TSTP Solution File: GRP084-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP084-1 : 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 : n011.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 01:16:55 EDT 2023
% Result : Unsatisfiable 4.99s 1.04s
% Output : Proof 10.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP084-1 : 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
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 00:31:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 4.99/1.04 Command-line arguments: --no-flatten-goal
% 4.99/1.04
% 4.99/1.04 % SZS status Unsatisfiable
% 4.99/1.04
% 9.59/1.62 % SZS output start Proof
% 9.59/1.62 Take the following subset of the input axioms:
% 9.59/1.62 fof(prove_these_axioms, negated_conjecture, multiply(inverse(a1), a1)!=multiply(inverse(b1), b1) | (multiply(multiply(inverse(b2), b2), a2)!=a2 | (multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3)) | multiply(a4, b4)!=multiply(b4, a4)))).
% 9.59/1.62 fof(single_axiom, axiom, ![X, Y, Z, U, V, W]: multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, U)), multiply(Z, inverse(multiply(multiply(V, inverse(W)), inverse(U))))))), W)=V).
% 9.59/1.62
% 9.59/1.62 Now clausify the problem and encode Horn clauses using encoding 3 of
% 9.59/1.62 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 9.59/1.62 We repeatedly replace C & s=t => u=v by the two clauses:
% 9.59/1.62 fresh(y, y, x1...xn) = u
% 9.59/1.62 C => fresh(s, t, x1...xn) = v
% 9.59/1.62 where fresh is a fresh function symbol and x1..xn are the free
% 9.59/1.62 variables of u and v.
% 9.59/1.62 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 9.59/1.62 input problem has no model of domain size 1).
% 9.59/1.62
% 9.59/1.62 The encoding turns the above axioms into the following unit equations and goals:
% 9.59/1.62
% 9.59/1.62 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.
% 9.59/1.62
% 9.59/1.62 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).
% 9.59/1.62 Proof:
% 9.59/1.62 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)))))))
% 9.59/1.62 = { by axiom 1 (single_axiom) R->L }
% 9.59/1.62 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)
% 9.59/1.62 = { by axiom 1 (single_axiom) }
% 9.59/1.62 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)
% 9.59/1.62
% 9.59/1.62 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.
% 9.59/1.62 Proof:
% 9.59/1.62 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))
% 9.59/1.62 = { by lemma 2 R->L }
% 9.59/1.62 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))
% 9.59/1.62 = { by axiom 1 (single_axiom) }
% 9.59/1.62 V
% 9.59/1.62
% 9.59/1.62 Lemma 4: 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) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, U)), multiply(X2, inverse(V))))), Y2), inverse(Y2)).
% 9.59/1.62 Proof:
% 9.59/1.62 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)
% 9.59/1.62 = { by lemma 2 R->L }
% 9.59/1.62 inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(V, inverse(inverse(U))), inverse(U2)))))))
% 9.59/1.62 = { by lemma 3 R->L }
% 9.59/1.62 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, U)), multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, U2)), multiply(V2, inverse(multiply(multiply(V, inverse(inverse(U))), inverse(U2))))))), inverse(U))))))), Y2), inverse(Y2))
% 9.59/1.62 = { by axiom 1 (single_axiom) }
% 9.59/1.62 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, U)), multiply(X2, inverse(V))))), Y2), inverse(Y2))
% 9.59/1.62
% 9.59/1.62 Lemma 5: 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.
% 9.59/1.62 Proof:
% 9.59/1.62 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))
% 9.59/1.62 = { by lemma 4 R->L }
% 9.59/1.62 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(V, inverse(Y2))))))), W), inverse(W))
% 9.59/1.62 = { by lemma 3 }
% 9.59/1.62 V
% 9.59/1.62
% 9.59/1.62 Lemma 6: 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))).
% 9.59/1.62 Proof:
% 9.59/1.62 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))
% 9.59/1.62 = { by lemma 2 R->L }
% 9.59/1.62 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))
% 9.59/1.62 = { by lemma 3 }
% 9.59/1.62 multiply(V, inverse(inverse(U)))
% 9.59/1.62
% 9.59/1.62 Lemma 7: multiply(multiply(X, inverse(Y)), inverse(inverse(Y))) = multiply(multiply(X, Z), inverse(Z)).
% 9.59/1.62 Proof:
% 9.59/1.62 multiply(multiply(X, inverse(Y)), inverse(inverse(Y)))
% 9.59/1.62 = { by lemma 6 R->L }
% 9.59/1.63 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))
% 9.59/1.63 = { by axiom 1 (single_axiom) }
% 9.59/1.63 multiply(multiply(X, Z), inverse(Z))
% 9.59/1.63
% 9.59/1.63 Lemma 8: 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))))))).
% 9.59/1.63 Proof:
% 9.59/1.63 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)
% 9.59/1.63 = { by lemma 2 R->L }
% 9.59/1.63 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)))))))
% 9.59/1.63 = { by lemma 7 }
% 9.59/1.63 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)))))))
% 9.59/1.63
% 9.59/1.63 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.
% 9.59/1.63 Proof:
% 9.59/1.63 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)))))))
% 9.59/1.63 = { by lemma 8 R->L }
% 9.59/1.63 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)
% 9.59/1.63 = { by axiom 1 (single_axiom) }
% 9.59/1.63 V
% 9.59/1.63
% 9.59/1.63 Lemma 10: multiply(multiply(X, Z), inverse(Z)) = multiply(multiply(X, Y), inverse(Y)).
% 9.59/1.63 Proof:
% 9.59/1.63 multiply(multiply(X, Z), inverse(Z))
% 9.59/1.63 = { by axiom 1 (single_axiom) R->L }
% 9.59/1.63 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))
% 9.59/1.63 = { by lemma 6 }
% 9.59/1.63 multiply(multiply(X, inverse(S)), inverse(inverse(S)))
% 9.59/1.63 = { by lemma 6 R->L }
% 9.59/1.63 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))
% 9.59/1.63 = { by axiom 1 (single_axiom) }
% 9.59/1.63 multiply(multiply(X, Y), inverse(Y))
% 9.59/1.63
% 9.59/1.63 Lemma 11: 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)))).
% 9.59/1.63 Proof:
% 9.59/1.63 multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, inverse(V))))
% 9.59/1.63 = { by lemma 5 R->L }
% 9.59/1.63 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))
% 9.59/1.63 = { by lemma 5 R->L }
% 9.59/1.63 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(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, W)), multiply(S2, inverse(V))))), X3), inverse(X3)), inverse(W))))))))))), V2), inverse(V2)), inverse(W2))
% 9.59/1.63 = { by axiom 1 (single_axiom) R->L }
% 9.59/1.64 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(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, W)), multiply(S2, inverse(V))))), X3), inverse(X3)), inverse(inverse(inverse(U3)))), inverse(V3))))))), inverse(inverse(U3))), inverse(W))))))))))), V2), inverse(V2)), inverse(W2))
% 9.59/1.64 = { by lemma 2 }
% 9.59/1.64 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(T3, S3)), multiply(S3, T3))), multiply(inverse(multiply(X4, Y4)), multiply(X4, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, W)), multiply(S2, inverse(V))))), X3), inverse(X3)), inverse(inverse(inverse(U3)))), inverse(V3))))))), inverse(Y4))))))), U3))))), V2), inverse(V2)), inverse(W2))
% 9.59/1.64 = { by lemma 2 R->L }
% 9.59/1.64 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(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, W)), multiply(S2, inverse(V))))), X3), inverse(X3)), inverse(inverse(inverse(U3)))), inverse(V3))))))), inverse(inverse(U3))), inverse(W))))))))))), V2), inverse(V2)), inverse(W2))
% 9.59/1.64 = { by axiom 1 (single_axiom) }
% 9.59/1.64 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(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, W)), multiply(S2, inverse(V))))), X3), inverse(X3)), inverse(W))))))))))), V2), inverse(V2)), inverse(W2))
% 9.59/1.64 = { by lemma 5 }
% 9.59/1.64 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))
% 9.59/1.64 = { by lemma 5 }
% 9.59/1.64 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(V))))
% 9.59/1.64
% 9.59/1.64 Lemma 12: 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)))).
% 9.59/1.64 Proof:
% 9.59/1.64 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(multiply(Z, W), V)), multiply(multiply(Z, U), inverse(U))))
% 9.59/1.64 = { by lemma 10 }
% 9.59/1.64 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(multiply(Z, W), V)), multiply(multiply(Z, W), inverse(W))))
% 9.59/1.64 = { by lemma 11 R->L }
% 9.59/1.64 multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, V)), multiply(X2, inverse(W))))
% 9.59/1.64
% 9.59/1.64 Lemma 13: 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)).
% 9.59/1.64 Proof:
% 9.59/1.64 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)
% 9.59/1.64 = { by lemma 9 R->L }
% 9.59/1.64 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))))))))
% 9.59/1.64 = { by lemma 10 R->L }
% 9.59/1.64 multiply(multiply(X, S), inverse(S))
% 9.59/1.64
% 9.59/1.64 Lemma 14: 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)).
% 9.59/1.64 Proof:
% 9.59/1.64 multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(U), U))
% 9.59/1.64 = { by lemma 3 R->L }
% 9.59/1.64 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))))
% 9.59/1.64 = { by lemma 3 R->L }
% 9.59/1.64 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))))
% 9.59/1.64 = { by lemma 9 R->L }
% 9.59/1.65 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))))))))))
% 9.59/1.65 = { by lemma 12 R->L }
% 9.59/1.65 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))))
% 9.59/1.65 = { by lemma 13 }
% 9.59/1.65 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))))
% 9.59/1.65 = { by lemma 3 }
% 9.59/1.65 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))))
% 9.59/1.65 = { by lemma 3 }
% 9.59/1.65 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(Z), Z))
% 9.59/1.65
% 9.59/1.65 Lemma 15: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 9.59/1.65 Proof:
% 9.59/1.65 multiply(inverse(Y), Y)
% 9.59/1.65 = { by lemma 5 R->L }
% 9.59/1.65 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))
% 9.59/1.65 = { by lemma 12 R->L }
% 9.59/1.65 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))
% 9.59/1.65 = { by lemma 14 }
% 9.59/1.65 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))
% 9.59/1.65 = { by lemma 5 }
% 9.59/1.65 multiply(inverse(X), X)
% 9.59/1.65
% 9.59/1.65 Lemma 16: multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(W), W)) = multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Y)).
% 9.59/1.65 Proof:
% 9.59/1.65 multiply(inverse(multiply(inverse(Z), Z)), multiply(inverse(W), W))
% 9.59/1.65 = { by lemma 15 }
% 9.59/1.65 multiply(inverse(multiply(inverse(multiply(U, U)), multiply(U, U))), multiply(inverse(W), W))
% 9.59/1.65 = { by lemma 14 }
% 9.59/1.65 multiply(inverse(multiply(inverse(multiply(V, V)), multiply(V, V))), multiply(inverse(Y), Y))
% 9.59/1.65 = { by lemma 15 R->L }
% 9.59/1.65 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Y))
% 9.59/1.65
% 9.59/1.65 Lemma 17: 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)).
% 9.59/1.65 Proof:
% 9.59/1.65 multiply(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Y)), inverse(multiply(inverse(Z), Z)))
% 9.59/1.65 = { by lemma 16 }
% 9.59/1.65 multiply(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(Z), Z)), inverse(multiply(inverse(Z), Z)))
% 9.59/1.65 = { by lemma 10 R->L }
% 9.59/1.65 multiply(multiply(inverse(multiply(inverse(W), W)), V), inverse(V))
% 9.59/1.65
% 9.59/1.65 Lemma 18: inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))) = inverse(multiply(inverse(Z), Z)).
% 9.59/1.65 Proof:
% 9.59/1.65 inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X)))
% 9.59/1.65 = { by lemma 9 R->L }
% 9.59/1.65 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)))))))
% 9.59/1.65 = { by lemma 14 R->L }
% 9.59/1.65 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)))))))
% 9.59/1.65 = { by lemma 17 }
% 9.59/1.65 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)))))))
% 9.59/1.65 = { by lemma 9 }
% 9.59/1.65 inverse(multiply(inverse(Z), Z))
% 9.59/1.65
% 9.59/1.65 Lemma 19: multiply(inverse(multiply(X, Y)), multiply(Y, X)) = multiply(inverse(Z), Z).
% 9.59/1.65 Proof:
% 9.59/1.65 multiply(inverse(multiply(X, Y)), multiply(Y, X))
% 9.59/1.65 = { by lemma 5 R->L }
% 9.59/1.65 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))
% 9.59/1.65 = { by lemma 18 }
% 9.59/1.65 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))
% 9.59/1.65 = { by lemma 5 }
% 9.59/1.65 multiply(inverse(Z), Z)
% 9.59/1.65
% 9.59/1.65 Lemma 20: multiply(multiply(inverse(multiply(X, Y)), Z), inverse(Z)) = multiply(multiply(inverse(W), W), inverse(multiply(Y, X))).
% 9.59/1.65 Proof:
% 9.59/1.65 multiply(multiply(inverse(multiply(X, Y)), Z), inverse(Z))
% 9.59/1.65 = { by lemma 10 }
% 9.59/1.65 multiply(multiply(inverse(multiply(X, Y)), multiply(Y, X)), inverse(multiply(Y, X)))
% 9.59/1.65 = { by lemma 19 }
% 9.59/1.65 multiply(multiply(inverse(W), W), inverse(multiply(Y, X)))
% 9.59/1.65
% 9.59/1.65 Lemma 21: multiply(multiply(multiply(inverse(X), X), inverse(multiply(Y, Z))), inverse(inverse(W))) = multiply(multiply(multiply(inverse(multiply(Z, Y)), W), V), inverse(V)).
% 9.59/1.65 Proof:
% 9.59/1.65 multiply(multiply(multiply(inverse(X), X), inverse(multiply(Y, Z))), inverse(inverse(W)))
% 9.59/1.65 = { by lemma 20 R->L }
% 9.59/1.65 multiply(multiply(multiply(inverse(multiply(Z, Y)), W), inverse(W)), inverse(inverse(W)))
% 9.59/1.65 = { by lemma 7 }
% 10.26/1.66 multiply(multiply(multiply(inverse(multiply(Z, Y)), W), V), inverse(V))
% 10.26/1.66
% 10.26/1.66 Lemma 22: multiply(inverse(Z), multiply(Y, Z)) = multiply(inverse(X), multiply(Y, X)).
% 10.26/1.66 Proof:
% 10.26/1.66 multiply(inverse(Z), multiply(Y, Z))
% 10.26/1.66 = { by lemma 5 R->L }
% 10.26/1.66 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), multiply(Y, Z))))))), S), inverse(S)), inverse(T))
% 10.26/1.66 = { by axiom 1 (single_axiom) R->L }
% 10.26/1.66 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(Z), multiply(Y, Z))), inverse(V2)), inverse(W2))))))), V2))))), S), inverse(S)), inverse(T))
% 10.26/1.66 = { by lemma 9 R->L }
% 10.26/1.66 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(Z), multiply(Y, Z))), inverse(V2)), W3), inverse(W3)), inverse(X3))))))), inverse(W2))))))), V2))))), S), inverse(S)), inverse(T))
% 10.26/1.66 = { by lemma 21 R->L }
% 10.26/1.66 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(Y, Z), inverse(Z)))), inverse(inverse(inverse(V2)))), inverse(X3))))))), inverse(W2))))))), V2))))), S), inverse(S)), inverse(T))
% 10.26/1.66 = { by lemma 10 }
% 10.26/1.66 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(Y, X), inverse(X)))), inverse(inverse(inverse(V2)))), inverse(X3))))))), inverse(W2))))))), V2))))), S), inverse(S)), inverse(T))
% 10.26/1.66 = { by lemma 21 }
% 10.26/1.66 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(Y, X))), inverse(V2)), Y3), inverse(Y3)), inverse(X3))))))), inverse(W2))))))), V2))))), S), inverse(S)), inverse(T))
% 10.26/1.66 = { by lemma 9 }
% 10.26/1.66 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(Y, X))), inverse(V2)), inverse(W2))))))), V2))))), S), inverse(S)), inverse(T))
% 10.26/1.66 = { by axiom 1 (single_axiom) }
% 10.26/1.66 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(Y, X))))))), S), inverse(S)), inverse(T))
% 10.26/1.66 = { by lemma 5 }
% 10.26/1.66 multiply(inverse(X), multiply(Y, X))
% 10.26/1.66
% 10.26/1.66 Lemma 23: 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)).
% 10.26/1.66 Proof:
% 10.26/1.66 multiply(multiply(inverse(multiply(inverse(multiply(X, inverse(X))), multiply(inverse(Y), Y))), Z), inverse(Z))
% 10.26/1.66 = { by lemma 10 }
% 10.26/1.66 multiply(multiply(inverse(multiply(inverse(multiply(X, inverse(X))), multiply(inverse(Y), Y))), multiply(inverse(U), U)), inverse(multiply(inverse(U), U)))
% 10.26/1.66 = { by lemma 15 }
% 10.26/1.66 multiply(multiply(inverse(multiply(inverse(multiply(X, inverse(X))), multiply(inverse(X), X))), multiply(inverse(U), U)), inverse(multiply(inverse(U), U)))
% 10.26/1.66 = { by lemma 14 R->L }
% 10.26/1.66 multiply(multiply(inverse(multiply(inverse(multiply(T, T)), multiply(T, T))), multiply(inverse(S), S)), inverse(multiply(inverse(U), U)))
% 10.26/1.66 = { by lemma 17 }
% 10.26/1.66 multiply(multiply(inverse(multiply(inverse(W), W)), V), inverse(V))
% 10.26/1.66
% 10.26/1.66 Lemma 24: multiply(inverse(X), multiply(inverse(multiply(inverse(Y), Y)), X)) = multiply(inverse(Z), Z).
% 10.26/1.66 Proof:
% 10.26/1.66 multiply(inverse(X), multiply(inverse(multiply(inverse(Y), Y)), X))
% 10.26/1.66 = { by lemma 22 }
% 10.26/1.66 multiply(inverse(multiply(W, inverse(W))), multiply(inverse(multiply(inverse(Y), Y)), multiply(W, inverse(W))))
% 10.26/1.66 = { by lemma 5 R->L }
% 10.26/1.66 multiply(inverse(multiply(W, inverse(W))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(W, inverse(W)))))))), X2), inverse(X2)), inverse(S)))
% 10.26/1.66 = { by lemma 9 R->L }
% 10.26/1.66 multiply(inverse(multiply(W, inverse(W))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Z2, Y2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(Y), Y)), multiply(W, inverse(W)))), multiply(inverse(U2), U2)), inverse(multiply(inverse(U2), U2))), inverse(V2))))))))))), X2), inverse(X2)), inverse(S)))
% 10.26/1.66 = { by lemma 15 }
% 10.26/1.66 multiply(inverse(multiply(W, inverse(W))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Z2, Y2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(W), W)), multiply(W, inverse(W)))), multiply(inverse(U2), U2)), inverse(multiply(inverse(U2), U2))), inverse(V2))))))))))), X2), inverse(X2)), inverse(S)))
% 10.26/1.66 = { by lemma 14 R->L }
% 10.26/1.66 multiply(inverse(multiply(W, inverse(W))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Z2, Y2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(T2, T2)), multiply(T2, T2))), multiply(inverse(U2), U2)), inverse(multiply(inverse(U2), U2))), inverse(V2))))))))))), X2), inverse(X2)), inverse(S)))
% 10.26/1.66 = { by lemma 9 }
% 10.26/1.66 multiply(inverse(multiply(W, inverse(W))), multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(inverse(multiply(T2, T2)), multiply(T2, T2))))))), X2), inverse(X2)), inverse(S)))
% 10.26/1.66 = { by lemma 5 }
% 10.26/1.66 multiply(inverse(multiply(W, inverse(W))), multiply(inverse(multiply(T2, T2)), multiply(T2, T2)))
% 10.26/1.66 = { by lemma 5 R->L }
% 10.26/1.66 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(W, inverse(W))), multiply(inverse(multiply(T2, T2)), multiply(T2, T2)))))))), W3), inverse(W3)), inverse(Z3))
% 10.26/1.66 = { by lemma 9 R->L }
% 10.26/1.67 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(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(W, inverse(W))), multiply(inverse(multiply(T2, T2)), multiply(T2, T2)))), X4), inverse(X4)), inverse(S3))))))))))), W3), inverse(W3)), inverse(Z3))
% 10.26/1.67 = { by lemma 23 }
% 10.26/1.67 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(inverse(multiply(V3, U3)), multiply(U3, V3))), multiply(inverse(multiply(T3, S3)), multiply(T3, inverse(multiply(multiply(multiply(inverse(multiply(inverse(Z), Z)), Y4), inverse(Y4)), inverse(S3))))))))))), W3), inverse(W3)), inverse(Z3))
% 10.26/1.67 = { by lemma 9 }
% 10.26/1.67 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(X3, S2))), multiply(inverse(multiply(Y3, Z3)), multiply(Y3, inverse(multiply(inverse(Z), Z)))))), W3), inverse(W3)), inverse(Z3))
% 10.26/1.67 = { by lemma 5 }
% 10.26/1.67 multiply(inverse(Z), Z)
% 10.26/1.67
% 10.26/1.67 Lemma 25: multiply(multiply(inverse(X), X), inverse(multiply(Y, inverse(Y)))) = multiply(Z, inverse(Z)).
% 10.26/1.67 Proof:
% 10.26/1.67 multiply(multiply(inverse(X), X), inverse(multiply(Y, inverse(Y))))
% 10.26/1.67 = { by lemma 20 R->L }
% 10.26/1.67 multiply(multiply(inverse(multiply(inverse(Y), Y)), multiply(inverse(W), W)), inverse(multiply(inverse(W), W)))
% 10.26/1.67 = { by lemma 16 }
% 10.26/1.67 multiply(multiply(inverse(multiply(inverse(V), V)), multiply(inverse(multiply(inverse(V), V)), multiply(inverse(V), V))), inverse(multiply(inverse(W), W)))
% 10.26/1.67 = { by lemma 24 }
% 10.26/1.67 multiply(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(W), W)), inverse(multiply(inverse(W), W)))
% 10.26/1.67 = { by lemma 5 R->L }
% 10.26/1.67 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))
% 10.26/1.67 = { by axiom 1 (single_axiom) R->L }
% 10.26/1.67 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))
% 10.26/1.67 = { by lemma 9 R->L }
% 10.26/1.67 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))
% 10.26/1.68 = { by lemma 21 R->L }
% 10.26/1.68 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))
% 10.26/1.68 = { by lemma 19 R->L }
% 10.26/1.68 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))
% 10.26/1.68 = { by lemma 20 }
% 10.26/1.68 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))
% 10.26/1.68 = { by lemma 20 }
% 10.51/1.68 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))
% 10.51/1.68 = { by lemma 18 }
% 10.51/1.69 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))
% 10.51/1.69 = { by lemma 21 }
% 10.51/1.69 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))
% 10.51/1.69 = { by lemma 9 }
% 10.51/1.69 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))
% 10.51/1.69 = { by axiom 1 (single_axiom) }
% 10.51/1.69 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))
% 10.51/1.69 = { by lemma 5 }
% 10.51/1.69 multiply(Z, inverse(Z))
% 10.51/1.69
% 10.51/1.69 Lemma 26: multiply(inverse(multiply(inverse(X), X)), Y) = multiply(inverse(multiply(Z, inverse(Z))), Y).
% 10.51/1.69 Proof:
% 10.51/1.69 multiply(inverse(multiply(inverse(X), X)), Y)
% 10.51/1.69 = { by lemma 9 R->L }
% 10.51/1.69 inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(X), X)), Y), S), inverse(S)), inverse(T)))))))
% 10.51/1.69 = { by lemma 21 R->L }
% 10.51/1.69 inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(multiply(inverse(X2), X2), inverse(multiply(X, inverse(X)))), inverse(inverse(Y))), inverse(T)))))))
% 10.51/1.69 = { by lemma 25 }
% 10.51/1.69 inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(Z), Z))), inverse(inverse(Y))), inverse(T)))))))
% 10.51/1.69 = { by lemma 21 }
% 10.51/1.69 inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(multiply(inverse(multiply(Z, inverse(Z))), Y), Y2), inverse(Y2)), inverse(T)))))))
% 10.51/1.69 = { by lemma 9 }
% 10.51/1.69 multiply(inverse(multiply(Z, inverse(Z))), Y)
% 10.51/1.69
% 10.51/1.69 Lemma 27: inverse(multiply(inverse(X), X)) = inverse(multiply(Y, inverse(Y))).
% 10.51/1.69 Proof:
% 10.51/1.69 inverse(multiply(inverse(X), X))
% 10.51/1.69 = { by lemma 9 R->L }
% 10.51/1.69 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)))))))
% 10.51/1.69 = { by lemma 26 }
% 10.51/1.69 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)))))))
% 10.51/1.69 = { by lemma 9 }
% 10.51/1.69 inverse(multiply(Y, inverse(Y)))
% 10.51/1.69
% 10.51/1.69 Lemma 28: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 10.51/1.69 Proof:
% 10.51/1.69 multiply(inverse(X), X)
% 10.51/1.69 = { by lemma 5 R->L }
% 10.51/1.69 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))
% 10.51/1.69 = { by lemma 27 }
% 10.51/1.69 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))
% 10.51/1.69 = { by lemma 5 }
% 10.51/1.69 multiply(Y, inverse(Y))
% 10.51/1.69
% 10.51/1.69 Lemma 29: multiply(multiply(inverse(inverse(inverse(multiply(inverse(X), X)))), Y), inverse(Y)) = multiply(Z, inverse(Z)).
% 10.51/1.69 Proof:
% 10.51/1.69 multiply(multiply(inverse(inverse(inverse(multiply(inverse(X), X)))), Y), inverse(Y))
% 10.51/1.69 = { by lemma 10 }
% 10.51/1.69 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))))))
% 10.51/1.69 = { by lemma 24 }
% 10.51/1.69 multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(inverse(X), X)), inverse(inverse(multiply(inverse(X), X))))))
% 10.51/1.69 = { by lemma 25 }
% 10.51/1.69 multiply(Z, inverse(Z))
% 10.51/1.69
% 10.51/1.69 Lemma 30: inverse(inverse(X)) = X.
% 10.51/1.69 Proof:
% 10.51/1.69 inverse(inverse(X))
% 10.51/1.69 = { by lemma 3 R->L }
% 10.51/1.69 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))
% 10.51/1.69 = { by lemma 27 }
% 10.51/1.69 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))
% 10.51/1.69 = { by lemma 29 R->L }
% 10.51/1.69 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))
% 10.51/1.69 = { by lemma 3 }
% 10.51/1.69 multiply(inverse(inverse(inverse(multiply(inverse(T), T)))), X)
% 10.51/1.69 = { by axiom 1 (single_axiom) R->L }
% 10.51/1.69 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)
% 10.51/1.69 = { by lemma 29 }
% 10.51/1.69 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)
% 10.51/1.69 = { by lemma 8 }
% 10.51/1.69 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)))))))
% 10.51/1.69 = { by lemma 9 }
% 10.51/1.69 X
% 10.51/1.69
% 10.51/1.69 Lemma 31: multiply(multiply(X, inverse(X)), inverse(Y)) = inverse(Y).
% 10.51/1.69 Proof:
% 10.51/1.69 multiply(multiply(X, inverse(X)), inverse(Y))
% 10.51/1.69 = { by lemma 25 R->L }
% 10.51/1.69 multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(multiply(inverse(multiply(Y, Y)), multiply(Y, Y)), inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y)))))), inverse(Y))
% 10.51/1.69 = { by lemma 20 R->L }
% 10.51/1.69 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, Y)))), W), inverse(W)), inverse(Y))
% 10.51/1.69 = { by lemma 30 R->L }
% 10.51/1.69 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, inverse(inverse(Y)))))), W), inverse(W)), inverse(Y))
% 10.51/1.69 = { by lemma 5 }
% 10.51/1.69 inverse(Y)
% 10.51/1.69
% 10.51/1.69 Lemma 32: multiply(multiply(Z, inverse(Z)), X) = multiply(multiply(X, Y), inverse(Y)).
% 10.51/1.69 Proof:
% 10.51/1.69 multiply(multiply(Z, inverse(Z)), X)
% 10.51/1.69 = { by lemma 28 R->L }
% 10.51/1.69 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)
% 10.51/1.69 = { by lemma 13 }
% 10.51/1.69 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))
% 10.51/1.69 = { by lemma 3 }
% 10.51/1.70 multiply(multiply(X, Y), inverse(Y))
% 10.51/1.70
% 10.51/1.70 Lemma 33: multiply(inverse(multiply(X, inverse(X))), Y) = inverse(inverse(Y)).
% 10.51/1.70 Proof:
% 10.51/1.70 multiply(inverse(multiply(X, inverse(X))), Y)
% 10.51/1.70 = { by lemma 28 R->L }
% 10.51/1.70 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(Z, W))), multiply(inverse(multiply(Z, W)), multiply(Z, W)))), Y)
% 10.51/1.70 = { by lemma 27 }
% 10.51/1.70 multiply(inverse(multiply(inverse(multiply(V, inverse(V))), multiply(inverse(multiply(Z, W)), multiply(Z, W)))), Y)
% 10.51/1.70 = { by lemma 30 R->L }
% 10.51/1.70 multiply(inverse(multiply(inverse(multiply(V, inverse(V))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(inverse(W)))))), Y)
% 10.51/1.70 = { by lemma 31 R->L }
% 10.51/1.70 multiply(inverse(multiply(inverse(multiply(V, inverse(V))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(U, inverse(U)), inverse(W))))))), Y)
% 10.51/1.70 = { by lemma 27 R->L }
% 10.51/1.70 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, T)), multiply(T, T))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(U, inverse(U)), inverse(W))))))), Y)
% 10.51/1.70 = { by lemma 2 R->L }
% 10.51/1.70 inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(multiply(U, inverse(U)), inverse(inverse(Y))), inverse(Z2)))))))
% 10.51/1.70 = { by lemma 32 }
% 10.51/1.70 inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(multiply(inverse(inverse(Y)), W2), inverse(W2)), inverse(Z2)))))))
% 10.51/1.70 = { by lemma 9 }
% 10.51/1.70 inverse(inverse(Y))
% 10.51/1.70
% 10.51/1.70 Lemma 34: inverse(multiply(X, inverse(X))) = multiply(Y, inverse(Y)).
% 10.51/1.70 Proof:
% 10.51/1.70 inverse(multiply(X, inverse(X)))
% 10.51/1.70 = { by lemma 3 R->L }
% 10.51/1.70 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))), multiply(inverse(multiply(Z, Z)), multiply(Z, inverse(multiply(inverse(multiply(X, inverse(X))), inverse(Z))))))), W), inverse(W))
% 10.51/1.70 = { by lemma 33 }
% 10.51/1.70 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))), multiply(inverse(multiply(Z, Z)), multiply(Z, inverse(inverse(inverse(inverse(Z)))))))), W), inverse(W))
% 10.51/1.70 = { by lemma 20 }
% 10.51/1.70 multiply(multiply(inverse(V), V), inverse(multiply(multiply(inverse(multiply(Z, Z)), multiply(Z, inverse(inverse(inverse(inverse(Z)))))), inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))))))
% 10.51/1.70 = { by lemma 28 }
% 10.51/1.70 multiply(multiply(U, inverse(U)), inverse(multiply(multiply(inverse(multiply(Z, Z)), multiply(Z, inverse(inverse(inverse(inverse(Z)))))), inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))))))
% 10.51/1.70 = { by lemma 30 }
% 10.51/1.70 multiply(multiply(U, inverse(U)), inverse(multiply(multiply(inverse(multiply(Z, Z)), multiply(Z, inverse(inverse(Z)))), inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))))))
% 10.51/1.70 = { by lemma 30 }
% 10.51/1.70 multiply(multiply(U, inverse(U)), inverse(multiply(multiply(inverse(multiply(Z, Z)), multiply(Z, Z)), inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))))))
% 10.51/1.70 = { by lemma 25 R->L }
% 10.51/1.70 multiply(multiply(U, inverse(U)), inverse(multiply(multiply(inverse(T), T), inverse(multiply(S, inverse(S))))))
% 10.51/1.70 = { by lemma 28 R->L }
% 10.51/1.70 multiply(multiply(inverse(X2), X2), inverse(multiply(multiply(inverse(T), T), inverse(multiply(S, inverse(S))))))
% 10.51/1.70 = { by lemma 20 R->L }
% 10.51/1.70 multiply(multiply(inverse(multiply(inverse(multiply(S, inverse(S))), multiply(inverse(T), T))), Y2), inverse(Y2))
% 10.51/1.70 = { by lemma 23 }
% 10.51/1.70 multiply(multiply(inverse(multiply(inverse(Z2), Z2)), W2), inverse(W2))
% 10.51/1.70 = { by lemma 20 }
% 10.51/1.70 multiply(multiply(inverse(V2), V2), inverse(multiply(Z2, inverse(Z2))))
% 10.51/1.70 = { by lemma 25 }
% 10.51/1.70 multiply(Y, inverse(Y))
% 10.51/1.70
% 10.51/1.70 Lemma 35: multiply(multiply(X, inverse(X)), Y) = Y.
% 10.51/1.70 Proof:
% 10.51/1.70 multiply(multiply(X, inverse(X)), Y)
% 10.51/1.70 = { by lemma 34 R->L }
% 10.51/1.70 multiply(inverse(multiply(Z, inverse(Z))), Y)
% 10.51/1.70 = { by lemma 33 }
% 10.51/1.70 inverse(inverse(Y))
% 10.51/1.70 = { by lemma 30 }
% 10.51/1.70 Y
% 10.51/1.70
% 10.51/1.70 Lemma 36: multiply(multiply(X, Y), inverse(Y)) = X.
% 10.51/1.70 Proof:
% 10.51/1.70 multiply(multiply(X, Y), inverse(Y))
% 10.51/1.70 = { by lemma 35 R->L }
% 10.51/1.70 multiply(multiply(multiply(multiply(Z, inverse(Z)), X), Y), inverse(Y))
% 10.51/1.70 = { by lemma 7 R->L }
% 10.51/1.70 multiply(multiply(multiply(multiply(Z, inverse(Z)), X), inverse(X)), inverse(inverse(X)))
% 10.51/1.70 = { by lemma 10 R->L }
% 10.51/1.70 multiply(multiply(multiply(multiply(Z, inverse(Z)), W), inverse(W)), inverse(inverse(X)))
% 10.51/1.70 = { by lemma 35 }
% 10.51/1.70 multiply(multiply(W, inverse(W)), inverse(inverse(X)))
% 10.51/1.70 = { by lemma 35 }
% 10.51/1.70 inverse(inverse(X))
% 10.51/1.70 = { by lemma 30 }
% 10.51/1.70 X
% 10.51/1.70
% 10.51/1.70 Lemma 37: inverse(multiply(Y, X)) = inverse(multiply(X, Y)).
% 10.51/1.70 Proof:
% 10.51/1.70 inverse(multiply(Y, X))
% 10.51/1.70 = { by lemma 36 R->L }
% 10.51/1.70 multiply(multiply(inverse(multiply(Y, X)), V), inverse(V))
% 10.51/1.70 = { by lemma 20 }
% 10.51/1.70 multiply(multiply(inverse(W), W), inverse(multiply(X, Y)))
% 10.51/1.70 = { by lemma 28 }
% 10.51/1.70 multiply(multiply(Z, inverse(Z)), inverse(multiply(X, Y)))
% 10.51/1.70 = { by lemma 35 }
% 10.51/1.70 inverse(multiply(X, Y))
% 10.51/1.70
% 10.51/1.70 Lemma 38: multiply(Y, X) = multiply(X, Y).
% 10.51/1.70 Proof:
% 10.51/1.70 multiply(Y, X)
% 10.51/1.70 = { by lemma 5 R->L }
% 10.51/1.70 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(Y, X)))))), T), inverse(T)), inverse(U))
% 10.51/1.70 = { by lemma 37 }
% 10.51/1.70 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(X, Y)))))), T), inverse(T)), inverse(U))
% 10.51/1.70 = { by lemma 5 }
% 10.51/1.70 multiply(X, Y)
% 10.51/1.70
% 10.51/1.70 Lemma 39: multiply(X, multiply(Y, inverse(X))) = Y.
% 10.51/1.70 Proof:
% 10.51/1.70 multiply(X, multiply(Y, inverse(X)))
% 10.51/1.70 = { by lemma 38 }
% 10.51/1.70 multiply(X, multiply(inverse(X), Y))
% 10.51/1.70 = { by lemma 38 }
% 10.51/1.70 multiply(multiply(inverse(X), Y), X)
% 10.51/1.70 = { by lemma 30 R->L }
% 10.51/1.70 multiply(multiply(inverse(X), Y), inverse(inverse(X)))
% 10.51/1.70 = { by lemma 38 }
% 10.51/1.70 multiply(multiply(Y, inverse(X)), inverse(inverse(X)))
% 10.51/1.70 = { by lemma 36 }
% 10.51/1.70 Y
% 10.51/1.70
% 10.51/1.70 Lemma 40: multiply(inverse(X), multiply(Y, X)) = multiply(Z, multiply(Y, inverse(Z))).
% 10.51/1.70 Proof:
% 10.51/1.70 multiply(inverse(X), multiply(Y, X))
% 10.51/1.70 = { by lemma 22 }
% 10.51/1.70 multiply(inverse(inverse(Z)), multiply(Y, inverse(Z)))
% 10.51/1.70 = { by lemma 30 }
% 10.51/1.70 multiply(Z, multiply(Y, inverse(Z)))
% 10.51/1.70
% 10.51/1.70 Lemma 41: multiply(multiply(X, Y), Z) = multiply(Y, multiply(X, Z)).
% 10.51/1.70 Proof:
% 10.51/1.70 multiply(multiply(X, Y), Z)
% 10.51/1.70 = { by lemma 38 }
% 10.51/1.70 multiply(Z, multiply(X, Y))
% 10.51/1.70 = { by lemma 30 R->L }
% 10.51/1.70 multiply(Z, inverse(inverse(multiply(X, Y))))
% 10.51/1.70 = { by lemma 39 R->L }
% 10.51/1.70 multiply(multiply(W, multiply(Z, inverse(W))), inverse(inverse(multiply(X, Y))))
% 10.51/1.70 = { by lemma 40 R->L }
% 10.51/1.70 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(inverse(multiply(X, Y))))
% 10.51/1.70 = { by lemma 35 R->L }
% 10.51/1.70 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(multiply(X, inverse(X)), inverse(multiply(X, Y)))))
% 10.51/1.71 = { by lemma 38 }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(X)))))
% 10.51/1.71 = { by lemma 30 R->L }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(inverse(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(X)))))))
% 10.51/1.71 = { by lemma 33 R->L }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(multiply(V, inverse(V))), multiply(inverse(multiply(X, Y)), multiply(X, inverse(X))))))
% 10.51/1.71 = { by lemma 27 R->L }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(multiply(inverse(multiply(U, U)), multiply(U, U))), multiply(inverse(multiply(X, Y)), multiply(X, inverse(X))))))
% 10.51/1.71 = { by lemma 9 R->L }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(multiply(inverse(multiply(U, U)), multiply(U, U))), multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(multiply(inverse(X), Z2), inverse(Z2)), inverse(Y2))))))))))))
% 10.51/1.71 = { by lemma 11 }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(W2), W2)), multiply(W2, inverse(W2)))), multiply(inverse(multiply(multiply(Z, X), Y)), multiply(multiply(Z, X), inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(multiply(inverse(X), Z2), inverse(Z2)), inverse(Y2))))))))))))
% 10.51/1.71 = { by lemma 9 }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(W2), W2)), multiply(W2, inverse(W2)))), multiply(inverse(multiply(multiply(Z, X), Y)), multiply(multiply(Z, X), inverse(X))))))
% 10.51/1.71 = { by lemma 9 R->L }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(W2), W2)), X3), inverse(X3)), inverse(S2))))))), multiply(W2, inverse(W2)))), multiply(inverse(multiply(multiply(Z, X), Y)), multiply(multiply(Z, X), inverse(X))))))
% 10.51/1.71 = { by lemma 28 R->L }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(W2), W2)), X3), inverse(X3)), inverse(S2))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(W2), W2)), X3), inverse(X3)), inverse(S2))))))), multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(W2), W2)), X3), inverse(X3)), inverse(S2))))))))), multiply(inverse(multiply(multiply(Z, X), Y)), multiply(multiply(Z, X), inverse(X))))))
% 10.51/1.71 = { by lemma 40 }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(W2), W2)), X3), inverse(X3)), inverse(S2))))))), inverse(multiply(inverse(W2), W2))))), multiply(inverse(multiply(multiply(Z, X), Y)), multiply(multiply(Z, X), inverse(X))))))
% 10.51/1.71 = { by lemma 38 R->L }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(multiply(inverse(W2), W2)), inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(W2), W2)), X3), inverse(X3)), inverse(S2)))))))))), multiply(inverse(multiply(multiply(Z, X), Y)), multiply(multiply(Z, X), inverse(X))))))
% 10.51/1.71 = { by lemma 9 }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(multiply(multiply(inverse(W2), W2), multiply(inverse(multiply(inverse(W2), W2)), inverse(multiply(inverse(W2), W2))))), multiply(inverse(multiply(multiply(Z, X), Y)), multiply(multiply(Z, X), inverse(X))))))
% 10.51/1.71 = { by lemma 39 }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(inverse(multiply(inverse(W2), W2))), multiply(inverse(multiply(multiply(Z, X), Y)), multiply(multiply(Z, X), inverse(X))))))
% 10.51/1.71 = { by lemma 27 }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(inverse(multiply(Y3, inverse(Y3)))), multiply(inverse(multiply(multiply(Z, X), Y)), multiply(multiply(Z, X), inverse(X))))))
% 10.51/1.71 = { by lemma 30 }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(multiply(Y3, inverse(Y3)), multiply(inverse(multiply(multiply(Z, X), Y)), multiply(multiply(Z, X), inverse(X))))))
% 10.51/1.71 = { by lemma 35 }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(multiply(multiply(Z, X), Y)), multiply(multiply(Z, X), inverse(X)))))
% 10.51/1.71 = { by lemma 37 R->L }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(inverse(multiply(Y, multiply(Z, X))), multiply(multiply(Z, X), inverse(X)))))
% 10.51/1.71 = { by lemma 38 R->L }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(multiply(multiply(Z, X), inverse(X)), inverse(multiply(Y, multiply(Z, X))))))
% 10.51/1.71 = { by lemma 38 R->L }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(multiply(inverse(X), multiply(Z, X)), inverse(multiply(Y, multiply(Z, X))))))
% 10.51/1.71 = { by lemma 40 }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(multiply(Z3, multiply(Z, inverse(Z3))), inverse(multiply(Y, multiply(Z, X))))))
% 10.51/1.71 = { by lemma 39 }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(Z, inverse(multiply(Y, multiply(Z, X))))))
% 10.51/1.71 = { by lemma 38 R->L }
% 10.51/1.71 multiply(multiply(inverse(inverse(multiply(Y, multiply(X, Z)))), multiply(Z, inverse(multiply(Y, multiply(X, Z))))), inverse(multiply(Z, inverse(multiply(Y, multiply(X, Z))))))
% 10.51/1.71 = { by lemma 36 }
% 10.51/1.71 inverse(inverse(multiply(Y, multiply(X, Z))))
% 10.51/1.71 = { by lemma 30 }
% 10.51/1.71 multiply(Y, multiply(X, Z))
% 10.51/1.71
% 10.51/1.71 Lemma 42: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
% 10.51/1.71 Proof:
% 10.51/1.71 inverse(multiply(X, inverse(Y)))
% 10.51/1.71 = { by lemma 37 }
% 10.51/1.72 inverse(multiply(inverse(Y), X))
% 10.51/1.72 = { by lemma 35 R->L }
% 10.51/1.72 multiply(multiply(Z, inverse(Z)), inverse(multiply(inverse(Y), X)))
% 10.51/1.72 = { by lemma 28 R->L }
% 10.51/1.72 multiply(multiply(inverse(W), W), inverse(multiply(inverse(Y), X)))
% 10.51/1.72 = { by lemma 20 R->L }
% 10.51/1.72 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(Y, multiply(X, inverse(Y)))), inverse(multiply(Y, multiply(X, inverse(Y)))))
% 10.51/1.72 = { by lemma 39 }
% 10.51/1.72 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(Y, multiply(X, inverse(Y)))), inverse(X))
% 10.51/1.72 = { by lemma 40 }
% 10.51/1.72 multiply(multiply(V, multiply(Y, inverse(V))), inverse(X))
% 10.51/1.72 = { by lemma 39 }
% 10.51/1.72 multiply(Y, inverse(X))
% 10.51/1.72
% 10.51/1.72 Lemma 43: inverse(multiply(inverse(X), Y)) = multiply(X, inverse(Y)).
% 10.51/1.72 Proof:
% 10.51/1.72 inverse(multiply(inverse(X), Y))
% 10.51/1.72 = { by lemma 37 }
% 10.51/1.72 inverse(multiply(Y, inverse(X)))
% 10.51/1.72 = { by lemma 42 }
% 10.51/1.72 multiply(X, inverse(Y))
% 10.51/1.72
% 10.51/1.72 Lemma 44: multiply(X, inverse(multiply(X, Y))) = inverse(Y).
% 10.51/1.72 Proof:
% 10.51/1.72 multiply(X, inverse(multiply(X, Y)))
% 10.51/1.72 = { by lemma 5 R->L }
% 10.51/1.72 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, inverse(multiply(X, inverse(multiply(X, Y)))))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.72 = { by lemma 37 }
% 10.51/1.72 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, inverse(multiply(inverse(multiply(X, Y)), X)))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.72 = { by lemma 39 R->L }
% 10.51/1.72 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, inverse(multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, inverse(X))))))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.72 = { by lemma 35 R->L }
% 10.51/1.72 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, inverse(multiply(multiply(W, inverse(W)), multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, inverse(X)))))))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.72 = { by lemma 37 }
% 10.51/1.72 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, inverse(multiply(multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, inverse(X)))), multiply(W, inverse(W)))))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.72 = { by lemma 34 R->L }
% 10.51/1.72 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, inverse(multiply(multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, inverse(X)))), inverse(multiply(V, inverse(V))))))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.72 = { by lemma 27 R->L }
% 10.51/1.72 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, inverse(multiply(multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, inverse(X)))), inverse(multiply(inverse(multiply(U, U)), multiply(U, U))))))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.72 = { by lemma 34 R->L }
% 10.51/1.72 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, inverse(multiply(multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(T, inverse(T))))), inverse(multiply(inverse(multiply(U, U)), multiply(U, U))))))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.72 = { by lemma 35 R->L }
% 10.51/1.72 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(multiply(S, inverse(S)), inverse(multiply(multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(T, inverse(T))))), inverse(multiply(inverse(multiply(U, U)), multiply(U, U)))))))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.72 = { by lemma 28 R->L }
% 10.51/1.72 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(multiply(inverse(X2), X2), inverse(multiply(multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(T, inverse(T))))), inverse(multiply(inverse(multiply(U, U)), multiply(U, U)))))))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.72 = { by lemma 20 R->L }
% 10.51/1.72 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, U)), multiply(U, U))), multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(T, inverse(T))))))), Y2), inverse(Y2)))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.72 = { by lemma 4 R->L }
% 10.51/1.72 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, Z2)), multiply(Z2, Z2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(multiply(multiply(T, inverse(T)), inverse(V2))))))), Y))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.72 = { by lemma 31 }
% 10.51/1.72 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, Z2)), multiply(Z2, Z2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(inverse(V2)))))), Y))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.73 = { by lemma 27 }
% 10.51/1.73 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(inverse(multiply(inverse(multiply(U2, inverse(U2))), multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(inverse(V2)))))), Y))))), Z), inverse(Z)), inverse(Y))
% 10.51/1.73 = { by lemma 33 }
% 10.51/1.73 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(inverse(inverse(inverse(multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(inverse(V2))))))), Y))))), Z), inverse(Z)), inverse(Y))
% 10.86/1.73 = { by lemma 30 }
% 10.86/1.73 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(inverse(multiply(inverse(multiply(W2, V2)), multiply(W2, inverse(inverse(V2))))), Y))))), Z), inverse(Z)), inverse(Y))
% 10.86/1.73 = { by lemma 30 }
% 10.86/1.73 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(inverse(multiply(inverse(multiply(W2, V2)), multiply(W2, V2))), Y))))), Z), inverse(Z)), inverse(Y))
% 10.86/1.73 = { by lemma 26 }
% 10.86/1.73 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(inverse(multiply(T2, inverse(T2))), Y))))), Z), inverse(Z)), inverse(Y))
% 10.86/1.73 = { by lemma 33 }
% 10.86/1.73 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, inverse(inverse(Y)))))), Z), inverse(Z)), inverse(Y))
% 10.86/1.73 = { by lemma 30 }
% 10.86/1.73 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, Y)))), Z), inverse(Z)), inverse(Y))
% 10.86/1.73 = { by lemma 20 }
% 10.86/1.73 multiply(multiply(multiply(inverse(S2), S2), inverse(multiply(multiply(inverse(multiply(Y, Y)), multiply(Y, Y)), inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y)))))), inverse(Y))
% 10.86/1.73 = { by lemma 25 }
% 10.86/1.73 multiply(multiply(X3, inverse(X3)), inverse(Y))
% 10.86/1.73 = { by lemma 31 }
% 10.86/1.73 inverse(Y)
% 10.86/1.73
% 10.86/1.73 Goal 1 (prove_these_axioms): tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4)) = tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4)).
% 10.86/1.73 Proof:
% 10.86/1.73 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 10.86/1.73 = { by lemma 28 }
% 10.86/1.73 tuple(multiply(multiply(X, inverse(X)), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 10.86/1.73 = { by lemma 28 }
% 10.86/1.73 tuple(multiply(multiply(X, inverse(X)), a2), multiply(multiply(a3, b3), c3), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 32 }
% 10.86/1.73 tuple(multiply(multiply(a2, Z), inverse(Z)), multiply(multiply(a3, b3), c3), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 36 }
% 10.86/1.73 tuple(a2, multiply(multiply(a3, b3), c3), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by axiom 1 (single_axiom) R->L }
% 10.86/1.73 tuple(a2, multiply(multiply(a3, b3), multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(c3, inverse(inverse(b3))), inverse(T))))))), inverse(b3))), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 38 }
% 10.86/1.73 tuple(a2, multiply(multiply(b3, a3), multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(c3, inverse(inverse(b3))), inverse(T))))))), inverse(b3))), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 42 R->L }
% 10.86/1.73 tuple(a2, multiply(multiply(b3, a3), inverse(multiply(b3, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(c3, inverse(inverse(b3))), inverse(T))))))))))), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 41 }
% 10.86/1.73 tuple(a2, multiply(a3, multiply(b3, inverse(multiply(b3, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(c3, inverse(inverse(b3))), inverse(T)))))))))))), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 44 }
% 10.86/1.73 tuple(a2, multiply(a3, inverse(inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(c3, inverse(inverse(b3))), inverse(T)))))))))), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 30 }
% 10.86/1.73 tuple(a2, multiply(a3, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(c3, inverse(inverse(b3))), inverse(T)))))))), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 2 }
% 10.86/1.73 tuple(a2, multiply(a3, multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, S)), multiply(S, S))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(c3, inverse(Y2))))))), b3)), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 43 }
% 10.86/1.73 tuple(a2, multiply(a3, multiply(multiply(multiply(inverse(multiply(S, S)), multiply(S, S)), inverse(multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(c3, inverse(Y2))))))), b3)), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 28 }
% 10.86/1.73 tuple(a2, multiply(a3, multiply(multiply(multiply(Z2, inverse(Z2)), inverse(multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(c3, inverse(Y2))))))), b3)), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 35 }
% 10.86/1.73 tuple(a2, multiply(a3, multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(c3, inverse(Y2)))))), b3)), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 43 }
% 10.86/1.73 tuple(a2, multiply(a3, multiply(multiply(multiply(X2, Y2), inverse(multiply(X2, inverse(multiply(c3, inverse(Y2)))))), b3)), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 41 }
% 10.86/1.73 tuple(a2, multiply(a3, multiply(multiply(Y2, multiply(X2, inverse(multiply(X2, inverse(multiply(c3, inverse(Y2))))))), b3)), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 44 }
% 10.86/1.73 tuple(a2, multiply(a3, multiply(multiply(Y2, inverse(inverse(multiply(c3, inverse(Y2))))), b3)), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 30 }
% 10.86/1.73 tuple(a2, multiply(a3, multiply(multiply(Y2, multiply(c3, inverse(Y2))), b3)), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 39 }
% 10.86/1.73 tuple(a2, multiply(a3, multiply(c3, b3)), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 38 R->L }
% 10.86/1.73 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(Y, inverse(Y)), multiply(a4, b4))
% 10.86/1.73 = { by lemma 38 }
% 10.86/1.73 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(Y, inverse(Y)), multiply(b4, a4))
% 10.86/1.73 = { by lemma 28 R->L }
% 10.86/1.73 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 10.86/1.73 % SZS output end Proof
% 10.86/1.73
% 10.86/1.73 RESULT: Unsatisfiable (the axioms are contradictory).
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