TSTP Solution File: GRP413-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP413-1 : 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 : n010.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 01:18:19 EDT 2023
% Result : Unsatisfiable 0.22s 0.46s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : GRP413-1 : TPTP v8.1.2. Released v2.6.0.
% 0.15/0.15 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.37 % Computer : n010.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon Aug 28 22:46:04 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.22/0.46 Command-line arguments: --no-flatten-goal
% 0.22/0.46
% 0.22/0.46 % SZS status Unsatisfiable
% 0.22/0.46
% 0.22/0.52 % SZS output start Proof
% 0.22/0.52 Axiom 1 (single_axiom): multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(X, inverse(Y))), Z))), Y))) = Z.
% 0.22/0.52
% 0.22/0.52 Lemma 2: inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X)) = multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(W)), Z))).
% 0.22/0.52 Proof:
% 0.22/0.52 inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X))
% 0.22/0.52 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.52 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X))))), Z)))
% 0.22/0.52 = { by axiom 1 (single_axiom) }
% 0.22/0.52 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(W)), Z)))
% 0.22/0.52
% 0.22/0.52 Lemma 3: inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), multiply(inverse(multiply(Y, inverse(Z))), W)))), X)) = W.
% 0.22/0.52 Proof:
% 0.22/0.52 inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), multiply(inverse(multiply(Y, inverse(Z))), W)))), X))
% 0.22/0.52 = { by lemma 2 }
% 0.22/0.52 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(Y, inverse(Z))), W))), Z)))
% 0.22/0.52 = { by axiom 1 (single_axiom) }
% 0.22/0.52 W
% 0.22/0.52
% 0.22/0.52 Lemma 4: multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y)))) = Z.
% 0.22/0.52 Proof:
% 0.22/0.52 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y))))
% 0.22/0.52 = { by lemma 2 R->L }
% 0.22/0.52 multiply(inverse(multiply(X, inverse(Y))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(Y))), inverse(W))), Z))), W)))
% 0.22/0.52 = { by axiom 1 (single_axiom) }
% 0.22/0.52 Z
% 0.22/0.52
% 0.22/0.52 Lemma 5: multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z)) = multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z)).
% 0.22/0.52 Proof:
% 0.22/0.52 multiply(inverse(multiply(W, inverse(Y))), multiply(W, Z))
% 0.22/0.52 = { by lemma 3 R->L }
% 0.22/0.52 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(inverse(multiply(V, inverse(U))), inverse(Y))), multiply(inverse(multiply(V, inverse(U))), Z)))), Y))))
% 0.22/0.52 = { by lemma 4 }
% 0.22/0.52 multiply(inverse(multiply(inverse(multiply(V, inverse(U))), inverse(Y))), multiply(inverse(multiply(V, inverse(U))), Z))
% 0.22/0.52 = { by lemma 4 R->L }
% 0.22/0.52 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(inverse(multiply(V, inverse(U))), inverse(Y))), multiply(inverse(multiply(V, inverse(U))), Z)))), Y))))
% 0.22/0.52 = { by lemma 3 }
% 0.22/0.53 multiply(inverse(multiply(X, inverse(Y))), multiply(X, Z))
% 0.22/0.53
% 0.22/0.53 Lemma 6: multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(X))), Z))), X) = multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(Z, Y)))).
% 0.22/0.53 Proof:
% 0.22/0.53 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(X))), Z))), X)
% 0.22/0.53 = { by lemma 4 R->L }
% 0.22/0.53 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(X))), Z))), X))), Y))))
% 0.22/0.53 = { by axiom 1 (single_axiom) }
% 0.22/0.53 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(Z, Y))))
% 0.22/0.53
% 0.22/0.53 Lemma 7: multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, Z)))), X) = multiply(inverse(multiply(W, inverse(V))), multiply(W, inverse(multiply(multiply(multiply(inverse(V), V), Z), V)))).
% 0.22/0.53 Proof:
% 0.22/0.53 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, Z)))), X)
% 0.22/0.53 = { by lemma 5 }
% 0.22/0.53 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(X))), multiply(multiply(inverse(V), V), Z)))), X)
% 0.22/0.53 = { by lemma 6 }
% 0.22/0.53 multiply(inverse(multiply(W, inverse(V))), multiply(W, inverse(multiply(multiply(multiply(inverse(V), V), Z), V))))
% 0.22/0.53
% 0.22/0.53 Lemma 8: multiply(X, multiply(inverse(multiply(Y, inverse(Z))), multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), X), Z))))) = multiply(inverse(multiply(W, V)), multiply(W, V)).
% 0.22/0.53 Proof:
% 0.22/0.53 multiply(X, multiply(inverse(multiply(Y, inverse(Z))), multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), X), Z)))))
% 0.22/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.53 multiply(multiply(U, inverse(multiply(multiply(multiply(inverse(T), T), inverse(multiply(inverse(multiply(U, inverse(T))), X))), T))), multiply(inverse(multiply(Y, inverse(Z))), multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), X), Z)))))
% 0.22/0.53 = { by lemma 2 R->L }
% 0.22/0.53 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), multiply(inverse(multiply(Y, inverse(Z))), multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), X), Z)))))
% 0.22/0.53 = { by lemma 7 R->L }
% 0.22/0.53 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V))
% 0.22/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.53 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(S))), multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V))))), S)))
% 0.22/0.53 = { by lemma 5 }
% 0.22/0.53 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(Z2))), inverse(X2))), multiply(inverse(multiply(Y2, inverse(Z2))), V)))), X2)))), inverse(S))), multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(Z2))), inverse(X2))), multiply(inverse(multiply(Y2, inverse(Z2))), V)))), X2)))), multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V))))), S)))
% 0.22/0.53 = { by lemma 5 }
% 0.22/0.53 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(Z2))), inverse(X2))), multiply(inverse(multiply(Y2, inverse(Z2))), V)))), X2)))), inverse(S))), multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(Z2))), inverse(X2))), multiply(inverse(multiply(Y2, inverse(Z2))), V)))), X2)))), multiply(W, V))))), S)))
% 0.22/0.53 = { by lemma 3 }
% 0.22/0.53 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(S))), multiply(inverse(multiply(W, inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(Z2))), inverse(X2))), multiply(inverse(multiply(Y2, inverse(Z2))), V)))), X2)))), multiply(W, V))))), S)))
% 0.22/0.53 = { by lemma 3 }
% 0.22/0.53 multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(T))), inverse(V))), multiply(inverse(multiply(U, inverse(T))), X)))), V)), inverse(S))), multiply(inverse(multiply(W, V)), multiply(W, V))))), S)))
% 0.22/0.53 = { by axiom 1 (single_axiom) }
% 0.22/0.53 multiply(inverse(multiply(W, V)), multiply(W, V))
% 0.22/0.53
% 0.22/0.53 Lemma 9: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.22/0.53 Proof:
% 0.22/0.53 multiply(inverse(Y), Y)
% 0.22/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.53 multiply(inverse(Y), multiply(inverse(multiply(S, inverse(X2))), inverse(multiply(multiply(multiply(inverse(Y2), Y2), inverse(multiply(inverse(multiply(inverse(multiply(S, inverse(X2))), inverse(Y2))), Y))), Y2))))
% 0.22/0.53 = { by lemma 2 }
% 0.22/0.53 multiply(inverse(Y), multiply(inverse(multiply(S, inverse(X2))), multiply(S, inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(Y)), X2)))))
% 0.22/0.53 = { by lemma 8 }
% 0.22/0.53 multiply(inverse(multiply(U, T)), multiply(U, T))
% 0.22/0.53 = { by lemma 8 R->L }
% 0.22/0.53 multiply(inverse(X), multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(multiply(multiply(multiply(inverse(W), W), inverse(X)), W)))))
% 0.22/0.53 = { by lemma 2 R->L }
% 0.22/0.53 multiply(inverse(X), multiply(inverse(multiply(Z, inverse(W))), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(W))), inverse(V))), X))), V))))
% 0.22/0.53 = { by axiom 1 (single_axiom) }
% 0.22/0.53 multiply(inverse(X), X)
% 0.22/0.53
% 0.22/0.53 Lemma 10: multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))), Z) = Z.
% 0.22/0.53 Proof:
% 0.22/0.53 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))), Z)
% 0.22/0.53 = { by lemma 9 }
% 0.22/0.53 multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(Y), Y))), Z)
% 0.22/0.53 = { by lemma 9 }
% 0.22/0.53 multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(inverse(W), inverse(Z))), multiply(inverse(W), inverse(Z))))), Z)
% 0.22/0.53 = { by lemma 4 R->L }
% 0.22/0.53 multiply(inverse(multiply(V, inverse(U))), multiply(V, inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(inverse(W), inverse(Z))), multiply(inverse(W), inverse(Z))))), Z))), U))))
% 0.22/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.53 multiply(inverse(multiply(V, inverse(U))), multiply(V, inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S)))), inverse(Z))), multiply(inverse(W), inverse(Z))))), Z))), U))))
% 0.22/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.53 multiply(inverse(multiply(V, inverse(U))), multiply(V, inverse(multiply(multiply(multiply(inverse(U), U), multiply(T, inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S)), multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S)), inverse(multiply(inverse(multiply(T, inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S)))), inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S)))), inverse(Z))), multiply(inverse(W), inverse(Z))))), Z))))), multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S))))), U))))
% 0.22/0.53 = { by axiom 1 (single_axiom) }
% 0.22/0.53 multiply(inverse(multiply(V, inverse(U))), multiply(V, inverse(multiply(multiply(multiply(inverse(U), U), multiply(T, inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S)), multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S)), inverse(multiply(inverse(W), inverse(Z)))), multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S))))), U))))
% 0.22/0.53 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.53 multiply(inverse(multiply(V, inverse(U))), multiply(V, inverse(multiply(multiply(multiply(inverse(U), U), multiply(T, inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S)), multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S)), inverse(multiply(inverse(multiply(T, inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S)))), inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S)))), inverse(X2))), multiply(inverse(W), inverse(Z))))), X2))))), multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S))))), U))))
% 0.22/0.53 = { by axiom 1 (single_axiom) }
% 0.22/0.53 multiply(inverse(multiply(V, inverse(U))), multiply(V, inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(T, inverse(S))), W))), S)))), inverse(X2))), multiply(inverse(W), inverse(Z))))), X2))), U))))
% 0.22/0.53 = { by axiom 1 (single_axiom) }
% 0.22/0.53 multiply(inverse(multiply(V, inverse(U))), multiply(V, inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(W), inverse(X2))), multiply(inverse(W), inverse(Z))))), X2))), U))))
% 0.22/0.53 = { by lemma 4 }
% 0.22/0.53 multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(inverse(multiply(inverse(W), inverse(X2))), multiply(inverse(W), inverse(Z))))), X2)
% 0.22/0.53 = { by lemma 7 }
% 0.22/0.53 multiply(inverse(multiply(Y2, inverse(Z2))), multiply(Y2, inverse(multiply(multiply(multiply(inverse(Z2), Z2), inverse(Z)), Z2))))
% 0.22/0.53 = { by lemma 4 }
% 0.22/0.54 Z
% 0.22/0.54
% 0.22/0.54 Lemma 11: multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(Y)), Z)) = multiply(inverse(inverse(Y)), Z).
% 0.22/0.54 Proof:
% 0.22/0.54 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(inverse(Y)), Z))
% 0.22/0.54 = { by lemma 9 }
% 0.22/0.54 multiply(inverse(multiply(inverse(inverse(Y)), inverse(Y))), multiply(inverse(inverse(Y)), Z))
% 0.22/0.54 = { by lemma 5 }
% 0.22/0.54 multiply(inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), inverse(Y))), multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z))
% 0.22/0.54 = { by lemma 10 }
% 0.22/0.54 multiply(inverse(inverse(Y)), multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(V), V))), Z))
% 0.22/0.54 = { by lemma 10 }
% 0.22/0.54 multiply(inverse(inverse(Y)), Z)
% 0.22/0.54
% 0.22/0.54 Lemma 12: multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(Z, X)))))) = Z.
% 0.22/0.54 Proof:
% 0.22/0.54 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(Z, X))))))
% 0.22/0.54 = { by lemma 6 R->L }
% 0.22/0.54 multiply(multiply(inverse(X), X), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(multiply(inverse(X), X), inverse(W))), Z))), W)))
% 0.22/0.54 = { by axiom 1 (single_axiom) }
% 0.22/0.54 Z
% 0.22/0.54
% 0.22/0.54 Lemma 13: multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y))) = inverse(multiply(inverse(Z), Z)).
% 0.22/0.54 Proof:
% 0.22/0.54 multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), Y)))
% 0.22/0.54 = { by lemma 9 }
% 0.22/0.54 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(inverse(V)), U)))), multiply(W, inverse(multiply(inverse(inverse(V)), U))))))
% 0.22/0.54 = { by lemma 9 }
% 0.22/0.54 multiply(multiply(inverse(multiply(inverse(inverse(V)), U)), multiply(inverse(inverse(V)), U)), inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(inverse(V)), U)))), multiply(W, inverse(multiply(inverse(inverse(V)), U))))))
% 0.22/0.54 = { by lemma 11 R->L }
% 0.22/0.54 multiply(multiply(inverse(multiply(inverse(inverse(V)), U)), multiply(inverse(inverse(V)), U)), inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(inverse(V)), U)))), multiply(W, inverse(multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(inverse(V)), U)))))))
% 0.22/0.54 = { by lemma 12 }
% 0.22/0.54 inverse(multiply(inverse(Z), Z))
% 0.22/0.54
% 0.22/0.54 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.22/0.54 Proof:
% 0.22/0.54 multiply(multiply(inverse(b2), b2), a2)
% 0.22/0.54 = { by lemma 12 R->L }
% 0.22/0.54 multiply(multiply(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))), inverse(multiply(inverse(multiply(Y, inverse(inverse(multiply(inverse(X), X))))), multiply(Y, inverse(multiply(multiply(inverse(b2), b2), inverse(multiply(inverse(X), X)))))))), a2)
% 0.22/0.54 = { by lemma 13 }
% 0.22/0.54 multiply(multiply(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))), inverse(multiply(inverse(multiply(Y, inverse(inverse(multiply(inverse(X), X))))), multiply(Y, inverse(inverse(multiply(inverse(X), X))))))), a2)
% 0.22/0.54 = { by lemma 13 }
% 0.22/0.54 multiply(inverse(multiply(inverse(Z), Z)), a2)
% 0.22/0.54 = { by axiom 1 (single_axiom) R->L }
% 0.22/0.54 multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(inverse(W)), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(inverse(W)), inverse(V))), a2))), V))))
% 0.22/0.54 = { by lemma 11 }
% 0.22/0.54 multiply(inverse(inverse(W)), inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(multiply(inverse(inverse(W)), inverse(V))), a2))), V)))
% 0.22/0.54 = { by axiom 1 (single_axiom) }
% 0.22/0.54 a2
% 0.22/0.54 % SZS output end Proof
% 0.22/0.54
% 0.22/0.54 RESULT: Unsatisfiable (the axioms are contradictory).
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