TSTP Solution File: GRP415-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP415-1 : 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 : n024.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 01:18:20 EDT 2023
% Result : Unsatisfiable 0.20s 0.54s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP415-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 20:10:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.54 Command-line arguments: --no-flatten-goal
% 0.20/0.54
% 0.20/0.54 % SZS status Unsatisfiable
% 0.20/0.54
% 0.20/0.59 % SZS output start Proof
% 0.20/0.59 Axiom 1 (single_axiom): inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(X), X)))))) = Z.
% 0.20/0.59
% 0.20/0.59 Lemma 2: inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, Z))), inverse(multiply(inverse(X), X)))))) = multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Z)))), inverse(multiply(inverse(W), W))))).
% 0.20/0.59 Proof:
% 0.20/0.59 inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, Z))), inverse(multiply(inverse(X), X))))))
% 0.20/0.59 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.59 inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Z)))), inverse(multiply(inverse(W), W))))))))), inverse(multiply(inverse(X), X))))))
% 0.20/0.59 = { by axiom 1 (single_axiom) }
% 0.20/0.59 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Z)))), inverse(multiply(inverse(W), W)))))
% 0.20/0.59
% 0.20/0.59 Lemma 3: multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(inverse(Z))))), inverse(multiply(inverse(X), X))))) = Z.
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(inverse(Z))))), inverse(multiply(inverse(X), X)))))
% 0.20/0.59 = { by lemma 2 R->L }
% 0.20/0.59 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Z)))), inverse(multiply(inverse(W), W))))))
% 0.20/0.59 = { by axiom 1 (single_axiom) }
% 0.20/0.59 Z
% 0.20/0.59
% 0.20/0.59 Lemma 4: multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Z)))), inverse(multiply(inverse(W), W))))) = multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(X), X))))).
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Z)))), inverse(multiply(inverse(W), W)))))
% 0.20/0.59 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.59 inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(T, U)), multiply(T, inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Z)))), inverse(multiply(inverse(W), W))))))))), inverse(multiply(inverse(U), U))))))
% 0.20/0.59 = { by axiom 1 (single_axiom) }
% 0.20/0.59 inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(T, U)), multiply(T, Z))), inverse(multiply(inverse(U), U))))))
% 0.20/0.59 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.59 inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(T, U)), multiply(T, inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(X), X))))))))), inverse(multiply(inverse(U), U))))))
% 0.20/0.59 = { by axiom 1 (single_axiom) }
% 0.20/0.59 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(X), X)))))
% 0.20/0.59
% 0.20/0.59 Lemma 5: inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), Z)), inverse(multiply(inverse(W), W)))))) = multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(Z))))), inverse(multiply(inverse(Y), Y))).
% 0.20/0.59 Proof:
% 0.20/0.59 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), Z)), inverse(multiply(inverse(W), W))))))
% 0.20/0.59 = { by lemma 3 R->L }
% 0.20/0.59 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(X, U)), multiply(X, inverse(inverse(Z))))), inverse(multiply(inverse(U), U))))))), inverse(multiply(inverse(W), W))))))
% 0.20/0.59 = { by lemma 3 R->L }
% 0.20/0.59 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(X, U)), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(V, X)), multiply(V, inverse(inverse(multiply(X, inverse(inverse(Z)))))))), inverse(multiply(inverse(X), X))))))), inverse(multiply(inverse(U), U))))))), inverse(multiply(inverse(W), W))))))
% 0.20/0.59 = { by lemma 4 }
% 0.20/0.59 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(V, X)), multiply(V, inverse(inverse(multiply(X, inverse(inverse(Z)))))))), inverse(multiply(inverse(X), X))))))), inverse(multiply(inverse(Y), Y))))))), inverse(multiply(inverse(W), W))))))
% 0.20/0.59 = { by lemma 3 }
% 0.20/0.59 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(Z))))), inverse(multiply(inverse(Y), Y))))))), inverse(multiply(inverse(W), W))))))
% 0.20/0.59 = { by axiom 1 (single_axiom) }
% 0.20/0.59 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(Z))))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.59
% 0.20/0.59 Lemma 6: multiply(X, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), inverse(multiply(inverse(Y), Y)))))))) = Z.
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(X, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), inverse(multiply(inverse(Y), Y))))))))
% 0.20/0.59 = { by lemma 5 }
% 0.20/0.59 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(W, X)), multiply(W, inverse(inverse(Z))))), inverse(multiply(inverse(X), X)))))
% 0.20/0.59 = { by lemma 4 R->L }
% 0.20/0.59 multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(inverse(Z))))), inverse(multiply(inverse(V), V)))))
% 0.20/0.59 = { by lemma 3 }
% 0.20/0.59 Z
% 0.20/0.59
% 0.20/0.59 Lemma 7: inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(W)))), inverse(multiply(inverse(inverse(multiply(Y, Z))), inverse(multiply(Y, Z)))))) = multiply(Y, inverse(inverse(multiply(Z, inverse(multiply(W, inverse(multiply(inverse(Z), Z)))))))).
% 0.20/0.59 Proof:
% 0.20/0.59 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(W)))), inverse(multiply(inverse(inverse(multiply(Y, Z))), inverse(multiply(Y, Z))))))
% 0.20/0.59 = { by lemma 6 R->L }
% 0.20/0.59 multiply(Y, inverse(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(W)))), inverse(multiply(inverse(inverse(multiply(Y, Z))), inverse(multiply(Y, Z)))))))), inverse(multiply(inverse(Z), Z))))))))
% 0.20/0.59 = { by axiom 1 (single_axiom) }
% 0.20/0.59 multiply(Y, inverse(inverse(multiply(Z, inverse(multiply(W, inverse(multiply(inverse(Z), Z))))))))
% 0.20/0.59
% 0.20/0.59 Lemma 8: multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Y), Y))))))))) = multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Z)))), inverse(multiply(inverse(W), W))))).
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Y), Y)))))))))
% 0.20/0.59 = { by lemma 7 R->L }
% 0.20/0.59 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(X, Y)))), multiply(U, inverse(Z)))), inverse(multiply(inverse(inverse(multiply(X, Y))), inverse(multiply(X, Y)))))))
% 0.20/0.59 = { by lemma 4 R->L }
% 0.20/0.59 multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Z)))), inverse(multiply(inverse(W), W)))))
% 0.20/0.59
% 0.20/0.59 Lemma 9: multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(Z))))))), inverse(multiply(inverse(Y), Y))) = Z.
% 0.20/0.59 Proof:
% 0.20/0.59 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(Z))))))), inverse(multiply(inverse(Y), Y)))
% 0.20/0.59 = { by lemma 5 R->L }
% 0.20/0.59 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(W), W))))))
% 0.20/0.59 = { by axiom 1 (single_axiom) }
% 0.20/0.59 Z
% 0.20/0.59
% 0.20/0.59 Lemma 10: inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Y), Y)))))))))) = Z.
% 0.20/0.59 Proof:
% 0.20/0.59 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Y), Y))))))))))
% 0.20/0.59 = { by lemma 7 R->L }
% 0.20/0.59 inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(X, Y)))), multiply(W, inverse(Z)))), inverse(multiply(inverse(inverse(multiply(X, Y))), inverse(multiply(X, Y))))))))
% 0.20/0.59 = { by axiom 1 (single_axiom) }
% 0.20/0.60 Z
% 0.20/0.60
% 0.20/0.60 Lemma 11: inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))))))) = multiply(inverse(X), X).
% 0.20/0.60 Proof:
% 0.20/0.60 inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))))))))
% 0.20/0.60 = { by lemma 9 R->L }
% 0.20/0.60 inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, X)), multiply(Z, inverse(inverse(multiply(X, inverse(Y))))))), inverse(multiply(inverse(X), X)))), Y)), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))))))))
% 0.20/0.60 = { by lemma 9 R->L }
% 0.20/0.60 inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, X)), multiply(Z, inverse(inverse(multiply(X, inverse(Y))))))), inverse(multiply(inverse(X), X)))), multiply(inverse(multiply(inverse(multiply(Z, X)), multiply(Z, inverse(inverse(multiply(X, inverse(Y))))))), inverse(multiply(inverse(X), X))))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))))))))
% 0.20/0.60 = { by axiom 1 (single_axiom) }
% 0.20/0.60 multiply(inverse(X), X)
% 0.20/0.60
% 0.20/0.60 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.20/0.60 Proof:
% 0.20/0.60 multiply(inverse(a1), a1)
% 0.20/0.60 = { by lemma 3 R->L }
% 0.20/0.60 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(inverse(multiply(inverse(a1), a1)))))), inverse(multiply(inverse(X), X)))))
% 0.20/0.60 = { by lemma 8 R->L }
% 0.20/0.60 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(W), W)))))))))
% 0.20/0.60 = { by lemma 6 R->L }
% 0.20/0.60 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(W), W))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.60 = { by lemma 3 R->L }
% 0.20/0.60 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(T, U)), multiply(T, inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(W), W))))))))), inverse(multiply(inverse(U), U)))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.60 = { by lemma 8 R->L }
% 0.20/0.60 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(S, inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(W), W))))), inverse(multiply(inverse(X2), X2)))))))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.61 = { by lemma 9 R->L }
% 0.20/0.61 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(S, inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(multiply(inverse(V), V)))), multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))))))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(W), W))))), inverse(multiply(inverse(X2), X2)))))))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.61 = { by lemma 11 }
% 0.20/0.61 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(S, inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(multiply(inverse(V), V)))), multiply(Y2, inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(W), W))))), inverse(multiply(inverse(X2), X2)))))))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.61 = { by lemma 11 R->L }
% 0.20/0.61 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(S, inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, inverse(multiply(inverse(V), V)))), multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(V), V)), inverse(multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))))))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(W), W))))), inverse(multiply(inverse(X2), X2)))))))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.61 = { by lemma 9 }
% 0.20/0.61 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(S, inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(W), W))))), inverse(multiply(inverse(X2), X2)))))))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.61 = { by lemma 8 }
% 0.20/0.61 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(multiply(Z2, inverse(multiply(inverse(multiply(inverse(multiply(W2, Z2)), multiply(W2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(W), W))))))))), inverse(multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.61 = { by lemma 3 }
% 0.20/0.61 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(W), W))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.62 = { by axiom 1 (single_axiom) R->L }
% 0.20/0.62 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(inverse(multiply(V2, inverse(multiply(inverse(multiply(inverse(multiply(U2, V2)), multiply(U2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(W), W)))))))), inverse(multiply(inverse(V2), V2))))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.62 = { by lemma 10 R->L }
% 0.20/0.62 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(inverse(multiply(V2, inverse(multiply(inverse(multiply(inverse(multiply(U2, V2)), multiply(U2, inverse(multiply(inverse(multiply(T2, inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(T2, inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(a1), a1)), inverse(multiply(inverse(W), W))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))), inverse(multiply(inverse(V2), V2))))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.62 = { by lemma 2 }
% 0.20/0.62 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(inverse(multiply(V2, inverse(multiply(inverse(multiply(inverse(multiply(U2, V2)), multiply(U2, inverse(multiply(inverse(multiply(T2, inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(T2, inverse(multiply(S2, inverse(multiply(inverse(multiply(inverse(multiply(X3, S2)), multiply(X3, inverse(inverse(multiply(inverse(W), W)))))), inverse(multiply(inverse(S2), S2)))))))))))), inverse(multiply(inverse(V2), V2))))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.62 = { by lemma 2 R->L }
% 0.20/0.62 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(inverse(multiply(V2, inverse(multiply(inverse(multiply(inverse(multiply(U2, V2)), multiply(U2, inverse(multiply(inverse(multiply(T2, inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(T2, inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(b1), b1)), inverse(multiply(inverse(W), W))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))), inverse(multiply(inverse(V2), V2))))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.62 = { by lemma 10 }
% 0.20/0.62 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(inverse(multiply(V2, inverse(multiply(inverse(multiply(inverse(multiply(U2, V2)), multiply(U2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(b1), b1)), inverse(multiply(inverse(W), W)))))))), inverse(multiply(inverse(V2), V2))))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.62 = { by axiom 1 (single_axiom) }
% 0.20/0.62 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(inverse(b1), b1)), inverse(multiply(inverse(W), W))))), inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))), inverse(multiply(inverse(inverse(multiply(inverse(V), V))), inverse(multiply(inverse(V), V))))))))))))))))))
% 0.20/0.62 = { by lemma 6 }
% 0.20/0.62 multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(b1), b1)), inverse(multiply(inverse(W), W)))))))))
% 0.20/0.62 = { by lemma 8 }
% 0.20/0.62 multiply(Y3, inverse(multiply(inverse(multiply(inverse(multiply(Z3, Y3)), multiply(Z3, inverse(inverse(multiply(inverse(b1), b1)))))), inverse(multiply(inverse(Y3), Y3)))))
% 0.20/0.62 = { by lemma 3 }
% 0.20/0.62 multiply(inverse(b1), b1)
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62
% 0.20/0.62 RESULT: Unsatisfiable (the axioms are contradictory).
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