TSTP Solution File: GRP437-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP437-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:18:25 EDT 2023
% Result : Unsatisfiable 0.14s 0.58s
% Output : Proof 3.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : GRP437-1 : TPTP v8.1.2. Released v2.6.0.
% 0.08/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Aug 28 23:03:01 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.58 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.14/0.58
% 0.14/0.58 % SZS status Unsatisfiable
% 0.14/0.58
% 2.40/0.70 % SZS output start Proof
% 2.40/0.70 Axiom 1 (single_axiom): multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, Y))), X))))) = W.
% 2.40/0.70
% 2.40/0.70 Lemma 2: multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V))), multiply(V, multiply(Z, X))))) = W.
% 2.40/0.71 Proof:
% 2.40/0.71 multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V))), multiply(V, multiply(Z, X)))))
% 2.40/0.71 = { by axiom 1 (single_axiom) R->L }
% 2.40/0.71 multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V))), multiply(V, multiply(multiply(inverse(V), inverse(multiply(W, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(V)))))), X)))))
% 2.40/0.71 = { by axiom 1 (single_axiom) }
% 2.40/0.71 W
% 2.40/0.71
% 2.40/0.71 Lemma 3: multiply(X, inverse(multiply(multiply(Y, multiply(Z, inverse(W))), multiply(W, multiply(V, X))))) = multiply(U, multiply(multiply(inverse(U), inverse(multiply(Z, V))), inverse(Y))).
% 2.40/0.71 Proof:
% 2.40/0.71 multiply(X, inverse(multiply(multiply(Y, multiply(Z, inverse(W))), multiply(W, multiply(V, X)))))
% 2.40/0.71 = { by axiom 1 (single_axiom) R->L }
% 2.40/0.71 multiply(X, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), inverse(multiply(Z, V))), inverse(Y)))))), inverse(W))), multiply(W, multiply(V, X)))))
% 2.40/0.71 = { by lemma 2 }
% 2.40/0.71 multiply(U, multiply(multiply(inverse(U), inverse(multiply(Z, V))), inverse(Y)))
% 2.40/0.71
% 2.40/0.71 Lemma 4: multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(Y, inverse(Z))))))))), inverse(V))) = W.
% 2.40/0.71 Proof:
% 2.40/0.71 multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(Y, inverse(Z))))))))), inverse(V)))
% 2.40/0.71 = { by lemma 3 R->L }
% 2.40/0.71 multiply(U, inverse(multiply(multiply(V, multiply(Y, inverse(Z))), multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, multiply(V, multiply(Y, inverse(Z)))))), U)))))
% 2.40/0.71 = { by axiom 1 (single_axiom) }
% 2.40/0.71 W
% 2.40/0.71
% 2.40/0.71 Lemma 5: multiply(inverse(X), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X)))))) = multiply(V, inverse(multiply(Y, multiply(Z, multiply(W, V))))).
% 2.40/0.71 Proof:
% 2.40/0.71 multiply(inverse(X), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X))))))
% 2.40/0.71 = { by lemma 2 R->L }
% 2.40/0.71 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(W, multiply(inverse(X), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X))))))))), inverse(Z))), multiply(Z, multiply(W, V)))))
% 2.40/0.71 = { by lemma 4 }
% 2.40/0.71 multiply(V, inverse(multiply(Y, multiply(Z, multiply(W, V)))))
% 2.40/0.71
% 2.40/0.71 Lemma 6: multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, inverse(Y)))))), Z))) = W.
% 2.40/0.71 Proof:
% 2.40/0.71 multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, inverse(Y)))))), Z)))
% 2.40/0.71 = { by lemma 4 R->L }
% 2.40/0.71 multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, inverse(Y)))))), multiply(V, multiply(multiply(inverse(V), inverse(multiply(W, multiply(inverse(Y), inverse(multiply(Z, multiply(X, multiply(W, inverse(Y))))))))), inverse(X))))))
% 2.40/0.71 = { by axiom 1 (single_axiom) }
% 2.40/0.71 W
% 2.40/0.71
% 2.40/0.71 Lemma 7: multiply(inverse(X), inverse(multiply(multiply(Y, inverse(multiply(Z, multiply(X, multiply(W, Y))))), Z))) = W.
% 2.40/0.71 Proof:
% 2.40/0.71 multiply(inverse(X), inverse(multiply(multiply(Y, inverse(multiply(Z, multiply(X, multiply(W, Y))))), Z)))
% 2.40/0.71 = { by lemma 5 R->L }
% 2.40/0.71 multiply(inverse(X), inverse(multiply(multiply(inverse(V), inverse(multiply(Z, multiply(X, multiply(W, inverse(V)))))), Z)))
% 2.40/0.71 = { by lemma 6 }
% 2.40/0.71 W
% 2.40/0.71
% 2.40/0.71 Lemma 8: multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, W))), Z))), inverse(Y))) = W.
% 2.40/0.71 Proof:
% 2.40/0.71 multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(Y), inverse(multiply(Z, W))), Z))), inverse(Y)))
% 2.40/0.71 = { by lemma 3 R->L }
% 2.40/0.71 multiply(V, inverse(multiply(multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, W))), inverse(U))), multiply(U, multiply(Z, V)))))
% 2.40/0.71 = { by lemma 2 }
% 2.40/0.71 W
% 2.40/0.71
% 2.40/0.71 Lemma 9: inverse(multiply(multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), X))))), Y)) = W.
% 2.40/0.71 Proof:
% 2.40/0.71 inverse(multiply(multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), X))))), Y))
% 2.40/0.71 = { by lemma 2 R->L }
% 2.40/0.71 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(Z), inverse(multiply(multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), W), X))))), Y))))), inverse(T))), multiply(T, multiply(inverse(Z), V)))))
% 2.40/0.71 = { by lemma 7 }
% 2.40/0.71 multiply(V, inverse(multiply(multiply(U, multiply(multiply(inverse(U), inverse(multiply(inverse(Z), W))), inverse(T))), multiply(T, multiply(inverse(Z), V)))))
% 2.40/0.71 = { by lemma 3 }
% 2.40/0.71 multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(inverse(U), inverse(multiply(inverse(Z), W))), inverse(Z)))), inverse(U)))
% 2.40/0.71 = { by lemma 8 }
% 2.40/0.71 W
% 2.40/0.71
% 2.40/0.71 Lemma 10: multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(Y, inverse(multiply(Z, W))), Z))), Y)) = W.
% 2.40/0.71 Proof:
% 2.40/0.71 multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(Y, inverse(multiply(Z, W))), Z))), Y))
% 2.40/0.71 = { by lemma 9 R->L }
% 2.40/0.71 multiply(X, multiply(multiply(inverse(X), inverse(multiply(multiply(Y, inverse(multiply(Z, W))), Z))), inverse(multiply(multiply(V, inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), Y), V))))), U))))
% 2.40/0.71 = { by lemma 3 R->L }
% 2.40/0.71 multiply(S, inverse(multiply(multiply(multiply(multiply(V, inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), Y), V))))), U), multiply(multiply(Y, inverse(multiply(Z, W))), inverse(X2))), multiply(X2, multiply(Z, S)))))
% 2.40/0.71 = { by lemma 9 R->L }
% 2.40/0.71 multiply(S, inverse(multiply(multiply(multiply(multiply(V, inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), Y), V))))), U), multiply(multiply(inverse(multiply(multiply(V, inverse(multiply(U, multiply(T, multiply(multiply(inverse(T), Y), V))))), U)), inverse(multiply(Z, W))), inverse(X2))), multiply(X2, multiply(Z, S)))))
% 2.40/0.71 = { by lemma 2 }
% 2.40/0.71 W
% 2.40/0.71
% 2.40/0.71 Lemma 11: inverse(multiply(multiply(X, multiply(Y, inverse(Z))), multiply(Z, multiply(W, V)))) = multiply(multiply(inverse(V), inverse(multiply(Y, W))), inverse(X)).
% 2.40/0.71 Proof:
% 2.40/0.71 inverse(multiply(multiply(X, multiply(Y, inverse(Z))), multiply(Z, multiply(W, V))))
% 2.40/0.71 = { by lemma 10 R->L }
% 2.40/0.71 multiply(U, multiply(multiply(inverse(U), inverse(multiply(multiply(T, inverse(multiply(V, inverse(multiply(multiply(X, multiply(Y, inverse(Z))), multiply(Z, multiply(W, V))))))), V))), T))
% 2.40/0.71 = { by lemma 3 }
% 2.40/0.71 multiply(U, multiply(multiply(inverse(U), inverse(multiply(multiply(T, inverse(multiply(V, multiply(multiply(inverse(V), inverse(multiply(Y, W))), inverse(X))))), V))), T))
% 2.40/0.71 = { by lemma 10 }
% 2.40/0.71 multiply(multiply(inverse(V), inverse(multiply(Y, W))), inverse(X))
% 2.40/0.71
% 2.40/0.71 Lemma 12: multiply(multiply(inverse(X), inverse(multiply(multiply(V, Z), W))), V) = multiply(multiply(inverse(X), inverse(multiply(multiply(Y, Z), W))), Y).
% 2.40/0.71 Proof:
% 2.40/0.71 multiply(multiply(inverse(X), inverse(multiply(multiply(V, Z), W))), V)
% 2.40/0.71 = { by lemma 9 R->L }
% 2.40/0.71 multiply(multiply(inverse(X), inverse(multiply(multiply(V, Z), W))), inverse(multiply(multiply(Z2, inverse(multiply(W2, multiply(V2, multiply(multiply(inverse(V2), V), Z2))))), W2)))
% 2.40/0.71 = { by lemma 9 R->L }
% 2.40/0.71 multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(multiply(Z2, inverse(multiply(W2, multiply(V2, multiply(multiply(inverse(V2), V), Z2))))), W2)), Z), W))), inverse(multiply(multiply(Z2, inverse(multiply(W2, multiply(V2, multiply(multiply(inverse(V2), V), Z2))))), W2)))
% 2.40/0.71 = { by lemma 11 R->L }
% 2.40/0.71 inverse(multiply(multiply(multiply(multiply(Z2, inverse(multiply(W2, multiply(V2, multiply(multiply(inverse(V2), V), Z2))))), W2), multiply(multiply(inverse(multiply(multiply(Z2, inverse(multiply(W2, multiply(V2, multiply(multiply(inverse(V2), V), Z2))))), W2)), Z), inverse(X2))), multiply(X2, multiply(W, X))))
% 2.40/0.71 = { by lemma 2 R->L }
% 2.40/0.71 inverse(multiply(multiply(U2, inverse(multiply(multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(Y2, multiply(multiply(multiply(Z2, inverse(multiply(W2, multiply(V2, multiply(multiply(inverse(V2), V), Z2))))), W2), multiply(multiply(inverse(multiply(multiply(Z2, inverse(multiply(W2, multiply(V2, multiply(multiply(inverse(V2), V), Z2))))), W2)), Z), inverse(X2)))))), inverse(T2))), multiply(T2, multiply(Y2, U2))))), multiply(X2, multiply(W, X))))
% 2.40/0.71 = { by lemma 3 }
% 2.40/0.71 inverse(multiply(multiply(multiply(multiply(U, inverse(multiply(T, multiply(S, multiply(multiply(inverse(S), Y), U))))), T), multiply(multiply(inverse(multiply(multiply(U, inverse(multiply(T, multiply(S, multiply(multiply(inverse(S), Y), U))))), T)), inverse(multiply(multiply(inverse(X2), inverse(multiply(Y2, multiply(multiply(multiply(Z2, inverse(multiply(W2, multiply(V2, multiply(multiply(inverse(V2), V), Z2))))), W2), multiply(multiply(inverse(multiply(multiply(Z2, inverse(multiply(W2, multiply(V2, multiply(multiply(inverse(V2), V), Z2))))), W2)), Z), inverse(X2)))))), Y2))), inverse(X2))), multiply(X2, multiply(W, X))))
% 2.40/0.71 = { by lemma 9 }
% 2.40/0.71 inverse(multiply(multiply(multiply(multiply(U, inverse(multiply(T, multiply(S, multiply(multiply(inverse(S), Y), U))))), T), multiply(multiply(inverse(multiply(multiply(U, inverse(multiply(T, multiply(S, multiply(multiply(inverse(S), Y), U))))), T)), Z), inverse(X2))), multiply(X2, multiply(W, X))))
% 2.40/0.71 = { by lemma 11 }
% 2.40/0.71 multiply(multiply(inverse(X), inverse(multiply(multiply(inverse(multiply(multiply(U, inverse(multiply(T, multiply(S, multiply(multiply(inverse(S), Y), U))))), T)), Z), W))), inverse(multiply(multiply(U, inverse(multiply(T, multiply(S, multiply(multiply(inverse(S), Y), U))))), T)))
% 2.40/0.71 = { by lemma 9 }
% 2.40/0.71 multiply(multiply(inverse(X), inverse(multiply(multiply(Y, Z), W))), inverse(multiply(multiply(U, inverse(multiply(T, multiply(S, multiply(multiply(inverse(S), Y), U))))), T)))
% 2.40/0.71 = { by lemma 9 }
% 2.40/0.71 multiply(multiply(inverse(X), inverse(multiply(multiply(Y, Z), W))), Y)
% 2.40/0.71
% 2.40/0.71 Lemma 13: multiply(multiply(X, inverse(multiply(multiply(Y, Z), multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, multiply(U, Z)))), X))))), Y) = multiply(V, U).
% 2.40/0.71 Proof:
% 2.40/0.71 multiply(multiply(X, inverse(multiply(multiply(Y, Z), multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, multiply(U, Z)))), X))))), Y)
% 2.40/0.71 = { by lemma 5 R->L }
% 2.40/0.71 multiply(multiply(inverse(T), inverse(multiply(multiply(Y, Z), multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, multiply(U, Z)))), inverse(T)))))), Y)
% 2.40/0.71 = { by lemma 12 }
% 2.40/0.71 multiply(multiply(inverse(T), inverse(multiply(multiply(U, Z), multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, multiply(U, Z)))), inverse(T)))))), U)
% 2.40/0.71 = { by axiom 1 (single_axiom) }
% 2.40/0.71 multiply(V, U)
% 2.40/0.71
% 2.40/0.71 Lemma 14: multiply(Z, multiply(inverse(Z), Y)) = multiply(X, multiply(inverse(X), Y)).
% 2.40/0.71 Proof:
% 2.40/0.71 multiply(Z, multiply(inverse(Z), Y))
% 2.40/0.71 = { by lemma 13 R->L }
% 2.40/0.71 multiply(multiply(W, inverse(multiply(multiply(V, U), multiply(T, multiply(multiply(inverse(T), inverse(multiply(Z, multiply(multiply(inverse(Z), Y), U)))), W))))), V)
% 2.40/0.71 = { by lemma 9 R->L }
% 2.40/0.71 multiply(multiply(W, inverse(multiply(multiply(V, U), multiply(T, multiply(multiply(inverse(T), inverse(multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(U, inverse(multiply(S, multiply(X, multiply(multiply(inverse(X), Y), U))))), S))), U)))), W))))), V)
% 2.40/0.71 = { by lemma 10 }
% 2.40/0.71 multiply(multiply(W, inverse(multiply(multiply(V, U), multiply(T, multiply(multiply(inverse(T), inverse(multiply(X, multiply(multiply(inverse(X), Y), U)))), W))))), V)
% 2.40/0.71 = { by lemma 13 }
% 2.40/0.71 multiply(X, multiply(inverse(X), Y))
% 2.40/0.71
% 2.40/0.71 Lemma 15: multiply(Y, inverse(Y)) = multiply(X, inverse(X)).
% 2.40/0.71 Proof:
% 2.40/0.71 multiply(Y, inverse(Y))
% 2.40/0.71 = { by lemma 13 R->L }
% 2.40/0.71 multiply(multiply(Z, inverse(multiply(multiply(W, V), multiply(U, multiply(multiply(inverse(U), inverse(multiply(Y, multiply(inverse(Y), V)))), Z))))), W)
% 2.40/0.71 = { by lemma 14 }
% 2.40/0.71 multiply(multiply(Z, inverse(multiply(multiply(W, V), multiply(U, multiply(multiply(inverse(U), inverse(multiply(X, multiply(inverse(X), V)))), Z))))), W)
% 2.40/0.72 = { by lemma 13 }
% 2.40/0.72 multiply(X, inverse(X))
% 2.40/0.72
% 2.40/0.72 Lemma 16: multiply(X, inverse(multiply(Y, inverse(Y)))) = X.
% 2.40/0.72 Proof:
% 2.40/0.72 multiply(X, inverse(multiply(Y, inverse(Y))))
% 2.40/0.72 = { by lemma 10 R->L }
% 2.40/0.72 multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(multiply(Y, inverse(Y)), inverse(multiply(Y, inverse(Y)))), Y))), multiply(Y, inverse(Y)))))))
% 2.40/0.72 = { by lemma 15 R->L }
% 2.40/0.72 multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(Y, inverse(Y)), Y))), multiply(Y, inverse(Y)))))))
% 2.40/0.72 = { by lemma 9 R->L }
% 2.40/0.72 multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(multiply(Y, inverse(Y)), Y))), inverse(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(Y, inverse(Y))), W))))), V)))))))
% 2.40/0.72 = { by lemma 9 R->L }
% 2.40/0.72 multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(Y, inverse(Y))), W))))), V)), Y))), inverse(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(Y, inverse(Y))), W))))), V)))))))
% 2.40/0.72 = { by lemma 11 R->L }
% 2.40/0.72 multiply(X, inverse(multiply(Y, multiply(Z, inverse(multiply(multiply(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(Y, inverse(Y))), W))))), V), multiply(inverse(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), multiply(Y, inverse(Y))), W))))), V)), inverse(T))), multiply(T, multiply(Y, Z))))))))
% 2.40/0.72 = { by lemma 14 }
% 2.40/0.72 multiply(X, inverse(multiply(Y, multiply(Z, inverse(multiply(multiply(multiply(multiply(S, inverse(multiply(X2, multiply(Y2, multiply(multiply(inverse(Y2), X), S))))), X2), multiply(inverse(multiply(multiply(S, inverse(multiply(X2, multiply(Y2, multiply(multiply(inverse(Y2), X), S))))), X2)), inverse(T))), multiply(T, multiply(Y, Z))))))))
% 2.40/0.72 = { by lemma 11 }
% 2.40/0.72 multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(inverse(multiply(multiply(S, inverse(multiply(X2, multiply(Y2, multiply(multiply(inverse(Y2), X), S))))), X2)), Y))), inverse(multiply(multiply(S, inverse(multiply(X2, multiply(Y2, multiply(multiply(inverse(Y2), X), S))))), X2)))))))
% 2.40/0.72 = { by lemma 9 }
% 2.40/0.72 multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(X, Y))), inverse(multiply(multiply(S, inverse(multiply(X2, multiply(Y2, multiply(multiply(inverse(Y2), X), S))))), X2)))))))
% 2.40/0.72 = { by lemma 9 }
% 2.40/0.72 multiply(X, inverse(multiply(Y, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(X, Y))), X)))))
% 2.40/0.72 = { by axiom 1 (single_axiom) }
% 2.40/0.72 X
% 2.40/0.72
% 2.40/0.72 Lemma 17: multiply(multiply(X, inverse(multiply(multiply(V, Z), W))), V) = multiply(multiply(X, inverse(multiply(multiply(Y, Z), W))), Y).
% 2.40/0.72 Proof:
% 2.40/0.72 multiply(multiply(X, inverse(multiply(multiply(V, Z), W))), V)
% 2.40/0.72 = { by lemma 10 R->L }
% 2.40/0.72 multiply(multiply(X, inverse(multiply(multiply(V, Z), multiply(U, multiply(multiply(inverse(U), inverse(multiply(multiply(X, inverse(multiply(T, W))), T))), X))))), V)
% 2.40/0.72 = { by lemma 5 R->L }
% 2.40/0.72 multiply(multiply(inverse(S), inverse(multiply(multiply(V, Z), multiply(U, multiply(multiply(inverse(U), inverse(multiply(multiply(X, inverse(multiply(T, W))), T))), inverse(S)))))), V)
% 2.40/0.72 = { by lemma 12 }
% 2.40/0.72 multiply(multiply(inverse(S), inverse(multiply(multiply(Y, Z), multiply(U, multiply(multiply(inverse(U), inverse(multiply(multiply(X, inverse(multiply(T, W))), T))), inverse(S)))))), Y)
% 2.40/0.72 = { by lemma 5 }
% 2.40/0.72 multiply(multiply(X, inverse(multiply(multiply(Y, Z), multiply(U, multiply(multiply(inverse(U), inverse(multiply(multiply(X, inverse(multiply(T, W))), T))), X))))), Y)
% 2.40/0.72 = { by lemma 10 }
% 3.14/0.72 multiply(multiply(X, inverse(multiply(multiply(Y, Z), W))), Y)
% 3.14/0.72
% 3.14/0.72 Lemma 18: multiply(X, multiply(Y, inverse(Y))) = X.
% 3.14/0.72 Proof:
% 3.14/0.72 multiply(X, multiply(Y, inverse(Y)))
% 3.14/0.72 = { by lemma 2 R->L }
% 3.14/0.72 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, multiply(X, multiply(Y, inverse(Y)))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 3.14/0.72 = { by axiom 1 (single_axiom) R->L }
% 3.14/0.72 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(T, inverse(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), multiply(S, multiply(multiply(inverse(S), inverse(multiply(V, multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y)))))))), T))))), multiply(X, multiply(Y, inverse(Y)))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 3.14/0.72 = { by lemma 16 R->L }
% 3.14/0.72 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(T, inverse(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(V, inverse(multiply(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), inverse(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))))), inverse(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), inverse(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))))))))), multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y)))))))), T))))), multiply(X, multiply(Y, inverse(Y)))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 3.14/0.72 = { by lemma 17 }
% 3.14/0.72 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(T, inverse(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(V, inverse(multiply(multiply(multiply(inverse(Y), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X))), inverse(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))))), inverse(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), inverse(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))))))))), multiply(inverse(Y), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X)))))), T))))), multiply(X, multiply(Y, inverse(Y)))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 3.14/0.72 = { by lemma 16 }
% 3.14/0.72 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(T, inverse(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(V, inverse(multiply(multiply(inverse(Y), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X))), inverse(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))))))), multiply(inverse(Y), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X)))))), T))))), multiply(X, multiply(Y, inverse(Y)))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 3.14/0.73 = { by lemma 16 }
% 3.14/0.73 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(T, inverse(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(V, inverse(multiply(inverse(Y), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X))))), multiply(inverse(Y), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X)))))), T))))), multiply(X, multiply(Y, inverse(Y)))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 3.14/0.73 = { by lemma 7 R->L }
% 3.14/0.73 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(T, inverse(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(V, inverse(multiply(multiply(inverse(X2), inverse(multiply(multiply(Y2, inverse(multiply(Z2, multiply(X2, multiply(inverse(Y), Y2))))), Z2))), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X))))), multiply(inverse(Y), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X)))))), T))))), multiply(X, multiply(Y, inverse(Y)))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 3.14/0.73 = { by lemma 6 R->L }
% 3.14/0.73 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(T, inverse(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(V, inverse(multiply(multiply(multiply(inverse(Y), inverse(multiply(multiply(inverse(multiply(multiply(Y2, inverse(multiply(Z2, multiply(X2, multiply(inverse(Y), Y2))))), Z2)), inverse(multiply(X, multiply(Y, multiply(inverse(X2), inverse(multiply(multiply(Y2, inverse(multiply(Z2, multiply(X2, multiply(inverse(Y), Y2))))), Z2))))))), X))), inverse(multiply(multiply(Y2, inverse(multiply(Z2, multiply(X2, multiply(inverse(Y), Y2))))), Z2))), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X))))), multiply(inverse(Y), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X)))))), T))))), multiply(X, multiply(Y, inverse(Y)))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 3.14/0.73 = { by lemma 7 }
% 3.14/0.73 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(T, inverse(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(V, inverse(multiply(multiply(multiply(inverse(Y), inverse(multiply(multiply(inverse(multiply(multiply(Y2, inverse(multiply(Z2, multiply(X2, multiply(inverse(Y), Y2))))), Z2)), inverse(multiply(X, multiply(Y, inverse(Y))))), X))), inverse(multiply(multiply(Y2, inverse(multiply(Z2, multiply(X2, multiply(inverse(Y), Y2))))), Z2))), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X))))), multiply(inverse(Y), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X)))))), T))))), multiply(X, multiply(Y, inverse(Y)))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 3.14/0.73 = { by lemma 12 R->L }
% 3.14/0.73 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(T, inverse(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(V, inverse(multiply(multiply(multiply(inverse(Y), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X))), X), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X))))), multiply(inverse(Y), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X)))))), T))))), multiply(X, multiply(Y, inverse(Y)))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 3.14/0.73 = { by lemma 17 R->L }
% 3.14/0.73 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(T, inverse(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), multiply(S, multiply(multiply(inverse(S), inverse(multiply(multiply(V, inverse(multiply(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X), inverse(multiply(multiply(X, inverse(multiply(X, multiply(Y, inverse(Y))))), X))))), multiply(X, inverse(multiply(X, multiply(Y, inverse(Y)))))))), T))))), multiply(X, multiply(Y, inverse(Y)))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 3.14/0.73 = { by lemma 16 }
% 3.14/0.73 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(multiply(T, inverse(multiply(multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(X, multiply(Y, inverse(Y))))), multiply(S, multiply(multiply(inverse(S), inverse(multiply(V, multiply(X, inverse(multiply(X, multiply(Y, inverse(Y)))))))), T))))), multiply(X, multiply(Y, inverse(Y)))))), inverse(U))), multiply(U, multiply(V, Z)))))
% 3.14/0.73 = { by lemma 13 }
% 3.14/0.73 multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(V, X))), inverse(U))), multiply(U, multiply(V, Z)))))
% 3.14/0.73 = { by lemma 3 }
% 3.14/0.73 multiply(W2, multiply(multiply(inverse(W2), inverse(multiply(multiply(inverse(W), inverse(multiply(V, X))), V))), inverse(W)))
% 3.14/0.73 = { by lemma 8 }
% 3.14/0.73 X
% 3.14/0.73
% 3.14/0.73 Lemma 19: multiply(multiply(X, inverse(X)), Y) = Y.
% 3.14/0.73 Proof:
% 3.14/0.73 multiply(multiply(X, inverse(X)), Y)
% 3.14/0.73 = { by lemma 18 R->L }
% 3.14/0.73 multiply(multiply(multiply(X, inverse(X)), Y), multiply(inverse(multiply(multiply(X, inverse(X)), Y)), inverse(inverse(multiply(multiply(X, inverse(X)), Y)))))
% 3.14/0.73 = { by lemma 15 }
% 3.14/0.73 multiply(multiply(multiply(X, inverse(X)), Y), multiply(inverse(multiply(multiply(X, inverse(X)), Y)), inverse(inverse(multiply(multiply(Y, inverse(Y)), Y)))))
% 3.14/0.73 = { by lemma 16 R->L }
% 3.14/0.73 multiply(multiply(multiply(X, inverse(X)), Y), multiply(inverse(multiply(multiply(X, inverse(X)), Y)), inverse(inverse(multiply(multiply(Y, inverse(multiply(Y, inverse(multiply(Z, inverse(Z)))))), Y)))))
% 3.14/0.73 = { by lemma 9 R->L }
% 3.14/0.73 multiply(multiply(multiply(X, inverse(X)), Y), multiply(inverse(multiply(multiply(X, inverse(X)), Y)), inverse(inverse(multiply(multiply(inverse(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), Y), W))))), V)), inverse(multiply(Y, inverse(multiply(Z, inverse(Z)))))), Y)))))
% 3.14/0.73 = { by lemma 2 R->L }
% 3.14/0.73 multiply(multiply(multiply(X, inverse(X)), Y), multiply(inverse(multiply(multiply(X, inverse(X)), Y)), inverse(multiply(T, inverse(multiply(multiply(S, multiply(multiply(inverse(S), inverse(multiply(inverse(X2), inverse(multiply(multiply(inverse(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), Y), W))))), V)), inverse(multiply(Y, inverse(multiply(Z, inverse(Z)))))), Y))))), inverse(Y2))), multiply(Y2, multiply(inverse(X2), T))))))))
% 3.14/0.73 = { by lemma 6 R->L }
% 3.14/0.73 multiply(multiply(multiply(X, inverse(X)), Y), multiply(inverse(multiply(multiply(X, inverse(X)), Y)), inverse(multiply(T, inverse(multiply(multiply(S, multiply(multiply(inverse(S), inverse(multiply(inverse(X2), inverse(multiply(multiply(inverse(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), Y), W))))), V)), inverse(multiply(multiply(Z, inverse(Z)), multiply(X2, multiply(multiply(inverse(X2), inverse(multiply(multiply(inverse(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), Y), W))))), V)), inverse(multiply(Y, inverse(multiply(Z, inverse(Z)))))), Y))), inverse(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), Y), W))))), V))))))), multiply(Z, inverse(Z))))))), inverse(Y2))), multiply(Y2, multiply(inverse(X2), T))))))))
% 3.14/0.73 = { by lemma 8 }
% 3.14/0.73 multiply(multiply(multiply(X, inverse(X)), Y), multiply(inverse(multiply(multiply(X, inverse(X)), Y)), inverse(multiply(T, inverse(multiply(multiply(S, multiply(multiply(inverse(S), inverse(multiply(inverse(X2), inverse(multiply(multiply(inverse(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), Y), W))))), V)), inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))))), multiply(Z, inverse(Z))))))), inverse(Y2))), multiply(Y2, multiply(inverse(X2), T))))))))
% 3.14/0.74 = { by lemma 2 }
% 3.14/0.74 multiply(multiply(multiply(X, inverse(X)), Y), multiply(inverse(multiply(multiply(X, inverse(X)), Y)), inverse(inverse(multiply(multiply(inverse(multiply(multiply(W, inverse(multiply(V, multiply(U, multiply(multiply(inverse(U), Y), W))))), V)), inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))))), multiply(Z, inverse(Z)))))))
% 3.14/0.74 = { by lemma 9 }
% 3.14/0.74 multiply(multiply(multiply(X, inverse(X)), Y), multiply(inverse(multiply(multiply(X, inverse(X)), Y)), inverse(inverse(multiply(multiply(Y, inverse(multiply(multiply(Z, inverse(Z)), inverse(multiply(Z, inverse(Z)))))), multiply(Z, inverse(Z)))))))
% 3.14/0.74 = { by lemma 16 }
% 3.14/0.74 multiply(multiply(multiply(X, inverse(X)), Y), multiply(inverse(multiply(multiply(X, inverse(X)), Y)), inverse(inverse(multiply(Y, multiply(Z, inverse(Z)))))))
% 3.14/0.74 = { by lemma 18 }
% 3.14/0.74 multiply(multiply(multiply(X, inverse(X)), Y), multiply(inverse(multiply(multiply(X, inverse(X)), Y)), inverse(inverse(Y))))
% 3.14/0.74 = { by lemma 14 }
% 3.14/0.74 multiply(Y, multiply(inverse(Y), inverse(inverse(Y))))
% 3.14/0.74 = { by lemma 18 }
% 3.14/0.74 Y
% 3.14/0.74
% 3.14/0.74 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 3.14/0.74 Proof:
% 3.14/0.74 multiply(multiply(inverse(b2), b2), a2)
% 3.14/0.74 = { by lemma 19 R->L }
% 3.14/0.74 multiply(multiply(multiply(multiply(X, inverse(X)), inverse(b2)), b2), a2)
% 3.14/0.74 = { by lemma 19 R->L }
% 3.14/0.74 multiply(multiply(multiply(multiply(Y, inverse(Y)), multiply(multiply(X, inverse(X)), inverse(b2))), b2), a2)
% 3.14/0.74 = { by lemma 13 R->L }
% 3.14/0.74 multiply(multiply(multiply(Z, inverse(multiply(multiply(W, multiply(V, inverse(U))), multiply(U, multiply(multiply(inverse(U), inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(multiply(X, inverse(X)), inverse(b2))), multiply(b2, multiply(V, inverse(U)))))), Z))))), W), a2)
% 3.14/0.74 = { by lemma 3 }
% 3.14/0.74 multiply(multiply(multiply(Z, inverse(multiply(multiply(W, multiply(V, inverse(U))), multiply(U, multiply(multiply(T, multiply(multiply(inverse(T), inverse(multiply(multiply(X, inverse(X)), V))), inverse(multiply(Y, inverse(Y))))), Z))))), W), a2)
% 3.14/0.74 = { by lemma 3 R->L }
% 3.14/0.74 multiply(multiply(multiply(Z, inverse(multiply(multiply(W, multiply(V, inverse(U))), multiply(U, multiply(multiply(inverse(U), inverse(multiply(multiply(multiply(Y, inverse(Y)), multiply(multiply(X, inverse(X)), inverse(multiply(X, inverse(X))))), multiply(multiply(X, inverse(X)), multiply(V, inverse(U)))))), Z))))), W), a2)
% 3.14/0.74 = { by lemma 13 }
% 3.14/0.74 multiply(multiply(multiply(multiply(Y, inverse(Y)), multiply(multiply(X, inverse(X)), inverse(multiply(X, inverse(X))))), multiply(X, inverse(X))), a2)
% 3.14/0.74 = { by lemma 19 }
% 3.14/0.74 multiply(multiply(multiply(multiply(X, inverse(X)), inverse(multiply(X, inverse(X)))), multiply(X, inverse(X))), a2)
% 3.14/0.74 = { by lemma 19 }
% 3.14/0.74 multiply(multiply(X, inverse(X)), a2)
% 3.14/0.74 = { by lemma 19 }
% 3.14/0.74 a2
% 3.14/0.74 % SZS output end Proof
% 3.14/0.74
% 3.14/0.74 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------