TSTP Solution File: GRP508-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP508-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n020.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 1.55s 0.66s
% Output : Proof 4.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP508-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.07/0.13 % 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 : n020.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 01:01:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 1.55/0.66 Command-line arguments: --ground-connectedness --complete-subsets
% 1.55/0.66
% 1.55/0.66 % SZS status Unsatisfiable
% 1.55/0.66
% 4.01/0.91 % SZS output start Proof
% 4.01/0.91 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.
% 4.01/0.91
% 4.01/0.91 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).
% 4.01/0.91 Proof:
% 4.01/0.91 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)))))))
% 4.01/0.91 = { by axiom 1 (single_axiom) R->L }
% 4.01/0.91 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)
% 4.01/0.91 = { by axiom 1 (single_axiom) }
% 4.01/0.91 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)
% 4.01/0.91
% 4.01/0.91 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.
% 4.01/0.91 Proof:
% 4.01/0.91 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))
% 4.01/0.91 = { by lemma 2 R->L }
% 4.01/0.91 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))
% 4.01/0.91 = { by axiom 1 (single_axiom) }
% 4.01/0.91 V
% 4.01/0.91
% 4.01/0.91 Lemma 4: 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))).
% 4.01/0.91 Proof:
% 4.01/0.91 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))
% 4.01/0.91 = { by lemma 2 R->L }
% 4.01/0.91 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))
% 4.01/0.91 = { by lemma 3 }
% 4.01/0.91 multiply(V, inverse(inverse(U)))
% 4.01/0.91
% 4.01/0.91 Lemma 5: multiply(multiply(X, Z), inverse(Z)) = multiply(multiply(X, Y), inverse(Y)).
% 4.01/0.91 Proof:
% 4.01/0.91 multiply(multiply(X, Z), inverse(Z))
% 4.01/0.91 = { by axiom 1 (single_axiom) R->L }
% 4.01/0.91 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))
% 4.01/0.91 = { by lemma 4 }
% 4.01/0.91 multiply(multiply(X, inverse(S)), inverse(inverse(S)))
% 4.01/0.91 = { by lemma 4 R->L }
% 4.01/0.91 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))
% 4.01/0.91 = { by axiom 1 (single_axiom) }
% 4.01/0.91 multiply(multiply(X, Y), inverse(Y))
% 4.01/0.91
% 4.01/0.91 Lemma 6: multiply(multiply(X, inverse(Y)), inverse(inverse(Y))) = multiply(multiply(X, Z), inverse(Z)).
% 4.01/0.91 Proof:
% 4.01/0.91 multiply(multiply(X, inverse(Y)), inverse(inverse(Y)))
% 4.01/0.91 = { by lemma 4 R->L }
% 4.01/0.91 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))
% 4.01/0.91 = { by axiom 1 (single_axiom) }
% 4.01/0.91 multiply(multiply(X, Z), inverse(Z))
% 4.01/0.91
% 4.01/0.91 Lemma 7: multiply(multiply(multiply(X, Y), inverse(Y)), inverse(inverse(Z))) = multiply(multiply(multiply(X, Z), W), inverse(W)).
% 4.01/0.91 Proof:
% 4.01/0.91 multiply(multiply(multiply(X, Y), inverse(Y)), inverse(inverse(Z)))
% 4.01/0.91 = { by lemma 5 }
% 4.01/0.91 multiply(multiply(multiply(X, Z), inverse(Z)), inverse(inverse(Z)))
% 4.01/0.91 = { by lemma 6 }
% 4.01/0.91 multiply(multiply(multiply(X, Z), W), inverse(W))
% 4.01/0.91
% 4.01/0.91 Lemma 8: 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.
% 4.01/0.91 Proof:
% 4.01/0.91 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))
% 4.01/0.91 = { by axiom 1 (single_axiom) R->L }
% 4.01/0.91 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))
% 4.01/0.91 = { by lemma 3 }
% 4.01/0.91 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))
% 4.01/0.91 = { by lemma 2 }
% 4.01/0.91 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))
% 4.01/0.91 = { by lemma 3 }
% 4.01/0.92 V
% 4.01/0.92
% 4.01/0.92 Lemma 9: 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.
% 4.01/0.92 Proof:
% 4.01/0.92 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)))))))
% 4.01/0.92 = { by axiom 1 (single_axiom) R->L }
% 4.01/0.92 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, inverse(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(multiply(V, U), inverse(U)), inverse(W))))))), inverse(Y2)), inverse(inverse(Y2)))))))), Y2)
% 4.01/0.92 = { by lemma 3 }
% 4.01/0.92 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, inverse(Y2))), multiply(X2, inverse(multiply(multiply(V, U), inverse(U))))))), Y2)
% 4.01/0.92 = { by lemma 6 R->L }
% 4.01/0.92 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, inverse(Y2))), multiply(X2, inverse(multiply(multiply(V, inverse(Y2)), inverse(inverse(Y2)))))))), Y2)
% 4.01/0.92 = { by axiom 1 (single_axiom) }
% 4.01/0.92 V
% 4.01/0.92
% 4.01/0.92 Lemma 10: multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, inverse(V)))) = multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(V)))).
% 4.01/0.92 Proof:
% 4.01/0.92 multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, inverse(V))))
% 4.01/0.92 = { by lemma 8 R->L }
% 4.01/0.92 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, inverse(V))))))))), V2), inverse(V2)), inverse(W2))
% 4.01/0.92 = { by axiom 1 (single_axiom) R->L }
% 4.01/0.92 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, inverse(V))))), inverse(Y3)), inverse(X3))))))), Y3))))), V2), inverse(V2)), inverse(W2))
% 4.01/0.92 = { by axiom 1 (single_axiom) R->L }
% 4.01/0.92 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z3, W3)), multiply(W3, Z3))), multiply(inverse(multiply(V3, U3)), multiply(V3, inverse(multiply(multiply(V, inverse(inverse(W))), inverse(U3))))))), inverse(W))))))), inverse(Y3)), inverse(X3))))))), Y3))))), V2), inverse(V2)), inverse(W2))
% 4.01/0.92 = { by axiom 1 (single_axiom) R->L }
% 4.01/0.92 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z3, W3)), multiply(W3, Z3))), multiply(inverse(multiply(V3, U3)), multiply(V3, inverse(multiply(multiply(V, inverse(inverse(W))), inverse(U3))))))), inverse(W))))))), inverse(Y3)), inverse(inverse(Y3))), inverse(W))))))), inverse(Y3)), inverse(X3))))))), Y3))))), V2), inverse(V2)), inverse(W2))
% 4.01/0.92 = { by lemma 3 }
% 4.01/0.92 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(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(Z3, W3)), multiply(W3, Z3))), multiply(inverse(multiply(V3, U3)), multiply(V3, inverse(multiply(multiply(V, inverse(inverse(W))), inverse(U3))))))), inverse(W))))))), inverse(Y3)), inverse(X3))))))), Y3))))), V2), inverse(V2)), inverse(W2))
% 4.01/0.92 = { by axiom 1 (single_axiom) }
% 4.01/0.92 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(V))))), inverse(Y3)), inverse(X3))))))), Y3))))), V2), inverse(V2)), inverse(W2))
% 4.01/0.92 = { by axiom 1 (single_axiom) }
% 4.01/0.92 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(V))))))))), V2), inverse(V2)), inverse(W2))
% 4.01/0.92 = { by lemma 8 }
% 4.01/0.92 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(V))))
% 4.01/0.92
% 4.01/0.92 Lemma 11: multiply(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), U), inverse(U)) = multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), Z), inverse(Z)).
% 4.01/0.92 Proof:
% 4.01/0.92 multiply(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), U), inverse(U))
% 4.01/0.92 = { by lemma 5 }
% 4.01/0.92 multiply(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(T, S)), multiply(T, inverse(X2)))), inverse(multiply(inverse(multiply(T, S)), multiply(T, inverse(X2)))))
% 4.01/0.92 = { by lemma 10 }
% 4.01/0.92 multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(T, S)), multiply(T, inverse(X2)))), inverse(multiply(inverse(multiply(T, S)), multiply(T, inverse(X2)))))
% 4.01/0.92 = { by lemma 5 R->L }
% 4.01/0.92 multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), Z), inverse(Z))
% 4.01/0.92
% 4.01/0.92 Lemma 12: multiply(multiply(inverse(multiply(W, V)), multiply(V, W)), inverse(multiply(Y, X))) = multiply(multiply(inverse(multiply(X, Y)), Z), inverse(Z)).
% 4.01/0.92 Proof:
% 4.01/0.92 multiply(multiply(inverse(multiply(W, V)), multiply(V, W)), inverse(multiply(Y, X)))
% 4.01/0.92 = { by lemma 8 R->L }
% 4.01/0.92 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(W, V)), multiply(V, W))))))), Y2), inverse(Y2)), inverse(X2)), inverse(multiply(Y, X)))
% 4.01/0.92 = { by lemma 9 R->L }
% 4.01/0.92 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(W, V)), multiply(V, W))), S2), inverse(S2)), inverse(U2))))))))))), Y2), inverse(Y2)), inverse(X2)), inverse(multiply(Y, X)))
% 4.01/0.92 = { by lemma 11 }
% 4.01/0.92 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(X, Y)), multiply(Y, X))), T2), inverse(T2)), inverse(U2))))))))))), Y2), inverse(Y2)), inverse(X2)), inverse(multiply(Y, X)))
% 4.01/0.92 = { by lemma 9 }
% 4.01/0.92 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(X, Y)), multiply(Y, X))))))), Y2), inverse(Y2)), inverse(X2)), inverse(multiply(Y, X)))
% 4.01/0.92 = { by lemma 8 }
% 4.01/0.92 multiply(multiply(inverse(multiply(X, Y)), multiply(Y, X)), inverse(multiply(Y, X)))
% 4.01/0.92 = { by lemma 5 R->L }
% 4.01/0.92 multiply(multiply(inverse(multiply(X, Y)), Z), inverse(Z))
% 4.01/0.92
% 4.01/0.92 Lemma 13: multiply(multiply(multiply(inverse(multiply(X, Y)), multiply(Y, X)), inverse(multiply(Z, W))), inverse(inverse(V))) = multiply(multiply(multiply(inverse(multiply(W, Z)), V), U), inverse(U)).
% 4.01/0.92 Proof:
% 4.01/0.92 multiply(multiply(multiply(inverse(multiply(X, Y)), multiply(Y, X)), inverse(multiply(Z, W))), inverse(inverse(V)))
% 4.01/0.92 = { by lemma 12 }
% 4.01/0.92 multiply(multiply(multiply(inverse(multiply(W, Z)), T), inverse(T)), inverse(inverse(V)))
% 4.01/0.92 = { by lemma 7 }
% 4.01/0.95 multiply(multiply(multiply(inverse(multiply(W, Z)), V), U), inverse(U))
% 4.01/0.95
% 4.01/0.95 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 4.01/0.95 Proof:
% 4.01/0.95 multiply(a, b)
% 4.01/0.95 = { by lemma 8 R->L }
% 4.01/0.95 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(a, b)))))), V), inverse(V)), inverse(W))
% 4.01/0.95 = { by axiom 1 (single_axiom) R->L }
% 4.01/0.95 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(multiply(inverse(multiply(a, b)), inverse(Y2)), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.01/0.95 = { by lemma 9 R->L }
% 4.01/0.95 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(a, b)), inverse(Y2)), T2), inverse(T2)), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.01/0.95 = { by lemma 7 R->L }
% 4.01/0.95 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(a, b)), multiply(a, b)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.01/0.96 = { by lemma 8 R->L }
% 4.01/0.96 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, inverse(multiply(inverse(multiply(a, b)), multiply(a, b))))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.01/0.96 = { by axiom 1 (single_axiom) R->L }
% 4.01/0.96 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(multiply(inverse(multiply(inverse(multiply(a, b)), multiply(a, b))), inverse(X4)), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.01/0.96 = { by lemma 9 R->L }
% 4.01/0.96 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(a, b)), multiply(a, b))), inverse(X4)), U4), inverse(U4)), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.01/0.97 = { by lemma 13 R->L }
% 4.01/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(inverse(multiply(T4, S4)), multiply(S4, T4)), inverse(multiply(multiply(a, b), inverse(multiply(a, b))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.01/0.97 = { by lemma 12 }
% 4.01/0.97 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(a, b)), multiply(a, b))), multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(a, b)), multiply(a, b)))), inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(a, b)), multiply(a, b))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.01/0.98 = { by lemma 9 R->L }
% 4.01/0.98 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(a, b)), multiply(a, b))), multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(a, b)), multiply(a, b)))), inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(a, b)), multiply(a, inverse(multiply(inverse(multiply(inverse(multiply(Z5, W5)), multiply(W5, Z5))), multiply(inverse(multiply(V5, U5)), multiply(V5, inverse(multiply(multiply(multiply(b, T5), inverse(T5)), inverse(U5)))))))))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.01/0.98 = { by lemma 10 }
% 4.60/0.98 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(a, b)), multiply(a, b))), multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(a, b)), multiply(a, b)))), inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, inverse(multiply(inverse(multiply(inverse(multiply(Z5, W5)), multiply(W5, Z5))), multiply(inverse(multiply(V5, U5)), multiply(V5, inverse(multiply(multiply(multiply(b, T5), inverse(T5)), inverse(U5)))))))))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/0.99 = { by lemma 9 }
% 4.60/0.99 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(a, b)), multiply(a, b))), multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(a, b)), multiply(a, b)))), inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.00 = { by lemma 8 R->L }
% 4.60/1.00 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S5, X6)), multiply(X6, S5))), multiply(inverse(multiply(Y6, Z6)), multiply(Y6, inverse(multiply(inverse(multiply(inverse(multiply(a, b)), multiply(a, b))), multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(a, b)), multiply(a, b))))))))), W6), inverse(W6)), inverse(Z6)), inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.00 = { by axiom 1 (single_axiom) R->L }
% 4.60/1.00 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S5, X6)), multiply(X6, S5))), multiply(inverse(multiply(Y6, Z6)), multiply(Y6, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V6, U6)), multiply(U6, V6))), multiply(inverse(multiply(T6, S6)), multiply(T6, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a, b)), multiply(a, b))), multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(a, b)), multiply(a, b))))), inverse(X7)), inverse(S6))))))), X7))))), W6), inverse(W6)), inverse(Z6)), inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.01 = { by lemma 9 R->L }
% 4.60/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S5, X6)), multiply(X6, S5))), multiply(inverse(multiply(Y6, Z6)), multiply(Y6, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V6, U6)), multiply(U6, V6))), multiply(inverse(multiply(T6, S6)), multiply(T6, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y7, Z7)), multiply(Z7, Y7))), multiply(inverse(multiply(W7, V7)), multiply(W7, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a, b)), multiply(a, b))), multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(a, b)), multiply(a, b))))), inverse(X7)), U7), inverse(U7)), inverse(V7))))))), inverse(S6))))))), X7))))), W6), inverse(W6)), inverse(Z6)), inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.02 = { by lemma 13 R->L }
% 4.60/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S5, X6)), multiply(X6, S5))), multiply(inverse(multiply(Y6, Z6)), multiply(Y6, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V6, U6)), multiply(U6, V6))), multiply(inverse(multiply(T6, S6)), multiply(T6, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y7, Z7)), multiply(Z7, Y7))), multiply(inverse(multiply(W7, V7)), multiply(W7, inverse(multiply(multiply(multiply(multiply(inverse(multiply(T7, S7)), multiply(S7, T7)), inverse(multiply(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(a, b)), multiply(a, b))), inverse(multiply(inverse(multiply(a, b)), multiply(a, b)))))), inverse(inverse(inverse(X7)))), inverse(V7))))))), inverse(S6))))))), X7))))), W6), inverse(W6)), inverse(Z6)), inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.02 = { by lemma 5 }
% 4.60/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S5, X6)), multiply(X6, S5))), multiply(inverse(multiply(Y6, Z6)), multiply(Y6, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V6, U6)), multiply(U6, V6))), multiply(inverse(multiply(T6, S6)), multiply(T6, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y7, Z7)), multiply(Z7, Y7))), multiply(inverse(multiply(W7, V7)), multiply(W7, inverse(multiply(multiply(multiply(multiply(inverse(multiply(T7, S7)), multiply(S7, T7)), inverse(multiply(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))), inverse(multiply(inverse(multiply(b, b)), multiply(b, b)))))), inverse(inverse(inverse(X7)))), inverse(V7))))))), inverse(S6))))))), X7))))), W6), inverse(W6)), inverse(Z6)), inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.03 = { by lemma 13 }
% 4.60/1.03 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S5, X6)), multiply(X6, S5))), multiply(inverse(multiply(Y6, Z6)), multiply(Y6, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V6, U6)), multiply(U6, V6))), multiply(inverse(multiply(T6, S6)), multiply(T6, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y7, Z7)), multiply(Z7, Y7))), multiply(inverse(multiply(W7, V7)), multiply(W7, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(b, b)), multiply(b, b))), multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))))), inverse(X7)), X8), inverse(X8)), inverse(V7))))))), inverse(S6))))))), X7))))), W6), inverse(W6)), inverse(Z6)), inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.03 = { by lemma 9 }
% 4.60/1.04 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S5, X6)), multiply(X6, S5))), multiply(inverse(multiply(Y6, Z6)), multiply(Y6, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V6, U6)), multiply(U6, V6))), multiply(inverse(multiply(T6, S6)), multiply(T6, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(b, b)), multiply(b, b))), multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))))), inverse(X7)), inverse(S6))))))), X7))))), W6), inverse(W6)), inverse(Z6)), inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.04 = { by axiom 1 (single_axiom) }
% 4.60/1.04 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S5, X6)), multiply(X6, S5))), multiply(inverse(multiply(Y6, Z6)), multiply(Y6, inverse(multiply(inverse(multiply(inverse(multiply(b, b)), multiply(b, b))), multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))))))))), W6), inverse(W6)), inverse(Z6)), inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.04 = { by lemma 8 }
% 4.60/1.04 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(b, b)), multiply(b, b))), multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b)))), inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(b, b)), multiply(b, b))))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.04 = { by lemma 11 }
% 4.60/1.04 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y4, Z4)), multiply(Z4, Y4))), multiply(inverse(multiply(W4, V4)), multiply(W4, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(Y8, Z8)), multiply(Z8, Y8))), inverse(X4)), inverse(inverse(X4))), inverse(inverse(inverse(X4)))), inverse(V4))))))), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.04 = { by lemma 9 }
% 4.60/1.04 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(multiply(inverse(multiply(inverse(multiply(Y8, Z8)), multiply(Z8, Y8))), inverse(X4)), inverse(S3))))))), X4))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.04 = { by axiom 1 (single_axiom) }
% 4.60/1.05 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, inverse(multiply(inverse(multiply(Y8, Z8)), multiply(Z8, Y8))))))), W3), inverse(W3)), inverse(Z3)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.05 = { by lemma 8 }
% 4.60/1.05 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(Y8, Z8)), multiply(Z8, Y8)), inverse(multiply(a, b))), inverse(inverse(inverse(Y2)))), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.05 = { by lemma 13 }
% 4.60/1.05 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, 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(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(b, a)), inverse(Y2)), W8), inverse(W8)), inverse(U2))))))), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.05 = { by lemma 9 }
% 4.60/1.05 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(multiply(inverse(multiply(b, a)), inverse(Y2)), inverse(X2))))))), Y2))))), V), inverse(V)), inverse(W))
% 4.60/1.05 = { by axiom 1 (single_axiom) }
% 4.60/1.05 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(b, a)))))), V), inverse(V)), inverse(W))
% 4.60/1.05 = { by lemma 8 }
% 4.60/1.05 multiply(b, a)
% 4.60/1.05 % SZS output end Proof
% 4.60/1.05
% 4.60/1.05 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------