TSTP Solution File: GRP506-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP506-1 : 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 : n007.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 2.86s 0.73s
% Output : Proof 5.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP506-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 21:58:43 EDT 2023
% 0.12/0.33 % CPUTime :
% 2.86/0.73 Command-line arguments: --no-flatten-goal
% 2.86/0.73
% 2.86/0.73 % SZS status Unsatisfiable
% 2.86/0.73
% 4.67/0.98 % SZS output start Proof
% 4.67/0.98 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.
% 4.67/0.98
% 4.67/0.98 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).
% 4.67/0.98 Proof:
% 4.67/0.98 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)))))))
% 4.67/0.98 = { by axiom 1 (single_axiom) R->L }
% 4.67/0.98 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)
% 4.67/0.98 = { by axiom 1 (single_axiom) }
% 4.67/0.98 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)
% 4.67/0.98
% 4.67/0.98 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.
% 4.67/0.98 Proof:
% 4.67/0.98 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))
% 4.67/0.98 = { by lemma 2 R->L }
% 4.67/0.98 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))
% 4.67/0.98 = { by axiom 1 (single_axiom) }
% 4.67/0.98 V
% 4.67/0.98
% 4.67/0.98 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))).
% 4.67/0.98 Proof:
% 4.67/0.98 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))
% 4.67/0.98 = { by lemma 2 R->L }
% 4.67/0.98 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))
% 4.67/0.98 = { by lemma 3 }
% 4.67/0.98 multiply(V, inverse(inverse(U)))
% 4.67/0.98
% 4.67/0.98 Lemma 5: multiply(multiply(X, inverse(Y)), inverse(inverse(Y))) = multiply(multiply(X, Z), inverse(Z)).
% 4.67/0.98 Proof:
% 4.67/0.98 multiply(multiply(X, inverse(Y)), inverse(inverse(Y)))
% 4.67/0.98 = { by lemma 4 R->L }
% 4.67/0.98 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))
% 4.67/0.98 = { by axiom 1 (single_axiom) }
% 4.67/0.98 multiply(multiply(X, Z), inverse(Z))
% 4.67/0.98
% 4.67/0.98 Lemma 6: 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) = inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(multiply(V, Z2), inverse(Z2)), inverse(Y2))))))).
% 4.67/0.98 Proof:
% 4.67/0.98 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)
% 4.67/0.98 = { by lemma 2 R->L }
% 4.67/0.98 inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(multiply(V, inverse(U)), inverse(inverse(U))), inverse(Y2)))))))
% 4.67/0.98 = { by lemma 5 }
% 4.67/0.98 inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(multiply(V, Z2), inverse(Z2)), inverse(Y2)))))))
% 4.67/0.98
% 4.67/0.98 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.
% 4.67/0.98 Proof:
% 4.67/0.98 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)))))))
% 4.67/0.98 = { by lemma 6 R->L }
% 4.67/0.98 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(V, inverse(Z2)), inverse(Y2))))))), Z2)
% 4.67/0.98 = { by axiom 1 (single_axiom) }
% 4.67/0.98 V
% 4.67/0.98
% 4.67/0.98 Lemma 8: multiply(multiply(X, Z), inverse(Z)) = multiply(multiply(X, Y), inverse(Y)).
% 4.67/0.98 Proof:
% 4.67/0.98 multiply(multiply(X, Z), inverse(Z))
% 4.67/0.98 = { by axiom 1 (single_axiom) R->L }
% 4.67/0.98 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))
% 4.67/0.98 = { by lemma 4 }
% 4.67/0.98 multiply(multiply(X, inverse(S)), inverse(inverse(S)))
% 4.67/0.98 = { by lemma 4 R->L }
% 4.67/0.98 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))
% 4.67/0.98 = { by axiom 1 (single_axiom) }
% 4.67/0.98 multiply(multiply(X, Y), inverse(Y))
% 4.67/0.98
% 4.67/0.98 Lemma 9: 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.
% 4.67/0.98 Proof:
% 4.67/0.98 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))
% 4.67/0.98 = { by axiom 1 (single_axiom) R->L }
% 4.67/0.98 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))
% 4.67/0.98 = { by lemma 3 }
% 4.67/0.98 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))
% 4.67/0.98 = { by lemma 2 }
% 4.67/0.98 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))
% 4.67/0.98 = { by lemma 3 }
% 4.67/0.98 V
% 4.67/0.98
% 4.67/0.98 Lemma 10: 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)))).
% 4.67/0.98 Proof:
% 4.67/0.98 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(multiply(Z, W), V)), multiply(multiply(Z, U), inverse(U))))
% 4.67/0.98 = { by lemma 8 }
% 4.67/0.98 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(multiply(Z, W), V)), multiply(multiply(Z, W), inverse(W))))
% 4.67/0.98 = { by lemma 9 R->L }
% 4.67/0.98 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))
% 4.67/0.99 = { by lemma 9 R->L }
% 4.67/0.99 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))
% 4.67/0.99 = { by axiom 1 (single_axiom) R->L }
% 4.67/0.99 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))
% 4.67/0.99 = { by lemma 2 }
% 4.67/0.99 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))
% 4.67/0.99 = { by lemma 2 R->L }
% 4.67/0.99 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))
% 4.67/0.99 = { by axiom 1 (single_axiom) }
% 4.67/0.99 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))
% 4.67/0.99 = { by lemma 9 }
% 4.67/0.99 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))
% 4.67/0.99 = { by lemma 9 }
% 4.67/0.99 multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, V)), multiply(X2, inverse(W))))
% 4.67/0.99
% 4.67/0.99 Lemma 11: multiply(multiply(X, multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Z, Y))), multiply(inverse(multiply(W, V)), multiply(W, inverse(multiply(multiply(multiply(U, T), inverse(T)), inverse(V))))))), U) = multiply(multiply(X, S), inverse(S)).
% 4.67/0.99 Proof:
% 4.67/0.99 multiply(multiply(X, multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Z, Y))), multiply(inverse(multiply(W, V)), multiply(W, inverse(multiply(multiply(multiply(U, T), inverse(T)), inverse(V))))))), U)
% 4.67/0.99 = { by lemma 7 R->L }
% 4.67/0.99 multiply(multiply(X, multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Z, Y))), multiply(inverse(multiply(W, V)), multiply(W, inverse(multiply(multiply(multiply(U, T), inverse(T)), inverse(V))))))), inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Z, Y))), multiply(inverse(multiply(W, V)), multiply(W, inverse(multiply(multiply(multiply(U, T), inverse(T)), inverse(V))))))))
% 4.67/0.99 = { by lemma 8 R->L }
% 4.67/0.99 multiply(multiply(X, S), inverse(S))
% 4.67/0.99
% 4.67/0.99 Lemma 12: 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)).
% 4.67/0.99 Proof:
% 4.67/0.99 multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(U), U))
% 4.67/0.99 = { by lemma 3 R->L }
% 4.67/0.99 multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(U), multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z3, W3)), multiply(W3, Z3))), multiply(inverse(multiply(V3, U3)), multiply(V3, inverse(multiply(U, inverse(U3))))))), X3), inverse(X3))))
% 4.67/0.99 = { by lemma 3 R->L }
% 4.67/0.99 multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z3, W3)), multiply(W3, Z3))), multiply(inverse(multiply(V3, U3)), multiply(V3, inverse(multiply(U, inverse(U3))))))), X3), inverse(X3))), multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z3, W3)), multiply(W3, Z3))), multiply(inverse(multiply(V3, U3)), multiply(V3, inverse(multiply(U, inverse(U3))))))), X3), inverse(X3))))
% 4.67/0.99 = { by lemma 7 R->L }
% 4.67/0.99 multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z3, W3)), multiply(W3, Z3))), multiply(inverse(multiply(V3, U3)), multiply(V3, inverse(multiply(U, inverse(U3))))))), X3), inverse(X3))), multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z3, W3)), multiply(W3, Z3))), multiply(inverse(multiply(V3, U3)), multiply(V3, inverse(multiply(U, inverse(U3))))))), X3), inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(inverse(X3), Y3), inverse(Y3)), inverse(S2))))))))))
% 4.67/0.99 = { by lemma 10 R->L }
% 4.67/0.99 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(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(inverse(X3), Y3), inverse(Y3)), inverse(S2))))))), inverse(X3))), 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))))
% 4.67/0.99 = { by lemma 11 }
% 4.67/0.99 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))))))), W2), inverse(W2))), 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))))
% 4.67/0.99 = { by lemma 3 }
% 4.67/0.99 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))))
% 4.67/0.99 = { by lemma 3 }
% 4.67/0.99 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(Z), Z))
% 4.67/0.99
% 4.67/0.99 Lemma 13: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 4.67/0.99 Proof:
% 4.67/0.99 multiply(inverse(Y), Y)
% 4.67/0.99 = { by lemma 9 R->L }
% 4.67/0.99 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))
% 4.67/0.99 = { by lemma 10 R->L }
% 4.67/0.99 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))
% 4.67/0.99 = { by lemma 12 }
% 4.67/0.99 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))
% 4.67/0.99 = { by lemma 9 }
% 4.67/0.99 multiply(inverse(X), X)
% 4.67/0.99
% 4.67/0.99 Lemma 14: multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(W), W)) = multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Y)).
% 4.67/0.99 Proof:
% 4.67/0.99 multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(W), W))
% 4.67/0.99 = { by lemma 13 }
% 4.67/0.99 multiply(inverse(multiply(inverse(multiply(U, U)), multiply(U, U))), multiply(inverse(W), W))
% 4.67/0.99 = { by lemma 12 }
% 4.67/0.99 multiply(inverse(multiply(inverse(multiply(V, V)), multiply(V, V))), multiply(inverse(Y), Y))
% 4.67/0.99 = { by lemma 13 R->L }
% 4.67/0.99 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Y))
% 4.67/0.99
% 4.67/0.99 Lemma 15: multiply(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Y)), inverse(multiply(inverse(Z), Z))) = multiply(multiply(inverse(multiply(inverse(W), W)), V), inverse(V)).
% 4.67/0.99 Proof:
% 4.67/0.99 multiply(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Y)), inverse(multiply(inverse(Z), Z)))
% 4.67/0.99 = { by lemma 14 }
% 4.67/0.99 multiply(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(Z), Z)), inverse(multiply(inverse(Z), Z)))
% 4.67/0.99 = { by lemma 8 R->L }
% 4.67/0.99 multiply(multiply(inverse(multiply(inverse(W), W)), V), inverse(V))
% 4.67/0.99
% 4.67/0.99 Lemma 16: inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))) = inverse(multiply(inverse(Z), Z)).
% 4.67/0.99 Proof:
% 4.67/0.99 inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X)))
% 4.67/0.99 = { by lemma 7 R->L }
% 4.67/0.99 inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(S), S)), inverse(multiply(inverse(S), S))), inverse(T)))))))
% 4.67/0.99 = { by lemma 12 R->L }
% 4.67/0.99 inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(X2, X2)), multiply(X2, X2))), multiply(inverse(Y2), Y2)), inverse(multiply(inverse(S), S))), inverse(T)))))))
% 4.67/0.99 = { by lemma 15 }
% 4.67/0.99 inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(inverse(multiply(inverse(Z), Z)), Z2), inverse(Z2)), inverse(T)))))))
% 4.67/0.99 = { by lemma 7 }
% 4.67/0.99 inverse(multiply(inverse(Z), Z))
% 4.67/0.99
% 4.67/0.99 Lemma 17: multiply(inverse(multiply(X, Y)), multiply(Y, X)) = multiply(inverse(Z), Z).
% 4.67/0.99 Proof:
% 4.67/0.99 multiply(inverse(multiply(X, Y)), multiply(Y, X))
% 4.67/0.99 = { by lemma 9 R->L }
% 4.67/0.99 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))))))), S), inverse(S)), inverse(T))
% 4.67/0.99 = { by lemma 16 }
% 4.67/0.99 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(inverse(Z), Z)))))), S), inverse(S)), inverse(T))
% 4.67/0.99 = { by lemma 9 }
% 4.67/0.99 multiply(inverse(Z), Z)
% 4.67/0.99
% 4.67/0.99 Lemma 18: multiply(multiply(inverse(multiply(X, Y)), Z), inverse(Z)) = multiply(multiply(inverse(W), W), inverse(multiply(Y, X))).
% 4.67/0.99 Proof:
% 4.67/0.99 multiply(multiply(inverse(multiply(X, Y)), Z), inverse(Z))
% 4.67/0.99 = { by lemma 8 }
% 4.67/0.99 multiply(multiply(inverse(multiply(X, Y)), multiply(Y, X)), inverse(multiply(Y, X)))
% 4.67/0.99 = { by lemma 17 }
% 4.67/1.00 multiply(multiply(inverse(W), W), inverse(multiply(Y, X)))
% 4.67/1.00
% 4.67/1.00 Lemma 19: multiply(multiply(multiply(inverse(X), X), inverse(multiply(Y, Z))), inverse(inverse(W))) = multiply(multiply(multiply(inverse(multiply(Z, Y)), W), V), inverse(V)).
% 4.67/1.00 Proof:
% 4.67/1.00 multiply(multiply(multiply(inverse(X), X), inverse(multiply(Y, Z))), inverse(inverse(W)))
% 4.67/1.00 = { by lemma 18 R->L }
% 4.67/1.00 multiply(multiply(multiply(inverse(multiply(Z, Y)), W), inverse(W)), inverse(inverse(W)))
% 4.67/1.00 = { by lemma 5 }
% 4.67/1.00 multiply(multiply(multiply(inverse(multiply(Z, Y)), W), V), inverse(V))
% 4.67/1.00
% 4.67/1.00 Lemma 20: multiply(multiply(inverse(multiply(inverse(multiply(X, inverse(X))), multiply(inverse(Y), Y))), Z), inverse(Z)) = multiply(multiply(inverse(multiply(inverse(W), W)), V), inverse(V)).
% 4.67/1.00 Proof:
% 4.67/1.00 multiply(multiply(inverse(multiply(inverse(multiply(X, inverse(X))), multiply(inverse(Y), Y))), Z), inverse(Z))
% 4.67/1.00 = { by lemma 8 }
% 4.67/1.00 multiply(multiply(inverse(multiply(inverse(multiply(X, inverse(X))), multiply(inverse(Y), Y))), multiply(inverse(U), U)), inverse(multiply(inverse(U), U)))
% 4.67/1.00 = { by lemma 13 }
% 4.67/1.00 multiply(multiply(inverse(multiply(inverse(multiply(X, inverse(X))), multiply(inverse(X), X))), multiply(inverse(U), U)), inverse(multiply(inverse(U), U)))
% 4.67/1.00 = { by lemma 12 R->L }
% 4.67/1.00 multiply(multiply(inverse(multiply(inverse(multiply(T, T)), multiply(T, T))), multiply(inverse(S), S)), inverse(multiply(inverse(U), U)))
% 4.67/1.00 = { by lemma 15 }
% 4.67/1.00 multiply(multiply(inverse(multiply(inverse(W), W)), V), inverse(V))
% 4.67/1.00
% 4.67/1.00 Lemma 21: multiply(inverse(X), multiply(inverse(multiply(inverse(Y), Y)), X)) = multiply(inverse(Z), Z).
% 4.67/1.00 Proof:
% 4.67/1.00 multiply(inverse(X), multiply(inverse(multiply(inverse(Y), Y)), X))
% 4.67/1.00 = { by lemma 9 R->L }
% 4.67/1.00 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(Y), Y)), X))))))), S), inverse(S)), inverse(T))
% 4.67/1.00 = { by axiom 1 (single_axiom) R->L }
% 4.67/1.00 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(Y), Y)), X))), inverse(V2)), inverse(W2))))))), V2))))), S), inverse(S)), inverse(T))
% 4.67/1.00 = { by lemma 7 R->L }
% 4.67/1.00 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, 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(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(Y), Y)), X))), inverse(V2)), Y3), inverse(Y3)), inverse(X3))))))), inverse(W2))))))), V2))))), S), inverse(S)), inverse(T))
% 4.67/1.00 = { by lemma 19 R->L }
% 4.67/1.00 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, 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(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(Z3), Z3), inverse(multiply(multiply(inverse(multiply(inverse(Y), Y)), X), inverse(X)))), inverse(inverse(inverse(V2)))), inverse(X3))))))), inverse(W2))))))), V2))))), S), inverse(S)), inverse(T))
% 4.67/1.00 = { by lemma 8 }
% 4.67/1.00 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, 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(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(Z3), Z3), inverse(multiply(multiply(inverse(multiply(inverse(Y), Y)), multiply(W3, inverse(W3))), inverse(multiply(W3, inverse(W3)))))), inverse(inverse(inverse(V2)))), inverse(X3))))))), inverse(W2))))))), V2))))), S), inverse(S)), inverse(T))
% 4.67/1.00 = { by lemma 19 }
% 4.67/1.00 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, 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(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(W3, inverse(W3))), multiply(inverse(multiply(inverse(Y), Y)), multiply(W3, inverse(W3))))), inverse(V2)), V3), inverse(V3)), inverse(X3))))))), inverse(W2))))))), V2))))), S), inverse(S)), inverse(T))
% 4.67/1.00 = { by lemma 7 }
% 4.67/1.00 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(W3, inverse(W3))), multiply(inverse(multiply(inverse(Y), Y)), multiply(W3, inverse(W3))))), inverse(V2)), inverse(W2))))))), V2))))), S), inverse(S)), inverse(T))
% 5.20/1.00 = { by axiom 1 (single_axiom) }
% 5.20/1.00 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(inverse(multiply(W3, inverse(W3))), multiply(inverse(multiply(inverse(Y), Y)), multiply(W3, inverse(W3))))))))), S), inverse(S)), inverse(T))
% 5.20/1.00 = { by lemma 9 }
% 5.20/1.00 multiply(inverse(multiply(W3, inverse(W3))), multiply(inverse(multiply(inverse(Y), Y)), multiply(W3, inverse(W3))))
% 5.20/1.00 = { by lemma 9 R->L }
% 5.20/1.00 multiply(inverse(multiply(W3, inverse(W3))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U3, T3)), multiply(T3, U3))), multiply(inverse(multiply(S3, X4)), multiply(S3, inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(W3, inverse(W3)))))))), Y4), inverse(Y4)), inverse(X4)))
% 5.20/1.00 = { by lemma 7 R->L }
% 5.20/1.00 multiply(inverse(multiply(W3, inverse(W3))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U3, T3)), multiply(T3, U3))), multiply(inverse(multiply(S3, X4)), multiply(S3, inverse(multiply(inverse(multiply(inverse(multiply(Z4, W4)), multiply(W4, Z4))), multiply(inverse(multiply(V4, U4)), multiply(V4, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(W3, inverse(W3)))), multiply(inverse(T4), T4)), inverse(multiply(inverse(T4), T4))), inverse(U4))))))))))), Y4), inverse(Y4)), inverse(X4)))
% 5.20/1.00 = { by lemma 13 }
% 5.20/1.00 multiply(inverse(multiply(W3, inverse(W3))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U3, T3)), multiply(T3, U3))), multiply(inverse(multiply(S3, X4)), multiply(S3, inverse(multiply(inverse(multiply(inverse(multiply(Z4, W4)), multiply(W4, Z4))), multiply(inverse(multiply(V4, U4)), multiply(V4, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(W3), W3)), multiply(W3, inverse(W3)))), multiply(inverse(T4), T4)), inverse(multiply(inverse(T4), T4))), inverse(U4))))))))))), Y4), inverse(Y4)), inverse(X4)))
% 5.20/1.00 = { by lemma 12 R->L }
% 5.20/1.01 multiply(inverse(multiply(W3, inverse(W3))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U3, T3)), multiply(T3, U3))), multiply(inverse(multiply(S3, X4)), multiply(S3, inverse(multiply(inverse(multiply(inverse(multiply(Z4, W4)), multiply(W4, Z4))), multiply(inverse(multiply(V4, U4)), multiply(V4, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(S4, S4)), multiply(S4, S4))), multiply(inverse(T4), T4)), inverse(multiply(inverse(T4), T4))), inverse(U4))))))))))), Y4), inverse(Y4)), inverse(X4)))
% 5.20/1.01 = { by lemma 7 }
% 5.20/1.01 multiply(inverse(multiply(W3, inverse(W3))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U3, T3)), multiply(T3, U3))), multiply(inverse(multiply(S3, X4)), multiply(S3, inverse(multiply(inverse(multiply(S4, S4)), multiply(S4, S4))))))), Y4), inverse(Y4)), inverse(X4)))
% 5.20/1.01 = { by lemma 9 }
% 5.20/1.01 multiply(inverse(multiply(W3, inverse(W3))), multiply(inverse(multiply(S4, S4)), multiply(S4, S4)))
% 5.20/1.01 = { by lemma 9 R->L }
% 5.20/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(Z5, W5)), multiply(Z5, inverse(multiply(inverse(multiply(W3, inverse(W3))), multiply(inverse(multiply(S4, S4)), multiply(S4, S4)))))))), V5), inverse(V5)), inverse(W5))
% 5.20/1.01 = { by lemma 7 R->L }
% 5.20/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(Z5, W5)), multiply(Z5, inverse(multiply(inverse(multiply(inverse(multiply(U5, T5)), multiply(T5, U5))), multiply(inverse(multiply(S5, X6)), multiply(S5, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(W3, inverse(W3))), multiply(inverse(multiply(S4, S4)), multiply(S4, S4)))), Y6), inverse(Y6)), inverse(X6))))))))))), V5), inverse(V5)), inverse(W5))
% 5.20/1.01 = { by lemma 20 }
% 5.20/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(Z5, W5)), multiply(Z5, inverse(multiply(inverse(multiply(inverse(multiply(U5, T5)), multiply(T5, U5))), multiply(inverse(multiply(S5, X6)), multiply(S5, inverse(multiply(multiply(multiply(inverse(multiply(inverse(Z), Z)), Z6), inverse(Z6)), inverse(X6))))))))))), V5), inverse(V5)), inverse(W5))
% 5.20/1.01 = { by lemma 7 }
% 5.20/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X5, Y5)), multiply(Y5, X5))), multiply(inverse(multiply(Z5, W5)), multiply(Z5, inverse(multiply(inverse(Z), Z)))))), V5), inverse(V5)), inverse(W5))
% 5.20/1.01 = { by lemma 9 }
% 5.20/1.01 multiply(inverse(Z), Z)
% 5.20/1.01
% 5.20/1.01 Lemma 22: multiply(multiply(inverse(X), X), inverse(multiply(Y, inverse(Y)))) = multiply(Z, inverse(Z)).
% 5.20/1.01 Proof:
% 5.20/1.01 multiply(multiply(inverse(X), X), inverse(multiply(Y, inverse(Y))))
% 5.20/1.01 = { by lemma 18 R->L }
% 5.20/1.01 multiply(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(W), W)), inverse(multiply(inverse(W), W)))
% 5.20/1.01 = { by lemma 14 }
% 5.20/1.01 multiply(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V))), inverse(multiply(inverse(W), W)))
% 5.20/1.01 = { by lemma 21 }
% 5.20/1.01 multiply(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W)), inverse(multiply(inverse(W), W)))
% 5.20/1.01 = { by lemma 9 R->L }
% 5.20/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W)), inverse(multiply(inverse(W), W)))))))), Y2), inverse(Y2)), inverse(X2))
% 5.20/1.01 = { by axiom 1 (single_axiom) R->L }
% 5.20/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W)), inverse(multiply(inverse(W), W)))), inverse(T2)), inverse(U2))))))), T2))))), Y2), inverse(Y2)), inverse(X2))
% 5.20/1.01 = { by lemma 7 R->L }
% 5.20/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, inverse(multiply(multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W)), inverse(multiply(inverse(W), W)))), inverse(T2)), W3), inverse(W3)), inverse(Z3))))))), inverse(U2))))))), T2))))), Y2), inverse(Y2)), inverse(X2))
% 5.20/1.01 = { by lemma 19 R->L }
% 5.20/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, inverse(multiply(multiply(multiply(multiply(inverse(V3), V3), inverse(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W))))), inverse(inverse(inverse(T2)))), inverse(Z3))))))), inverse(U2))))))), T2))))), Y2), inverse(Y2)), inverse(X2))
% 5.20/1.01 = { by lemma 17 R->L }
% 5.20/1.01 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, inverse(multiply(multiply(multiply(multiply(inverse(multiply(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W)), inverse(multiply(inverse(W), W)))), multiply(inverse(multiply(inverse(W), W)), multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W)))), inverse(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W))))), inverse(inverse(inverse(T2)))), inverse(Z3))))))), inverse(U2))))))), T2))))), Y2), inverse(Y2)), inverse(X2))
% 5.20/1.02 = { by lemma 18 }
% 5.20/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, inverse(multiply(multiply(multiply(multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(W, inverse(W))))), multiply(inverse(multiply(inverse(W), W)), multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W)))), inverse(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W))))), inverse(inverse(inverse(T2)))), inverse(Z3))))))), inverse(U2))))))), T2))))), Y2), inverse(Y2)), inverse(X2))
% 5.20/1.02 = { by lemma 18 }
% 5.20/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, inverse(multiply(multiply(multiply(multiply(inverse(U3), U3), inverse(multiply(inverse(multiply(W, inverse(W))), multiply(inverse(W), W)))), inverse(inverse(inverse(T2)))), inverse(Z3))))))), inverse(U2))))))), T2))))), Y2), inverse(Y2)), inverse(X2))
% 5.20/1.02 = { by lemma 16 }
% 5.20/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, inverse(multiply(multiply(multiply(multiply(inverse(U3), U3), inverse(multiply(inverse(Z), Z))), inverse(inverse(inverse(T2)))), inverse(Z3))))))), inverse(U2))))))), T2))))), Y2), inverse(Y2)), inverse(X2))
% 5.20/1.02 = { by lemma 19 }
% 5.20/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, inverse(multiply(multiply(multiply(multiply(inverse(multiply(Z, inverse(Z))), inverse(T2)), T3), inverse(T3)), inverse(Z3))))))), inverse(U2))))))), T2))))), Y2), inverse(Y2)), inverse(X2))
% 5.20/1.02 = { by lemma 7 }
% 5.20/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(inverse(multiply(Z, inverse(Z))), inverse(T2)), inverse(U2))))))), T2))))), Y2), inverse(Y2)), inverse(X2))
% 5.20/1.02 = { by axiom 1 (single_axiom) }
% 5.20/1.02 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, X2)), multiply(S, inverse(multiply(Z, inverse(Z))))))), Y2), inverse(Y2)), inverse(X2))
% 5.20/1.02 = { by lemma 9 }
% 5.20/1.02 multiply(Z, inverse(Z))
% 5.20/1.02
% 5.20/1.02 Lemma 23: inverse(multiply(inverse(X), X)) = inverse(multiply(Y, inverse(Y))).
% 5.20/1.02 Proof:
% 5.20/1.02 inverse(multiply(inverse(X), X))
% 5.20/1.02 = { by lemma 7 R->L }
% 5.20/1.02 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(multiply(inverse(multiply(inverse(X), X)), T), inverse(T)), inverse(U)))))))
% 5.20/1.02 = { by lemma 7 R->L }
% 5.20/1.02 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(X), X)), T), W2), inverse(W2)), inverse(Z2))))))), inverse(T)), inverse(U)))))))
% 5.20/1.02 = { by lemma 19 R->L }
% 5.20/1.02 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(multiply(multiply(inverse(V2), V2), inverse(multiply(X, inverse(X)))), inverse(inverse(T))), inverse(Z2))))))), inverse(T)), inverse(U)))))))
% 5.20/1.02 = { by lemma 22 }
% 5.20/1.02 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(inverse(Y), Y))), inverse(inverse(T))), inverse(Z2))))))), inverse(T)), inverse(U)))))))
% 5.20/1.02 = { by lemma 19 }
% 5.20/1.02 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(Y, inverse(Y))), T), U2), inverse(U2)), inverse(Z2))))))), inverse(T)), inverse(U)))))))
% 5.20/1.02 = { by lemma 7 }
% 5.20/1.02 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(multiply(inverse(multiply(Y, inverse(Y))), T), inverse(T)), inverse(U)))))))
% 5.20/1.02 = { by lemma 7 }
% 5.20/1.02 inverse(multiply(Y, inverse(Y)))
% 5.20/1.02
% 5.20/1.02 Lemma 24: multiply(multiply(inverse(inverse(inverse(multiply(inverse(X), X)))), Y), inverse(Y)) = multiply(Z, inverse(Z)).
% 5.20/1.02 Proof:
% 5.20/1.02 multiply(multiply(inverse(inverse(inverse(multiply(inverse(X), X)))), Y), inverse(Y))
% 5.20/1.02 = { by lemma 8 }
% 5.20/1.02 multiply(multiply(inverse(inverse(inverse(multiply(inverse(X), X)))), multiply(inverse(multiply(inverse(X), X)), inverse(inverse(multiply(inverse(X), X))))), inverse(multiply(inverse(multiply(inverse(X), X)), inverse(inverse(multiply(inverse(X), X))))))
% 5.20/1.02 = { by lemma 21 }
% 5.20/1.02 multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(X), X)), inverse(inverse(multiply(inverse(X), X))))))
% 5.20/1.02 = { by lemma 22 }
% 5.20/1.02 multiply(Z, inverse(Z))
% 5.20/1.02
% 5.20/1.02 Lemma 25: inverse(inverse(X)) = X.
% 5.20/1.02 Proof:
% 5.20/1.02 inverse(inverse(X))
% 5.20/1.02 = { by lemma 3 R->L }
% 5.20/1.02 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Z, Y))), multiply(inverse(multiply(W, X)), multiply(W, inverse(multiply(inverse(inverse(X)), inverse(X))))))), V), inverse(V))
% 5.20/1.02 = { by lemma 23 }
% 5.20/1.02 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Z, Y))), multiply(inverse(multiply(W, X)), multiply(W, inverse(multiply(U, inverse(U))))))), V), inverse(V))
% 5.20/1.02 = { by lemma 24 R->L }
% 5.20/1.02 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Z, Y))), multiply(inverse(multiply(W, X)), multiply(W, inverse(multiply(multiply(inverse(inverse(inverse(multiply(inverse(T), T)))), X), inverse(X))))))), V), inverse(V))
% 5.20/1.02 = { by lemma 3 }
% 5.20/1.02 multiply(inverse(inverse(inverse(multiply(inverse(T), T)))), X)
% 5.20/1.02 = { by axiom 1 (single_axiom) R->L }
% 5.20/1.02 multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(multiply(inverse(inverse(inverse(multiply(inverse(T), T)))), X), inverse(X)), inverse(Z2))))))), X)
% 5.20/1.02 = { by lemma 24 }
% 5.20/1.02 multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(X, inverse(X)), inverse(Z2))))))), X)
% 5.20/1.02 = { by lemma 6 }
% 5.20/1.02 inverse(multiply(inverse(multiply(inverse(multiply(W2, V2)), multiply(V2, W2))), multiply(inverse(multiply(U2, T2)), multiply(U2, inverse(multiply(multiply(multiply(X, S2), inverse(S2)), inverse(T2)))))))
% 5.20/1.02 = { by lemma 7 }
% 5.20/1.02 X
% 5.20/1.02
% 5.20/1.02 Lemma 26: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 5.20/1.02 Proof:
% 5.20/1.02 multiply(inverse(X), X)
% 5.20/1.02 = { by lemma 9 R->L }
% 5.20/1.03 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))
% 5.20/1.03 = { by lemma 23 }
% 5.20/1.03 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))
% 5.20/1.03 = { by lemma 9 }
% 5.20/1.03 multiply(Y, inverse(Y))
% 5.20/1.03
% 5.20/1.03 Lemma 27: multiply(multiply(Z, inverse(Z)), X) = multiply(multiply(X, Y), inverse(Y)).
% 5.20/1.03 Proof:
% 5.20/1.03 multiply(multiply(Z, inverse(Z)), X)
% 5.20/1.03 = { by lemma 26 R->L }
% 5.20/1.03 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(X, Y), inverse(Y)), inverse(T))))))), multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(X, Y), inverse(Y)), inverse(T))))))), X)
% 5.20/1.03 = { by lemma 11 }
% 5.20/1.03 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(X, Y), inverse(Y)), inverse(T))))))), S), inverse(S))
% 5.20/1.03 = { by lemma 3 }
% 5.20/1.03 multiply(multiply(X, Y), inverse(Y))
% 5.20/1.03
% 5.20/1.03 Lemma 28: multiply(inverse(multiply(X, inverse(X))), Y) = inverse(inverse(Y)).
% 5.20/1.03 Proof:
% 5.20/1.03 multiply(inverse(multiply(X, inverse(X))), Y)
% 5.20/1.03 = { by lemma 26 R->L }
% 5.20/1.03 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))), multiply(inverse(multiply(Z, W)), multiply(Z, W)))), Y)
% 5.20/1.03 = { by lemma 23 }
% 5.20/1.03 multiply(inverse(multiply(inverse(multiply(V, inverse(V))), multiply(inverse(multiply(Z, W)), multiply(Z, W)))), Y)
% 5.20/1.03 = { by lemma 25 R->L }
% 5.20/1.03 multiply(inverse(multiply(inverse(multiply(V, inverse(V))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(W)))))), Y)
% 5.20/1.03 = { by lemma 9 R->L }
% 5.20/1.03 multiply(inverse(multiply(inverse(multiply(V, inverse(V))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, W)), multiply(W, W))), multiply(inverse(multiply(W, W)), multiply(W, inverse(inverse(W)))))), U), inverse(U)), inverse(W))))))), Y)
% 5.20/1.03 = { by lemma 25 }
% 5.20/1.03 multiply(inverse(multiply(inverse(multiply(V, inverse(V))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, W)), multiply(W, W))), multiply(inverse(multiply(W, W)), multiply(W, W)))), U), inverse(U)), inverse(W))))))), Y)
% 5.20/1.03 = { by lemma 18 }
% 5.20/1.03 multiply(inverse(multiply(inverse(multiply(V, inverse(V))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(inverse(T), T), inverse(multiply(multiply(inverse(multiply(W, W)), multiply(W, W)), inverse(multiply(inverse(multiply(W, W)), multiply(W, W)))))), inverse(W))))))), Y)
% 5.20/1.03 = { by lemma 22 }
% 5.20/1.03 multiply(inverse(multiply(inverse(multiply(V, inverse(V))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(S, inverse(S)), inverse(W))))))), Y)
% 5.20/1.03 = { by lemma 23 R->L }
% 5.20/1.03 multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, X2)), multiply(X2, X2))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(S, inverse(S)), inverse(W))))))), Y)
% 5.20/1.03 = { by lemma 2 R->L }
% 5.20/1.03 inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Z2, Y2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(multiply(multiply(multiply(S, inverse(S)), inverse(inverse(Y))), inverse(V2)))))))
% 5.20/1.03 = { by lemma 27 }
% 5.20/1.03 inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Z2, Y2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(multiply(multiply(multiply(inverse(inverse(Y)), U2), inverse(U2)), inverse(V2)))))))
% 5.20/1.03 = { by lemma 7 }
% 5.20/1.03 inverse(inverse(Y))
% 5.20/1.03
% 5.20/1.03 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 5.20/1.03 Proof:
% 5.20/1.03 multiply(multiply(inverse(b2), b2), a2)
% 5.20/1.03 = { by lemma 26 }
% 5.20/1.03 multiply(multiply(X, inverse(X)), a2)
% 5.20/1.03 = { by lemma 27 }
% 5.20/1.03 multiply(multiply(a2, inverse(a2)), inverse(inverse(a2)))
% 5.20/1.03 = { by lemma 22 R->L }
% 5.20/1.03 multiply(multiply(multiply(inverse(Y), Y), inverse(multiply(Z, inverse(Z)))), inverse(inverse(a2)))
% 5.20/1.03 = { by lemma 18 R->L }
% 5.20/1.03 multiply(multiply(multiply(inverse(multiply(inverse(Z), Z)), W), inverse(W)), inverse(inverse(a2)))
% 5.20/1.03 = { by lemma 20 R->L }
% 5.20/1.03 multiply(multiply(multiply(inverse(multiply(inverse(multiply(V, inverse(V))), multiply(inverse(U), U))), T), inverse(T)), inverse(inverse(a2)))
% 5.20/1.03 = { by lemma 18 }
% 5.20/1.03 multiply(multiply(multiply(inverse(S), S), inverse(multiply(multiply(inverse(U), U), inverse(multiply(V, inverse(V)))))), inverse(inverse(a2)))
% 5.20/1.03 = { by lemma 26 }
% 5.20/1.03 multiply(multiply(multiply(X2, inverse(X2)), inverse(multiply(multiply(inverse(U), U), inverse(multiply(V, inverse(V)))))), inverse(inverse(a2)))
% 5.20/1.03 = { by lemma 22 }
% 5.20/1.03 multiply(multiply(multiply(X2, inverse(X2)), inverse(multiply(multiply(inverse(multiply(Y2, Y2)), multiply(Y2, Y2)), inverse(multiply(inverse(multiply(Y2, Y2)), multiply(Y2, Y2)))))), inverse(inverse(a2)))
% 5.20/1.03 = { by lemma 25 R->L }
% 5.20/1.03 multiply(multiply(multiply(X2, inverse(X2)), inverse(multiply(multiply(inverse(multiply(Y2, Y2)), multiply(Y2, inverse(inverse(Y2)))), inverse(multiply(inverse(multiply(Y2, Y2)), multiply(Y2, Y2)))))), inverse(inverse(a2)))
% 5.20/1.03 = { by lemma 25 R->L }
% 5.20/1.03 multiply(multiply(multiply(X2, inverse(X2)), inverse(multiply(multiply(inverse(multiply(Y2, Y2)), multiply(Y2, inverse(inverse(inverse(inverse(Y2)))))), inverse(multiply(inverse(multiply(Y2, Y2)), multiply(Y2, Y2)))))), inverse(inverse(a2)))
% 5.20/1.03 = { by lemma 26 R->L }
% 5.20/1.03 multiply(multiply(multiply(inverse(Z2), Z2), inverse(multiply(multiply(inverse(multiply(Y2, Y2)), multiply(Y2, inverse(inverse(inverse(inverse(Y2)))))), inverse(multiply(inverse(multiply(Y2, Y2)), multiply(Y2, Y2)))))), inverse(inverse(a2)))
% 5.20/1.03 = { by lemma 18 R->L }
% 5.20/1.03 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Y2)), multiply(Y2, Y2))), multiply(inverse(multiply(Y2, Y2)), multiply(Y2, inverse(inverse(inverse(inverse(Y2)))))))), W2), inverse(W2)), inverse(inverse(a2)))
% 5.20/1.03 = { by lemma 28 R->L }
% 5.20/1.03 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Y2)), multiply(Y2, Y2))), multiply(inverse(multiply(Y2, Y2)), multiply(Y2, inverse(multiply(inverse(multiply(V2, inverse(V2))), inverse(Y2))))))), W2), inverse(W2)), inverse(inverse(a2)))
% 5.20/1.03 = { by lemma 3 }
% 5.20/1.03 multiply(inverse(multiply(V2, inverse(V2))), inverse(inverse(a2)))
% 5.20/1.03 = { by lemma 28 }
% 5.20/1.03 inverse(inverse(inverse(inverse(a2))))
% 5.20/1.03 = { by lemma 25 }
% 5.20/1.03 inverse(inverse(a2))
% 5.20/1.03 = { by lemma 25 }
% 5.20/1.03 a2
% 5.20/1.03 % SZS output end Proof
% 5.20/1.03
% 5.20/1.03 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------