%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP050-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 10:09:09 AM UTC 2026
% Result : Unsatisfiable 7.85s 1.41s
% Output : Proof 7.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP050-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:16:46 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.85/1.41 Command-line arguments: --flatten --complete-subsets
% 7.85/1.41
% 7.85/1.41 % SZS status Unsatisfiable
% 7.85/1.41
% 7.85/1.48 % SZS output start Proof
% 7.85/1.48 Axiom 1 (single_axiom): multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(Y), multiply(inverse(Y), Y))))) = Z.
% 7.85/1.48
% 7.85/1.48 Lemma 2: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z)))) = multiply(X, inverse(multiply(inverse(W), multiply(inverse(Y), multiply(inverse(Y), Y))))).
% 7.85/1.48 Proof:
% 7.85/1.48 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z))))
% 7.85/1.48 = { by axiom 1 (single_axiom) R->L }
% 7.85/1.48 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z)))))), multiply(inverse(Y), multiply(inverse(Y), Y)))))
% 7.85/1.48 = { by axiom 1 (single_axiom) }
% 7.85/1.48 multiply(X, inverse(multiply(inverse(W), multiply(inverse(Y), multiply(inverse(Y), Y)))))
% 7.85/1.48
% 7.85/1.48 Lemma 3: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(Y), Y)))))) = Z.
% 7.85/1.48 Proof:
% 7.85/1.48 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(Y), Y))))))
% 7.85/1.48 = { by lemma 2 R->L }
% 7.85/1.48 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), Z)), multiply(inverse(W), multiply(inverse(W), W)))))
% 7.85/1.48 = { by axiom 1 (single_axiom) }
% 7.85/1.48 Z
% 7.85/1.48
% 7.85/1.48 Lemma 4: multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W)) = multiply(inverse(multiply(V, Z)), multiply(V, W)).
% 7.85/1.48 Proof:
% 7.85/1.48 multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))
% 7.85/1.48 = { by lemma 3 R->L }
% 7.85/1.48 multiply(inverse(multiply(V, Z)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), W))), multiply(inverse(Z), multiply(inverse(Z), Z))))))
% 7.85/1.48 = { by lemma 2 }
% 7.85/1.48 multiply(inverse(multiply(V, Z)), multiply(V, multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), W)), multiply(inverse(Y), multiply(inverse(Y), Y)))))))
% 7.85/1.48 = { by axiom 1 (single_axiom) }
% 7.85/1.48 multiply(inverse(multiply(V, Z)), multiply(V, W))
% 7.85/1.48
% 7.85/1.48 Lemma 5: inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), multiply(inverse(Y), multiply(inverse(Y), Y)))) = Z.
% 7.85/1.48 Proof:
% 7.85/1.48 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 7.85/1.48 = { by lemma 4 R->L }
% 7.85/1.48 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(multiply(W, V)), Z))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 7.85/1.48 = { by lemma 2 }
% 7.85/1.48 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Z)), multiply(inverse(V), multiply(inverse(V), V)))))
% 7.85/1.48 = { by axiom 1 (single_axiom) }
% 7.85/1.48 Z
% 7.85/1.48
% 7.85/1.48 Lemma 6: multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, multiply(Y, multiply(Z, W)))) = multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V))).
% 7.85/1.48 Proof:
% 7.85/1.48 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, multiply(Y, multiply(Z, W))))
% 7.85/1.48 = { by axiom 1 (single_axiom) R->L }
% 7.85/1.48 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(Y, multiply(Z, W)))), multiply(inverse(W), multiply(inverse(W), W)))))))
% 7.85/1.48 = { by lemma 2 R->L }
% 7.85/1.48 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(Y, multiply(Z, W)))), multiply(inverse(multiply(Y, W)), multiply(Y, multiply(Z, W))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 7.85/1.48 = { by lemma 4 R->L }
% 7.85/1.48 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(Y, multiply(Z, W)))), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), multiply(Z, W))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 7.85/1.48 = { by lemma 4 R->L }
% 7.85/1.48 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(Y, multiply(Z, W)))), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 7.85/1.48 = { by lemma 4 R->L }
% 7.85/1.48 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), multiply(Z, W)))), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 7.85/1.48 = { by lemma 4 R->L }
% 7.85/1.48 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W)))), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 7.85/1.48 = { by lemma 3 R->L }
% 7.85/1.48 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W)))), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W))))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 7.85/1.48 = { by axiom 1 (single_axiom) R->L }
% 7.85/1.49 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W)))), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W))))))), multiply(inverse(X2), multiply(inverse(X2), X2))))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 7.85/1.49 = { by lemma 2 R->L }
% 7.85/1.49 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(S, inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(inverse(multiply(Z, W)), W))), Y2)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(inverse(multiply(Z, W)), W)), multiply(inverse(multiply(Z, W)), W))))), multiply(inverse(Y2), multiply(inverse(Y2), Y2))))), multiply(inverse(X2), multiply(inverse(X2), X2))))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 7.85/1.49 = { by lemma 2 }
% 7.85/1.49 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(S, inverse(multiply(inverse(inverse(multiply(multiply(S, inverse(multiply(inverse(Y2), multiply(inverse(X2), multiply(inverse(X2), X2))))), multiply(inverse(Y2), multiply(inverse(Y2), Y2))))), multiply(inverse(X2), multiply(inverse(X2), X2))))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 7.85/1.49 = { by lemma 2 R->L }
% 7.85/1.49 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(S, inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), V)), Y2)), multiply(inverse(V), multiply(inverse(V), V)))), multiply(inverse(Y2), multiply(inverse(Y2), Y2))))), multiply(inverse(X2), multiply(inverse(X2), X2))))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 7.85/1.49 = { by lemma 2 }
% 7.85/1.49 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), inverse(multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V)))))), multiply(inverse(X2), multiply(inverse(X2), X2))))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 7.85/1.49 = { by axiom 1 (single_axiom) }
% 7.85/1.49 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V)))), multiply(inverse(T), multiply(inverse(T), T))))))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 7.85/1.49 = { by lemma 3 }
% 7.85/1.49 multiply(inverse(multiply(X, multiply(Y, multiply(Z, W)))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V)))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(inverse(multiply(Y, multiply(Z, W))), multiply(Y, multiply(Z, W))))))))
% 7.85/1.49 = { by lemma 3 }
% 7.85/1.49 multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V)))
% 7.85/1.49
% 7.85/1.49 Lemma 7: multiply(X, multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(X, multiply(inverse(Z), multiply(inverse(Z), Z))))))) = multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W))).
% 7.85/1.49 Proof:
% 7.85/1.49 multiply(X, multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(X, multiply(inverse(Z), multiply(inverse(Z), Z)))))))
% 7.85/1.49 = { by lemma 5 R->L }
% 7.85/1.49 multiply(X, multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(Z), multiply(inverse(Z), Z)))))))
% 7.85/1.49 = { by lemma 3 }
% 7.85/1.49 multiply(X, multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U))))
% 7.85/1.49 = { by lemma 5 R->L }
% 7.85/1.49 multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U)))), multiply(inverse(multiply(inverse(multiply(V, U)), multiply(V, X))), multiply(inverse(U), multiply(inverse(U), U))))
% 7.85/1.49 = { by lemma 6 }
% 7.85/1.49 multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W)))
% 7.85/1.49
% 7.85/1.49 Lemma 8: multiply(inverse(multiply(inverse(X), multiply(inverse(X), X))), multiply(inverse(X), multiply(inverse(X), X))) = multiply(inverse(Y), Y).
% 7.85/1.49 Proof:
% 7.85/1.49 multiply(inverse(multiply(inverse(X), multiply(inverse(X), X))), multiply(inverse(X), multiply(inverse(X), X)))
% 7.85/1.49 = { by lemma 7 R->L }
% 7.85/1.49 multiply(inverse(Y), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(inverse(Y), multiply(inverse(W), multiply(inverse(W), W)))))))
% 7.85/1.49 = { by lemma 3 }
% 7.85/1.49 multiply(inverse(Y), Y)
% 7.85/1.49
% 7.85/1.49 Lemma 9: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 7.85/1.49 Proof:
% 7.85/1.49 multiply(inverse(Y), Y)
% 7.85/1.49 = { by lemma 8 R->L }
% 7.85/1.49 multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V)))
% 7.85/1.49 = { by lemma 7 R->L }
% 7.85/1.49 multiply(inverse(X), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(inverse(X), multiply(inverse(W), multiply(inverse(W), W)))))))
% 7.85/1.49 = { by lemma 3 }
% 7.85/1.49 multiply(inverse(X), X)
% 7.85/1.49
% 7.85/1.49 Lemma 10: multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Y)) = multiply(inverse(Z), Z).
% 7.85/1.49 Proof:
% 7.85/1.49 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Y))
% 7.85/1.49 = { by lemma 8 R->L }
% 7.85/1.49 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.49 = { by lemma 8 R->L }
% 7.85/1.49 multiply(inverse(multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W)))), multiply(inverse(multiply(inverse(W), multiply(inverse(W), W))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.49 = { by lemma 6 }
% 7.85/1.49 multiply(inverse(multiply(inverse(V), multiply(inverse(V), V))), multiply(inverse(V), multiply(inverse(V), V)))
% 7.85/1.49 = { by lemma 8 }
% 7.85/1.49 multiply(inverse(Z), Z)
% 7.85/1.49
% 7.85/1.49 Lemma 11: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 7.85/1.49 Proof:
% 7.85/1.49 inverse(multiply(inverse(X), X))
% 7.85/1.49 = { by lemma 5 R->L }
% 7.85/1.49 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(inverse(X), X))))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.49 = { by lemma 10 R->L }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Z, multiply(inverse(Y), Y))), multiply(Z, multiply(inverse(Y), Y)))), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Y))))))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.50 = { by lemma 10 R->L }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Z, multiply(inverse(Y), Y))), multiply(Z, multiply(inverse(Y), Y)))), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Y)))))))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.50 = { by axiom 1 (single_axiom) }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(Z, multiply(inverse(Y), Y)))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.50 = { by lemma 5 }
% 7.85/1.50 multiply(inverse(Y), Y)
% 7.85/1.50
% 7.85/1.50 Lemma 12: inverse(multiply(inverse(X), multiply(inverse(X), X))) = X.
% 7.85/1.50 Proof:
% 7.85/1.50 inverse(multiply(inverse(X), multiply(inverse(X), X)))
% 7.85/1.50 = { by lemma 3 R->L }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(X), X))), multiply(inverse(X), multiply(inverse(X), X)))))))
% 7.85/1.50 = { by lemma 11 }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), multiply(inverse(X), X))))
% 7.85/1.50 = { by lemma 11 }
% 7.85/1.50 inverse(multiply(multiply(inverse(Y), Y), multiply(inverse(X), multiply(inverse(X), X))))
% 7.85/1.50 = { by lemma 11 R->L }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), multiply(inverse(multiply(Z, W)), X))), multiply(inverse(X), multiply(inverse(X), X))))
% 7.85/1.50 = { by lemma 2 }
% 7.85/1.50 multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), multiply(inverse(W), multiply(inverse(W), W)))))
% 7.85/1.50 = { by axiom 1 (single_axiom) }
% 7.85/1.50 X
% 7.85/1.50
% 7.85/1.50 Lemma 13: multiply(multiply(inverse(X), X), multiply(inverse(Y), Y)) = multiply(inverse(Z), Z).
% 7.85/1.50 Proof:
% 7.85/1.50 multiply(multiply(inverse(X), X), multiply(inverse(Y), Y))
% 7.85/1.50 = { by lemma 11 R->L }
% 7.85/1.50 multiply(inverse(multiply(inverse(W), W)), multiply(inverse(Y), Y))
% 7.85/1.50 = { by lemma 10 }
% 7.85/1.50 multiply(inverse(Z), Z)
% 7.85/1.50
% 7.85/1.50 Lemma 14: multiply(X, multiply(inverse(X), Y)) = Y.
% 7.85/1.50 Proof:
% 7.85/1.50 multiply(X, multiply(inverse(X), Y))
% 7.85/1.50 = { by lemma 12 R->L }
% 7.85/1.50 multiply(X, multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(Y), Y)))))
% 7.85/1.50 = { by lemma 13 R->L }
% 7.85/1.50 multiply(X, multiply(inverse(X), inverse(multiply(inverse(Y), multiply(multiply(inverse(Z), Z), multiply(inverse(W), W))))))
% 7.85/1.50 = { by lemma 13 R->L }
% 7.85/1.50 multiply(X, multiply(inverse(X), inverse(multiply(inverse(Y), multiply(multiply(inverse(Z), Z), multiply(multiply(inverse(V), V), multiply(inverse(X), X)))))))
% 7.85/1.50 = { by lemma 11 R->L }
% 7.85/1.50 multiply(X, multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(multiply(inverse(X), X)), multiply(multiply(inverse(V), V), multiply(inverse(X), X)))))))
% 7.85/1.50 = { by lemma 11 R->L }
% 7.85/1.50 multiply(X, multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X)))))))
% 7.85/1.50 = { by lemma 12 R->L }
% 7.85/1.50 multiply(inverse(multiply(inverse(X), multiply(inverse(X), X))), multiply(inverse(X), inverse(multiply(inverse(Y), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X)))))))
% 7.85/1.50 = { by lemma 3 }
% 7.85/1.50 Y
% 7.85/1.50
% 7.85/1.50 Lemma 15: multiply(inverse(multiply(X, Y)), multiply(X, multiply(inverse(Z), Z))) = multiply(inverse(Y), multiply(inverse(W), W)).
% 7.85/1.50 Proof:
% 7.85/1.50 multiply(inverse(multiply(X, Y)), multiply(X, multiply(inverse(Z), Z)))
% 7.85/1.50 = { by lemma 11 R->L }
% 7.85/1.50 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(inverse(Y), multiply(inverse(Y), Y))), multiply(inverse(Y), multiply(inverse(Y), Y))))))
% 7.85/1.50 = { by lemma 3 }
% 7.85/1.50 multiply(inverse(Y), multiply(inverse(Y), Y))
% 7.85/1.50 = { by lemma 9 R->L }
% 7.85/1.50 multiply(inverse(Y), multiply(inverse(W), W))
% 7.85/1.50
% 7.85/1.50 Lemma 16: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 7.85/1.50 Proof:
% 7.85/1.50 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 7.85/1.50 = { by lemma 4 R->L }
% 7.85/1.50 multiply(inverse(multiply(inverse(multiply(V, U)), Y)), multiply(inverse(multiply(V, U)), Z))
% 7.85/1.50 = { by lemma 4 }
% 7.85/1.50 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 7.85/1.50
% 7.85/1.50 Lemma 17: inverse(multiply(multiply(inverse(X), X), multiply(inverse(Y), multiply(inverse(Z), Z)))) = Y.
% 7.85/1.50 Proof:
% 7.85/1.50 inverse(multiply(multiply(inverse(X), X), multiply(inverse(Y), multiply(inverse(Z), Z))))
% 7.85/1.50 = { by lemma 9 }
% 7.85/1.50 inverse(multiply(multiply(inverse(X), X), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 7.85/1.50 = { by lemma 11 R->L }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(multiply(W, V)), Y))), multiply(inverse(Y), multiply(inverse(Y), Y))))
% 7.85/1.50 = { by lemma 2 }
% 7.85/1.50 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), Y)), multiply(inverse(V), multiply(inverse(V), V)))))
% 7.85/1.50 = { by axiom 1 (single_axiom) }
% 7.85/1.50 Y
% 7.85/1.50
% 7.85/1.50 Lemma 18: multiply(inverse(multiply(X, Y)), multiply(X, Z)) = multiply(multiply(inverse(W), W), multiply(inverse(Y), Z)).
% 7.85/1.50 Proof:
% 7.85/1.50 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 7.85/1.50 = { by lemma 16 }
% 7.85/1.50 multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Z))
% 7.85/1.50 = { by lemma 9 R->L }
% 7.85/1.50 multiply(inverse(multiply(inverse(V), V)), multiply(inverse(Y), Z))
% 7.85/1.50 = { by lemma 11 }
% 7.85/1.50 multiply(multiply(inverse(W), W), multiply(inverse(Y), Z))
% 7.85/1.50
% 7.85/1.50 Lemma 19: multiply(X, multiply(inverse(Y), Y)) = X.
% 7.85/1.50 Proof:
% 7.85/1.50 multiply(X, multiply(inverse(Y), Y))
% 7.85/1.50 = { by lemma 5 R->L }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), W)), multiply(inverse(Z), multiply(X, multiply(inverse(Y), Y))))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.50 = { by lemma 14 R->L }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), W)), multiply(inverse(multiply(X, multiply(inverse(X), Z))), multiply(X, multiply(inverse(Y), Y))))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.50 = { by lemma 15 }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), W)), multiply(inverse(multiply(inverse(X), Z)), multiply(inverse(X), X)))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.50 = { by lemma 16 R->L }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), W)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), X)))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.50 = { by lemma 11 }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), W)), multiply(multiply(inverse(V), V), multiply(inverse(Z), X)))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.50 = { by lemma 17 R->L }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), W)), multiply(multiply(inverse(V), V), multiply(inverse(Z), inverse(multiply(multiply(inverse(U), U), multiply(inverse(X), multiply(inverse(Z), Z)))))))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.50 = { by lemma 11 R->L }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), W)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), inverse(multiply(multiply(inverse(U), U), multiply(inverse(X), multiply(inverse(Z), Z)))))))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.50 = { by lemma 18 R->L }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), W)), multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), inverse(multiply(inverse(multiply(inverse(Z), X)), multiply(inverse(Z), multiply(inverse(Z), Z)))))))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.50 = { by lemma 3 }
% 7.85/1.50 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), W)), multiply(inverse(Z), X))), multiply(inverse(W), multiply(inverse(W), W))))
% 7.85/1.50 = { by lemma 5 }
% 7.85/1.50 X
% 7.85/1.50
% 7.85/1.50 Goal 1 (prove_these_axioms): tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1)) = tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1)).
% 7.85/1.50 Proof:
% 7.85/1.50 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1))
% 7.85/1.50 = { by lemma 9 }
% 7.85/1.50 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(b1), b1))
% 7.85/1.50 = { by lemma 17 R->L }
% 7.85/1.50 tuple(inverse(multiply(multiply(inverse(X), X), multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Y))))), multiply(multiply(a3, b3), c3), multiply(inverse(b1), b1))
% 7.85/1.50 = { by lemma 11 R->L }
% 7.85/1.50 tuple(inverse(multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), a2)), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Y))))), multiply(multiply(a3, b3), c3), multiply(inverse(b1), b1))
% 7.85/1.50 = { by lemma 15 }
% 7.85/1.50 tuple(inverse(multiply(multiply(inverse(X), X), multiply(inverse(a2), multiply(inverse(Z), Z)))), multiply(multiply(a3, b3), c3), multiply(inverse(b1), b1))
% 7.85/1.50 = { by lemma 17 }
% 7.85/1.50 tuple(a2, multiply(multiply(a3, b3), c3), multiply(inverse(b1), b1))
% 7.85/1.50 = { by lemma 19 R->L }
% 7.85/1.50 tuple(a2, multiply(multiply(a3, b3), multiply(c3, multiply(inverse(multiply(b3, c3)), multiply(b3, c3)))), multiply(inverse(b1), b1))
% 7.85/1.50 = { by lemma 17 R->L }
% 7.85/1.50 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(c3), multiply(inverse(V), V)))), multiply(inverse(multiply(b3, c3)), multiply(b3, c3)))), multiply(inverse(b1), b1))
% 7.85/1.50 = { by lemma 18 R->L }
% 7.85/1.50 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(inverse(multiply(b3, c3)), multiply(b3, multiply(inverse(V), V)))), multiply(inverse(multiply(b3, c3)), multiply(b3, c3)))), multiply(inverse(b1), b1))
% 7.85/1.50 = { by lemma 19 }
% 7.85/1.50 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(inverse(multiply(b3, c3)), b3)), multiply(inverse(multiply(b3, c3)), multiply(b3, c3)))), multiply(inverse(b1), b1))
% 7.85/1.50 = { by lemma 16 R->L }
% 7.85/1.50 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(a3, b3)), multiply(a3, multiply(b3, c3)))), multiply(inverse(b1), b1))
% 7.85/1.50 = { by lemma 14 }
% 7.85/1.50 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1))
% 7.85/1.50 % SZS output end Proof
% 7.85/1.50
% 7.85/1.50 RESULT: Unsatisfiable (the axioms are contradictory).
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