%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP096-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 0.17s 0.48s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP096-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 09:19:16 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.48 Command-line arguments: --no-flatten-goal
% 0.17/0.48
% 0.17/0.48 % SZS status Unsatisfiable
% 0.17/0.48
% 0.17/0.50 % SZS output start Proof
% 0.17/0.50 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.17/0.51 Axiom 2 (single_axiom): divide(divide(X, inverse(divide(Y, divide(X, Z)))), Z) = Y.
% 0.17/0.51
% 0.17/0.51 Lemma 3: divide(X, inverse(divide(Y, divide(X, divide(Z, W))))) = divide(divide(Z, inverse(Y)), W).
% 0.17/0.51 Proof:
% 0.17/0.51 divide(X, inverse(divide(Y, divide(X, divide(Z, W)))))
% 0.17/0.51 = { by axiom 2 (single_axiom) R->L }
% 0.17/0.51 divide(divide(Z, inverse(divide(divide(X, inverse(divide(Y, divide(X, divide(Z, W))))), divide(Z, W)))), W)
% 0.17/0.51 = { by axiom 2 (single_axiom) }
% 0.17/0.51 divide(divide(Z, inverse(Y)), W)
% 0.17/0.51
% 0.17/0.51 Lemma 4: divide(divide(divide(X, inverse(Y)), Z), divide(X, Z)) = Y.
% 0.17/0.51 Proof:
% 0.17/0.51 divide(divide(divide(X, inverse(Y)), Z), divide(X, Z))
% 0.17/0.51 = { by lemma 3 R->L }
% 0.17/0.51 divide(divide(W, inverse(divide(Y, divide(W, divide(X, Z))))), divide(X, Z))
% 0.17/0.51 = { by axiom 2 (single_axiom) }
% 0.17/0.51 Y
% 0.17/0.51
% 0.17/0.51 Lemma 5: divide(X, divide(divide(Y, inverse(X)), divide(Y, inverse(Z)))) = Z.
% 0.17/0.51 Proof:
% 0.17/0.51 divide(X, divide(divide(Y, inverse(X)), divide(Y, inverse(Z))))
% 0.17/0.51 = { by lemma 4 R->L }
% 0.17/0.51 divide(divide(divide(divide(Y, inverse(X)), inverse(Z)), divide(Y, inverse(Z))), divide(divide(Y, inverse(X)), divide(Y, inverse(Z))))
% 0.17/0.51 = { by lemma 4 }
% 0.17/0.51 Z
% 0.17/0.51
% 0.17/0.51 Lemma 6: divide(divide(X, Y), divide(Z, divide(Z, inverse(W)))) = divide(divide(X, inverse(W)), Y).
% 0.17/0.51 Proof:
% 0.17/0.51 divide(divide(X, Y), divide(Z, divide(Z, inverse(W))))
% 0.17/0.51 = { by axiom 2 (single_axiom) R->L }
% 0.17/0.51 divide(divide(X, inverse(divide(divide(divide(X, Y), divide(Z, divide(Z, inverse(W)))), divide(X, Y)))), Y)
% 0.17/0.51 = { by axiom 2 (single_axiom) R->L }
% 0.17/0.51 divide(divide(X, inverse(divide(divide(divide(X, Y), divide(Z, divide(Z, inverse(W)))), divide(divide(Z, inverse(divide(divide(X, Y), divide(Z, divide(Z, inverse(W)))))), divide(Z, inverse(W)))))), Y)
% 0.17/0.51 = { by lemma 5 }
% 0.17/0.51 divide(divide(X, inverse(W)), Y)
% 0.17/0.51
% 0.17/0.51 Lemma 7: divide(divide(X, inverse(divide(Y, Z))), inverse(W)) = divide(X, inverse(divide(divide(Y, inverse(W)), Z))).
% 0.17/0.51 Proof:
% 0.17/0.51 divide(divide(X, inverse(divide(Y, Z))), inverse(W))
% 0.17/0.51 = { by lemma 3 R->L }
% 0.17/0.51 divide(X, inverse(divide(divide(Y, Z), divide(X, divide(X, inverse(W))))))
% 0.17/0.51 = { by lemma 6 }
% 0.17/0.51 divide(X, inverse(divide(divide(Y, inverse(W)), Z)))
% 0.17/0.51
% 0.17/0.51 Lemma 8: divide(divide(X, inverse(Y)), inverse(Z)) = divide(X, inverse(divide(Y, inverse(Z)))).
% 0.17/0.51 Proof:
% 0.17/0.51 divide(divide(X, inverse(Y)), inverse(Z))
% 0.17/0.51 = { by axiom 2 (single_axiom) R->L }
% 0.17/0.51 divide(divide(X, inverse(divide(divide(W, inverse(divide(Y, divide(W, V)))), V))), inverse(Z))
% 0.17/0.51 = { by lemma 7 }
% 0.17/0.51 divide(X, inverse(divide(divide(divide(W, inverse(divide(Y, divide(W, V)))), inverse(Z)), V)))
% 0.17/0.51 = { by lemma 7 }
% 0.17/0.51 divide(X, inverse(divide(divide(W, inverse(divide(divide(Y, inverse(Z)), divide(W, V)))), V)))
% 0.17/0.51 = { by axiom 2 (single_axiom) }
% 0.17/0.51 divide(X, inverse(divide(Y, inverse(Z))))
% 0.17/0.51
% 0.17/0.51 Lemma 9: divide(divide(X, inverse(Z)), Y) = divide(divide(X, Y), inverse(Z)).
% 0.17/0.51 Proof:
% 0.17/0.51 divide(divide(X, inverse(Z)), Y)
% 0.17/0.51 = { by axiom 2 (single_axiom) R->L }
% 0.17/0.51 divide(divide(X, inverse(divide(divide(W, inverse(divide(Z, divide(W, inverse(V))))), inverse(V)))), Y)
% 0.17/0.51 = { by lemma 8 R->L }
% 0.17/0.51 divide(divide(divide(X, inverse(divide(W, inverse(divide(Z, divide(W, inverse(V))))))), inverse(V)), Y)
% 0.17/0.51 = { by lemma 3 R->L }
% 0.17/0.51 divide(T, inverse(divide(V, divide(T, divide(divide(X, inverse(divide(W, inverse(divide(Z, divide(W, inverse(V))))))), Y)))))
% 0.17/0.51 = { by lemma 6 R->L }
% 0.17/0.51 divide(T, inverse(divide(V, divide(T, divide(divide(X, Y), divide(U, divide(U, inverse(divide(W, inverse(divide(Z, divide(W, inverse(V)))))))))))))
% 0.17/0.51 = { by lemma 3 }
% 0.17/0.51 divide(divide(divide(X, Y), inverse(V)), divide(U, divide(U, inverse(divide(W, inverse(divide(Z, divide(W, inverse(V)))))))))
% 0.17/0.51 = { by lemma 6 }
% 0.17/0.51 divide(divide(divide(X, Y), inverse(divide(W, inverse(divide(Z, divide(W, inverse(V))))))), inverse(V))
% 0.17/0.51 = { by lemma 8 }
% 0.17/0.51 divide(divide(X, Y), inverse(divide(divide(W, inverse(divide(Z, divide(W, inverse(V))))), inverse(V))))
% 0.17/0.51 = { by axiom 2 (single_axiom) }
% 0.17/0.51 divide(divide(X, Y), inverse(Z))
% 0.17/0.51
% 0.17/0.51 Lemma 10: divide(divide(X, X), inverse(Y)) = Y.
% 0.17/0.51 Proof:
% 0.17/0.51 divide(divide(X, X), inverse(Y))
% 0.17/0.51 = { by lemma 9 R->L }
% 0.17/0.51 divide(divide(X, inverse(Y)), X)
% 0.17/0.51 = { by axiom 2 (single_axiom) R->L }
% 0.17/0.51 divide(divide(X, inverse(Y)), divide(divide(Z, inverse(divide(X, divide(Z, inverse(Y))))), inverse(Y)))
% 0.17/0.51 = { by axiom 2 (single_axiom) R->L }
% 0.17/0.51 divide(divide(divide(divide(Z, inverse(divide(X, divide(Z, inverse(Y))))), inverse(Y)), inverse(Y)), divide(divide(Z, inverse(divide(X, divide(Z, inverse(Y))))), inverse(Y)))
% 0.17/0.51 = { by lemma 4 }
% 0.17/0.51 Y
% 0.17/0.51
% 0.17/0.51 Lemma 11: divide(Y, inverse(X)) = divide(X, inverse(Y)).
% 0.17/0.51 Proof:
% 0.17/0.51 divide(Y, inverse(X))
% 0.17/0.51 = { by lemma 10 R->L }
% 0.17/0.51 divide(divide(divide(Z, Z), inverse(Y)), inverse(X))
% 0.17/0.51 = { by lemma 9 R->L }
% 0.17/0.51 divide(divide(divide(Z, Z), inverse(X)), inverse(Y))
% 0.17/0.51 = { by lemma 8 }
% 0.17/0.51 divide(divide(Z, Z), inverse(divide(X, inverse(Y))))
% 0.17/0.51 = { by lemma 10 }
% 0.17/0.51 divide(X, inverse(Y))
% 0.17/0.51
% 0.17/0.51 Lemma 12: divide(X, divide(X, Y)) = Y.
% 0.17/0.51 Proof:
% 0.17/0.51 divide(X, divide(X, Y))
% 0.17/0.51 = { by lemma 10 R->L }
% 0.17/0.51 divide(X, divide(X, divide(divide(Z, Z), inverse(Y))))
% 0.17/0.51 = { by lemma 10 R->L }
% 0.17/0.51 divide(X, divide(divide(divide(Z, Z), inverse(X)), divide(divide(Z, Z), inverse(Y))))
% 0.17/0.51 = { by lemma 5 }
% 0.17/0.51 Y
% 0.17/0.51
% 0.17/0.51 Lemma 13: divide(X, inverse(divide(Y, X))) = Y.
% 0.17/0.51 Proof:
% 0.17/0.51 divide(X, inverse(divide(Y, X)))
% 0.17/0.51 = { by axiom 2 (single_axiom) R->L }
% 0.17/0.51 divide(X, inverse(divide(Y, divide(divide(Z, inverse(divide(X, divide(Z, W)))), W))))
% 0.17/0.51 = { by axiom 2 (single_axiom) R->L }
% 0.17/0.51 divide(divide(divide(Z, inverse(divide(X, divide(Z, W)))), W), inverse(divide(Y, divide(divide(Z, inverse(divide(X, divide(Z, W)))), W))))
% 0.17/0.51 = { by lemma 9 R->L }
% 0.17/0.51 divide(divide(divide(Z, inverse(divide(X, divide(Z, W)))), inverse(divide(Y, divide(divide(Z, inverse(divide(X, divide(Z, W)))), W)))), W)
% 0.17/0.51 = { by axiom 2 (single_axiom) }
% 0.17/0.51 Y
% 0.17/0.51
% 0.17/0.51 Lemma 14: inverse(divide(X, Y)) = divide(Y, X).
% 0.17/0.51 Proof:
% 0.17/0.51 inverse(divide(X, Y))
% 0.17/0.51 = { by lemma 12 R->L }
% 0.17/0.51 divide(Y, divide(Y, inverse(divide(X, Y))))
% 0.17/0.51 = { by lemma 13 }
% 0.17/0.51 divide(Y, X)
% 0.17/0.51
% 0.17/0.51 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)).
% 0.17/0.51 Proof:
% 0.17/0.51 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.17/0.51 = { by axiom 1 (multiply) }
% 0.17/0.51 tuple(divide(inverse(a1), inverse(a1)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.17/0.51 = { by axiom 1 (multiply) }
% 0.17/0.51 tuple(divide(inverse(a1), inverse(a1)), multiply(divide(inverse(b2), inverse(b2)), a2), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.17/0.51 = { by axiom 1 (multiply) }
% 0.17/0.51 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(multiply(a3, b3), c3), multiply(a4, b4))
% 0.17/0.51 = { by axiom 1 (multiply) }
% 0.17/0.51 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), multiply(divide(a3, inverse(b3)), c3), multiply(a4, b4))
% 0.17/0.51 = { by axiom 1 (multiply) }
% 0.17/0.51 tuple(divide(inverse(a1), inverse(a1)), divide(divide(inverse(b2), inverse(b2)), inverse(a2)), divide(divide(a3, inverse(b3)), inverse(c3)), multiply(a4, b4))
% 0.17/0.51 = { by axiom 1 (multiply) }
% 0.17/0.51 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)))
% 0.17/0.51 = { by lemma 8 }
% 0.17/0.51 tuple(divide(inverse(a1), inverse(a1)), divide(inverse(b2), inverse(divide(b2, inverse(a2)))), divide(divide(a3, inverse(b3)), inverse(c3)), divide(a4, inverse(b4)))
% 0.17/0.51 = { by lemma 8 }
% 0.17/0.51 tuple(divide(inverse(a1), inverse(a1)), divide(inverse(b2), inverse(divide(b2, inverse(a2)))), divide(a3, inverse(divide(b3, inverse(c3)))), divide(a4, inverse(b4)))
% 0.17/0.51 = { by lemma 14 }
% 0.17/0.51 tuple(divide(inverse(a1), inverse(a1)), divide(inverse(b2), divide(inverse(a2), b2)), divide(a3, inverse(divide(b3, inverse(c3)))), divide(a4, inverse(b4)))
% 0.17/0.51 = { by lemma 14 }
% 0.17/0.51 tuple(divide(inverse(a1), inverse(a1)), divide(inverse(b2), divide(inverse(a2), b2)), divide(a3, divide(inverse(c3), b3)), divide(a4, inverse(b4)))
% 0.17/0.51 = { by lemma 14 R->L }
% 0.17/0.51 tuple(divide(inverse(a1), inverse(a1)), divide(inverse(b2), inverse(divide(b2, inverse(a2)))), divide(a3, divide(inverse(c3), b3)), divide(a4, inverse(b4)))
% 0.17/0.51 = { by lemma 11 R->L }
% 0.17/0.51 tuple(divide(inverse(a1), inverse(a1)), divide(inverse(b2), inverse(divide(a2, inverse(b2)))), divide(a3, divide(inverse(c3), b3)), divide(a4, inverse(b4)))
% 0.17/0.51 = { by lemma 14 }
% 0.17/0.51 tuple(divide(inverse(a1), inverse(a1)), divide(inverse(b2), divide(inverse(b2), a2)), divide(a3, divide(inverse(c3), b3)), divide(a4, inverse(b4)))
% 0.17/0.52 = { by lemma 12 }
% 0.17/0.52 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, divide(inverse(c3), b3)), divide(a4, inverse(b4)))
% 0.17/0.52 = { by lemma 14 R->L }
% 0.17/0.52 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(a4, inverse(b4)))
% 0.17/0.52 = { by lemma 11 }
% 0.17/0.52 tuple(divide(inverse(a1), inverse(a1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(b4, inverse(a4)))
% 0.17/0.52 = { by lemma 13 R->L }
% 0.17/0.52 tuple(divide(inverse(b1), inverse(divide(divide(inverse(a1), inverse(a1)), inverse(b1)))), a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(b4, inverse(a4)))
% 0.17/0.52 = { by lemma 10 }
% 0.17/0.52 tuple(divide(inverse(b1), inverse(b1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))), divide(b4, inverse(a4)))
% 0.17/0.52 = { by axiom 1 (multiply) R->L }
% 0.17/0.52 tuple(divide(inverse(b1), inverse(b1)), a2, divide(a3, inverse(divide(b3, inverse(c3)))), multiply(b4, a4))
% 0.17/0.52 = { by axiom 1 (multiply) R->L }
% 0.17/0.52 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, divide(b3, inverse(c3))), multiply(b4, a4))
% 0.17/0.52 = { by axiom 1 (multiply) R->L }
% 0.17/0.52 tuple(divide(inverse(b1), inverse(b1)), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.17/0.52 = { by axiom 1 (multiply) R->L }
% 0.17/0.52 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)), multiply(b4, a4))
% 0.17/0.52 % SZS output end Proof
% 0.17/0.52
% 0.17/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------