TSTP Solution File: GRP505-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP505-1 : 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 : n013.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 01:18:42 EDT 2023
% Result : Unsatisfiable 2.13s 0.70s
% Output : Proof 4.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP505-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.14 % 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 : n013.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 01:40:16 EDT 2023
% 0.13/0.35 % CPUTime :
% 2.13/0.70 Command-line arguments: --no-flatten-goal
% 2.13/0.70
% 2.13/0.70 % SZS status Unsatisfiable
% 2.13/0.70
% 4.49/0.96 % SZS output start Proof
% 4.49/0.96 Axiom 1 (single_axiom): multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(V, inverse(U)), inverse(W))))))), U) = V.
% 4.49/0.96
% 4.49/0.96 Lemma 2: inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(V, inverse(inverse(U))), inverse(W))))))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(V, inverse(Y2))))))), U).
% 4.49/0.96 Proof:
% 4.49/0.96 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(V, inverse(inverse(U))), inverse(W)))))))
% 4.49/0.96 = { by axiom 1 (single_axiom) R->L }
% 4.49/0.96 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(V, inverse(inverse(U))), inverse(W))))))), inverse(U)), inverse(Y2))))))), U)
% 4.49/0.96 = { by axiom 1 (single_axiom) }
% 4.49/0.96 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(V, inverse(Y2))))))), U)
% 4.49/0.96
% 4.49/0.96 Lemma 3: multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W))))))), U), inverse(U)) = V.
% 4.49/0.96 Proof:
% 4.49/0.97 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W))))))), U), inverse(U))
% 4.49/0.97 = { by lemma 2 R->L }
% 4.49/0.97 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(V, inverse(inverse(U))), inverse(Y2))))))), inverse(U))
% 4.49/0.97 = { by axiom 1 (single_axiom) }
% 4.49/0.97 V
% 4.49/0.97
% 4.49/0.97 Lemma 4: multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(V))))), U), inverse(U)), inverse(W)) = V.
% 4.49/0.97 Proof:
% 4.49/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(V))))), U), inverse(U)), inverse(W))
% 4.49/0.97 = { by axiom 1 (single_axiom) R->L }
% 4.49/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(V, inverse(inverse(W))), inverse(Y2))))))), inverse(W))))))), U), inverse(U)), inverse(W))
% 4.49/0.97 = { by lemma 3 }
% 4.49/0.97 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(V, inverse(inverse(W))), inverse(Y2))))))), inverse(W))
% 4.49/0.97 = { by lemma 2 }
% 4.49/0.97 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(V, inverse(U2))))))), W), inverse(W))
% 4.49/0.97 = { by lemma 3 }
% 4.49/0.97 V
% 4.49/0.97
% 4.49/0.97 Lemma 5: multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W))))))), U), T), inverse(T)) = multiply(V, inverse(inverse(U))).
% 4.49/0.97 Proof:
% 4.49/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W))))))), U), T), inverse(T))
% 4.49/0.97 = { by lemma 2 R->L }
% 4.49/0.97 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(V, inverse(inverse(U))), inverse(Z2))))))), T), inverse(T))
% 4.49/0.97 = { by lemma 3 }
% 4.49/0.97 multiply(V, inverse(inverse(U)))
% 4.49/0.97
% 4.49/0.97 Lemma 6: multiply(multiply(X, inverse(Y)), inverse(inverse(Y))) = multiply(multiply(X, Z), inverse(Z)).
% 4.49/0.97 Proof:
% 4.49/0.97 multiply(multiply(X, inverse(Y)), inverse(inverse(Y)))
% 4.49/0.97 = { by lemma 5 R->L }
% 4.49/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(Y)), inverse(T))))))), Y), Z), inverse(Z))
% 4.49/0.97 = { by axiom 1 (single_axiom) }
% 4.49/0.97 multiply(multiply(X, Z), inverse(Z))
% 4.49/0.97
% 4.49/0.97 Lemma 7: inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(V, U), inverse(U)), inverse(W))))))) = V.
% 4.49/0.97 Proof:
% 4.49/0.97 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(V, U), inverse(U)), inverse(W)))))))
% 4.49/0.97 = { by lemma 6 R->L }
% 4.49/0.97 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(V, inverse(T)), inverse(inverse(T))), inverse(W)))))))
% 4.49/0.97 = { by lemma 2 }
% 4.49/0.97 multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(V, inverse(T)), inverse(Z2))))))), T)
% 4.49/0.97 = { by axiom 1 (single_axiom) }
% 4.49/0.97 V
% 4.49/0.97
% 4.49/0.97 Lemma 8: multiply(multiply(X, Z), inverse(Z)) = multiply(multiply(X, Y), inverse(Y)).
% 4.49/0.97 Proof:
% 4.49/0.97 multiply(multiply(X, Z), inverse(Z))
% 4.49/0.97 = { by axiom 1 (single_axiom) R->L }
% 4.49/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(multiply(multiply(X, inverse(S)), inverse(W2))))))), S), Z), inverse(Z))
% 4.49/0.97 = { by lemma 5 }
% 4.49/0.97 multiply(multiply(X, inverse(S)), inverse(inverse(S)))
% 4.49/0.97 = { by lemma 5 R->L }
% 4.49/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(S)), inverse(T))))))), S), Y), inverse(Y))
% 4.49/0.97 = { by axiom 1 (single_axiom) }
% 4.49/0.97 multiply(multiply(X, Y), inverse(Y))
% 4.49/0.97
% 4.49/0.97 Lemma 9: multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(multiply(Z, W), V)), multiply(multiply(Z, U), inverse(U)))) = multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, V)), multiply(X2, inverse(W)))).
% 4.49/0.97 Proof:
% 4.49/0.97 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(multiply(Z, W), V)), multiply(multiply(Z, U), inverse(U))))
% 4.49/0.97 = { by lemma 8 }
% 4.49/0.97 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(multiply(Z, W), V)), multiply(multiply(Z, W), inverse(W))))
% 4.49/0.97 = { by lemma 4 R->L }
% 4.49/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Z2, Y2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(multiply(Z, W), V)), multiply(multiply(Z, W), inverse(W))))))))), U2), inverse(U2)), inverse(V2))
% 4.49/0.97 = { by lemma 4 R->L }
% 4.49/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Z2, Y2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(multiply(Z, W), V)), multiply(multiply(Z, W), inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T2, S2)), multiply(S2, T2))), multiply(inverse(multiply(X3, V)), multiply(X3, inverse(W))))), Y3), inverse(Y3)), inverse(V))))))))))), U2), inverse(U2)), inverse(V2))
% 4.49/0.97 = { by axiom 1 (single_axiom) R->L }
% 4.49/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Z2, Y2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(multiply(Z, W), V)), multiply(multiply(Z, W), inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z3, W3)), multiply(W3, Z3))), multiply(inverse(multiply(V3, U3)), multiply(V3, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T2, S2)), multiply(S2, T2))), multiply(inverse(multiply(X3, V)), multiply(X3, inverse(W))))), Y3), inverse(Y3)), inverse(inverse(inverse(T3)))), inverse(U3))))))), inverse(inverse(T3))), inverse(V))))))))))), U2), inverse(U2)), inverse(V2))
% 4.49/0.97 = { by lemma 2 }
% 4.49/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Z2, Y2))), multiply(inverse(multiply(W2, V2)), multiply(W2, multiply(inverse(multiply(inverse(multiply(inverse(multiply(S3, X4)), multiply(X4, S3))), multiply(inverse(multiply(Y4, Z4)), multiply(Y4, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z3, W3)), multiply(W3, Z3))), multiply(inverse(multiply(V3, U3)), multiply(V3, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T2, S2)), multiply(S2, T2))), multiply(inverse(multiply(X3, V)), multiply(X3, inverse(W))))), Y3), inverse(Y3)), inverse(inverse(inverse(T3)))), inverse(U3))))))), inverse(Z4))))))), T3))))), U2), inverse(U2)), inverse(V2))
% 4.49/0.97 = { by lemma 2 R->L }
% 4.49/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Z2, Y2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, V)), multiply(X2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z3, W3)), multiply(W3, Z3))), multiply(inverse(multiply(V3, U3)), multiply(V3, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T2, S2)), multiply(S2, T2))), multiply(inverse(multiply(X3, V)), multiply(X3, inverse(W))))), Y3), inverse(Y3)), inverse(inverse(inverse(T3)))), inverse(U3))))))), inverse(inverse(T3))), inverse(V))))))))))), U2), inverse(U2)), inverse(V2))
% 4.49/0.97 = { by axiom 1 (single_axiom) }
% 4.49/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Z2, Y2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, V)), multiply(X2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T2, S2)), multiply(S2, T2))), multiply(inverse(multiply(X3, V)), multiply(X3, inverse(W))))), Y3), inverse(Y3)), inverse(V))))))))))), U2), inverse(U2)), inverse(V2))
% 4.49/0.97 = { by lemma 4 }
% 4.49/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Z2, Y2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, V)), multiply(X2, inverse(W))))))))), U2), inverse(U2)), inverse(V2))
% 4.49/0.97 = { by lemma 4 }
% 4.49/0.98 multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, V)), multiply(X2, inverse(W))))
% 4.49/0.98
% 4.49/0.98 Lemma 10: multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(U), U)) = multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(Z), Z)).
% 4.49/0.98 Proof:
% 4.49/0.98 multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(U), U))
% 4.49/0.98 = { by lemma 3 R->L }
% 4.49/0.98 multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(U), multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, inverse(multiply(U, inverse(V3))))))), S2), inverse(S2))))
% 4.49/0.98 = { by lemma 3 R->L }
% 4.49/0.98 multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, inverse(multiply(U, inverse(V3))))))), S2), inverse(S2))), multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, inverse(multiply(U, inverse(V3))))))), S2), inverse(S2))))
% 4.49/0.98 = { by lemma 7 R->L }
% 4.49/0.98 multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, inverse(multiply(U, inverse(V3))))))), S2), inverse(S2))), multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, inverse(multiply(U, inverse(V3))))))), S2), inverse(multiply(inverse(multiply(inverse(multiply(W2, V2)), multiply(V2, W2))), multiply(inverse(multiply(U2, T2)), multiply(U2, inverse(multiply(multiply(multiply(inverse(S2), X3), inverse(X3)), inverse(T2))))))))))
% 4.49/0.98 = { by lemma 9 R->L }
% 4.49/0.98 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(Z, inverse(Y2))))))), multiply(inverse(multiply(inverse(multiply(W2, V2)), multiply(V2, W2))), multiply(inverse(multiply(U2, T2)), multiply(U2, inverse(multiply(multiply(multiply(inverse(S2), X3), inverse(X3)), inverse(T2))))))), inverse(S2))), multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(Z, inverse(Y2))))))), Z2), inverse(Z2))))
% 4.49/0.98 = { by lemma 7 R->L }
% 4.49/0.98 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(Z, inverse(Y2))))))), multiply(inverse(multiply(inverse(multiply(W2, V2)), multiply(V2, W2))), multiply(inverse(multiply(U2, T2)), multiply(U2, inverse(multiply(multiply(multiply(inverse(S2), X3), inverse(X3)), inverse(T2))))))), inverse(multiply(inverse(multiply(inverse(multiply(W2, V2)), multiply(V2, W2))), multiply(inverse(multiply(U2, T2)), multiply(U2, inverse(multiply(multiply(multiply(inverse(S2), X3), inverse(X3)), inverse(T2))))))))), multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(Z, inverse(Y2))))))), Z2), inverse(Z2))))
% 4.49/0.98 = { by lemma 3 }
% 4.49/0.98 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(Z), multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(Z, inverse(Y2))))))), Z2), inverse(Z2))))
% 4.49/0.98 = { by lemma 3 }
% 4.49/0.98 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(Z), Z))
% 4.49/0.98
% 4.49/0.98 Lemma 11: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 4.49/0.98 Proof:
% 4.49/0.98 multiply(inverse(Y), Y)
% 4.49/0.98 = { by lemma 4 R->L }
% 4.49/0.98 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, T)), multiply(Z2, inverse(multiply(inverse(Y), Y)))))), S), inverse(S)), inverse(T))
% 4.49/0.98 = { by lemma 9 R->L }
% 4.49/0.98 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(Y), Y)), T)), multiply(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(X), X)), inverse(multiply(inverse(X), X)))))), S), inverse(S)), inverse(T))
% 4.49/0.98 = { by lemma 10 }
% 4.49/0.98 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(X), X)), T)), multiply(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(X), X)), inverse(multiply(inverse(X), X)))))), S), inverse(S)), inverse(T))
% 4.49/0.98 = { by lemma 4 }
% 4.49/0.98 multiply(inverse(X), X)
% 4.49/0.98
% 4.49/0.98 Lemma 12: multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(W), W)) = multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Y)).
% 4.49/0.98 Proof:
% 4.49/0.98 multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(W), W))
% 4.49/0.98 = { by lemma 11 }
% 4.49/0.98 multiply(inverse(multiply(inverse(multiply(U, U)), multiply(U, U))), multiply(inverse(W), W))
% 4.49/0.98 = { by lemma 10 }
% 4.49/0.98 multiply(inverse(multiply(inverse(multiply(V, V)), multiply(V, V))), multiply(inverse(Y), Y))
% 4.49/0.98 = { by lemma 11 R->L }
% 4.49/0.98 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Y))
% 4.49/0.98
% 4.49/0.98 Lemma 13: multiply(multiply(multiply(inverse(X), X), inverse(multiply(Y, Z))), inverse(inverse(W))) = multiply(multiply(multiply(inverse(multiply(Z, Y)), W), V), inverse(V)).
% 4.49/0.98 Proof:
% 4.49/0.98 multiply(multiply(multiply(inverse(X), X), inverse(multiply(Y, Z))), inverse(inverse(W)))
% 4.49/0.98 = { by lemma 4 R->L }
% 4.49/0.98 multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(inverse(X), X)))))), Y2), inverse(Y2)), inverse(X2)), inverse(multiply(Y, Z))), inverse(inverse(W)))
% 4.49/0.98 = { by lemma 7 R->L }
% 4.77/0.98 multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(T2), T2)), inverse(multiply(inverse(T2), T2))), inverse(U2))))))))))), Y2), inverse(Y2)), inverse(X2)), inverse(multiply(Y, Z))), inverse(inverse(W)))
% 4.77/0.98 = { by lemma 12 R->L }
% 4.77/0.98 multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(S2, S2)), multiply(S2, S2))), multiply(inverse(X3), X3)), inverse(multiply(inverse(T2), T2))), inverse(U2))))))))))), Y2), inverse(Y2)), inverse(X2)), inverse(multiply(Y, Z))), inverse(inverse(W)))
% 4.77/0.98 = { by lemma 10 }
% 4.77/0.98 multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(Z, Y)), multiply(Y, Z))), multiply(inverse(T2), T2)), inverse(multiply(inverse(T2), T2))), inverse(U2))))))))))), Y2), inverse(Y2)), inverse(X2)), inverse(multiply(Y, Z))), inverse(inverse(W)))
% 4.77/0.98 = { by lemma 7 }
% 4.77/0.98 multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(inverse(multiply(Z, Y)), multiply(Y, Z))))))), Y2), inverse(Y2)), inverse(X2)), inverse(multiply(Y, Z))), inverse(inverse(W)))
% 4.77/0.98 = { by lemma 4 }
% 4.77/0.98 multiply(multiply(multiply(inverse(multiply(Z, Y)), multiply(Y, Z)), inverse(multiply(Y, Z))), inverse(inverse(W)))
% 4.77/0.98 = { by lemma 8 R->L }
% 4.77/0.98 multiply(multiply(multiply(inverse(multiply(Z, Y)), W), inverse(W)), inverse(inverse(W)))
% 4.77/0.98 = { by lemma 6 }
% 4.77/0.99 multiply(multiply(multiply(inverse(multiply(Z, Y)), W), V), inverse(V))
% 4.77/0.99
% 4.77/0.99 Lemma 14: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 4.77/0.99 Proof:
% 4.77/0.99 multiply(inverse(X), X)
% 4.77/0.99 = { by lemma 4 R->L }
% 4.77/0.99 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(X), X)))))), T), inverse(T)), inverse(U))
% 4.77/0.99 = { by lemma 7 R->L }
% 4.77/0.99 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(W2, W2)), multiply(W2, W2))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/0.99 = { by lemma 7 R->L }
% 4.77/0.99 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(W2, W2)), multiply(W2, W2))), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/0.99 = { by lemma 12 }
% 4.77/0.99 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Y))), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.00 = { by lemma 4 R->L }
% 4.77/1.00 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Y)))))))), U3), inverse(U3)), inverse(V3)), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.00 = { by axiom 1 (single_axiom) R->L }
% 4.77/1.00 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(T3, S3)), multiply(S3, T3))), multiply(inverse(multiply(X4, Y4)), multiply(X4, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Y)))), inverse(Z4)), inverse(Y4))))))), Z4))))), U3), inverse(U3)), inverse(V3)), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.00 = { by lemma 7 R->L }
% 4.77/1.00 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(T3, S3)), multiply(S3, T3))), multiply(inverse(multiply(X4, Y4)), multiply(X4, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W4, V4)), multiply(V4, W4))), multiply(inverse(multiply(U4, T4)), multiply(U4, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Y)))), inverse(Z4)), S4), inverse(S4)), inverse(T4))))))), inverse(Y4))))))), Z4))))), U3), inverse(U3)), inverse(V3)), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.01 = { by lemma 13 R->L }
% 4.77/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(T3, S3)), multiply(S3, T3))), multiply(inverse(multiply(X4, Y4)), multiply(X4, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W4, V4)), multiply(V4, W4))), multiply(inverse(multiply(U4, T4)), multiply(U4, inverse(multiply(multiply(multiply(multiply(inverse(X5), X5), inverse(multiply(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(Y), Y)), inverse(multiply(inverse(Y), Y))))), inverse(inverse(inverse(Z4)))), inverse(T4))))))), inverse(Y4))))))), Z4))))), U3), inverse(U3)), inverse(V3)), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.01 = { by lemma 8 }
% 4.77/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(T3, S3)), multiply(S3, T3))), multiply(inverse(multiply(X4, Y4)), multiply(X4, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W4, V4)), multiply(V4, W4))), multiply(inverse(multiply(U4, T4)), multiply(U4, inverse(multiply(multiply(multiply(multiply(inverse(X5), X5), inverse(multiply(multiply(inverse(multiply(inverse(Y), Y)), multiply(Y, inverse(Y))), inverse(multiply(Y, inverse(Y)))))), inverse(inverse(inverse(Z4)))), inverse(T4))))))), inverse(Y4))))))), Z4))))), U3), inverse(U3)), inverse(V3)), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.01 = { by lemma 13 }
% 4.77/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(T3, S3)), multiply(S3, T3))), multiply(inverse(multiply(X4, Y4)), multiply(X4, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W4, V4)), multiply(V4, W4))), multiply(inverse(multiply(U4, T4)), multiply(U4, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(Y, inverse(Y))), multiply(inverse(multiply(inverse(Y), Y)), multiply(Y, inverse(Y))))), inverse(Z4)), Y5), inverse(Y5)), inverse(T4))))))), inverse(Y4))))))), Z4))))), U3), inverse(U3)), inverse(V3)), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.01 = { by lemma 7 }
% 4.77/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(T3, S3)), multiply(S3, T3))), multiply(inverse(multiply(X4, Y4)), multiply(X4, inverse(multiply(multiply(inverse(multiply(inverse(multiply(Y, inverse(Y))), multiply(inverse(multiply(inverse(Y), Y)), multiply(Y, inverse(Y))))), inverse(Z4)), inverse(Y4))))))), Z4))))), U3), inverse(U3)), inverse(V3)), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.01 = { by axiom 1 (single_axiom) }
% 4.77/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, inverse(multiply(inverse(multiply(Y, inverse(Y))), multiply(inverse(multiply(inverse(Y), Y)), multiply(Y, inverse(Y))))))))), U3), inverse(U3)), inverse(V3)), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.02 = { by lemma 4 }
% 4.77/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(Y, inverse(Y))), multiply(inverse(multiply(inverse(Y), Y)), multiply(Y, inverse(Y)))), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.02 = { by lemma 4 R->L }
% 4.77/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(Y, inverse(Y))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z5, W5)), multiply(W5, Z5))), multiply(inverse(multiply(V5, U5)), multiply(V5, inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(Y, inverse(Y)))))))), T5), inverse(T5)), inverse(U5))), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.02 = { by lemma 7 R->L }
% 4.77/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(Y, inverse(Y))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z5, W5)), multiply(W5, Z5))), multiply(inverse(multiply(V5, U5)), multiply(V5, inverse(multiply(inverse(multiply(inverse(multiply(S5, X6)), multiply(X6, S5))), multiply(inverse(multiply(Y6, Z6)), multiply(Y6, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(Y, inverse(Y)))), multiply(inverse(W6), W6)), inverse(multiply(inverse(W6), W6))), inverse(Z6))))))))))), T5), inverse(T5)), inverse(U5))), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.02 = { by lemma 10 R->L }
% 4.77/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(Y, inverse(Y))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z5, W5)), multiply(W5, Z5))), multiply(inverse(multiply(V5, U5)), multiply(V5, inverse(multiply(inverse(multiply(inverse(multiply(S5, X6)), multiply(X6, S5))), multiply(inverse(multiply(Y6, Z6)), multiply(Y6, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2))), multiply(inverse(W6), W6)), inverse(multiply(inverse(W6), W6))), inverse(Z6))))))))))), T5), inverse(T5)), inverse(U5))), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.02 = { by lemma 7 }
% 4.77/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(Y, inverse(Y))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z5, W5)), multiply(W5, Z5))), multiply(inverse(multiply(V5, U5)), multiply(V5, inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2))))))), T5), inverse(T5)), inverse(U5))), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.02 = { by lemma 4 }
% 4.77/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(Y, inverse(Y))), multiply(inverse(multiply(W2, W2)), multiply(W2, W2))), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.02 = { by lemma 7 }
% 4.77/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(multiply(inverse(multiply(Y, inverse(Y))), multiply(inverse(multiply(W2, W2)), multiply(W2, W2))), inverse(multiply(inverse(multiply(W2, W2)), multiply(W2, W2)))), inverse(Z2))))))))))), T), inverse(T)), inverse(U))
% 4.77/1.02 = { by lemma 7 }
% 4.77/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(Y, inverse(Y))))))), T), inverse(T)), inverse(U))
% 4.77/1.02 = { by lemma 4 }
% 4.77/1.02 multiply(Y, inverse(Y))
% 4.77/1.02
% 4.77/1.02 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 4.77/1.02 Proof:
% 4.77/1.02 multiply(inverse(a1), a1)
% 4.77/1.02 = { by lemma 14 }
% 4.77/1.02 multiply(X, inverse(X))
% 4.77/1.02 = { by lemma 14 R->L }
% 4.77/1.02 multiply(inverse(b1), b1)
% 4.77/1.02 % SZS output end Proof
% 4.77/1.02
% 4.77/1.02 RESULT: Unsatisfiable (the axioms are contradictory).
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