 Lemma 8: divide(X, divide(Y, inverse(divide(Z, Z)))) = divide(X, Y).
% 0.21/0.53 Proof:
% 0.21/0.53 divide(X, divide(Y, inverse(divide(Z, Z))))
% 0.21/0.53 = { by lemma 7 R->L }
% 0.21/0.53 divide(divide(inverse(divide(divide(divide(W, W), Y), divide(X, Y))), inverse(divide(Z, Z))), divide(Y, inverse(divide(Z, Z))))
% 0.21/0.53 = { by lemma 4 }
% 0.21/0.53 divide(X, Y)
% 0.21/0.53
% 0.21/0.53 Lemma 9: divide(X, inverse(divide(Y, Y))) = X.
% 0.21/0.53 Proof:
% 0.21/0.53 divide(X, inverse(divide(Y, Y)))
% 0.21/0.53 = { by lemma 4 R->L }
% 0.21/0.53 divide(divide(inverse(divide(divide(divide(Z, Z), W), divide(X, inverse(divide(Y, Y))))), V), divide(W, V))
% 0.21/0.53 = { by lemma 8 }
% 0.21/0.53 divide(divide(inverse(divide(divide(divide(Z, Z), W), X)), V), divide(W, V))
% 0.21/0.53 = { by lemma 4 }
% 0.21/0.53 X
% 0.21/0.53
% 0.21/0.53 Lemma 10: inverse(divide(X, X)) = divide(Y, Y).
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(divide(X, X))
% 0.21/0.53 = { by lemma 9 R->L }
% 0.21/0.53 divide(inverse(divide(X, X)), inverse(divide(Z, Z)))
% 0.21/0.53 = { by lemma 9 R->L }
% 0.21/0.53 divide(inverse(divide(divide(X, X), inverse(divide(W, W)))), inverse(divide(Z, Z)))
% 0.21/0.53 = { by lemma 9 R->L }
% 0.21/0.53 divide(inverse(divide(divide(divide(X, X), inverse(divide(W, W))), inverse(divide(V, V)))), inverse(divide(Z, Z)))
% 0.21/0.53 = { by lemma 5 }
% 0.21/0.53 divide(inverse(divide(divide(divide(divide(divide(Y, Y), U), divide(divide(Y, Y), U)), inverse(divide(W, W))), inverse(divide(V, V)))), inverse(divide(Z, Z)))
% 0.21/0.53 = { by lemma 9 }
% 0.21/0.53 divide(inverse(divide(divide(divide(divide(Y, Y), U), divide(divide(Y, Y), U)), inverse(divide(W, W)))), inverse(divide(Z, Z)))
% 0.21/0.53 = { by lemma 9 }
% 0.21/0.53 divide(inverse(divide(divide(divide(Y, Y), U), divide(divide(Y, Y), U))), inverse(divide(Z, Z)))
% 0.21/0.53 = { by lemma 7 }
% 0.21/0.53 divide(Y, Y)
% 0.21/0.53
% 0.21/0.53 Lemma 11: divide(divide(X, Y), divide(Z, Y)) = divide(X, Z).
% 0.21/0.53 Proof:
% 0.21/0.53 divide(divide(X, Y), divide(Z, Y))
% 0.21/0.53 = { by axiom 2 (single_axiom) R->L }
% 0.21/0.53 divide(divide(divide(inverse(divide(divide(divide(W, W), V), divide(X, divide(V, U)))), U), Y), divide(Z, Y))
% 0.21/0.53 = { by lemma 6 }
% 0.21/0.53 divide(divide(X, divide(V, U)), divide(Z, divide(V, U)))
% 0.21/0.53 = { by lemma 6 R->L }
% 0.21/0.53 divide(divide(divide(inverse(divide(divide(divide(T, T), V), divide(X, divide(V, U)))), U), inverse(divide(S, S))), divide(Z, inverse(divide(S, S))))
% 0.21/0.53 = { by axiom 2 (single_axiom) }
% 0.21/0.53 divide(divide(X, inverse(divide(S, S))), divide(Z, inverse(divide(S, S))))
% 0.21/0.53 = { by lemma 9 }
% 0.21/0.53 divide(X, divide(Z, inverse(divide(S, S))))
% 0.21/0.53 = { by lemma 8 }
% 0.21/0.53 divide(X, Z)
% 0.21/0.53
% 0.21/0.53 Lemma 12: divide(X, divide(Y, Y)) = X.
% 0.21/0.53 Proof:
% 0.21/0.53 divide(X, divide(Y, Y))
% 0.21/0.53 = { by lemma 10 R->L }
% 0.21/0.53 divide(X, inverse(divide(Z, Z)))
% 0.21/0.53 = { by lemma 9 }
% 0.21/0.53 X
% 0.21/0.53
% 0.21/0.53 Lemma 13: inverse(divide(divide(X, X), Y)) = Y.
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(divide(divide(X, X), Y))
% 0.21/0.53 = { by lemma 11 R->L }
% 0.21/0.53 inverse(divide(divide(divide(X, X), Z), divide(Y, Z)))
% 0.21/0.53 = { by lemma 11 R->L }
% 0.21/0.53 inverse(divide(divide(divide(X, X), Z), divide(divide(Y, divide(W, V)), divide(Z, divide(W, V)))))
% 0.21/0.53 = { by lemma 3 }
% 0.21/0.53 divide(inverse(divide(divide(divide(U, U), W), divide(Y, divide(W, V)))), V)
% 0.21/0.53 = { by axiom 2 (single_axiom) }
% 0.21/0.53 Y
% 0.21/0.53
% 0.21/0.53 Lemma 14: inverse(divide(X, Y)) = divide(Y, X).
% 0.21/0.53 Proof:
% 0.21/0.53 inverse(divide(X, Y))
% 0.21/0.53 = { by lemma 11 R->L }
% 0.21/0.54 inverse(divide(divide(X, X), divide(Y, X)))
% 0.21/0.54 = { by lemma 12 R->L }
% 0.21/0.54 inverse(divide(divide(divide(X, X), divide(Y, X)), divide(Z, Z)))
% 0.21/0.54 = { by lemma 5 R->L }
% 0.21/0.54 inverse(divide(divide(divide(W, W), divide(Y, X)), divide(Z, Z)))
% 0.21/0.54 = { by lemma 12 }
% 0.21/0.54 inverse(divide(divide(W, W), divide(Y, X)))
% 0.21/0.54 = { by lemma 13 }
% 0.21/0.54 divide(Y, X)
% 0.21/0.54
% 0.21/0.54 Lemma 15: divide(divide(X, X), Y) = inverse(Y).
% 0.21/0.54 Proof:
% 0.21/0.54 divide(divide(X, X), Y)
% 0.21/0.54 = { by lemma 12 R->L }
% 0.21/0.54 divide(divide(X, X), divide(Y, divide(Z, Z)))
% 0.21/0.54 = { by lemma 11 R->L }
% 0.21/0.54 divide(divide(X, X), divide(divide(Y, W), divide(divide(Z, Z), W)))
% 0.21/0.54 = { by lemma 14 R->L }
% 0.21/0.54 divide(divide(X, X), inverse(divide(divide(divide(Z, Z), W), divide(Y, W))))
% 0.21/0.54 = { by lemma 10 R->L }
% 0.21/0.54 divide(inverse(divide(V, V)), inverse(divide(divide(divide(Z, Z), W), divide(Y, W))))
% 0.21/0.54 = { by lemma 14 R->L }
% 0.21/0.54 inverse(divide(inverse(divide(divide(divide(Z, Z), W), divide(Y, W))), inverse(divide(V, V))))
% 0.21/0.54 = { by lemma 7 }
% 0.21/0.54 inverse(Y)
% 0.21/0.54
% 0.21/0.54 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3))).
% 0.21/0.54 Proof:
% 0.21/0.54 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.21/0.54 = { by axiom 1 (multiply) }
% 0.21/0.54 tuple(divide(inverse(a1), inverse(a1)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 0.21/0.54 = { by axiom 1 (multiply) }
% 0.21/0.54 tuple(divide(inverse(a1), inverse(a1)), multiply(divide(inverse(b2), inverse(b2)), a2), multiply(multiply(a3, b3), c3))
% 0.21/0.54 = { by axiom 1 (multiply) }
% 0.21/0.54 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(multiply(a3, b3), c3))
% 0.21/0.54 = { by axiom 1 (multiply) }
% 0.21/0.54 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(divide(a3, inverse(b3)), c3))
% 0.21/0.54 = { by axiom 1 (multiply) }
% 0.21/0.54 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)))
% 0.21/0.54 = { by lemma 15 }
% 0.21/0.54 tuple(divide(inverse(a1), inverse(a1)), inverse(inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)))
% 0.21/0.54 = { by lemma 15 R->L }
% 0.21/0.54 tuple(divide(inverse(a1), inverse(a1)), inverse(divide(divide(X, X), a2)), divide(divide(a3, inverse(b3)), inverse(c3)))
% 0.21/0.54 = { by lemma 13 }
% 0.21/0.54 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, inverse(b3)), inverse(c3)))
% 0.21/0.54 = { by lemma 15 R->L }
% 0.21/0.54 tuple(divide(inverse(a1), inverse(a1)), a2, divide(divide(a3, divide(divide(Y, Y), b3)), inverse(c3)))
% 0.21/0.54 = { by lemma 14 R->L }
% 0.21/0.54 tuple(divide(inverse(a1), inverse(a1)), a2, divide(inverse(divide(divide(divide(Y, Y), b3), a3)), inverse(c3)))
% 0.21/0.54 = { by lemma 3 R->L }
% 0.21/0.54 tuple(divide(inverse(a1), inverse(a1)), a2, inverse(divide(divide(divide(Z, Z), divide(Z, Z)), divide(a3, divide(divide(Z, Z), divide(b3, inverse(c3)))))))
% 0.21/0.54 = { by lemma 15 }
% 0.21/0.54 tuple(divide(inverse(a1), inverse(a1)), a2, inverse(divide(divide(divide(Z, Z), divide(Z, Z)), divide(a3, inverse(divide(b3, inverse(c3)))))))
% 0.21/0.54 = { by lemma 13 }
% 0.21/0.54 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 0.21/0.54 = { by lemma 4 R->L }
% 0.21/0.54 tuple(divide(divide(inverse(divide(divide(divide(divide(inverse(b1), inverse(b1)), divide(inverse(b1), inverse(b1))), divide(inverse(b1), inverse(b1))), divide(inverse(a1), inverse(a1)))), W), divide(divide(inverse(b1), inverse(b1)), W)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 0.21/0.54 = { by lemma 12 }
% 0.21/0.54 tuple(divide(divide(inverse(divide(divide(divide(inverse(b1), inverse(b1)), divide(inverse(b1), inverse(b1))), divide(inverse(b1), inverse(b1)))), W), divide(divide(inverse(b1), inverse(b1)), W)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 0.21/0.54 = { by lemma 4 }
% 0.21/0.54 tuple(divide(inverse(b1), inverse(b1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))))
% 0.21/0.54 = { by axiom 1 (multiply) R->L }
% 0.21/0.54 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, divide(b3, inverse(c3))))
% 0.21/0.54 = { by axiom 1 (multiply) R->L }
% 0.21/0.54 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, multiply(b3, c3)))
% 0.21/0.54 = { by axiom 1 (multiply) R->L }
% 0.21/0.54 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 0.21/0.54 % SZS output end Proof
% 0.21/0.54
% 0.21/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------