%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP086-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 0.15s 0.46s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP086-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:21:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.46 Command-line arguments: --no-flatten-goal
% 0.15/0.46
% 0.15/0.46 % SZS status Unsatisfiable
% 0.15/0.46
% 0.15/0.47 % SZS output start Proof
% 0.15/0.47 Axiom 1 (single_axiom): multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, Z)))) = Y.
% 0.15/0.47
% 0.15/0.47 Lemma 2: multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z))))))) = W.
% 0.15/0.47 Proof:
% 0.15/0.47 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))))))
% 0.15/0.47 = { by axiom 1 (single_axiom) R->L }
% 0.15/0.47 multiply(X, multiply(multiply(W, multiply(multiply(Y, Z), inverse(multiply(W, Z)))), inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(W, Z)))))))
% 0.15/0.47 = { by axiom 1 (single_axiom) }
% 0.15/0.47 W
% 0.15/0.47
% 0.15/0.47 Lemma 3: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.15/0.47 Proof:
% 0.15/0.47 multiply(X, multiply(Y, inverse(Y)))
% 0.15/0.47 = { by axiom 1 (single_axiom) R->L }
% 0.15/0.47 multiply(X, multiply(Y, inverse(multiply(X, multiply(multiply(Y, Z), inverse(multiply(X, Z)))))))
% 0.15/0.47 = { by lemma 2 }
% 0.15/0.47 X
% 0.15/0.47
% 0.15/0.47 Lemma 4: multiply(X, multiply(Y, inverse(X))) = Y.
% 0.15/0.47 Proof:
% 0.15/0.47 multiply(X, multiply(Y, inverse(X)))
% 0.15/0.47 = { by lemma 3 R->L }
% 0.15/0.47 multiply(X, multiply(Y, inverse(multiply(X, multiply(Z, inverse(Z))))))
% 0.15/0.47 = { by lemma 3 R->L }
% 0.15/0.47 multiply(X, multiply(multiply(Y, multiply(Z, inverse(Z))), inverse(multiply(X, multiply(Z, inverse(Z))))))
% 0.15/0.47 = { by axiom 1 (single_axiom) }
% 0.15/0.47 Y
% 0.15/0.47
% 0.15/0.47 Lemma 5: multiply(multiply(X, Y), multiply(Z, inverse(X))) = multiply(Z, Y).
% 0.15/0.47 Proof:
% 0.15/0.47 multiply(multiply(X, Y), multiply(Z, inverse(X)))
% 0.15/0.47 = { by lemma 2 R->L }
% 0.15/0.47 multiply(multiply(X, Y), multiply(Z, inverse(multiply(multiply(X, Y), multiply(multiply(Z, Y), inverse(multiply(multiply(X, Y), multiply(multiply(multiply(Z, Y), Y), inverse(multiply(X, Y))))))))))
% 0.15/0.47 = { by lemma 4 }
% 0.15/0.47 multiply(multiply(X, Y), multiply(Z, inverse(multiply(multiply(X, Y), multiply(multiply(Z, Y), inverse(multiply(multiply(Z, Y), Y)))))))
% 0.15/0.47 = { by lemma 2 }
% 0.15/0.47 multiply(Z, Y)
% 0.15/0.47
% 0.15/0.47 Lemma 6: multiply(X, multiply(Y, inverse(Z))) = multiply(Y, multiply(X, inverse(Z))).
% 0.15/0.47 Proof:
% 0.15/0.47 multiply(X, multiply(Y, inverse(Z)))
% 0.15/0.47 = { by lemma 5 R->L }
% 0.15/0.47 multiply(multiply(Z, multiply(Y, inverse(Z))), multiply(X, inverse(Z)))
% 0.15/0.47 = { by lemma 4 }
% 0.15/0.47 multiply(Y, multiply(X, inverse(Z)))
% 0.15/0.47
% 0.15/0.47 Lemma 7: multiply(X, multiply(multiply(Y, Z), inverse(Y))) = multiply(X, Z).
% 0.15/0.47 Proof:
% 0.15/0.47 multiply(X, multiply(multiply(Y, Z), inverse(Y)))
% 0.15/0.47 = { by lemma 6 R->L }
% 0.15/0.47 multiply(multiply(Y, Z), multiply(X, inverse(Y)))
% 0.15/0.47 = { by lemma 5 }
% 0.15/0.47 multiply(X, Z)
% 0.15/0.47
% 0.15/0.47 Lemma 8: multiply(multiply(X, Y), Z) = multiply(multiply(X, Z), Y).
% 0.15/0.47 Proof:
% 0.15/0.47 multiply(multiply(X, Y), Z)
% 0.15/0.47 = { by lemma 5 R->L }
% 0.15/0.47 multiply(multiply(X, Z), multiply(multiply(X, Y), inverse(X)))
% 0.15/0.47 = { by lemma 7 }
% 0.15/0.47 multiply(multiply(X, Z), Y)
% 0.15/0.47
% 0.15/0.47 Lemma 9: multiply(X, multiply(multiply(Y, inverse(X)), Z)) = multiply(Y, Z).
% 0.15/0.47 Proof:
% 0.15/0.47 multiply(X, multiply(multiply(Y, inverse(X)), Z))
% 0.15/0.47 = { by lemma 8 R->L }
% 0.15/0.47 multiply(X, multiply(multiply(Y, Z), inverse(X)))
% 0.15/0.47 = { by lemma 4 }
% 0.15/0.47 multiply(Y, Z)
% 0.15/0.47
% 0.15/0.47 Lemma 10: multiply(X, inverse(multiply(Y, inverse(Y)))) = X.
% 0.15/0.47 Proof:
% 0.15/0.47 multiply(X, inverse(multiply(Y, inverse(Y))))
% 0.15/0.47 = { by lemma 9 R->L }
% 0.15/0.47 multiply(Y, multiply(multiply(X, inverse(Y)), inverse(multiply(Y, inverse(Y)))))
% 0.15/0.48 = { by axiom 1 (single_axiom) }
% 0.15/0.48 X
% 0.15/0.48
% 0.15/0.48 Lemma 11: multiply(Y, X) = multiply(X, Y).
% 0.15/0.48 Proof:
% 0.15/0.48 multiply(Y, X)
% 0.15/0.48 = { by lemma 10 R->L }
% 0.15/0.48 multiply(Y, multiply(X, inverse(multiply(Z, inverse(Z)))))
% 0.15/0.48 = { by lemma 6 }
% 0.15/0.48 multiply(X, multiply(Y, inverse(multiply(Z, inverse(Z)))))
% 0.15/0.48 = { by lemma 10 }
% 0.15/0.48 multiply(X, Y)
% 0.15/0.48
% 0.15/0.48 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)).
% 0.15/0.48 Proof:
% 0.15/0.48 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.15/0.48 = { by lemma 11 R->L }
% 0.15/0.48 tuple(multiply(a2, multiply(inverse(b2), b2)), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.15/0.48 = { by lemma 11 R->L }
% 0.15/0.48 tuple(multiply(a2, multiply(b2, inverse(b2))), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.15/0.48 = { by lemma 3 }
% 0.15/0.48 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.15/0.48 = { by lemma 11 R->L }
% 0.15/0.48 tuple(a2, multiply(c3, multiply(a3, b3)), multiply(inverse(a1), a1), multiply(a4, b4))
% 0.15/0.48 = { by lemma 11 R->L }
% 0.15/0.48 tuple(a2, multiply(c3, multiply(a3, b3)), multiply(a1, inverse(a1)), multiply(a4, b4))
% 0.15/0.48 = { by lemma 11 }
% 0.15/0.48 tuple(a2, multiply(c3, multiply(b3, a3)), multiply(a1, inverse(a1)), multiply(a4, b4))
% 0.15/0.48 = { by lemma 11 }
% 0.15/0.48 tuple(a2, multiply(multiply(b3, a3), c3), multiply(a1, inverse(a1)), multiply(a4, b4))
% 0.15/0.48 = { by lemma 8 R->L }
% 0.15/0.48 tuple(a2, multiply(multiply(b3, c3), a3), multiply(a1, inverse(a1)), multiply(a4, b4))
% 0.15/0.48 = { by lemma 11 R->L }
% 0.15/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(a1, inverse(a1)), multiply(a4, b4))
% 0.15/0.48 = { by lemma 9 R->L }
% 0.15/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(b1, multiply(multiply(a1, inverse(b1)), inverse(a1))), multiply(a4, b4))
% 0.15/0.48 = { by lemma 7 }
% 0.15/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(b1, inverse(b1)), multiply(a4, b4))
% 0.15/0.48 = { by lemma 11 }
% 0.15/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(b1, inverse(b1)), multiply(b4, a4))
% 0.15/0.48 = { by lemma 11 }
% 0.15/0.48 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 0.15/0.48 % SZS output end Proof
% 0.15/0.48
% 0.15/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------