TSTP Solution File: GRP412-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP412-1 : 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 : n019.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 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP412-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 01:04:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.43 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.43
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 Axiom 1 (single_axiom): multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(multiply(X, inverse(Y))), Z))), Y))) = Z.
% 0.20/0.46
% 0.20/0.46 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))).
% 0.20/0.46 Proof:
% 0.20/0.46 inverse(multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(Y, inverse(Z))), inverse(X))), W))), X))
% 0.20/0.46 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.46 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)))
% 0.20/0.46 = { by axiom 1 (single_axiom) }
% 0.20/0.46 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(W)), Z)))
% 0.20/0.46
% 0.20/0.46 Lemma 3: multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y)))) = Z.
% 0.20/0.46 Proof:
% 0.20/0.46 multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(multiply(multiply(multiply(inverse(Y), Y), inverse(Z)), Y))))
% 0.20/0.46 = { by lemma 2 R->L }
% 0.20/0.46 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)))
% 0.20/0.46 = { by axiom 1 (single_axiom) }
% 0.20/0.46 Z
% 0.20/0.46
% 0.20/0.46 Lemma 4: 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)))).
% 0.20/0.46 Proof:
% 0.20/0.46 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(Y), Y), inverse(X))), Z))), X)
% 0.20/0.46 = { by lemma 3 R->L }
% 0.20/0.46 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))))
% 0.20/0.46 = { by axiom 1 (single_axiom) }
% 0.20/0.46 multiply(inverse(multiply(W, inverse(Y))), multiply(W, inverse(multiply(Z, Y))))
% 0.20/0.46
% 0.20/0.46 Lemma 5: multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(Z, X)))))) = Z.
% 0.20/0.46 Proof:
% 0.20/0.46 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(Z, X))))))
% 0.20/0.46 = { by lemma 4 R->L }
% 0.20/0.46 multiply(multiply(inverse(X), X), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(multiply(inverse(X), X), inverse(W))), Z))), W)))
% 0.20/0.46 = { by axiom 1 (single_axiom) }
% 0.20/0.46 Z
% 0.20/0.46
% 0.20/0.46 Lemma 6: 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.
% 0.20/0.46 Proof:
% 0.20/0.46 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))
% 0.20/0.46 = { by lemma 2 }
% 0.20/0.46 multiply(Y, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(Y, inverse(Z))), W))), Z)))
% 0.20/0.46 = { by axiom 1 (single_axiom) }
% 0.20/0.46 W
% 0.20/0.46
% 0.20/0.46 Lemma 7: multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(multiply(V, W))))))) = multiply(inverse(multiply(multiply(inverse(W), W), Y)), V).
% 0.20/0.46 Proof:
% 0.20/0.46 multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(multiply(V, W)))))))
% 0.20/0.46 = { by lemma 6 R->L }
% 0.20/0.46 multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))), multiply(X, inverse(multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(multiply(V, W)))))))
% 0.20/0.46 = { by lemma 4 R->L }
% 0.20/0.47 multiply(inverse(multiply(X, inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))), multiply(X, inverse(multiply(multiply(multiply(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)), multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)), inverse(multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))), V))), multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))))
% 0.20/0.47 = { by lemma 3 }
% 0.20/0.47 multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(S))), inverse(U))), multiply(inverse(multiply(T, inverse(S))), Y)))), U)))), V)
% 0.20/0.47 = { by lemma 6 }
% 0.20/0.47 multiply(inverse(multiply(multiply(inverse(W), W), Y)), V)
% 0.20/0.47
% 0.20/0.47 Lemma 8: multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(Z))))), X) = Z.
% 0.20/0.47 Proof:
% 0.20/0.47 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(Z))))), X)
% 0.20/0.47 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.47 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(inverse(multiply(W, inverse(V))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(V))), inverse(U))), Z))), U)))))))), X)
% 0.20/0.47 = { by lemma 2 }
% 0.20/0.47 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(Y, inverse(X))), multiply(Y, inverse(multiply(inverse(multiply(W, inverse(V))), multiply(W, inverse(multiply(multiply(multiply(inverse(V), V), inverse(Z)), V))))))))), X)
% 0.20/0.47 = { by lemma 7 }
% 0.20/0.47 multiply(multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(X))), multiply(multiply(inverse(V), V), inverse(Z))))), X)
% 0.20/0.47 = { by lemma 4 }
% 0.20/0.47 multiply(inverse(multiply(T, inverse(V))), multiply(T, inverse(multiply(multiply(multiply(inverse(V), V), inverse(Z)), V))))
% 0.20/0.47 = { by lemma 3 }
% 0.20/0.47 Z
% 0.20/0.47
% 0.20/0.47 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.20/0.47 Proof:
% 0.20/0.47 multiply(inverse(a1), a1)
% 0.20/0.47 = { by lemma 5 R->L }
% 0.20/0.47 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(inverse(X)))), multiply(Y, inverse(multiply(multiply(inverse(a1), a1), inverse(X)))))))
% 0.20/0.47 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.47 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(inverse(X)))), multiply(Y, inverse(multiply(multiply(inverse(a1), a1), inverse(multiply(inverse(multiply(Z, inverse(b1))), inverse(multiply(multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(b1))), inverse(W))), X))), W))))))))))
% 0.20/0.47 = { by lemma 2 }
% 0.20/0.47 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(inverse(X)))), multiply(Y, inverse(multiply(multiply(inverse(a1), a1), inverse(multiply(inverse(multiply(Z, inverse(b1))), multiply(Z, inverse(multiply(multiply(multiply(inverse(b1), b1), inverse(X)), b1)))))))))))
% 0.20/0.47 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.47 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(inverse(X)))), multiply(Y, inverse(multiply(multiply(inverse(a1), multiply(multiply(inverse(V), V), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))), inverse(multiply(inverse(multiply(Z, inverse(b1))), multiply(Z, inverse(multiply(multiply(multiply(inverse(b1), b1), inverse(X)), b1)))))))))))
% 0.20/0.47 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.47 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(inverse(X)))), multiply(Y, inverse(multiply(multiply(inverse(multiply(multiply(inverse(V), V), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))), multiply(multiply(inverse(V), V), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))), inverse(multiply(inverse(multiply(Z, inverse(b1))), multiply(Z, inverse(multiply(multiply(multiply(inverse(b1), b1), inverse(X)), b1)))))))))))
% 0.20/0.47 = { by lemma 8 R->L }
% 0.20/0.47 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(inverse(X)))), multiply(Y, inverse(multiply(multiply(inverse(multiply(multiply(inverse(V), V), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))), multiply(multiply(inverse(V), V), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))), inverse(multiply(inverse(multiply(Z, inverse(b1))), multiply(Z, inverse(multiply(multiply(multiply(inverse(b1), b1), inverse(X)), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))))))))))))
% 0.20/0.48 = { by lemma 8 R->L }
% 0.20/0.48 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(inverse(X)))), multiply(Y, inverse(multiply(multiply(inverse(multiply(multiply(inverse(V), V), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))), multiply(multiply(inverse(V), V), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))), inverse(multiply(inverse(multiply(Z, inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))))), multiply(Z, inverse(multiply(multiply(multiply(inverse(b1), b1), inverse(X)), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))))))))))))
% 0.20/0.48 = { by lemma 6 R->L }
% 0.20/0.48 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(inverse(X)))), multiply(Y, inverse(multiply(multiply(inverse(multiply(multiply(inverse(V), V), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))), multiply(multiply(inverse(V), V), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(X2, inverse(Y2))), inverse(S))), multiply(inverse(multiply(X2, inverse(Y2))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))))), S)))), inverse(multiply(inverse(multiply(Z, inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))))), multiply(Z, inverse(multiply(multiply(multiply(inverse(b1), b1), inverse(X)), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))))))))))))
% 0.20/0.49 = { by lemma 7 R->L }
% 0.20/0.49 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(inverse(X)))), multiply(Y, inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(inverse(multiply(Z2, inverse(V))), multiply(Z2, inverse(multiply(multiply(multiply(inverse(V), V), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(X2, inverse(Y2))), inverse(S))), multiply(inverse(multiply(X2, inverse(Y2))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))))), S))), V))))))), inverse(multiply(inverse(multiply(Z, inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))))), multiply(Z, inverse(multiply(multiply(multiply(inverse(b1), b1), inverse(X)), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))))))))))))
% 0.20/0.49 = { by lemma 2 R->L }
% 0.20/0.49 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(inverse(X)))), multiply(Y, inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(inverse(multiply(Z2, inverse(V))), inverse(multiply(multiply(multiply(inverse(W2), W2), inverse(multiply(inverse(multiply(inverse(multiply(Z2, inverse(V))), inverse(W2))), multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(X2, inverse(Y2))), inverse(S))), multiply(inverse(multiply(X2, inverse(Y2))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))))), S)))), W2)))))), inverse(multiply(inverse(multiply(Z, inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))))), multiply(Z, inverse(multiply(multiply(multiply(inverse(b1), b1), inverse(X)), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))))))))))))
% 0.20/0.49 = { by axiom 1 (single_axiom) }
% 0.20/0.50 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(inverse(X)))), multiply(Y, inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(S), S), inverse(multiply(inverse(multiply(inverse(multiply(X2, inverse(Y2))), inverse(S))), multiply(inverse(multiply(X2, inverse(Y2))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))))), S)))), inverse(multiply(inverse(multiply(Z, inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))))), multiply(Z, inverse(multiply(multiply(multiply(inverse(b1), b1), inverse(X)), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))))))))))))
% 0.20/0.50 = { by lemma 6 }
% 0.20/0.50 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(inverse(X)))), multiply(Y, inverse(multiply(multiply(inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))), inverse(multiply(inverse(multiply(Z, inverse(multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U)))))), multiply(Z, inverse(multiply(multiply(multiply(inverse(b1), b1), inverse(X)), multiply(multiply(multiply(inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))), inverse(multiply(inverse(multiply(T, inverse(inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))), multiply(T, inverse(b1))))), inverse(multiply(multiply(multiply(inverse(U), U), inverse(multiply(inverse(multiply(multiply(inverse(V), V), inverse(U))), a1))), U))))))))))))))
% 0.20/0.50 = { by lemma 5 }
% 0.20/0.50 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(multiply(inverse(multiply(Y, inverse(inverse(X)))), multiply(Y, inverse(multiply(multiply(inverse(b1), b1), inverse(X)))))))
% 0.20/0.50 = { by lemma 5 }
% 0.20/0.50 multiply(inverse(b1), b1)
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50
% 0.20/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------