%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP085-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 0.13s 0.45s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP085-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 09:24:30 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.45 Command-line arguments: --no-flatten-goal
% 0.13/0.45
% 0.13/0.45 % SZS status Unsatisfiable
% 0.13/0.45
% 0.13/0.47 % SZS output start Proof
% 0.13/0.47 Axiom 1 (single_axiom): multiply(multiply(multiply(X, Y), Z), inverse(multiply(X, Z))) = Y.
% 0.13/0.47
% 0.13/0.47 Lemma 2: multiply(X, inverse(multiply(multiply(Y, X), inverse(multiply(Y, Z))))) = Z.
% 0.13/0.47 Proof:
% 0.13/0.47 multiply(X, inverse(multiply(multiply(Y, X), inverse(multiply(Y, Z)))))
% 0.13/0.47 = { by axiom 1 (single_axiom) R->L }
% 0.13/0.47 multiply(multiply(multiply(multiply(Y, X), Z), inverse(multiply(Y, Z))), inverse(multiply(multiply(Y, X), inverse(multiply(Y, Z)))))
% 0.13/0.47 = { by axiom 1 (single_axiom) }
% 0.13/0.47 Z
% 0.13/0.47
% 0.13/0.47 Lemma 3: multiply(X, multiply(multiply(Y, Z), inverse(multiply(Y, Z)))) = X.
% 0.13/0.47 Proof:
% 0.13/0.47 multiply(X, multiply(multiply(Y, Z), inverse(multiply(Y, Z))))
% 0.13/0.47 = { by lemma 2 R->L }
% 0.13/0.47 multiply(X, multiply(multiply(multiply(Y, inverse(multiply(multiply(W, Y), inverse(multiply(W, Y))))), Z), inverse(multiply(Y, Z))))
% 0.13/0.47 = { by axiom 1 (single_axiom) }
% 0.13/0.47 multiply(X, inverse(multiply(multiply(W, Y), inverse(multiply(W, Y)))))
% 0.13/0.47 = { by lemma 2 R->L }
% 0.13/0.47 multiply(X, inverse(multiply(multiply(multiply(W, inverse(multiply(multiply(V, W), inverse(multiply(V, W))))), Y), inverse(multiply(W, Y)))))
% 0.13/0.47 = { by axiom 1 (single_axiom) }
% 0.13/0.47 multiply(X, inverse(inverse(multiply(multiply(V, W), inverse(multiply(V, W))))))
% 0.13/0.47 = { by axiom 1 (single_axiom) R->L }
% 0.13/0.47 multiply(X, inverse(multiply(multiply(multiply(W, inverse(multiply(multiply(V, W), inverse(multiply(V, W))))), X), inverse(multiply(W, X)))))
% 0.13/0.47 = { by lemma 2 }
% 0.13/0.47 multiply(X, inverse(multiply(multiply(W, X), inverse(multiply(W, X)))))
% 0.13/0.47 = { by lemma 2 }
% 0.13/0.47 X
% 0.13/0.47
% 0.13/0.47 Lemma 4: multiply(multiply(X, Y), inverse(X)) = Y.
% 0.13/0.47 Proof:
% 0.13/0.47 multiply(multiply(X, Y), inverse(X))
% 0.13/0.47 = { by lemma 3 R->L }
% 0.13/0.47 multiply(multiply(X, Y), inverse(multiply(X, multiply(multiply(Z, W), inverse(multiply(Z, W))))))
% 0.13/0.47 = { by lemma 3 R->L }
% 0.13/0.47 multiply(multiply(multiply(X, Y), multiply(multiply(Z, W), inverse(multiply(Z, W)))), inverse(multiply(X, multiply(multiply(Z, W), inverse(multiply(Z, W))))))
% 0.13/0.47 = { by axiom 1 (single_axiom) }
% 0.13/0.47 Y
% 0.13/0.47
% 0.13/0.47 Lemma 5: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 0.13/0.47 Proof:
% 0.13/0.47 multiply(X, inverse(multiply(Y, X)))
% 0.13/0.47 = { by lemma 4 R->L }
% 0.13/0.47 multiply(multiply(multiply(Y, X), inverse(Y)), inverse(multiply(Y, X)))
% 0.13/0.47 = { by lemma 4 }
% 0.13/0.47 inverse(Y)
% 0.13/0.47
% 0.13/0.47 Lemma 6: multiply(Y, inverse(inverse(X))) = multiply(X, Y).
% 0.13/0.47 Proof:
% 0.13/0.47 multiply(Y, inverse(inverse(X)))
% 0.13/0.47 = { by lemma 5 R->L }
% 0.13/0.47 multiply(Y, inverse(multiply(multiply(X, Y), inverse(multiply(X, multiply(X, Y))))))
% 0.13/0.47 = { by lemma 2 }
% 0.13/0.47 multiply(X, Y)
% 0.13/0.47
% 0.13/0.47 Lemma 7: inverse(multiply(X, Y)) = multiply(inverse(X), inverse(Y)).
% 0.13/0.47 Proof:
% 0.13/0.47 inverse(multiply(X, Y))
% 0.13/0.47 = { by lemma 4 R->L }
% 0.13/0.47 multiply(multiply(Y, inverse(multiply(X, Y))), inverse(Y))
% 0.13/0.47 = { by lemma 5 }
% 0.13/0.47 multiply(inverse(X), inverse(Y))
% 0.13/0.47
% 0.13/0.47 Lemma 8: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.13/0.47 Proof:
% 0.13/0.47 multiply(X, multiply(Y, inverse(Y)))
% 0.13/0.47 = { by lemma 6 R->L }
% 0.13/0.47 multiply(X, multiply(inverse(Y), inverse(inverse(Y))))
% 0.13/0.47 = { by lemma 7 R->L }
% 0.13/0.47 multiply(X, inverse(multiply(Y, inverse(Y))))
% 0.13/0.47 = { by lemma 4 R->L }
% 0.13/0.47 multiply(multiply(multiply(Y, X), inverse(Y)), inverse(multiply(Y, inverse(Y))))
% 0.13/0.47 = { by axiom 1 (single_axiom) }
% 0.13/0.47 X
% 0.13/0.47
% 0.13/0.47 Lemma 9: inverse(inverse(X)) = X.
% 0.13/0.47 Proof:
% 0.13/0.47 inverse(inverse(X))
% 0.13/0.47 = { by lemma 4 R->L }
% 0.13/0.47 multiply(multiply(inverse(X), inverse(inverse(X))), inverse(inverse(X)))
% 0.13/0.47 = { by lemma 6 }
% 0.13/0.47 multiply(X, multiply(inverse(X), inverse(inverse(X))))
% 0.13/0.47 = { by lemma 6 R->L }
% 0.13/0.47 multiply(X, multiply(inverse(inverse(X)), inverse(inverse(inverse(X)))))
% 0.13/0.47 = { by lemma 8 }
% 0.13/0.47 X
% 0.13/0.47
% 0.13/0.47 Lemma 10: multiply(Y, X) = multiply(X, Y).
% 0.13/0.47 Proof:
% 0.13/0.47 multiply(Y, X)
% 0.13/0.47 = { by lemma 9 R->L }
% 0.13/0.47 multiply(Y, inverse(inverse(X)))
% 0.13/0.47 = { by lemma 6 }
% 0.13/0.47 multiply(X, Y)
% 0.13/0.47
% 0.13/0.47 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)).
% 0.13/0.47 Proof:
% 0.13/0.47 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.13/0.47 = { by lemma 6 R->L }
% 0.13/0.47 tuple(multiply(multiply(b2, inverse(inverse(inverse(b2)))), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.13/0.47 = { by lemma 6 R->L }
% 0.13/0.47 tuple(multiply(a2, inverse(inverse(multiply(b2, inverse(inverse(inverse(b2))))))), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.13/0.47 = { by lemma 6 R->L }
% 0.13/0.47 tuple(multiply(a2, inverse(inverse(multiply(b2, inverse(inverse(inverse(b2))))))), multiply(c3, inverse(inverse(multiply(a3, b3)))), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.13/0.47 = { by lemma 6 R->L }
% 0.13/0.47 tuple(multiply(a2, inverse(inverse(multiply(b2, inverse(inverse(inverse(b2))))))), multiply(c3, inverse(inverse(multiply(a3, b3)))), multiply(a1, inverse(inverse(inverse(a1)))), multiply(a4, b4))
% 0.13/0.47 = { by lemma 7 }
% 0.13/0.47 tuple(multiply(a2, inverse(inverse(multiply(b2, inverse(inverse(inverse(b2))))))), multiply(c3, inverse(multiply(inverse(a3), inverse(b3)))), multiply(a1, inverse(inverse(inverse(a1)))), multiply(a4, b4))
% 0.13/0.47 = { by lemma 7 }
% 0.13/0.47 tuple(multiply(a2, inverse(inverse(multiply(b2, inverse(inverse(inverse(b2))))))), multiply(c3, multiply(inverse(inverse(a3)), inverse(inverse(b3)))), multiply(a1, inverse(inverse(inverse(a1)))), multiply(a4, b4))
% 0.13/0.47 = { by lemma 6 }
% 0.13/0.47 tuple(multiply(a2, inverse(inverse(multiply(b2, inverse(inverse(inverse(b2))))))), multiply(c3, multiply(b3, inverse(inverse(a3)))), multiply(a1, inverse(inverse(inverse(a1)))), multiply(a4, b4))
% 0.13/0.47 = { by lemma 6 }
% 0.13/0.47 tuple(multiply(a2, inverse(inverse(multiply(b2, inverse(inverse(inverse(b2))))))), multiply(c3, multiply(a3, b3)), multiply(a1, inverse(inverse(inverse(a1)))), multiply(a4, b4))
% 0.13/0.47 = { by lemma 7 }
% 0.13/0.47 tuple(multiply(a2, inverse(multiply(inverse(b2), inverse(inverse(inverse(inverse(b2))))))), multiply(c3, multiply(a3, b3)), multiply(a1, inverse(inverse(inverse(a1)))), multiply(a4, b4))
% 0.13/0.47 = { by lemma 7 }
% 0.13/0.47 tuple(multiply(a2, multiply(inverse(inverse(b2)), inverse(inverse(inverse(inverse(inverse(b2))))))), multiply(c3, multiply(a3, b3)), multiply(a1, inverse(inverse(inverse(a1)))), multiply(a4, b4))
% 0.13/0.47 = { by lemma 9 }
% 0.13/0.47 tuple(multiply(a2, multiply(b2, inverse(inverse(inverse(inverse(inverse(b2))))))), multiply(c3, multiply(a3, b3)), multiply(a1, inverse(inverse(inverse(a1)))), multiply(a4, b4))
% 0.13/0.47 = { by lemma 9 }
% 0.13/0.47 tuple(multiply(a2, multiply(b2, inverse(inverse(inverse(b2))))), multiply(c3, multiply(a3, b3)), multiply(a1, inverse(inverse(inverse(a1)))), multiply(a4, b4))
% 0.13/0.47 = { by lemma 9 }
% 0.13/0.47 tuple(multiply(a2, multiply(b2, inverse(b2))), multiply(c3, multiply(a3, b3)), multiply(a1, inverse(inverse(inverse(a1)))), multiply(a4, b4))
% 0.13/0.47 = { by lemma 8 }
% 0.13/0.47 tuple(a2, multiply(c3, multiply(a3, b3)), multiply(a1, inverse(inverse(inverse(a1)))), multiply(a4, b4))
% 0.13/0.47 = { by lemma 9 }
% 0.13/0.47 tuple(a2, multiply(c3, multiply(a3, b3)), multiply(a1, inverse(a1)), multiply(a4, b4))
% 0.13/0.47 = { by lemma 10 }
% 0.13/0.47 tuple(a2, multiply(c3, multiply(b3, a3)), multiply(a1, inverse(a1)), multiply(a4, b4))
% 0.13/0.47 = { by lemma 10 }
% 0.13/0.47 tuple(a2, multiply(multiply(b3, a3), c3), multiply(a1, inverse(a1)), multiply(a4, b4))
% 0.13/0.48 = { by lemma 4 R->L }
% 0.13/0.48 tuple(a2, multiply(multiply(inverse(multiply(b3, c3)), multiply(multiply(b3, a3), c3)), inverse(inverse(multiply(b3, c3)))), multiply(a1, inverse(a1)), multiply(a4, b4))
% 0.13/0.48 = { by lemma 6 }
% 0.13/0.48 tuple(a2, multiply(multiply(b3, c3), multiply(inverse(multiply(b3, c3)), multiply(multiply(b3, a3), c3))), multiply(a1, inverse(a1)), multiply(a4, b4))
% 0.13/0.48 = { by lemma 10 R->L }
% 0.13/0.48 tuple(a2, multiply(multiply(b3, c3), multiply(multiply(multiply(b3, a3), c3), inverse(multiply(b3, c3)))), multiply(a1, inverse(a1)), multiply(a4, b4))
% 0.13/0.48 = { by axiom 1 (single_axiom) }
% 0.13/0.48 tuple(a2, multiply(multiply(b3, c3), a3), multiply(a1, inverse(a1)), multiply(a4, b4))
% 0.13/0.48 = { by lemma 10 R->L }
% 0.13/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(a1, inverse(a1)), multiply(a4, b4))
% 0.13/0.48 = { by lemma 2 R->L }
% 0.13/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(multiply(multiply(Y, X), inverse(multiply(Y, multiply(a1, inverse(a1))))))), multiply(a4, b4))
% 0.13/0.48 = { by lemma 8 }
% 0.13/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(multiply(multiply(Y, X), inverse(Y)))), multiply(a4, b4))
% 0.13/0.48 = { by lemma 8 R->L }
% 0.13/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(X, inverse(multiply(multiply(Y, X), inverse(multiply(Y, multiply(b1, inverse(b1))))))), multiply(a4, b4))
% 0.13/0.48 = { by lemma 2 }
% 0.13/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(b1, inverse(b1)), multiply(a4, b4))
% 0.13/0.48 = { by lemma 9 R->L }
% 0.13/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(b1, inverse(b1)), multiply(a4, inverse(inverse(b4))))
% 0.13/0.48 = { by lemma 9 R->L }
% 0.13/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(b1, inverse(inverse(inverse(b1)))), multiply(a4, inverse(inverse(b4))))
% 0.13/0.48 = { by lemma 6 }
% 0.13/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(b1, inverse(inverse(inverse(b1)))), multiply(b4, a4))
% 0.13/0.48 = { by lemma 6 }
% 0.13/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.13/0.48 % SZS output end Proof
% 0.13/0.48
% 0.13/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------