TSTP Solution File: GRP053-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP053-1 : TPTP v8.1.2. Released v1.0.0.
% 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 01:16:48 EDT 2023
% Result : Unsatisfiable 5.05s 1.06s
% Output : Proof 10.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP053-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % 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 00:13:26 EDT 2023
% 0.13/0.34 % CPUTime :
% 5.05/1.06 Command-line arguments: --no-flatten-goal
% 5.05/1.06
% 5.05/1.06 % SZS status Unsatisfiable
% 5.05/1.06
% 9.13/1.54 % SZS output start Proof
% 9.13/1.54 Take the following subset of the input axioms:
% 9.13/1.54 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)))).
% 9.13/1.54 fof(single_axiom, axiom, ![Y, Z, X]: inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, inverse(X)))), inverse(multiply(inverse(Y), Y))))))=X).
% 9.13/1.54
% 9.13/1.54 Now clausify the problem and encode Horn clauses using encoding 3 of
% 9.13/1.54 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 9.13/1.54 We repeatedly replace C & s=t => u=v by the two clauses:
% 9.13/1.54 fresh(y, y, x1...xn) = u
% 9.13/1.54 C => fresh(s, t, x1...xn) = v
% 9.13/1.54 where fresh is a fresh function symbol and x1..xn are the free
% 9.13/1.54 variables of u and v.
% 9.13/1.54 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 9.13/1.54 input problem has no model of domain size 1).
% 9.13/1.54
% 9.13/1.54 The encoding turns the above axioms into the following unit equations and goals:
% 9.13/1.54
% 9.13/1.55 Axiom 1 (single_axiom): inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(X), X)))))) = Z.
% 9.13/1.55
% 9.13/1.55 Lemma 2: multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(X), X))))) = inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, Z))), inverse(multiply(inverse(W), W)))))).
% 9.13/1.55 Proof:
% 9.13/1.55 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(X), X)))))
% 9.13/1.55 = { by axiom 1 (single_axiom) R->L }
% 9.13/1.55 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, inverse(Z)))), inverse(multiply(inverse(X), X))))))))), inverse(multiply(inverse(W), W))))))
% 9.13/1.55 = { by axiom 1 (single_axiom) }
% 9.13/1.55 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, Z))), inverse(multiply(inverse(W), W))))))
% 9.13/1.55
% 9.13/1.55 Lemma 3: inverse(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, Z))), inverse(multiply(inverse(X), X))))))) = Z.
% 9.13/1.55 Proof:
% 9.13/1.55 inverse(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(Y, X)), multiply(Y, Z))), inverse(multiply(inverse(X), X)))))))
% 9.13/1.55 = { by lemma 2 R->L }
% 9.13/1.55 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Z)))), inverse(multiply(inverse(W), W))))))
% 9.13/1.55 = { by axiom 1 (single_axiom) }
% 9.13/1.55 Z
% 9.13/1.55
% 9.13/1.55 Lemma 4: inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(Z))))), inverse(multiply(inverse(Y), Y)))) = inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), Z)), inverse(multiply(inverse(W), W))))))).
% 9.13/1.55 Proof:
% 9.13/1.55 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(Z))))), inverse(multiply(inverse(Y), Y))))
% 9.13/1.55 = { by lemma 3 R->L }
% 9.13/1.55 inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(Z))))), inverse(multiply(inverse(Y), Y))))))), inverse(multiply(inverse(W), W)))))))
% 9.13/1.55 = { by lemma 2 }
% 9.13/1.55 inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(Z)))), inverse(multiply(inverse(V), V)))))))), inverse(multiply(inverse(W), W)))))))
% 9.13/1.55 = { by axiom 1 (single_axiom) }
% 9.13/1.55 inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), Z)), inverse(multiply(inverse(W), W)))))))
% 9.13/1.55
% 9.13/1.55 Lemma 5: multiply(X, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), inverse(multiply(inverse(Y), Y)))))))) = Z.
% 9.13/1.55 Proof:
% 9.13/1.55 multiply(X, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), inverse(multiply(inverse(Y), Y))))))))
% 9.13/1.55 = { by lemma 4 R->L }
% 9.13/1.55 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(W, X)), multiply(W, inverse(inverse(Z))))), inverse(multiply(inverse(X), X)))))
% 9.13/1.55 = { by lemma 2 }
% 9.13/1.55 inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(Z)))), inverse(multiply(inverse(V), V))))))
% 9.13/1.55 = { by axiom 1 (single_axiom) }
% 9.13/1.55 Z
% 9.13/1.55
% 9.13/1.55 Lemma 6: multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(Z))))), inverse(multiply(inverse(Y), Y))) = inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), Z)), inverse(multiply(inverse(W), W)))))).
% 9.13/1.55 Proof:
% 9.13/1.55 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(Z))))), inverse(multiply(inverse(Y), Y)))
% 9.13/1.55 = { by axiom 1 (single_axiom) R->L }
% 9.13/1.55 inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(Z))))), inverse(multiply(inverse(Y), Y))))))), inverse(multiply(inverse(V), V))))))
% 9.13/1.55 = { by lemma 4 }
% 9.13/1.55 inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), Z)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(V), V))))))
% 9.13/1.55 = { by axiom 1 (single_axiom) }
% 9.13/1.55 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Y, W)), Z)), inverse(multiply(inverse(W), W))))))
% 9.13/1.55
% 9.13/1.55 Lemma 7: inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(W)))), inverse(multiply(inverse(inverse(multiply(Y, Z))), inverse(multiply(Y, Z)))))) = multiply(Y, inverse(inverse(multiply(Z, inverse(multiply(W, inverse(multiply(inverse(Z), Z)))))))).
% 9.13/1.55 Proof:
% 9.13/1.55 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(W)))), inverse(multiply(inverse(inverse(multiply(Y, Z))), inverse(multiply(Y, Z))))))
% 9.13/1.55 = { by lemma 5 R->L }
% 9.13/1.55 multiply(Y, inverse(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(Y, Z)))), multiply(X, inverse(W)))), inverse(multiply(inverse(inverse(multiply(Y, Z))), inverse(multiply(Y, Z)))))))), inverse(multiply(inverse(Z), Z))))))))
% 9.13/1.55 = { by axiom 1 (single_axiom) }
% 9.13/1.55 multiply(Y, inverse(inverse(multiply(Z, inverse(multiply(W, inverse(multiply(inverse(Z), Z))))))))
% 9.13/1.55
% 9.13/1.55 Lemma 8: multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Y), Y))))))))) = inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, Z))), inverse(multiply(inverse(W), W)))))).
% 9.13/1.55 Proof:
% 9.13/1.55 multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Y), Y)))))))))
% 9.13/1.55 = { by lemma 7 R->L }
% 9.13/1.55 multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(U, inverse(multiply(X, Y)))), multiply(U, inverse(Z)))), inverse(multiply(inverse(inverse(multiply(X, Y))), inverse(multiply(X, Y)))))))
% 9.13/1.55 = { by lemma 2 }
% 9.13/1.55 inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, Z))), inverse(multiply(inverse(W), W))))))
% 9.13/1.55
% 9.13/1.55 Lemma 9: inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Y), Y)))))))))) = Z.
% 9.13/1.55 Proof:
% 9.13/1.55 inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(Y, inverse(multiply(Z, inverse(multiply(inverse(Y), Y))))))))))
% 9.13/1.55 = { by lemma 7 R->L }
% 9.13/1.55 inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(X, Y)))), multiply(W, inverse(Z)))), inverse(multiply(inverse(inverse(multiply(X, Y))), inverse(multiply(X, Y))))))))
% 9.13/1.55 = { by axiom 1 (single_axiom) }
% 9.13/1.55 Z
% 9.13/1.55
% 9.13/1.55 Lemma 10: inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z))) = inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))).
% 9.13/1.55 Proof:
% 9.13/1.55 inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z)))
% 9.13/1.55 = { by lemma 9 R->L }
% 9.13/1.55 inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z))), inverse(multiply(inverse(Y), Y))))))))))
% 9.13/1.55 = { by axiom 1 (single_axiom) R->L }
% 9.13/1.55 inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(W, Y)), multiply(W, inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(T, U)), multiply(T, inverse(Z)))), inverse(multiply(inverse(U), U))))))))), inverse(multiply(inverse(Y), Y))))))))))
% 9.13/1.55 = { by axiom 1 (single_axiom) }
% 9.13/1.55 inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(T, U)), multiply(T, inverse(Z)))), inverse(multiply(inverse(U), U)))))))))
% 9.13/1.55 = { by axiom 1 (single_axiom) R->L }
% 9.13/1.55 inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(T, U)), multiply(T, inverse(Z)))), inverse(multiply(inverse(U), U))))))))), inverse(multiply(inverse(Y), Y))))))))))
% 9.13/1.55 = { by axiom 1 (single_axiom) }
% 9.13/1.55 inverse(multiply(inverse(multiply(V, Y)), multiply(V, inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), inverse(multiply(inverse(Y), Y))))))))))
% 9.13/1.55 = { by lemma 9 }
% 9.13/1.55 inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))
% 9.13/1.55
% 9.13/1.55 Lemma 11: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 9.13/1.55 Proof:
% 9.13/1.55 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 9.13/1.55 = { by axiom 1 (single_axiom) R->L }
% 9.13/1.55 inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z)))))), inverse(multiply(inverse(V), V))))))
% 9.13/1.55 = { by lemma 10 }
% 9.13/1.55 inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))))), inverse(multiply(inverse(V), V))))))
% 9.13/1.55 = { by axiom 1 (single_axiom) }
% 9.13/1.55 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 9.13/1.55
% 9.13/1.55 Lemma 12: multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(W, Y)), multiply(W, V))) = multiply(inverse(multiply(U, Z)), multiply(U, multiply(X, V))).
% 9.13/1.55 Proof:
% 9.13/1.55 multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(W, Y)), multiply(W, V)))
% 9.13/1.55 = { by lemma 11 }
% 9.13/1.55 multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), multiply(X, V)))
% 9.13/1.55 = { by lemma 11 R->L }
% 9.13/1.56 multiply(inverse(multiply(U, Z)), multiply(U, multiply(X, V)))
% 9.13/1.56
% 9.13/1.56 Lemma 13: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 9.13/1.56 Proof:
% 9.13/1.56 multiply(inverse(Y), Y)
% 9.13/1.56 = { by lemma 5 R->L }
% 9.13/1.56 multiply(inverse(Y), multiply(V2, inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))
% 9.13/1.56 = { by lemma 5 R->L }
% 9.13/1.56 multiply(inverse(multiply(V2, inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2))))))))), multiply(V2, inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))
% 9.13/1.56 = { by axiom 1 (single_axiom) R->L }
% 9.13/1.56 multiply(inverse(multiply(V2, inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2))))))))), multiply(V2, inverse(multiply(X5, inverse(multiply(inverse(multiply(inverse(multiply(Z2, X5)), multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2))))))))))), inverse(multiply(inverse(X5), X5))))))))
% 9.13/1.57 = { by axiom 1 (single_axiom) R->L }
% 9.13/1.57 multiply(inverse(multiply(V2, inverse(multiply(S4, inverse(multiply(inverse(multiply(inverse(multiply(Z2, S4)), multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2))))))))))), inverse(multiply(inverse(S4), S4)))))))), multiply(V2, inverse(multiply(X5, inverse(multiply(inverse(multiply(inverse(multiply(Z2, X5)), multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2))))))))))), inverse(multiply(inverse(X5), X5))))))))
% 9.13/1.57 = { by lemma 6 R->L }
% 9.13/1.57 multiply(inverse(multiply(V2, inverse(multiply(S4, inverse(multiply(inverse(multiply(inverse(multiply(Z2, S4)), multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2))))))))))), inverse(multiply(inverse(S4), S4)))))))), multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))
% 9.13/1.57 = { by lemma 6 R->L }
% 9.13/1.57 multiply(inverse(multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))), multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))
% 9.13/1.57 = { by axiom 1 (single_axiom) R->L }
% 9.13/1.57 inverse(multiply(U4, inverse(multiply(inverse(multiply(inverse(multiply(T4, U4)), multiply(T4, inverse(multiply(inverse(multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))), multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))))), inverse(multiply(inverse(U4), U4))))))
% 9.13/1.57 = { by lemma 8 R->L }
% 9.13/1.57 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))), multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(S), S)))))))))
% 9.13/1.57 = { by lemma 3 R->L }
% 9.13/1.58 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(V4, X2)), multiply(V4, multiply(inverse(multiply(inverse(multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))), multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 9.13/1.58 = { by lemma 12 R->L }
% 9.13/1.58 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))), multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), X2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 9.13/1.59 = { by axiom 1 (single_axiom) R->L }
% 9.13/1.59 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(inverse(multiply(Z4, inverse(multiply(inverse(multiply(inverse(multiply(W4, Z4)), multiply(W4, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))), multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), X2))))), inverse(multiply(inverse(Z4), Z4))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 9.72/1.60 = { by lemma 8 R->L }
% 9.72/1.60 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))), multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), X2)), inverse(multiply(inverse(X3), X3)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 9.72/1.60 = { by axiom 1 (single_axiom) R->L }
% 9.72/1.61 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(inverse(multiply(U3, inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))), U3)), multiply(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))), inverse(multiply(inverse(multiply(inverse(multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))), multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))))))), inverse(multiply(inverse(U3), U3))))))), X2)), inverse(multiply(inverse(X3), X3)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 9.72/1.61 = { by axiom 1 (single_axiom) R->L }
% 9.72/1.62 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(inverse(multiply(U3, inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))), U3)), multiply(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))), inverse(multiply(inverse(multiply(inverse(multiply(V2, multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))), multiply(V2, inverse(multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(S3, T3)), multiply(S3, inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), inverse(multiply(inverse(T3), T3))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))))))), inverse(multiply(inverse(U3), U3))))))), X2)), inverse(multiply(inverse(X3), X3)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 9.72/1.62 = { by lemma 2 }
% 9.72/1.63 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(inverse(multiply(U3, inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))), U3)), inverse(multiply(X4, inverse(multiply(inverse(multiply(inverse(multiply(Y4, X4)), multiply(Y4, multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(S3, T3)), multiply(S3, inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), inverse(multiply(inverse(T3), T3)))))))), inverse(multiply(inverse(X4), X4)))))))), inverse(multiply(inverse(U3), U3))))))), X2)), inverse(multiply(inverse(X3), X3)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 9.72/1.63 = { by lemma 2 R->L }
% 9.72/1.64 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(inverse(multiply(U3, inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))), U3)), multiply(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), W3)), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), W3)), inverse(multiply(T3, inverse(multiply(inverse(multiply(inverse(multiply(S3, T3)), multiply(S3, inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), inverse(multiply(inverse(T3), T3))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))))))), inverse(multiply(inverse(U3), U3))))))), X2)), inverse(multiply(inverse(X3), X3)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 9.72/1.64 = { by axiom 1 (single_axiom) }
% 9.72/1.65 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(inverse(multiply(U3, inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))), U3)), multiply(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), W3)), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), W3)), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))))))), inverse(multiply(inverse(U3), U3))))))), X2)), inverse(multiply(inverse(X3), X3)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 9.72/1.66 = { by axiom 1 (single_axiom) }
% 9.72/1.66 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), W3)), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), W3)), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), X2)), inverse(multiply(inverse(X3), X3)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 9.72/1.66 = { by lemma 10 R->L }
% 9.72/1.67 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z3, Z2)), multiply(Z3, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))))))), W3)), multiply(inverse(multiply(inverse(multiply(Z3, Z2)), multiply(Z3, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))))))), inverse(multiply(inverse(Z2), Z2))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), W3)), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), X2)), inverse(multiply(inverse(X3), X3)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 9.72/1.67 = { by lemma 6 }
% 10.33/1.67 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z3, Z2)), multiply(Z3, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))))))), W3)), inverse(multiply(V3, inverse(multiply(inverse(multiply(inverse(multiply(Z2, V3)), multiply(Z2, inverse(inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))))), inverse(multiply(inverse(V3), V3)))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), W3)), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), X2)), inverse(multiply(inverse(X3), X3)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 10.37/1.67 = { by axiom 1 (single_axiom) }
% 10.37/1.68 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z3, Z2)), multiply(Z3, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))))))), W3)), inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), W3)), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), X2)), inverse(multiply(inverse(X3), X3)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 10.37/1.68 = { by lemma 12 }
% 10.37/1.68 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, multiply(inverse(multiply(inverse(multiply(Z3, Z2)), multiply(Z3, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))))))), inverse(multiply(inverse(Z2), Z2)))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), X2)), inverse(multiply(inverse(X3), X3)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 10.37/1.69 = { by lemma 6 }
% 10.37/1.69 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(multiply(Y3, inverse(multiply(inverse(multiply(inverse(multiply(Z2, Y3)), multiply(Z2, inverse(inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))))), inverse(multiply(inverse(Y3), Y3))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), X2)), inverse(multiply(inverse(X3), X3)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 10.37/1.69 = { by axiom 1 (single_axiom) }
% 10.37/1.69 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(inverse(multiply(X3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), X2)), inverse(multiply(inverse(X3), X3)))))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 10.37/1.69 = { by lemma 8 }
% 10.37/1.69 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(inverse(multiply(U2, inverse(multiply(inverse(multiply(inverse(multiply(T2, U2)), multiply(T2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), X2))))), inverse(multiply(inverse(U2), U2))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 10.37/1.69 = { by axiom 1 (single_axiom) }
% 10.37/1.70 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(inverse(inverse(multiply(X2, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), X2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2)))), multiply(inverse(multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(inverse(multiply(Z2, inverse(inverse(inverse(multiply(W2, inverse(multiply(inverse(multiply(inverse(multiply(V2, W2)), Y)), inverse(multiply(inverse(W2), W2)))))))))))))), inverse(multiply(inverse(Z2), Z2))))))), multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(X2), X2)))))))))))))
% 10.37/1.70 = { by lemma 3 }
% 10.37/1.70 multiply(inverse(multiply(T, S)), multiply(T, inverse(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))), inverse(multiply(inverse(S), S)))))))))
% 10.37/1.70 = { by lemma 8 }
% 10.37/1.70 inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))))))), inverse(multiply(inverse(V), V))))))
% 10.37/1.70 = { by axiom 1 (single_axiom) }
% 10.37/1.70 multiply(inverse(multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W))))))))), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))
% 10.37/1.70 = { by lemma 5 }
% 10.37/1.70 multiply(inverse(X), multiply(Z, inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), X)), inverse(multiply(inverse(W), W)))))))))
% 10.37/1.70 = { by lemma 5 }
% 10.37/1.70 multiply(inverse(X), X)
% 10.37/1.70
% 10.37/1.70 Lemma 14: inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(Z), Z)))))) = X.
% 10.37/1.70 Proof:
% 10.37/1.70 inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(Z), Z))))))
% 10.37/1.70 = { by lemma 13 }
% 10.37/1.70 inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(inverse(X)), inverse(X)))))))
% 10.37/1.70 = { by lemma 13 }
% 10.37/1.70 inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(X))), multiply(W, inverse(X)))), inverse(multiply(inverse(inverse(X)), inverse(X)))))))
% 10.37/1.70 = { by axiom 1 (single_axiom) }
% 10.37/1.70 X
% 10.37/1.70
% 10.37/1.70 Lemma 15: inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y)))) = inverse(multiply(inverse(Z), Z)).
% 10.37/1.70 Proof:
% 10.37/1.70 inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y))))
% 10.37/1.70 = { by lemma 14 R->L }
% 10.37/1.70 inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y))))), inverse(multiply(inverse(multiply(inverse(X), X)), inverse(multiply(inverse(Y), Y))))))
% 10.37/1.70 = { by lemma 13 R->L }
% 10.37/1.70 inverse(multiply(inverse(Z), Z))
% 10.37/1.70
% 10.37/1.70 Lemma 16: inverse(multiply(inverse(X), inverse(multiply(inverse(Y), Y)))) = X.
% 10.37/1.70 Proof:
% 10.37/1.70 inverse(multiply(inverse(X), inverse(multiply(inverse(Y), Y))))
% 10.37/1.70 = { by lemma 15 R->L }
% 10.37/1.70 inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(Z), Z)), inverse(multiply(inverse(W), W))))))
% 10.37/1.70 = { by lemma 14 }
% 10.37/1.70 X
% 10.37/1.70
% 10.37/1.70 Lemma 17: inverse(multiply(inverse(X), multiply(inverse(Y), Y))) = X.
% 10.37/1.70 Proof:
% 10.37/1.70 inverse(multiply(inverse(X), multiply(inverse(Y), Y)))
% 10.37/1.70 = { by lemma 16 R->L }
% 10.37/1.70 inverse(multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(Z), Z))))))
% 10.37/1.70 = { by lemma 14 }
% 10.37/1.70 X
% 10.37/1.70
% 10.37/1.70 Lemma 18: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 10.37/1.70 Proof:
% 10.37/1.70 inverse(multiply(inverse(X), X))
% 10.37/1.70 = { by lemma 15 R->L }
% 10.37/1.70 inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(Z), Z))))
% 10.37/1.70 = { by lemma 16 }
% 10.37/1.70 multiply(inverse(Y), Y)
% 10.37/1.70
% 10.37/1.70 Lemma 19: multiply(inverse(X), multiply(inverse(Y), Y)) = inverse(multiply(X, multiply(inverse(Z), Z))).
% 10.37/1.70 Proof:
% 10.37/1.70 multiply(inverse(X), multiply(inverse(Y), Y))
% 10.37/1.70 = { by lemma 14 R->L }
% 10.37/1.70 inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), inverse(multiply(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(V), V))))))
% 10.37/1.70 = { by lemma 17 }
% 10.37/1.70 inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(W), W)), inverse(multiply(inverse(V), V))))))
% 10.37/1.70 = { by lemma 15 }
% 10.37/1.70 inverse(multiply(X, inverse(multiply(inverse(U), U))))
% 10.37/1.70 = { by lemma 18 }
% 10.37/1.70 inverse(multiply(X, multiply(inverse(Z), Z)))
% 10.37/1.70
% 10.37/1.70 Lemma 20: multiply(X, inverse(multiply(X, multiply(inverse(Y), Y)))) = multiply(inverse(Z), Z).
% 10.58/1.70 Proof:
% 10.58/1.70 multiply(X, inverse(multiply(X, multiply(inverse(Y), Y))))
% 10.58/1.70 = { by lemma 19 R->L }
% 10.58/1.70 multiply(X, multiply(inverse(X), multiply(inverse(W), W)))
% 10.58/1.70 = { by lemma 17 R->L }
% 10.58/1.70 multiply(inverse(multiply(inverse(X), multiply(inverse(W), W))), multiply(inverse(X), multiply(inverse(W), W)))
% 10.58/1.70 = { by lemma 13 R->L }
% 10.58/1.70 multiply(inverse(Z), Z)
% 10.58/1.70
% 10.58/1.70 Lemma 21: inverse(inverse(multiply(X, multiply(inverse(Y), Y)))) = X.
% 10.58/1.70 Proof:
% 10.58/1.70 inverse(inverse(multiply(X, multiply(inverse(Y), Y))))
% 10.58/1.70 = { by lemma 19 R->L }
% 10.58/1.70 inverse(multiply(inverse(X), multiply(inverse(Z), Z)))
% 10.58/1.70 = { by lemma 17 }
% 10.58/1.70 X
% 10.58/1.70
% 10.58/1.70 Lemma 22: inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))) = multiply(inverse(Z), Y).
% 10.58/1.70 Proof:
% 10.58/1.70 inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z)))
% 10.58/1.70 = { by lemma 11 }
% 10.58/1.70 inverse(multiply(inverse(multiply(inverse(Z), Y)), multiply(inverse(Z), Z)))
% 10.58/1.70 = { by lemma 13 R->L }
% 10.58/1.70 inverse(multiply(inverse(multiply(inverse(Z), Y)), multiply(inverse(W), W)))
% 10.58/1.70 = { by lemma 17 }
% 10.58/1.70 multiply(inverse(Z), Y)
% 10.58/1.70
% 10.58/1.70 Lemma 23: multiply(inverse(inverse(inverse(multiply(X, Y)))), X) = inverse(Y).
% 10.58/1.70 Proof:
% 10.58/1.70 multiply(inverse(inverse(inverse(multiply(X, Y)))), X)
% 10.58/1.70 = { by lemma 22 R->L }
% 10.58/1.70 inverse(multiply(inverse(multiply(Z, X)), multiply(Z, inverse(inverse(multiply(X, Y))))))
% 10.58/1.70 = { by lemma 16 R->L }
% 10.58/1.70 inverse(multiply(inverse(multiply(Z, X)), multiply(Z, inverse(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(inverse(X), X))))))))))
% 10.58/1.70 = { by lemma 8 }
% 10.58/1.70 inverse(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(V, W)), multiply(V, inverse(Y)))), inverse(multiply(inverse(W), W)))))))
% 10.58/1.70 = { by lemma 2 }
% 10.58/1.70 inverse(inverse(inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(T, U)), multiply(T, Y))), inverse(multiply(inverse(U), U))))))))
% 10.58/1.70 = { by lemma 3 }
% 10.58/1.70 inverse(Y)
% 10.58/1.70
% 10.58/1.70 Lemma 24: multiply(multiply(inverse(X), X), Y) = Y.
% 10.58/1.70 Proof:
% 10.58/1.70 multiply(multiply(inverse(X), X), Y)
% 10.58/1.70 = { by lemma 18 R->L }
% 10.58/1.70 multiply(inverse(multiply(inverse(Z), Z)), Y)
% 10.58/1.70 = { by lemma 18 R->L }
% 10.58/1.70 multiply(inverse(inverse(multiply(inverse(W), W))), Y)
% 10.58/1.70 = { by lemma 18 R->L }
% 10.58/1.70 multiply(inverse(inverse(inverse(multiply(inverse(V), V)))), Y)
% 10.58/1.70 = { by lemma 20 R->L }
% 10.58/1.70 multiply(inverse(inverse(inverse(multiply(Y, inverse(multiply(Y, multiply(inverse(U), U))))))), Y)
% 10.58/1.70 = { by lemma 23 }
% 10.58/1.70 inverse(inverse(multiply(Y, multiply(inverse(U), U))))
% 10.58/1.70 = { by lemma 21 }
% 10.58/1.70 Y
% 10.58/1.70
% 10.58/1.70 Lemma 25: multiply(X, multiply(inverse(X), Y)) = Y.
% 10.58/1.70 Proof:
% 10.58/1.70 multiply(X, multiply(inverse(X), Y))
% 10.58/1.70 = { by lemma 21 R->L }
% 10.58/1.70 multiply(X, multiply(inverse(X), inverse(inverse(multiply(Y, multiply(inverse(Y), Y))))))
% 10.58/1.70 = { by lemma 24 R->L }
% 10.58/1.70 multiply(X, multiply(inverse(X), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y))))))
% 10.58/1.70 = { by lemma 24 R->L }
% 10.58/1.70 multiply(X, multiply(inverse(multiply(multiply(inverse(W), W), X)), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y))))))
% 10.58/1.70 = { by axiom 1 (single_axiom) R->L }
% 10.58/1.70 multiply(X, multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V)))))))), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y))))))
% 10.58/1.70 = { by axiom 1 (single_axiom) R->L }
% 10.58/1.70 multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V)))))), multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V)))))))), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y))))))
% 10.58/1.71 = { by lemma 17 R->L }
% 10.58/1.71 multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V)))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V)))))))), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y)))))), multiply(inverse(T), T))))
% 10.58/1.71 = { by lemma 22 R->L }
% 10.58/1.71 multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V)))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V)))))))), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y)))))), inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(T, multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V))))))))), T)), multiply(inverse(inverse(inverse(multiply(T, multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V))))))))), T))))))
% 10.58/1.71 = { by lemma 23 R->L }
% 10.58/1.71 multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V)))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(inverse(inverse(multiply(T, multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V))))))))), T))), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y)))))), inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(T, multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V))))))))), T)), multiply(inverse(inverse(inverse(multiply(T, multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V))))))))), T))))))
% 10.58/1.71 = { by lemma 23 R->L }
% 10.58/1.71 multiply(multiply(inverse(inverse(inverse(multiply(T, multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V))))))))), T), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(inverse(inverse(multiply(T, multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V))))))))), T))), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y)))))), inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(T, multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V))))))))), T)), multiply(inverse(inverse(inverse(multiply(T, multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V))))))))), T))))))
% 10.58/1.71 = { by lemma 5 R->L }
% 10.58/1.71 multiply(multiply(inverse(inverse(inverse(multiply(T, multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V))))))))), T), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(inverse(inverse(multiply(T, multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V))))))))), T))), multiply(multiply(inverse(W), W), inverse(inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S)))))))), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y)))))), inverse(multiply(inverse(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S))))))), inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S)))))))))))))))), inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(T, multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V))))))))), T)), multiply(inverse(inverse(inverse(multiply(T, multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(X)))), inverse(multiply(inverse(V), V))))))))), T))))))
% 10.58/1.71 = { by lemma 2 }
% 10.58/1.71 inverse(multiply(Z2, inverse(multiply(inverse(multiply(inverse(multiply(W2, Z2)), multiply(W2, inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S)))))))), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y)))))), inverse(multiply(inverse(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S))))))), inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S))))))))))))))), inverse(multiply(inverse(Z2), Z2))))))
% 10.58/1.71 = { by axiom 1 (single_axiom) }
% 10.58/1.71 multiply(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S)))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S)))))))), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y)))))), inverse(multiply(inverse(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S))))))), inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S)))))))))))
% 10.58/1.71 = { by lemma 16 }
% 10.58/1.71 multiply(inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S)))))), multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S)))))))), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y))))))
% 10.58/1.71 = { by axiom 1 (single_axiom) }
% 10.58/1.71 multiply(multiply(inverse(Y2), Y2), multiply(inverse(multiply(multiply(inverse(W), W), inverse(multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, S)), multiply(X2, inverse(multiply(inverse(Y2), Y2))))), inverse(multiply(inverse(S), S)))))))), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y))))))
% 10.58/1.71 = { by axiom 1 (single_axiom) }
% 10.58/1.71 multiply(multiply(inverse(Y2), Y2), multiply(inverse(multiply(multiply(inverse(W), W), multiply(inverse(Y2), Y2))), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y))))))
% 10.58/1.71 = { by lemma 18 R->L }
% 10.58/1.71 multiply(multiply(inverse(Y2), Y2), multiply(inverse(multiply(inverse(multiply(inverse(Y2), Y2)), multiply(inverse(Y2), Y2))), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y))))))
% 10.58/1.71 = { by lemma 18 }
% 10.58/1.71 multiply(multiply(inverse(Y2), Y2), multiply(multiply(inverse(Z), Z), inverse(inverse(multiply(Y, multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y))))))
% 10.58/1.71 = { by lemma 16 R->L }
% 10.58/1.71 multiply(multiply(inverse(Y2), Y2), multiply(multiply(inverse(Z), Z), inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y)), inverse(multiply(inverse(Y), Y)))))))))
% 10.58/1.71 = { by lemma 5 R->L }
% 10.58/1.71 multiply(multiply(inverse(Y2), Y2), multiply(multiply(inverse(Z), Z), inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y)), multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y))), inverse(multiply(inverse(Y), Y))))))))), inverse(multiply(inverse(Y), Y)))))))))
% 10.58/1.71 = { by lemma 5 }
% 10.58/1.71 multiply(multiply(inverse(Y2), Y2), inverse(inverse(multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y)), multiply(inverse(multiply(multiply(inverse(Z), Z), Y)), Y))), inverse(multiply(inverse(Y), Y))))))))
% 10.58/1.71 = { by lemma 15 }
% 10.58/1.71 multiply(multiply(inverse(Y2), Y2), inverse(inverse(multiply(Y, inverse(multiply(inverse(V2), V2))))))
% 10.58/1.71 = { by lemma 18 }
% 10.58/1.71 multiply(multiply(inverse(Y2), Y2), inverse(inverse(multiply(Y, multiply(inverse(U2), U2)))))
% 10.58/1.71 = { by lemma 21 }
% 10.58/1.71 multiply(multiply(inverse(Y2), Y2), Y)
% 10.58/1.71 = { by lemma 24 }
% 10.58/1.71 Y
% 10.58/1.71
% 10.58/1.71 Lemma 26: multiply(inverse(X), X) = multiply(Y, inverse(Y)).
% 10.58/1.71 Proof:
% 10.58/1.71 multiply(inverse(X), X)
% 10.58/1.71 = { by lemma 20 R->L }
% 10.58/1.71 multiply(Y, inverse(multiply(Y, multiply(inverse(Y), Y))))
% 10.58/1.71 = { by lemma 25 }
% 10.58/1.71 multiply(Y, inverse(Y))
% 10.58/1.71
% 10.58/1.71 Lemma 27: multiply(X, multiply(inverse(multiply(inverse(Y), X)), Z)) = multiply(multiply(inverse(W), W), multiply(Y, Z)).
% 10.58/1.71 Proof:
% 10.58/1.71 multiply(X, multiply(inverse(multiply(inverse(Y), X)), Z))
% 10.58/1.71 = { by lemma 16 R->L }
% 10.58/1.71 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), X)), Z)), inverse(multiply(inverse(X), X)))))
% 10.58/1.71 = { by lemma 5 R->L }
% 10.58/1.71 multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), X)), multiply(inverse(Y), inverse(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), V)), Z)), inverse(multiply(inverse(V), V)))))))))), inverse(multiply(inverse(X), X)))))
% 10.58/1.71 = { by lemma 2 }
% 10.58/1.71 inverse(multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(T, U)), multiply(T, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), V)), Z)), inverse(multiply(inverse(V), V))))))))), inverse(multiply(inverse(U), U))))))
% 10.58/1.71 = { by lemma 2 R->L }
% 10.58/1.71 multiply(inverse(multiply(inverse(S), S)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(S), S)))), multiply(inverse(Y), inverse(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), V)), Z)), inverse(multiply(inverse(V), V)))))))))), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))))
% 10.58/1.71 = { by lemma 5 }
% 10.58/1.71 multiply(inverse(multiply(inverse(S), S)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), inverse(multiply(inverse(S), S)))), Z)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))))
% 10.58/1.71 = { by lemma 16 }
% 10.58/1.71 multiply(inverse(multiply(inverse(S), S)), inverse(multiply(inverse(multiply(Y, Z)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))))
% 10.58/1.71 = { by lemma 18 }
% 10.58/1.71 multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(Y, Z)), inverse(multiply(inverse(inverse(multiply(inverse(S), S))), inverse(multiply(inverse(S), S)))))))
% 10.58/1.71 = { by lemma 18 }
% 10.58/1.71 multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(Y, Z)), inverse(multiply(inverse(multiply(inverse(X2), X2)), inverse(multiply(inverse(S), S)))))))
% 10.58/1.71 = { by lemma 18 }
% 10.58/1.72 multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(Y, Z)), inverse(multiply(inverse(multiply(inverse(X2), X2)), multiply(inverse(X2), X2))))))
% 10.58/1.72 = { by lemma 22 }
% 10.58/1.72 multiply(multiply(inverse(W), W), inverse(multiply(inverse(multiply(Y, Z)), multiply(inverse(X2), X2))))
% 10.58/1.72 = { by lemma 17 }
% 10.58/1.72 multiply(multiply(inverse(W), W), multiply(Y, Z))
% 10.58/1.72
% 10.58/1.72 Lemma 28: multiply(multiply(X, inverse(X)), Y) = Y.
% 10.58/1.72 Proof:
% 10.58/1.72 multiply(multiply(X, inverse(X)), Y)
% 10.58/1.72 = { by lemma 25 R->L }
% 10.58/1.72 multiply(multiply(X, inverse(X)), multiply(Y, multiply(inverse(Y), Y)))
% 10.58/1.72 = { by lemma 26 R->L }
% 10.58/1.72 multiply(multiply(inverse(Z), Z), multiply(Y, multiply(inverse(Y), Y)))
% 10.58/1.72 = { by lemma 18 R->L }
% 10.58/1.72 multiply(multiply(inverse(Z), Z), multiply(Y, inverse(multiply(inverse(W), W))))
% 10.58/1.72 = { by lemma 27 R->L }
% 10.58/1.72 multiply(Y, multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(W), W))))
% 10.58/1.72 = { by axiom 1 (single_axiom) R->L }
% 10.58/1.72 multiply(Y, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(inverse(W), W))))))), inverse(multiply(inverse(V), V)))))))
% 10.58/1.72 = { by lemma 15 }
% 10.58/1.72 multiply(Y, inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(U, V)), multiply(U, inverse(multiply(inverse(Y), Y))))), inverse(multiply(inverse(V), V)))))))
% 10.58/1.72 = { by axiom 1 (single_axiom) }
% 10.58/1.72 multiply(Y, multiply(inverse(Y), Y))
% 10.58/1.72 = { by lemma 25 }
% 10.58/1.72 Y
% 10.58/1.72
% 10.58/1.72 Goal 1 (prove_these_axioms): tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3)) = tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3))).
% 10.58/1.72 Proof:
% 10.58/1.72 tuple(multiply(inverse(a1), a1), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 10.58/1.72 = { by lemma 26 }
% 10.58/1.72 tuple(multiply(X, inverse(X)), multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3))
% 10.58/1.72 = { by lemma 26 }
% 10.58/1.72 tuple(multiply(X, inverse(X)), multiply(multiply(Y, inverse(Y)), a2), multiply(multiply(a3, b3), c3))
% 10.58/1.72 = { by lemma 28 }
% 10.58/1.72 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, b3), c3))
% 10.58/1.72 = { by lemma 28 R->L }
% 10.58/1.72 tuple(multiply(X, inverse(X)), a2, multiply(multiply(Z, inverse(Z)), multiply(multiply(a3, b3), c3)))
% 10.58/1.72 = { by lemma 26 R->L }
% 10.58/1.72 tuple(multiply(X, inverse(X)), a2, multiply(multiply(inverse(W), W), multiply(multiply(a3, b3), c3)))
% 10.58/1.72 = { by lemma 27 R->L }
% 10.58/1.72 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, multiply(V, inverse(V))), multiply(inverse(multiply(inverse(multiply(a3, b3)), multiply(a3, multiply(V, inverse(V))))), c3)))
% 10.58/1.72 = { by lemma 16 R->L }
% 10.58/1.72 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, multiply(V, inverse(V))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, b3)), multiply(a3, multiply(V, inverse(V))))), c3)), inverse(multiply(inverse(U), U))))))
% 10.58/1.72 = { by lemma 26 R->L }
% 10.58/1.72 tuple(multiply(X, inverse(X)), a2, multiply(multiply(a3, multiply(inverse(a3), a3)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, b3)), multiply(a3, multiply(V, inverse(V))))), c3)), inverse(multiply(inverse(U), U))))))
% 10.58/1.72 = { by lemma 25 }
% 10.58/1.72 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(a3, b3)), multiply(a3, multiply(V, inverse(V))))), c3)), inverse(multiply(inverse(U), U))))))
% 10.58/1.72 = { by lemma 22 }
% 10.58/1.72 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(inverse(multiply(multiply(inverse(multiply(V, inverse(V))), b3), c3)), inverse(multiply(inverse(U), U))))))
% 10.58/1.72 = { by lemma 26 R->L }
% 10.58/1.72 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(inverse(multiply(multiply(inverse(multiply(inverse(T), T)), b3), c3)), inverse(multiply(inverse(U), U))))))
% 10.58/1.72 = { by lemma 18 }
% 10.58/1.72 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(inverse(multiply(multiply(multiply(inverse(S), S), b3), c3)), inverse(multiply(inverse(U), U))))))
% 10.58/1.72 = { by lemma 26 }
% 10.58/1.72 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(inverse(multiply(multiply(multiply(X2, inverse(X2)), b3), c3)), inverse(multiply(inverse(U), U))))))
% 10.58/1.72 = { by lemma 28 }
% 10.58/1.72 tuple(multiply(X, inverse(X)), a2, multiply(a3, inverse(multiply(inverse(multiply(b3, c3)), inverse(multiply(inverse(U), U))))))
% 10.58/1.72 = { by lemma 16 }
% 10.58/1.72 tuple(multiply(X, inverse(X)), a2, multiply(a3, multiply(b3, c3)))
% 10.58/1.72 = { by lemma 26 R->L }
% 10.58/1.72 tuple(multiply(inverse(b1), b1), a2, multiply(a3, multiply(b3, c3)))
% 10.58/1.72 % SZS output end Proof
% 10.58/1.72
% 10.58/1.72 RESULT: Unsatisfiable (the axioms are contradictory).
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