%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP054-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 10:09:10 AM UTC 2026
% Result : Unsatisfiable 0.54s 0.53s
% Output : Proof 1.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP054-1 : 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 : n003.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 09:19:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.54/0.53 Command-line arguments: --no-flatten-goal
% 0.54/0.53
% 0.54/0.53 % SZS status Unsatisfiable
% 0.54/0.53
% 0.54/0.60 % SZS output start Proof
% 0.54/0.60 Axiom 1 (single_axiom): inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))) = Y.
% 0.54/0.60
% 0.54/0.60 Lemma 2: multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z)) = Y.
% 0.54/0.60 Proof:
% 0.54/0.60 multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))
% 0.54/0.60 = { by axiom 1 (single_axiom) R->L }
% 0.54/0.60 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V)))
% 0.54/0.60 = { by axiom 1 (single_axiom) }
% 0.54/0.60 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(Y), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V)))
% 0.54/0.60 = { by axiom 1 (single_axiom) }
% 0.54/0.60 Y
% 0.54/0.60
% 0.54/0.60 Lemma 3: inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), Y)) = W.
% 0.54/0.61 Proof:
% 0.54/0.61 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), Y))
% 0.54/0.61 = { by lemma 2 R->L }
% 0.54/0.61 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))))
% 0.54/0.61 = { by axiom 1 (single_axiom) }
% 0.54/0.61 W
% 0.54/0.61
% 0.54/0.61 Lemma 4: inverse(multiply(inverse(Y), Y)) = inverse(multiply(inverse(X), X)).
% 0.54/0.61 Proof:
% 0.54/0.61 inverse(multiply(inverse(Y), Y))
% 0.54/0.61 = { by axiom 1 (single_axiom) R->L }
% 0.54/0.61 inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(Y)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W))), Y))
% 0.54/0.61 = { by lemma 3 R->L }
% 0.54/0.61 inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(Y)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), inverse(multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(inverse(inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))))))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), inverse(multiply(inverse(multiply(Z, W)), inverse(multiply(multiply(V, U), inverse(multiply(inverse(multiply(V, U)), multiply(V, U))))))))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))))))))), Y))
% 0.54/0.61 = { by lemma 3 }
% 0.54/0.61 multiply(inverse(multiply(V, inverse(multiply(inverse(inverse(inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))))))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), inverse(multiply(inverse(multiply(Z, W)), inverse(multiply(multiply(V, U), inverse(multiply(inverse(multiply(V, U)), multiply(V, U))))))))
% 0.54/0.61 = { by lemma 3 R->L }
% 0.54/0.61 inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(X)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), inverse(multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(inverse(inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))))))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), inverse(multiply(inverse(multiply(Z, W)), inverse(multiply(multiply(V, U), inverse(multiply(inverse(multiply(V, U)), multiply(V, U))))))))), inverse(multiply(multiply(Z, W), inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))))))))), X))
% 0.54/0.61 = { by lemma 3 }
% 0.54/0.61 inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(X)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W))), X))
% 0.54/0.61 = { by axiom 1 (single_axiom) }
% 0.54/0.61 inverse(multiply(inverse(X), X))
% 0.54/0.61
% 0.54/0.61 Lemma 5: multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z)) = multiply(Z, inverse(multiply(inverse(W), W))).
% 0.54/0.61 Proof:
% 0.54/0.61 multiply(inverse(multiply(X, inverse(multiply(inverse(Y), Y)))), multiply(X, Z))
% 0.54/0.61 = { by lemma 4 }
% 0.54/0.61 multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z))))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))
% 0.54/0.61 = { by axiom 1 (single_axiom) R->L }
% 0.54/0.61 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z))))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 0.54/0.61 = { by axiom 1 (single_axiom) }
% 0.54/0.61 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 0.54/0.61 = { by axiom 1 (single_axiom) R->L }
% 0.54/0.61 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z))))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), multiply(T, S))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 0.54/0.61 = { by axiom 1 (single_axiom) }
% 0.54/0.61 multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z))))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), multiply(T, S))
% 0.54/0.61 = { by lemma 2 }
% 0.54/0.61 multiply(Z, inverse(multiply(inverse(Z), Z)))
% 0.54/0.61 = { by lemma 4 R->L }
% 0.54/0.61 multiply(Z, inverse(multiply(inverse(W), W)))
% 0.54/0.61
% 0.54/0.61 Lemma 6: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.54/0.61 Proof:
% 0.54/0.61 multiply(inverse(Y), Y)
% 0.54/0.61 = { by axiom 1 (single_axiom) R->L }
% 0.54/0.61 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W)))
% 0.54/0.61 = { by lemma 4 }
% 0.54/0.61 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W)))
% 0.54/0.61 = { by axiom 1 (single_axiom) }
% 0.54/0.61 multiply(inverse(X), X)
% 0.54/0.61
% 0.54/0.61 Lemma 7: multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y))) = multiply(inverse(Z), Z).
% 0.54/0.61 Proof:
% 0.54/0.61 multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y)))
% 0.54/0.61 = { by lemma 5 R->L }
% 0.54/0.61 multiply(inverse(multiply(W, inverse(multiply(inverse(X), X)))), multiply(W, inverse(multiply(inverse(X), X))))
% 0.54/0.61 = { by lemma 6 R->L }
% 0.54/0.61 multiply(inverse(Z), Z)
% 0.54/0.61
% 0.54/0.61 Lemma 8: multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(inverse(Y), Y)), Z)) = multiply(Z, inverse(multiply(inverse(W), W))).
% 0.54/0.61 Proof:
% 0.54/0.61 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(inverse(Y), Y)), Z))
% 0.54/0.61 = { by lemma 7 R->L }
% 0.54/0.61 multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(V), V)))), multiply(inverse(multiply(inverse(Y), Y)), Z))
% 0.54/0.61 = { by lemma 5 }
% 0.54/0.61 multiply(Z, inverse(multiply(inverse(W), W)))
% 0.54/0.61
% 0.54/0.61 Lemma 9: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))) = multiply(inverse(Z), Z).
% 0.54/0.61 Proof:
% 0.54/0.61 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y)))
% 0.54/0.61 = { by lemma 8 R->L }
% 0.54/0.61 multiply(inverse(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X))), multiply(inverse(multiply(inverse(X), X)), multiply(inverse(X), X)))
% 0.54/0.61 = { by lemma 6 R->L }
% 0.54/0.61 multiply(inverse(Z), Z)
% 0.54/0.61
% 0.54/0.61 Lemma 10: multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(Y), Y)))), multiply(inverse(Z), Z)) = multiply(X, inverse(multiply(inverse(W), W))).
% 0.54/0.61 Proof:
% 0.54/0.61 multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(Y), Y)))), multiply(inverse(Z), Z))
% 0.54/0.61 = { by lemma 6 }
% 0.54/0.61 multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(Y), Y)))), multiply(inverse(X), X))
% 0.54/0.61 = { by lemma 5 }
% 0.54/0.62 multiply(X, inverse(multiply(inverse(W), W)))
% 0.54/0.62
% 0.54/0.62 Lemma 11: inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))))), multiply(inverse(W), W))) = Y.
% 0.54/0.62 Proof:
% 0.54/0.62 inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))))), multiply(inverse(W), W)))
% 0.54/0.62 = { by lemma 7 R->L }
% 0.54/0.62 inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))))))), multiply(inverse(W), W)))
% 0.54/0.62 = { by lemma 7 R->L }
% 0.54/0.62 inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))))))), multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(V), V)))))
% 0.54/0.62 = { by axiom 1 (single_axiom) }
% 0.54/0.62 Y
% 0.54/0.62
% 0.54/0.62 Lemma 12: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.54/0.62 Proof:
% 0.54/0.62 inverse(multiply(inverse(X), X))
% 0.54/0.62 = { by lemma 9 R->L }
% 0.54/0.62 inverse(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(W), W))))
% 0.54/0.62 = { by lemma 10 R->L }
% 0.54/0.62 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(V), V)))), multiply(inverse(U), U)))
% 0.54/0.62 = { by lemma 7 R->L }
% 0.54/0.62 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(T), T)))))), multiply(inverse(U), U)))
% 0.54/0.62 = { by lemma 11 }
% 0.54/0.62 multiply(inverse(Y), Y)
% 0.54/0.62
% 0.54/0.62 Lemma 13: multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), multiply(inverse(Z), Z)) = multiply(X, multiply(inverse(W), W)).
% 0.54/0.62 Proof:
% 0.54/0.62 multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), multiply(inverse(Z), Z))
% 0.54/0.62 = { by lemma 12 R->L }
% 0.54/0.62 multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(V), V)))), multiply(inverse(Z), Z))
% 0.54/0.62 = { by lemma 10 }
% 0.54/0.62 multiply(X, inverse(multiply(inverse(U), U)))
% 0.54/0.62 = { by lemma 12 }
% 0.54/0.62 multiply(X, multiply(inverse(W), W))
% 0.54/0.62
% 0.54/0.62 Lemma 14: multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), Z)) = multiply(Z, multiply(inverse(W), W)).
% 0.54/0.62 Proof:
% 0.54/0.62 multiply(multiply(inverse(X), X), multiply(multiply(inverse(Y), Y), Z))
% 0.54/0.62 = { by lemma 12 R->L }
% 0.54/0.62 multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(V), V)), Z))
% 0.54/0.62 = { by lemma 12 R->L }
% 0.54/0.62 multiply(inverse(multiply(inverse(U), U)), multiply(inverse(multiply(inverse(V), V)), Z))
% 0.54/0.62 = { by lemma 8 }
% 0.54/0.62 multiply(Z, inverse(multiply(inverse(T), T)))
% 0.54/0.62 = { by lemma 12 }
% 0.54/0.62 multiply(Z, multiply(inverse(W), W))
% 0.54/0.62
% 0.54/0.62 Lemma 15: multiply(multiply(multiply(inverse(X), X), Y), multiply(inverse(Z), Z)) = multiply(multiply(inverse(W), W), multiply(Y, multiply(inverse(V), V))).
% 0.54/0.62 Proof:
% 0.54/0.62 multiply(multiply(multiply(inverse(X), X), Y), multiply(inverse(Z), Z))
% 0.54/0.62 = { by lemma 14 R->L }
% 0.54/0.62 multiply(multiply(inverse(W), W), multiply(multiply(inverse(U), U), multiply(multiply(inverse(X), X), Y)))
% 0.54/0.62 = { by lemma 14 }
% 0.54/0.62 multiply(multiply(inverse(W), W), multiply(Y, multiply(inverse(V), V)))
% 0.54/0.62
% 0.54/0.62 Lemma 16: multiply(multiply(inverse(X), X), multiply(Y, multiply(inverse(Z), Z))) = multiply(Y, multiply(inverse(W), W)).
% 0.54/0.62 Proof:
% 0.54/0.62 multiply(multiply(inverse(X), X), multiply(Y, multiply(inverse(Z), Z)))
% 0.54/0.62 = { by lemma 13 R->L }
% 0.54/0.62 multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(Y), multiply(inverse(V), V))), multiply(inverse(U), U)))
% 0.54/0.62 = { by lemma 15 R->L }
% 0.54/0.62 multiply(multiply(multiply(inverse(T), T), inverse(multiply(inverse(Y), multiply(inverse(V), V)))), multiply(inverse(S), S))
% 0.54/0.62 = { by lemma 12 R->L }
% 0.54/0.62 multiply(multiply(inverse(multiply(inverse(X2), X2)), inverse(multiply(inverse(Y), multiply(inverse(V), V)))), multiply(inverse(S), S))
% 0.54/0.62 = { by lemma 12 R->L }
% 0.54/0.62 multiply(multiply(inverse(multiply(inverse(X2), X2)), inverse(multiply(inverse(Y), inverse(multiply(inverse(Y2), Y2))))), multiply(inverse(S), S))
% 0.54/0.62 = { by lemma 13 R->L }
% 0.54/0.62 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(X2), X2)), inverse(multiply(inverse(Y), inverse(multiply(inverse(Y2), Y2)))))), multiply(inverse(Z2), Z2))), multiply(inverse(W), W))
% 0.54/0.62 = { by lemma 11 }
% 0.54/0.62 multiply(Y, multiply(inverse(W), W))
% 0.54/0.62
% 0.54/0.62 Lemma 17: multiply(multiply(X, multiply(inverse(Y), Y)), multiply(inverse(Z), Z)) = multiply(X, multiply(inverse(W), W)).
% 0.54/0.62 Proof:
% 0.54/0.62 multiply(multiply(X, multiply(inverse(Y), Y)), multiply(inverse(Z), Z))
% 0.54/0.62 = { by lemma 12 R->L }
% 0.54/0.62 multiply(multiply(X, multiply(inverse(Y), Y)), inverse(multiply(inverse(V), V)))
% 0.54/0.62 = { by lemma 5 R->L }
% 0.54/0.62 multiply(inverse(multiply(multiply(inverse(U), U), inverse(multiply(inverse(T), T)))), multiply(multiply(inverse(U), U), multiply(X, multiply(inverse(Y), Y))))
% 0.54/0.62 = { by lemma 16 }
% 0.54/0.62 multiply(inverse(multiply(multiply(inverse(U), U), inverse(multiply(inverse(T), T)))), multiply(X, multiply(inverse(S), S)))
% 1.50/0.62 = { by lemma 9 }
% 1.50/0.62 multiply(inverse(multiply(inverse(X2), X2)), multiply(X, multiply(inverse(S), S)))
% 1.50/0.62 = { by lemma 12 }
% 1.50/0.62 multiply(multiply(inverse(Y2), Y2), multiply(X, multiply(inverse(S), S)))
% 1.50/0.62 = { by lemma 16 }
% 1.50/0.62 multiply(X, multiply(inverse(W), W))
% 1.50/0.62
% 1.50/0.62 Lemma 18: multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(inverse(Z), Z)) = multiply(inverse(X), multiply(inverse(W), W)).
% 1.50/0.62 Proof:
% 1.50/0.62 multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(inverse(Z), Z))
% 1.50/0.62 = { by lemma 12 R->L }
% 1.50/0.62 multiply(inverse(multiply(X, inverse(multiply(inverse(V), V)))), multiply(inverse(Z), Z))
% 1.50/0.62 = { by lemma 10 R->L }
% 1.50/0.62 multiply(inverse(multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(U), U)))), multiply(inverse(T), T))), multiply(inverse(Z), Z))
% 1.50/0.62 = { by lemma 13 }
% 1.50/0.62 multiply(multiply(inverse(X), inverse(multiply(inverse(U), U))), multiply(inverse(S), S))
% 1.50/0.62 = { by lemma 12 }
% 1.50/0.62 multiply(multiply(inverse(X), multiply(inverse(X2), X2)), multiply(inverse(S), S))
% 1.50/0.62 = { by lemma 17 }
% 1.50/0.62 multiply(inverse(X), multiply(inverse(W), W))
% 1.50/0.62
% 1.50/0.62 Lemma 19: multiply(inverse(inverse(X)), multiply(inverse(Y), Y)) = multiply(X, multiply(inverse(Z), Z)).
% 1.50/0.62 Proof:
% 1.50/0.62 multiply(inverse(inverse(X)), multiply(inverse(Y), Y))
% 1.50/0.62 = { by lemma 18 R->L }
% 1.50/0.62 multiply(inverse(multiply(inverse(X), multiply(inverse(W), W))), multiply(inverse(V), V))
% 1.50/0.62 = { by lemma 13 }
% 1.50/0.62 multiply(X, multiply(inverse(Z), Z))
% 1.50/0.62
% 1.50/0.62 Lemma 20: inverse(multiply(inverse(X), multiply(inverse(Y), Y))) = X.
% 1.50/0.62 Proof:
% 1.50/0.62 inverse(multiply(inverse(X), multiply(inverse(Y), Y)))
% 1.50/0.62 = { by lemma 17 R->L }
% 1.50/0.62 inverse(multiply(multiply(inverse(X), multiply(inverse(Z), Z)), multiply(inverse(W), W)))
% 1.50/0.62 = { by lemma 12 R->L }
% 1.50/0.62 inverse(multiply(multiply(inverse(X), inverse(multiply(inverse(V), V))), multiply(inverse(W), W)))
% 1.50/0.62 = { by lemma 19 R->L }
% 1.50/0.62 inverse(multiply(inverse(inverse(multiply(inverse(X), inverse(multiply(inverse(V), V))))), multiply(inverse(U), U)))
% 1.50/0.62 = { by lemma 18 R->L }
% 1.50/0.62 inverse(multiply(inverse(multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(V), V)))), multiply(inverse(T), T))), multiply(inverse(S), S)))
% 1.50/0.62 = { by lemma 16 R->L }
% 1.50/0.62 inverse(multiply(inverse(multiply(multiply(inverse(X2), X2), multiply(inverse(multiply(inverse(X), inverse(multiply(inverse(V), V)))), multiply(inverse(Y2), Y2)))), multiply(inverse(S), S)))
% 1.50/0.62 = { by lemma 15 R->L }
% 1.50/0.62 inverse(multiply(inverse(multiply(multiply(multiply(inverse(Z2), Z2), inverse(multiply(inverse(X), inverse(multiply(inverse(V), V))))), multiply(inverse(W2), W2))), multiply(inverse(S), S)))
% 1.50/0.62 = { by lemma 18 }
% 1.50/0.62 inverse(multiply(inverse(multiply(multiply(inverse(Z2), Z2), inverse(multiply(inverse(X), inverse(multiply(inverse(V), V)))))), multiply(inverse(V2), V2)))
% 1.50/0.62 = { by lemma 12 R->L }
% 1.50/0.62 inverse(multiply(inverse(multiply(inverse(multiply(inverse(U2), U2)), inverse(multiply(inverse(X), inverse(multiply(inverse(V), V)))))), multiply(inverse(V2), V2)))
% 1.50/0.62 = { by lemma 11 }
% 1.50/0.62 X
% 1.50/0.62
% 1.50/0.62 Lemma 21: multiply(multiply(inverse(X), X), Y) = Y.
% 1.50/0.62 Proof:
% 1.50/0.62 multiply(multiply(inverse(X), X), Y)
% 1.50/0.62 = { by lemma 20 R->L }
% 1.50/0.62 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), multiply(inverse(Z), Z))))
% 1.50/0.62 = { by lemma 12 R->L }
% 1.50/0.62 multiply(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(Y), multiply(inverse(Z), Z))))
% 1.50/0.62 = { by lemma 12 R->L }
% 1.50/0.62 multiply(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(Y), inverse(multiply(inverse(V), V)))))
% 1.50/0.62 = { by lemma 20 R->L }
% 1.50/0.62 inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(Y), inverse(multiply(inverse(V), V)))))), multiply(inverse(U), U)))
% 1.50/0.62 = { by lemma 11 }
% 1.50/0.62 Y
% 1.50/0.62
% 1.50/0.62 Lemma 22: multiply(X, multiply(inverse(Y), Y)) = X.
% 1.50/0.62 Proof:
% 1.50/0.62 multiply(X, multiply(inverse(Y), Y))
% 1.50/0.62 = { by lemma 20 R->L }
% 1.50/0.62 inverse(multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(inverse(Z), Z)))
% 1.50/0.62 = { by lemma 18 }
% 1.50/0.62 inverse(multiply(inverse(X), multiply(inverse(W), W)))
% 1.50/0.62 = { by lemma 20 }
% 1.50/0.62 X
% 1.50/0.62
% 1.50/0.62 Lemma 23: inverse(inverse(X)) = X.
% 1.50/0.62 Proof:
% 1.50/0.62 inverse(inverse(X))
% 1.50/0.63 = { by lemma 20 R->L }
% 1.50/0.63 inverse(inverse(inverse(multiply(inverse(X), multiply(inverse(Y), Y)))))
% 1.50/0.63 = { by lemma 21 R->L }
% 1.50/0.63 inverse(inverse(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(X), multiply(inverse(Y), Y))))))
% 1.50/0.63 = { by lemma 12 R->L }
% 1.50/0.63 inverse(inverse(multiply(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(X), multiply(inverse(Y), Y))))))
% 1.50/0.63 = { by lemma 12 R->L }
% 1.50/0.63 inverse(inverse(multiply(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(X), inverse(multiply(inverse(V), V)))))))
% 1.50/0.63 = { by lemma 22 R->L }
% 1.50/0.63 inverse(multiply(inverse(multiply(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(X), inverse(multiply(inverse(V), V)))))), multiply(inverse(U), U)))
% 1.50/0.63 = { by lemma 11 }
% 1.50/0.63 X
% 1.50/0.63
% 1.50/0.63 Lemma 24: inverse(multiply(inverse(multiply(X, Y)), X)) = Y.
% 1.50/0.63 Proof:
% 1.50/0.63 inverse(multiply(inverse(multiply(X, Y)), X))
% 1.50/0.63 = { by lemma 22 R->L }
% 1.50/0.63 inverse(multiply(inverse(multiply(X, Y)), multiply(X, multiply(inverse(Z), Z))))
% 1.50/0.63 = { by lemma 20 R->L }
% 1.50/0.63 inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), multiply(inverse(W), W))))), multiply(X, multiply(inverse(Z), Z))))
% 1.50/0.63 = { by lemma 12 R->L }
% 1.50/0.63 inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(inverse(Z), Z)))))), multiply(X, multiply(inverse(Z), Z))))
% 1.50/0.63 = { by lemma 23 R->L }
% 1.50/0.63 inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(inverse(inverse(multiply(inverse(Z), Z)))))))), multiply(X, multiply(inverse(Z), Z))))
% 1.50/0.63 = { by lemma 21 R->L }
% 1.50/0.63 inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(Z), Z), inverse(inverse(multiply(inverse(Z), Z))))))))), multiply(X, multiply(inverse(Z), Z))))
% 1.50/0.63 = { by lemma 22 R->L }
% 1.50/0.63 inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(Z), Z))))))))), multiply(X, multiply(inverse(Z), Z))))
% 1.50/0.63 = { by axiom 1 (single_axiom) }
% 1.50/0.63 Y
% 1.50/0.63
% 1.50/0.63 Lemma 25: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 1.50/0.63 Proof:
% 1.50/0.63 inverse(multiply(inverse(X), Y))
% 1.50/0.63 = { by lemma 22 R->L }
% 1.50/0.63 inverse(multiply(inverse(multiply(X, multiply(inverse(Z), Z))), Y))
% 1.50/0.63 = { by lemma 12 R->L }
% 1.50/0.63 inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(W), W)))), Y))
% 1.50/0.63 = { by lemma 5 R->L }
% 1.50/0.63 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(V), V)))), multiply(inverse(Y), X))), Y))
% 1.50/0.63 = { by lemma 12 }
% 1.50/0.63 inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(inverse(U), U))), multiply(inverse(Y), X))), Y))
% 1.50/0.63 = { by lemma 20 }
% 1.50/0.63 inverse(multiply(inverse(multiply(Y, multiply(inverse(Y), X))), Y))
% 1.50/0.63 = { by lemma 24 }
% 1.50/0.63 multiply(inverse(Y), X)
% 1.50/0.63
% 1.50/0.63 Lemma 26: inverse(multiply(X, Y)) = multiply(inverse(Y), inverse(X)).
% 1.50/0.63 Proof:
% 1.50/0.63 inverse(multiply(X, Y))
% 1.50/0.63 = { by lemma 11 R->L }
% 1.50/0.63 inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(X), inverse(multiply(inverse(W), W)))))), multiply(inverse(V), V))), Y))
% 1.50/0.63 = { by lemma 25 }
% 1.50/0.63 multiply(inverse(Y), multiply(inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(X), inverse(multiply(inverse(W), W)))))), multiply(inverse(V), V)))
% 1.50/0.63 = { by lemma 22 }
% 1.50/0.63 multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(X), inverse(multiply(inverse(W), W)))))))
% 1.50/0.63 = { by lemma 25 }
% 1.50/0.63 multiply(inverse(Y), multiply(inverse(inverse(multiply(inverse(X), inverse(multiply(inverse(W), W))))), multiply(inverse(Z), Z)))
% 1.50/0.63 = { by lemma 19 }
% 1.50/0.63 multiply(inverse(Y), multiply(multiply(inverse(X), inverse(multiply(inverse(W), W))), multiply(inverse(U), U)))
% 1.50/0.63 = { by lemma 22 }
% 1.50/0.63 multiply(inverse(Y), multiply(inverse(X), inverse(multiply(inverse(W), W))))
% 1.50/0.63 = { by lemma 12 }
% 1.50/0.63 multiply(inverse(Y), multiply(inverse(X), multiply(inverse(T), T)))
% 1.50/0.63 = { by lemma 22 }
% 1.50/0.63 multiply(inverse(Y), inverse(X))
% 1.50/0.63
% 1.50/0.63 Lemma 27: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 1.50/0.63 Proof:
% 1.50/0.63 multiply(inverse(X), X)
% 1.50/0.63 = { by lemma 6 }
% 1.50/0.63 multiply(inverse(inverse(Y)), inverse(Y))
% 1.50/0.63 = { by lemma 23 }
% 1.50/0.63 multiply(Y, inverse(Y))
% 1.50/0.63
% 1.50/0.63 Lemma 28: multiply(inverse(multiply(X, Y)), X) = inverse(Y).
% 1.50/0.63 Proof:
% 1.50/0.63 multiply(inverse(multiply(X, Y)), X)
% 1.50/0.63 = { by lemma 22 R->L }
% 1.50/0.63 multiply(multiply(inverse(multiply(X, Y)), X), multiply(inverse(Z), Z))
% 1.50/0.63 = { by lemma 12 R->L }
% 1.50/0.63 multiply(multiply(inverse(multiply(X, Y)), X), inverse(multiply(inverse(W), W)))
% 1.50/0.63 = { by lemma 10 R->L }
% 1.50/0.63 multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), X)), inverse(multiply(inverse(V), V)))), multiply(inverse(U), U))
% 1.50/0.63 = { by lemma 24 }
% 1.50/0.63 multiply(inverse(multiply(Y, inverse(multiply(inverse(V), V)))), multiply(inverse(U), U))
% 1.50/0.63 = { by lemma 22 }
% 1.50/0.63 inverse(multiply(Y, inverse(multiply(inverse(V), V))))
% 1.50/0.63 = { by lemma 12 }
% 1.50/0.63 inverse(multiply(Y, multiply(inverse(T), T)))
% 1.50/0.63 = { by lemma 22 }
% 1.50/0.63 inverse(Y)
% 1.50/0.63
% 1.50/0.63 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))).
% 1.50/0.63 Proof:
% 1.50/0.63 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 1.50/0.63 = { by lemma 21 }
% 1.50/0.63 tuple(multiply(inverse(a1), a1), a2, multiply(multiply(a3, b3), c3))
% 1.50/0.63 = { by lemma 27 }
% 1.50/0.63 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), c3))
% 1.50/0.63 = { by lemma 23 R->L }
% 1.50/0.63 tuple(multiply(X, inverse(X)), a2, multiply(multiply(inverse(inverse(a3)), b3), c3))
% 1.50/0.63 = { by lemma 25 R->L }
% 1.50/0.63 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(inverse(b3), inverse(a3))), c3))
% 1.50/0.63 = { by lemma 26 R->L }
% 1.50/0.63 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(multiply(a3, b3))), c3))
% 1.50/0.63 = { by lemma 28 R->L }
% 1.50/0.63 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))))), multiply(a3, b3))), inverse(multiply(a3, inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))))))), c3))
% 1.50/0.63 = { by axiom 1 (single_axiom) }
% 1.50/0.63 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, inverse(multiply(a3, inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3)))))))))), c3))
% 1.50/0.63 = { by lemma 26 }
% 1.50/0.63 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, multiply(inverse(inverse(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3))))))), inverse(a3)))), c3))
% 1.50/0.63 = { by lemma 23 }
% 1.50/0.63 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, multiply(multiply(inverse(c3), inverse(multiply(b3, inverse(multiply(inverse(b3), b3))))), inverse(a3)))), c3))
% 1.50/0.63 = { by lemma 26 }
% 1.50/0.63 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, multiply(multiply(inverse(c3), multiply(inverse(inverse(multiply(inverse(b3), b3))), inverse(b3))), inverse(a3)))), c3))
% 1.50/0.63 = { by lemma 23 }
% 1.50/0.63 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, multiply(multiply(inverse(c3), multiply(multiply(inverse(b3), b3), inverse(b3))), inverse(a3)))), c3))
% 1.50/0.63 = { by lemma 21 R->L }
% 1.50/0.63 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, multiply(multiply(inverse(c3), multiply(multiply(multiply(inverse(Y), Y), multiply(inverse(b3), b3)), inverse(b3))), inverse(a3)))), c3))
% 1.50/0.63 = { by lemma 23 R->L }
% 1.50/0.64 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, multiply(multiply(inverse(c3), multiply(multiply(inverse(inverse(multiply(inverse(Y), Y))), multiply(inverse(b3), b3)), inverse(b3))), inverse(a3)))), c3))
% 1.50/0.64 = { by lemma 25 R->L }
% 1.50/0.64 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, multiply(multiply(inverse(c3), multiply(inverse(multiply(inverse(multiply(inverse(b3), b3)), inverse(multiply(inverse(Y), Y)))), inverse(b3))), inverse(a3)))), c3))
% 1.50/0.64 = { by lemma 28 R->L }
% 1.50/0.64 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, multiply(multiply(inverse(c3), multiply(inverse(multiply(inverse(multiply(inverse(b3), b3)), inverse(multiply(inverse(Y), Y)))), multiply(inverse(multiply(inverse(b3), b3)), inverse(b3)))), inverse(a3)))), c3))
% 1.50/0.64 = { by lemma 5 }
% 1.50/0.64 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, multiply(multiply(inverse(c3), multiply(inverse(b3), inverse(multiply(inverse(Z), Z)))), inverse(a3)))), c3))
% 1.50/0.64 = { by lemma 12 }
% 1.50/0.64 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, multiply(multiply(inverse(c3), multiply(inverse(b3), multiply(inverse(W), W))), inverse(a3)))), c3))
% 1.50/0.64 = { by lemma 22 }
% 1.50/0.64 tuple(multiply(X, inverse(X)), a2, multiply(inverse(multiply(c3, multiply(multiply(inverse(c3), inverse(b3)), inverse(a3)))), c3))
% 1.50/0.64 = { by lemma 28 }
% 1.50/0.64 tuple(multiply(X, inverse(X)), a2, inverse(multiply(multiply(inverse(c3), inverse(b3)), inverse(a3))))
% 1.50/0.64 = { by lemma 26 }
% 1.50/0.64 tuple(multiply(X, inverse(X)), a2, multiply(inverse(inverse(a3)), inverse(multiply(inverse(c3), inverse(b3)))))
% 1.50/0.64 = { by lemma 23 }
% 1.50/0.64 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(inverse(c3), inverse(b3)))))
% 1.50/0.64 = { by lemma 25 }
% 1.50/0.64 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(inverse(inverse(b3)), c3)))
% 1.50/0.64 = { by lemma 23 }
% 1.50/0.64 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)))
% 1.50/0.64 = { by lemma 27 R->L }
% 1.50/0.64 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 1.50/0.64 % SZS output end Proof
% 1.50/0.64
% 1.50/0.64 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------