%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP084-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:14 AM UTC 2026
% Result : Unsatisfiable 8.70s 1.57s
% Output : Proof 15.02s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP084-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:21:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.70/1.57 Command-line arguments: --no-flatten-goal
% 8.70/1.57
% 8.70/1.57 % SZS status Unsatisfiable
% 8.70/1.57
% 13.81/2.18 % SZS output start Proof
% 13.81/2.18 Axiom 1 (single_axiom): multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(V, inverse(U)), inverse(W))))))), U) = V.
% 13.81/2.18
% 13.81/2.18 Lemma 2: inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(V, inverse(inverse(U))), inverse(W))))))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(V, inverse(Y2))))))), U).
% 13.81/2.18 Proof:
% 13.81/2.18 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(V, inverse(inverse(U))), inverse(W)))))))
% 13.81/2.18 = { by axiom 1 (single_axiom) R->L }
% 13.81/2.18 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(V, inverse(inverse(U))), inverse(W))))))), inverse(U)), inverse(Y2))))))), U)
% 13.81/2.18 = { by axiom 1 (single_axiom) }
% 13.81/2.18 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(V, inverse(Y2))))))), U)
% 13.81/2.18
% 13.81/2.18 Lemma 3: multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W))))))), U), inverse(U)) = V.
% 13.81/2.18 Proof:
% 13.81/2.18 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W))))))), U), inverse(U))
% 13.81/2.18 = { by lemma 2 R->L }
% 13.81/2.18 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(V, inverse(inverse(U))), inverse(Y2))))))), inverse(U))
% 13.81/2.18 = { by axiom 1 (single_axiom) }
% 13.81/2.18 V
% 13.81/2.18
% 13.81/2.18 Lemma 4: multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W))))))), U), T), inverse(T)) = multiply(V, inverse(inverse(U))).
% 13.81/2.18 Proof:
% 13.81/2.18 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W))))))), U), T), inverse(T))
% 13.81/2.18 = { by lemma 2 R->L }
% 13.81/2.18 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(S, X2)), multiply(X2, S))), multiply(inverse(multiply(Y2, Z2)), multiply(Y2, inverse(multiply(multiply(V, inverse(inverse(U))), inverse(Z2))))))), T), inverse(T))
% 13.81/2.18 = { by lemma 3 }
% 13.81/2.18 multiply(V, inverse(inverse(U)))
% 13.81/2.18
% 13.81/2.18 Lemma 5: multiply(multiply(X, Z), inverse(Z)) = multiply(multiply(X, Y), inverse(Y)).
% 13.81/2.18 Proof:
% 13.81/2.18 multiply(multiply(X, Z), inverse(Z))
% 13.81/2.18 = { by axiom 1 (single_axiom) R->L }
% 13.81/2.19 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(multiply(multiply(X, inverse(S)), inverse(W2))))))), S), Z), inverse(Z))
% 13.81/2.19 = { by lemma 4 }
% 13.81/2.19 multiply(multiply(X, inverse(S)), inverse(inverse(S)))
% 13.81/2.19 = { by lemma 4 R->L }
% 13.81/2.19 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(S)), inverse(T))))))), S), Y), inverse(Y))
% 13.81/2.19 = { by axiom 1 (single_axiom) }
% 13.81/2.19 multiply(multiply(X, Y), inverse(Y))
% 13.81/2.19
% 13.81/2.19 Lemma 6: multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(V, U), inverse(U)), inverse(W))))))), T) = multiply(V, T).
% 13.81/2.19 Proof:
% 13.81/2.19 multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(V, U), inverse(U)), inverse(W))))))), T)
% 13.81/2.19 = { by lemma 5 }
% 13.81/2.19 multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(V, T), inverse(T)), inverse(W))))))), T)
% 13.81/2.19 = { by axiom 1 (single_axiom) }
% 13.81/2.19 multiply(V, T)
% 13.81/2.19
% 13.81/2.19 Lemma 7: multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(V))))), U), inverse(U)), inverse(W)) = V.
% 13.81/2.19 Proof:
% 13.81/2.19 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(V))))), U), inverse(U)), inverse(W))
% 13.81/2.19 = { by axiom 1 (single_axiom) R->L }
% 13.81/2.19 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(V, inverse(inverse(W))), inverse(Y2))))))), inverse(W))))))), U), inverse(U)), inverse(W))
% 13.81/2.19 = { by lemma 3 }
% 13.81/2.19 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(V, inverse(inverse(W))), inverse(Y2))))))), inverse(W))
% 13.81/2.19 = { by axiom 1 (single_axiom) }
% 13.81/2.19 V
% 13.81/2.19
% 13.81/2.19 Lemma 8: inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(V, U), inverse(U)), inverse(W))))))) = V.
% 13.81/2.19 Proof:
% 13.81/2.19 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(V, U), inverse(U)), inverse(W)))))))
% 13.81/2.19 = { by axiom 1 (single_axiom) R->L }
% 13.81/2.19 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(V, U), inverse(U)), inverse(W))))))), inverse(Z2)), inverse(Y2))))))), Z2)
% 13.81/2.19 = { by lemma 6 }
% 13.81/2.19 multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(multiply(V, inverse(Z2)), inverse(Y2))))))), Z2)
% 13.81/2.19 = { by axiom 1 (single_axiom) }
% 13.81/2.19 V
% 13.81/2.19
% 13.81/2.19 Lemma 9: multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(multiply(multiply(V, U), inverse(U))))))), W) = V.
% 13.81/2.19 Proof:
% 13.81/2.19 multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(multiply(multiply(V, U), inverse(U))))))), W)
% 13.81/2.19 = { by lemma 5 }
% 13.81/2.19 multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(multiply(multiply(V, inverse(W)), inverse(inverse(W)))))))), W)
% 13.81/2.19 = { by axiom 1 (single_axiom) }
% 13.81/2.19 V
% 13.81/2.19
% 13.81/2.19 Lemma 10: inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, inverse(V))))) = inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(V))))).
% 13.81/2.19 Proof:
% 13.81/2.19 inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, inverse(V)))))
% 13.81/2.19 = { by lemma 7 R->L }
% 13.81/2.19 inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W)), multiply(Z2, inverse(V))))), W2), inverse(W2)), inverse(W)))))))
% 13.81/2.19 = { by axiom 1 (single_axiom) R->L }
% 13.81/2.19 inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W)), multiply(Z2, inverse(V))))), W2), inverse(W2)), inverse(inverse(inverse(X3)))), inverse(S2))))))), inverse(inverse(X3))), inverse(W)))))))
% 13.81/2.19 = { by lemma 2 }
% 13.81/2.19 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W)), multiply(Z2, inverse(V))))), W2), inverse(W2)), inverse(inverse(inverse(X3)))), inverse(S2))))))), inverse(V3))))))), X3)
% 13.81/2.19 = { by lemma 2 R->L }
% 13.81/2.19 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V2, U2)), multiply(U2, V2))), multiply(inverse(multiply(T2, S2)), multiply(T2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W)), multiply(Z2, inverse(V))))), W2), inverse(W2)), inverse(inverse(inverse(X3)))), inverse(S2))))))), inverse(inverse(X3))), inverse(W)))))))
% 13.81/2.19 = { by axiom 1 (single_axiom) }
% 13.81/2.19 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W)), multiply(Z2, inverse(V))))), W2), inverse(W2)), inverse(W)))))))
% 13.81/2.19 = { by lemma 7 }
% 13.81/2.19 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(V)))))
% 13.81/2.20
% 13.81/2.20 Lemma 11: multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, V))) = multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, V))).
% 13.81/2.20 Proof:
% 13.81/2.20 multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, V)))
% 13.81/2.20 = { by lemma 8 R->L }
% 13.81/2.20 multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(multiply(multiply(multiply(V, V2), inverse(V2)), inverse(W2))))))))))
% 13.81/2.20 = { by lemma 7 R->L }
% 13.81/2.20 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, W)), multiply(S, inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(multiply(multiply(multiply(V, V2), inverse(V2)), inverse(W2))))))))))))))), Y3), inverse(Y3)), inverse(X3))
% 13.81/2.20 = { by lemma 10 }
% 13.81/2.20 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(multiply(multiply(multiply(V, V2), inverse(V2)), inverse(W2))))))))))))))), Y3), inverse(Y3)), inverse(X3))
% 13.81/2.20 = { by lemma 7 }
% 13.81/2.20 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(multiply(multiply(multiply(V, V2), inverse(V2)), inverse(W2))))))))))
% 13.81/2.20 = { by lemma 8 }
% 13.81/2.20 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, V)))
% 13.81/2.20
% 13.81/2.20 Lemma 12: multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(U), U)) = multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(Z), Z)).
% 13.81/2.20 Proof:
% 13.81/2.20 multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(U), U))
% 13.81/2.20 = { by lemma 9 R->L }
% 13.81/2.20 multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W2, V2)), multiply(V2, W2))), multiply(inverse(multiply(U2, inverse(Y2))), multiply(U2, inverse(multiply(multiply(U, T2), inverse(T2))))))), Y2)), U))
% 13.81/2.20 = { by lemma 9 R->L }
% 13.81/2.20 multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W2, V2)), multiply(V2, W2))), multiply(inverse(multiply(U2, inverse(Y2))), multiply(U2, inverse(multiply(multiply(U, T2), inverse(T2))))))), Y2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(W2, V2)), multiply(V2, W2))), multiply(inverse(multiply(U2, inverse(Y2))), multiply(U2, inverse(multiply(multiply(U, T2), inverse(T2))))))), Y2)))
% 13.81/2.20 = { by lemma 11 }
% 13.81/2.20 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, inverse(Y2))), multiply(X2, inverse(multiply(multiply(Z, Z2), inverse(Z2))))))), Y2)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, inverse(Y2))), multiply(X2, inverse(multiply(multiply(Z, Z2), inverse(Z2))))))), Y2)))
% 13.81/2.20 = { by lemma 9 }
% 13.81/2.20 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, inverse(Y2))), multiply(X2, inverse(multiply(multiply(Z, Z2), inverse(Z2))))))), Y2)), Z))
% 14.20/2.20 = { by lemma 9 }
% 14.20/2.20 multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(Z), Z))
% 14.20/2.20
% 14.20/2.20 Lemma 13: inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))) = inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))).
% 14.20/2.20 Proof:
% 14.20/2.20 inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z)))
% 14.20/2.20 = { by lemma 8 R->L }
% 14.20/2.20 inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(X2), X2)), inverse(multiply(inverse(X2), X2))), inverse(S)))))))
% 14.20/2.20 = { by lemma 12 }
% 14.20/2.20 inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(X2), X2)), inverse(multiply(inverse(X2), X2))), inverse(S)))))))
% 14.20/2.20 = { by lemma 8 }
% 14.20/2.20 inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X)))
% 14.20/2.20
% 14.20/2.20 Lemma 14: multiply(inverse(multiply(Z, W)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(Y, X)).
% 14.20/2.20 Proof:
% 14.20/2.20 multiply(inverse(multiply(Z, W)), multiply(W, Z))
% 14.20/2.20 = { by lemma 7 R->L }
% 14.20/2.20 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))))))), X2), inverse(X2)), inverse(S))
% 14.20/2.20 = { by lemma 13 }
% 14.20/2.20 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))))))), X2), inverse(X2)), inverse(S))
% 14.20/2.20 = { by lemma 7 }
% 14.20/2.20 multiply(inverse(multiply(X, Y)), multiply(Y, X))
% 14.20/2.20
% 14.20/2.20 Lemma 15: multiply(multiply(inverse(multiply(X, Y)), multiply(Y, X)), inverse(multiply(Z, W))) = multiply(multiply(inverse(multiply(W, Z)), V), inverse(V)).
% 14.20/2.20 Proof:
% 14.20/2.20 multiply(multiply(inverse(multiply(X, Y)), multiply(Y, X)), inverse(multiply(Z, W)))
% 14.20/2.20 = { by lemma 14 }
% 14.20/2.20 multiply(multiply(inverse(multiply(W, Z)), multiply(Z, W)), inverse(multiply(Z, W)))
% 14.20/2.20 = { by lemma 5 R->L }
% 14.20/2.20 multiply(multiply(inverse(multiply(W, Z)), V), inverse(V))
% 14.20/2.20
% 14.20/2.20 Lemma 16: multiply(inverse(Z), multiply(Y, Z)) = multiply(inverse(X), multiply(Y, X)).
% 14.20/2.20 Proof:
% 14.20/2.20 multiply(inverse(Z), multiply(Y, Z))
% 14.20/2.20 = { by lemma 7 R->L }
% 14.20/2.20 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(inverse(Z), multiply(Y, Z))))))), S), inverse(S)), inverse(T))
% 14.20/2.20 = { by lemma 8 R->L }
% 14.20/2.20 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(Z), multiply(Y, Z))), V2), inverse(V2)), inverse(W2))))))))))), S), inverse(S)), inverse(T))
% 14.20/2.20 = { by lemma 15 R->L }
% 14.20/2.20 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(X), multiply(Y, X))), multiply(multiply(Y, X), inverse(X))), inverse(multiply(multiply(Y, Z), inverse(Z)))), inverse(W2))))))))))), S), inverse(S)), inverse(T))
% 14.20/2.20 = { by lemma 5 }
% 14.20/2.20 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(inverse(multiply(inverse(multiply(X2, Y2)), multiply(Y2, X2))), multiply(inverse(multiply(Z2, W2)), multiply(Z2, inverse(multiply(multiply(multiply(inverse(multiply(inverse(X), multiply(Y, X))), multiply(multiply(Y, X), inverse(X))), inverse(multiply(multiply(Y, X), inverse(X)))), inverse(W2))))))))))), S), inverse(S)), inverse(T))
% 14.20/2.20 = { by lemma 8 }
% 14.20/2.20 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(inverse(X), multiply(Y, X))))))), S), inverse(S)), inverse(T))
% 14.20/2.20 = { by lemma 7 }
% 14.20/2.20 multiply(inverse(X), multiply(Y, X))
% 14.20/2.20
% 14.20/2.20 Lemma 17: multiply(multiply(inverse(X), multiply(Y, X)), inverse(multiply(Y, Z))) = multiply(multiply(inverse(Z), W), inverse(W)).
% 14.20/2.20 Proof:
% 14.20/2.21 multiply(multiply(inverse(X), multiply(Y, X)), inverse(multiply(Y, Z)))
% 14.20/2.21 = { by lemma 16 }
% 14.20/2.21 multiply(multiply(inverse(Z), multiply(Y, Z)), inverse(multiply(Y, Z)))
% 14.20/2.21 = { by lemma 5 R->L }
% 14.20/2.21 multiply(multiply(inverse(Z), W), inverse(W))
% 14.20/2.21
% 14.20/2.21 Lemma 18: inverse(multiply(inverse(Y), Y)) = inverse(multiply(inverse(X), X)).
% 14.20/2.21 Proof:
% 14.20/2.21 inverse(multiply(inverse(Y), Y))
% 14.20/2.21 = { by lemma 8 R->L }
% 14.20/2.21 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(multiply(inverse(multiply(inverse(Y), Y)), X2), inverse(X2)), inverse(U)))))))
% 14.20/2.21 = { by lemma 17 R->L }
% 14.20/2.21 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(X), X))), inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(Y), Y)))), inverse(U)))))))
% 14.20/2.21 = { by lemma 12 R->L }
% 14.20/2.21 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(multiply(inverse(multiply(inverse(X), X)), multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(X), X))), inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(X), X)))), inverse(U)))))))
% 14.20/2.21 = { by lemma 8 }
% 14.20/2.21 inverse(multiply(inverse(X), X))
% 14.20/2.21
% 14.20/2.21 Lemma 19: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 14.20/2.21 Proof:
% 14.20/2.21 multiply(inverse(Y), Y)
% 14.20/2.21 = { by lemma 7 R->L }
% 14.20/2.21 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(Y), Y)))))), T), inverse(T)), inverse(U))
% 14.20/2.21 = { by lemma 18 }
% 14.20/2.21 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(X), X)))))), T), inverse(T)), inverse(U))
% 14.20/2.21 = { by lemma 7 }
% 14.20/2.21 multiply(inverse(X), X)
% 14.20/2.21
% 14.20/2.21 Lemma 20: multiply(multiply(inverse(Z), Z), inverse(X)) = multiply(multiply(inverse(X), Y), inverse(Y)).
% 14.20/2.21 Proof:
% 14.20/2.21 multiply(multiply(inverse(Z), Z), inverse(X))
% 14.20/2.21 = { by lemma 19 }
% 14.20/2.21 multiply(multiply(inverse(X), X), inverse(X))
% 14.20/2.21 = { by lemma 5 R->L }
% 14.20/2.21 multiply(multiply(inverse(X), Y), inverse(Y))
% 14.20/2.21
% 14.20/2.21 Lemma 21: multiply(multiply(inverse(X), X), Y) = multiply(multiply(Y, Z), inverse(Z)).
% 14.20/2.21 Proof:
% 14.20/2.21 multiply(multiply(inverse(X), X), Y)
% 14.20/2.21 = { by lemma 8 R->L }
% 14.20/2.21 multiply(multiply(inverse(X), X), inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(Y, S), inverse(S)), inverse(T))))))))
% 14.20/2.21 = { by lemma 20 }
% 14.20/2.21 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(Y, S), inverse(S)), inverse(T))))))), Z), inverse(Z))
% 14.20/2.21 = { by lemma 6 }
% 14.20/2.21 multiply(multiply(Y, Z), inverse(Z))
% 14.20/2.21
% 14.20/2.21 Lemma 22: multiply(inverse(Z), multiply(X, Z)) = multiply(X, multiply(inverse(Y), Y)).
% 14.20/2.21 Proof:
% 14.20/2.21 multiply(inverse(Z), multiply(X, Z))
% 14.20/2.21 = { by lemma 6 R->L }
% 14.20/2.21 multiply(inverse(Z), multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(X, S), inverse(S)), inverse(T))))))), Z))
% 14.20/2.21 = { by lemma 16 }
% 14.20/2.21 multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(X, S), inverse(S)), inverse(T))))))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(X, S), inverse(S)), inverse(T))))))), multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(X, S), inverse(S)), inverse(T))))))))
% 14.20/2.21 = { by lemma 19 R->L }
% 14.20/2.21 multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(X, S), inverse(S)), inverse(T))))))), multiply(inverse(Y), Y))
% 14.20/2.21 = { by lemma 6 }
% 14.20/2.21 multiply(X, multiply(inverse(Y), Y))
% 14.20/2.21
% 14.20/2.21 Lemma 23: multiply(inverse(multiply(X, Y)), multiply(inverse(Z), multiply(X, Z))) = multiply(inverse(W), multiply(inverse(Y), W)).
% 14.20/2.21 Proof:
% 14.20/2.21 multiply(inverse(multiply(X, Y)), multiply(inverse(Z), multiply(X, Z)))
% 14.20/2.21 = { by lemma 16 }
% 14.20/2.21 multiply(inverse(multiply(X, Y)), multiply(inverse(Y), multiply(X, Y)))
% 14.20/2.21 = { by lemma 16 R->L }
% 14.20/2.21 multiply(inverse(W), multiply(inverse(Y), W))
% 14.20/2.21
% 14.20/2.21 Lemma 24: multiply(inverse(X), multiply(inverse(multiply(inverse(Y), Y)), X)) = multiply(inverse(Z), Z).
% 14.20/2.21 Proof:
% 14.20/2.21 multiply(inverse(X), multiply(inverse(multiply(inverse(Y), Y)), X))
% 14.20/2.21 = { by lemma 23 R->L }
% 14.20/2.21 multiply(inverse(multiply(inverse(Y), multiply(inverse(Y), Y))), multiply(inverse(Y), multiply(inverse(Y), Y)))
% 14.20/2.21 = { by lemma 19 R->L }
% 14.20/2.21 multiply(inverse(Z), Z)
% 14.20/2.21
% 14.20/2.21 Lemma 25: inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W))))))) = multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, inverse(X2))), multiply(S, inverse(V))))), X2).
% 14.20/2.21 Proof:
% 14.20/2.21 inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W)))))))
% 14.20/2.21 = { by axiom 1 (single_axiom) R->L }
% 14.20/2.21 multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, inverse(X2))), multiply(S, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W))))))), inverse(X2)), inverse(inverse(X2)))))))), X2)
% 14.20/2.21 = { by lemma 3 }
% 14.20/2.21 multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, inverse(X2))), multiply(S, inverse(V))))), X2)
% 14.20/2.21
% 14.20/2.21 Lemma 26: multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(V))))), W), U), inverse(U)) = V.
% 14.20/2.21 Proof:
% 14.20/2.21 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, inverse(W))), multiply(Z, inverse(V))))), W), U), inverse(U))
% 14.20/2.21 = { by lemma 25 R->L }
% 14.20/2.21 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, Y2)), multiply(X2, inverse(multiply(V, inverse(Y2))))))), U), inverse(U))
% 14.20/2.21 = { by lemma 3 }
% 14.20/2.21 V
% 14.20/2.21
% 14.20/2.21 Lemma 27: multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(Z), Z))), W), V), inverse(V)) = W.
% 14.20/2.21 Proof:
% 14.20/2.21 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(Z), Z))), W), V), inverse(V))
% 14.20/2.21 = { by lemma 12 }
% 14.20/2.21 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(U, T)), multiply(T, U))), multiply(inverse(multiply(S, inverse(W))), multiply(S, inverse(W))))), W), V), inverse(V))
% 14.20/2.21 = { by lemma 26 }
% 14.20/2.21 W
% 14.20/2.21
% 14.20/2.21 Lemma 28: multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(Y), Y)), Z)) = Z.
% 14.20/2.21 Proof:
% 14.20/2.21 multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(Y), Y)), Z))
% 14.20/2.21 = { by lemma 24 R->L }
% 14.20/2.21 multiply(multiply(inverse(X), X), multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, W)), multiply(W, W))), multiply(inverse(multiply(inverse(multiply(W, W)), multiply(W, W))), multiply(inverse(multiply(W, W)), multiply(W, W))))), Z))
% 14.20/2.21 = { by lemma 21 }
% 14.20/2.22 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, W)), multiply(W, W))), multiply(inverse(multiply(inverse(multiply(W, W)), multiply(W, W))), multiply(inverse(multiply(W, W)), multiply(W, W))))), Z), V), inverse(V))
% 14.20/2.22 = { by lemma 27 }
% 14.20/2.22 Z
% 14.20/2.22
% 14.20/2.22 Lemma 29: multiply(inverse(X), multiply(multiply(X, Y), inverse(Y))) = multiply(inverse(Z), Z).
% 14.20/2.22 Proof:
% 14.20/2.22 multiply(inverse(X), multiply(multiply(X, Y), inverse(Y)))
% 14.20/2.22 = { by axiom 1 (single_axiom) R->L }
% 14.20/2.22 multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(inverse(X), multiply(multiply(X, Y), inverse(Y))), inverse(S)), inverse(T))))))), S)
% 14.20/2.22 = { by lemma 21 R->L }
% 14.20/2.22 multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(inverse(X), multiply(multiply(inverse(X2), X2), X)), inverse(S)), inverse(T))))))), S)
% 14.20/2.22 = { by lemma 22 }
% 14.20/2.22 multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(multiply(inverse(X2), X2), multiply(inverse(Y2), Y2)), inverse(S)), inverse(T))))))), S)
% 14.20/2.22 = { by lemma 28 R->L }
% 14.20/2.22 multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(multiply(inverse(X2), X2), multiply(inverse(Y2), Y2)), inverse(multiply(multiply(inverse(X2), X2), multiply(inverse(multiply(inverse(Z2), Z2)), S)))), inverse(T))))))), S)
% 14.20/2.22 = { by lemma 22 R->L }
% 14.20/2.22 multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(Z2), Z2)), S)), multiply(multiply(inverse(X2), X2), multiply(inverse(multiply(inverse(Z2), Z2)), S))), inverse(multiply(multiply(inverse(X2), X2), multiply(inverse(multiply(inverse(Z2), Z2)), S)))), inverse(T))))))), S)
% 14.20/2.22 = { by lemma 20 R->L }
% 14.20/2.22 multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(inverse(W2), W2), inverse(multiply(inverse(multiply(inverse(Z2), Z2)), S))), inverse(T))))))), S)
% 14.20/2.22 = { by lemma 24 R->L }
% 14.20/2.22 multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(inverse(S), multiply(inverse(multiply(inverse(Z2), Z2)), S)), inverse(multiply(inverse(multiply(inverse(Z2), Z2)), S))), inverse(T))))))), S)
% 14.20/2.22 = { by lemma 20 R->L }
% 14.20/2.22 multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(multiply(inverse(Z), Z), inverse(S)), inverse(T))))))), S)
% 14.20/2.22 = { by axiom 1 (single_axiom) }
% 14.20/2.22 multiply(inverse(Z), Z)
% 14.20/2.22
% 14.20/2.22 Lemma 30: multiply(multiply(inverse(Z), Z), inverse(multiply(W, inverse(W)))) = multiply(multiply(inverse(X), Y), inverse(multiply(inverse(X), Y))).
% 14.20/2.22 Proof:
% 14.20/2.22 multiply(multiply(inverse(Z), Z), inverse(multiply(W, inverse(W))))
% 14.20/2.22 = { by lemma 19 }
% 14.20/2.22 multiply(multiply(inverse(multiply(Y2, Y2)), multiply(Y2, Y2)), inverse(multiply(W, inverse(W))))
% 14.20/2.22 = { by lemma 15 }
% 14.20/2.22 multiply(multiply(inverse(multiply(inverse(W), W)), X2), inverse(X2))
% 14.20/2.22 = { by lemma 17 R->L }
% 14.20/2.22 multiply(multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(multiply(Y, inverse(X)), inverse(S))))))), X)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(multiply(Y, inverse(X)), inverse(S))))))), multiply(inverse(W), W))))
% 14.20/2.22 = { by lemma 22 R->L }
% 14.20/2.22 multiply(multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(multiply(Y, inverse(X)), inverse(S))))))), X)), inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(multiply(Y, inverse(X)), inverse(S))))))), X))))
% 14.20/2.22 = { by axiom 1 (single_axiom) }
% 14.20/2.22 multiply(multiply(inverse(X), Y), inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, U)), multiply(U, V))), multiply(inverse(multiply(T, S)), multiply(T, inverse(multiply(multiply(Y, inverse(X)), inverse(S))))))), X))))
% 14.20/2.22 = { by axiom 1 (single_axiom) }
% 14.20/2.22 multiply(multiply(inverse(X), Y), inverse(multiply(inverse(X), Y)))
% 14.20/2.22
% 14.20/2.22 Lemma 31: multiply(multiply(inverse(X), X), inverse(multiply(Y, inverse(Y)))) = multiply(inverse(Z), Z).
% 14.20/2.22 Proof:
% 14.20/2.22 multiply(multiply(inverse(X), X), inverse(multiply(Y, inverse(Y))))
% 14.20/2.22 = { by lemma 30 }
% 14.20/2.22 multiply(multiply(inverse(W), W), inverse(multiply(inverse(W), W)))
% 14.20/2.22 = { by lemma 29 R->L }
% 14.20/2.22 multiply(multiply(inverse(inverse(V)), multiply(multiply(inverse(V), V), inverse(V))), inverse(multiply(inverse(W), W)))
% 14.20/2.22 = { by lemma 22 }
% 14.20/2.22 multiply(multiply(multiply(inverse(V), V), multiply(inverse(W), W)), inverse(multiply(inverse(W), W)))
% 14.20/2.22 = { by lemma 21 R->L }
% 14.20/2.22 multiply(multiply(inverse(U), U), multiply(inverse(V), V))
% 14.20/2.22 = { by lemma 22 R->L }
% 14.20/2.22 multiply(inverse(inverse(U)), multiply(multiply(inverse(U), U), inverse(U)))
% 14.20/2.22 = { by lemma 29 }
% 14.20/2.22 multiply(inverse(Z), Z)
% 14.20/2.22
% 14.20/2.22 Lemma 32: multiply(multiply(multiply(inverse(X), X), Y), inverse(inverse(Z))) = multiply(multiply(inverse(W), W), multiply(Y, Z)).
% 14.20/2.22 Proof:
% 14.20/2.22 multiply(multiply(multiply(inverse(X), X), Y), inverse(inverse(Z)))
% 14.20/2.22 = { by lemma 21 }
% 14.20/2.22 multiply(multiply(multiply(Y, Z), inverse(Z)), inverse(inverse(Z)))
% 14.20/2.22 = { by lemma 21 R->L }
% 14.20/2.22 multiply(multiply(inverse(W), W), multiply(Y, Z))
% 14.20/2.22
% 14.20/2.22 Lemma 33: multiply(multiply(inverse(X), X), inverse(inverse(Y))) = Y.
% 14.20/2.22 Proof:
% 14.20/2.22 multiply(multiply(inverse(X), X), inverse(inverse(Y)))
% 14.20/2.22 = { by lemma 31 R->L }
% 14.20/2.22 multiply(multiply(multiply(inverse(Z), Z), inverse(multiply(W, inverse(W)))), inverse(inverse(Y)))
% 14.20/2.22 = { by lemma 30 }
% 14.20/2.22 multiply(multiply(multiply(inverse(V), V), inverse(multiply(inverse(V), V))), inverse(inverse(Y)))
% 14.20/2.22 = { by lemma 32 }
% 14.20/2.22 multiply(multiply(inverse(U), U), multiply(inverse(multiply(inverse(V), V)), Y))
% 14.20/2.22 = { by lemma 28 }
% 14.20/2.22 Y
% 14.20/2.22
% 14.20/2.22 Lemma 34: multiply(inverse(X), X) = multiply(Y, inverse(inverse(inverse(Y)))).
% 14.20/2.22 Proof:
% 14.20/2.22 multiply(inverse(X), X)
% 14.20/2.22 = { by lemma 29 R->L }
% 14.20/2.22 multiply(inverse(inverse(Z)), multiply(multiply(inverse(Z), Z), inverse(Z)))
% 14.20/2.22 = { by lemma 22 }
% 14.20/2.22 multiply(multiply(inverse(Z), Z), multiply(inverse(W), W))
% 14.20/2.22 = { by lemma 21 }
% 14.20/2.22 multiply(multiply(multiply(inverse(W), W), inverse(inverse(Y))), inverse(inverse(inverse(Y))))
% 14.20/2.22 = { by lemma 33 }
% 14.20/2.23 multiply(Y, inverse(inverse(inverse(Y))))
% 14.20/2.23
% 14.20/2.23 Lemma 35: multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z)) = multiply(inverse(Y), Z).
% 14.20/2.23 Proof:
% 14.20/2.23 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), Z))
% 14.20/2.23 = { by axiom 1 (single_axiom) R->L }
% 14.20/2.23 multiply(inverse(multiply(inverse(X), X)), multiply(inverse(Y), multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(Z, inverse(Y)), inverse(T))))))), Y)))
% 14.20/2.23 = { by lemma 18 }
% 14.20/2.23 multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(Z, inverse(Y)), inverse(T))))))), multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(Z, inverse(Y)), inverse(T)))))))), multiply(inverse(Y), multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(Z, inverse(Y)), inverse(T))))))), Y)))
% 14.20/2.23 = { by lemma 23 }
% 14.20/2.23 multiply(inverse(Y), multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(Z, inverse(Y)), inverse(T))))))), Y))
% 14.20/2.23 = { by axiom 1 (single_axiom) }
% 14.20/2.23 multiply(inverse(Y), Z)
% 14.20/2.23
% 14.20/2.23 Lemma 36: multiply(multiply(X, Y), inverse(Y)) = X.
% 14.20/2.23 Proof:
% 14.20/2.23 multiply(multiply(X, Y), inverse(Y))
% 14.20/2.23 = { by lemma 5 }
% 14.20/2.23 multiply(multiply(X, inverse(inverse(inverse(X)))), inverse(inverse(inverse(inverse(X)))))
% 14.20/2.23 = { by lemma 34 R->L }
% 14.20/2.23 multiply(multiply(inverse(Z), Z), inverse(inverse(inverse(inverse(X)))))
% 14.20/2.23 = { by lemma 20 }
% 14.20/2.23 multiply(multiply(inverse(inverse(inverse(inverse(X)))), multiply(multiply(inverse(X), X), inverse(inverse(inverse(X))))), inverse(multiply(multiply(inverse(X), X), inverse(inverse(inverse(X))))))
% 14.20/2.23 = { by lemma 19 }
% 14.20/2.23 multiply(multiply(inverse(inverse(inverse(inverse(X)))), multiply(multiply(inverse(X), X), inverse(inverse(inverse(X))))), inverse(multiply(multiply(inverse(multiply(W, W)), multiply(W, W)), inverse(inverse(inverse(X))))))
% 14.20/2.23 = { by lemma 14 }
% 14.20/2.23 multiply(multiply(inverse(inverse(inverse(inverse(X)))), multiply(multiply(inverse(X), X), inverse(inverse(inverse(X))))), inverse(multiply(multiply(inverse(multiply(inverse(inverse(X)), inverse(X))), multiply(inverse(X), inverse(inverse(X)))), inverse(inverse(inverse(X))))))
% 14.20/2.23 = { by lemma 35 }
% 14.20/2.23 multiply(multiply(inverse(inverse(inverse(inverse(X)))), multiply(multiply(inverse(X), X), inverse(inverse(inverse(X))))), inverse(multiply(multiply(inverse(X), inverse(inverse(X))), inverse(inverse(inverse(X))))))
% 14.20/2.23 = { by lemma 5 R->L }
% 14.20/2.23 multiply(multiply(inverse(inverse(inverse(inverse(X)))), multiply(multiply(inverse(X), X), inverse(inverse(inverse(X))))), inverse(multiply(multiply(inverse(X), X), inverse(X))))
% 14.20/2.23 = { by lemma 17 }
% 14.20/2.23 multiply(multiply(inverse(inverse(X)), inverse(X)), inverse(inverse(X)))
% 14.20/2.23 = { by lemma 33 }
% 14.20/2.23 X
% 14.20/2.23
% 14.20/2.23 Lemma 37: multiply(multiply(multiply(X, Y), inverse(Y)), inverse(X)) = multiply(inverse(Z), multiply(multiply(Z, W), inverse(W))).
% 14.20/2.23 Proof:
% 14.20/2.23 multiply(multiply(multiply(X, Y), inverse(Y)), inverse(X))
% 14.20/2.23 = { by lemma 21 R->L }
% 14.20/2.23 multiply(multiply(multiply(inverse(V), V), X), inverse(X))
% 14.20/2.23 = { by lemma 21 R->L }
% 14.20/2.23 multiply(multiply(inverse(U), U), multiply(inverse(V), V))
% 14.20/2.23 = { by lemma 22 R->L }
% 14.20/2.23 multiply(inverse(Z), multiply(multiply(inverse(U), U), Z))
% 14.20/2.23 = { by lemma 21 }
% 14.20/2.23 multiply(inverse(Z), multiply(multiply(Z, W), inverse(W)))
% 14.20/2.23
% 14.20/2.23 Lemma 38: multiply(Y, inverse(Y)) = multiply(X, inverse(inverse(inverse(X)))).
% 14.20/2.23 Proof:
% 14.20/2.23 multiply(Y, inverse(Y))
% 14.20/2.23 = { by lemma 36 R->L }
% 14.20/2.23 multiply(multiply(multiply(Y, V), inverse(V)), inverse(Y))
% 14.20/2.23 = { by lemma 37 }
% 14.20/2.23 multiply(inverse(Z), multiply(multiply(Z, W), inverse(W)))
% 14.20/2.23 = { by lemma 36 }
% 14.20/2.23 multiply(inverse(Z), Z)
% 14.20/2.23 = { by lemma 34 }
% 14.20/2.23 multiply(X, inverse(inverse(inverse(X))))
% 14.20/2.23
% 14.20/2.23 Lemma 39: inverse(inverse(X)) = X.
% 14.20/2.23 Proof:
% 14.20/2.23 inverse(inverse(X))
% 14.20/2.23 = { by lemma 26 R->L }
% 14.20/2.23 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Z, Y))), multiply(inverse(multiply(X, inverse(X))), multiply(X, inverse(inverse(inverse(X))))))), X), W), inverse(W))
% 14.20/2.23 = { by lemma 38 R->L }
% 14.20/2.23 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), multiply(Z, Y))), multiply(inverse(multiply(X, inverse(X))), multiply(X, inverse(X))))), X), W), inverse(W))
% 14.20/2.23 = { by lemma 27 }
% 14.20/2.23 X
% 14.20/2.23
% 14.20/2.23 Lemma 40: multiply(multiply(X, inverse(X)), inverse(Y)) = inverse(Y).
% 14.20/2.23 Proof:
% 14.20/2.23 multiply(multiply(X, inverse(X)), inverse(Y))
% 14.20/2.23 = { by lemma 38 }
% 14.20/2.23 multiply(multiply(Z, inverse(inverse(inverse(Z)))), inverse(Y))
% 14.20/2.23 = { by lemma 34 R->L }
% 14.20/2.23 multiply(multiply(inverse(W), W), inverse(Y))
% 14.20/2.23 = { by lemma 31 R->L }
% 14.20/2.23 multiply(multiply(multiply(inverse(V), V), inverse(multiply(U, inverse(U)))), inverse(Y))
% 14.20/2.23 = { by lemma 30 }
% 14.20/2.23 multiply(multiply(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, Y))))), inverse(Y))
% 14.20/2.23 = { by lemma 20 }
% 14.20/2.23 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, Y)))), T), inverse(T)), inverse(Y))
% 14.20/2.23 = { by lemma 39 R->L }
% 14.20/2.23 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, inverse(inverse(Y)))))), T), inverse(T)), inverse(Y))
% 14.20/2.23 = { by lemma 7 }
% 14.20/2.23 inverse(Y)
% 14.20/2.23
% 14.20/2.23 Lemma 41: multiply(inverse(X), multiply(Y, X)) = multiply(Z, multiply(Y, inverse(Z))).
% 14.20/2.23 Proof:
% 14.20/2.23 multiply(inverse(X), multiply(Y, X))
% 14.20/2.23 = { by lemma 16 }
% 14.20/2.23 multiply(inverse(inverse(Z)), multiply(Y, inverse(Z)))
% 14.20/2.23 = { by lemma 39 }
% 14.20/2.23 multiply(Z, multiply(Y, inverse(Z)))
% 14.20/2.23
% 14.20/2.23 Lemma 42: multiply(Z, multiply(X, inverse(Z))) = multiply(X, multiply(Y, inverse(Y))).
% 14.20/2.23 Proof:
% 14.20/2.23 multiply(Z, multiply(X, inverse(Z)))
% 14.20/2.23 = { by lemma 41 R->L }
% 14.20/2.23 multiply(inverse(U), multiply(X, U))
% 14.20/2.23 = { by lemma 22 }
% 14.20/2.23 multiply(X, multiply(inverse(V), V))
% 14.20/2.23 = { by lemma 34 }
% 14.20/2.23 multiply(X, multiply(W, inverse(inverse(inverse(W)))))
% 14.20/2.23 = { by lemma 38 R->L }
% 14.20/2.23 multiply(X, multiply(Y, inverse(Y)))
% 14.20/2.23
% 14.20/2.23 Lemma 43: multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W))))))), U) = multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, U)), multiply(X2, inverse(V))))), Y2), inverse(Y2)).
% 14.20/2.23 Proof:
% 14.20/2.23 multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W))))))), U)
% 14.20/2.23 = { by lemma 3 R->L }
% 14.20/2.23 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, U)), multiply(X2, inverse(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(Y, X))), multiply(inverse(multiply(Z, W)), multiply(Z, inverse(multiply(V, inverse(W))))))), U), inverse(U))))))), Y2), inverse(Y2))
% 14.20/2.23 = { by lemma 3 }
% 14.20/2.23 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(T, S)), multiply(S, T))), multiply(inverse(multiply(X2, U)), multiply(X2, inverse(V))))), Y2), inverse(Y2))
% 14.20/2.24
% 14.20/2.24 Lemma 44: multiply(X, multiply(inverse(Y), inverse(X))) = inverse(Y).
% 14.20/2.24 Proof:
% 14.20/2.24 multiply(X, multiply(inverse(Y), inverse(X)))
% 14.20/2.24 = { by lemma 7 R->L }
% 14.20/2.24 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, inverse(multiply(X, multiply(inverse(Y), inverse(X)))))))), Z), inverse(Z)), inverse(Y))
% 14.20/2.24 = { by axiom 1 (single_axiom) R->L }
% 14.20/2.24 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(inverse(multiply(X, multiply(inverse(Y), inverse(X)))), inverse(Y)), inverse(T))))))), Y))))), Z), inverse(Z)), inverse(Y))
% 14.20/2.24 = { by lemma 40 R->L }
% 14.20/2.24 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(inverse(multiply(X, multiply(inverse(Y), inverse(X)))), multiply(multiply(S, inverse(S)), inverse(Y))), inverse(T))))))), Y))))), Z), inverse(Z)), inverse(Y))
% 14.20/2.24 = { by lemma 42 }
% 14.20/2.24 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(inverse(multiply(inverse(Y), multiply(S, inverse(S)))), multiply(multiply(S, inverse(S)), inverse(Y))), inverse(T))))))), Y))))), Z), inverse(Z)), inverse(Y))
% 14.20/2.24 = { by lemma 14 R->L }
% 14.20/2.24 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(inverse(multiply(X2, X2)), multiply(X2, X2)), inverse(T))))))), Y))))), Z), inverse(Z)), inverse(Y))
% 14.20/2.24 = { by lemma 34 }
% 14.20/2.24 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(Y2, inverse(inverse(inverse(Y2)))), inverse(T))))))), Y))))), Z), inverse(Z)), inverse(Y))
% 14.20/2.24 = { by lemma 38 R->L }
% 14.20/2.24 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(Y, inverse(Y)), inverse(T))))))), Y))))), Z), inverse(Z)), inverse(Y))
% 14.20/2.24 = { by lemma 43 }
% 14.20/2.24 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, W2)), multiply(W2, Z2))), multiply(inverse(multiply(V2, Y)), multiply(V2, inverse(multiply(Y, inverse(Y))))))), U2), inverse(U2)))))), Z), inverse(Z)), inverse(Y))
% 14.20/2.24 = { by lemma 3 }
% 14.20/2.24 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, Y)))), Z), inverse(Z)), inverse(Y))
% 14.20/2.24 = { by lemma 20 R->L }
% 14.20/2.24 multiply(multiply(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), inverse(multiply(inverse(multiply(inverse(multiply(Y, Y)), multiply(Y, Y))), multiply(inverse(multiply(Y, Y)), multiply(Y, Y))))), inverse(Y))
% 14.20/2.24 = { by lemma 40 }
% 14.20/2.24 inverse(Y)
% 14.20/2.24
% 14.20/2.24 Lemma 45: multiply(X, multiply(Y, inverse(X))) = Y.
% 14.20/2.24 Proof:
% 14.20/2.24 multiply(X, multiply(Y, inverse(X)))
% 14.20/2.24 = { by lemma 6 R->L }
% 14.20/2.24 multiply(X, multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(multiply(Y, T), inverse(T)), inverse(U))))))), inverse(X)))
% 14.20/2.24 = { by lemma 44 }
% 14.20/2.24 inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(multiply(Y, T), inverse(T)), inverse(U)))))))
% 14.20/2.24 = { by lemma 8 }
% 14.20/2.24 Y
% 14.20/2.24
% 14.20/2.24 Lemma 46: multiply(inverse(multiply(X, multiply(Y, inverse(X)))), Y) = multiply(Z, inverse(Z)).
% 14.20/2.24 Proof:
% 14.20/2.24 multiply(inverse(multiply(X, multiply(Y, inverse(X)))), Y)
% 14.20/2.24 = { by lemma 33 R->L }
% 14.20/2.24 multiply(inverse(multiply(X, multiply(Y, inverse(X)))), multiply(multiply(inverse(inverse(Y)), inverse(Y)), inverse(inverse(Y))))
% 14.20/2.24 = { by lemma 41 R->L }
% 14.20/2.24 multiply(inverse(multiply(inverse(W), multiply(Y, W))), multiply(multiply(inverse(inverse(Y)), inverse(Y)), inverse(inverse(Y))))
% 14.20/2.24 = { by lemma 17 R->L }
% 14.20/2.24 multiply(inverse(multiply(inverse(W), multiply(Y, W))), multiply(multiply(inverse(W), multiply(Y, W)), inverse(multiply(Y, inverse(Y)))))
% 14.20/2.24 = { by lemma 38 }
% 14.20/2.24 multiply(inverse(multiply(inverse(W), multiply(Y, W))), multiply(multiply(inverse(W), multiply(Y, W)), inverse(multiply(V, inverse(inverse(inverse(V)))))))
% 14.20/2.24 = { by lemma 34 R->L }
% 14.20/2.24 multiply(inverse(multiply(inverse(W), multiply(Y, W))), multiply(multiply(inverse(W), multiply(Y, W)), inverse(multiply(inverse(U), U))))
% 14.20/2.24 = { by lemma 35 R->L }
% 14.20/2.24 multiply(inverse(multiply(inverse(multiply(inverse(U), U)), multiply(inverse(W), multiply(Y, W)))), multiply(multiply(inverse(W), multiply(Y, W)), inverse(multiply(inverse(U), U))))
% 14.20/2.24 = { by lemma 14 R->L }
% 14.20/2.24 multiply(inverse(multiply(T, T)), multiply(T, T))
% 14.20/2.24 = { by lemma 34 }
% 14.20/2.24 multiply(S, inverse(inverse(inverse(S))))
% 14.20/2.24 = { by lemma 38 R->L }
% 14.20/2.24 multiply(Z, inverse(Z))
% 14.20/2.24
% 14.20/2.24 Lemma 47: multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(Z, inverse(Z))))) = inverse(Y).
% 14.20/2.24 Proof:
% 14.20/2.24 multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(Z, inverse(Z)))))
% 14.20/2.24 = { by lemma 38 }
% 14.20/2.24 multiply(multiply(W, inverse(inverse(inverse(W)))), inverse(multiply(Y, multiply(Z, inverse(Z)))))
% 14.20/2.24 = { by lemma 34 R->L }
% 14.20/2.24 multiply(multiply(inverse(multiply(V, V)), multiply(V, V)), inverse(multiply(Y, multiply(Z, inverse(Z)))))
% 14.20/2.24 = { by lemma 14 }
% 14.20/2.24 multiply(multiply(inverse(multiply(multiply(inverse(inverse(Y)), inverse(Y)), inverse(inverse(Y)))), multiply(inverse(inverse(Y)), multiply(inverse(inverse(Y)), inverse(Y)))), inverse(multiply(Y, multiply(Z, inverse(Z)))))
% 14.20/2.25 = { by lemma 33 }
% 14.20/2.25 multiply(multiply(inverse(Y), multiply(inverse(inverse(Y)), multiply(inverse(inverse(Y)), inverse(Y)))), inverse(multiply(Y, multiply(Z, inverse(Z)))))
% 14.20/2.25 = { by lemma 41 }
% 14.20/2.25 multiply(multiply(inverse(Y), multiply(Y, multiply(inverse(inverse(Y)), inverse(Y)))), inverse(multiply(Y, multiply(Z, inverse(Z)))))
% 14.20/2.25 = { by lemma 34 }
% 14.20/2.25 multiply(multiply(inverse(Y), multiply(Y, multiply(U, inverse(inverse(inverse(U)))))), inverse(multiply(Y, multiply(Z, inverse(Z)))))
% 14.20/2.25 = { by lemma 38 R->L }
% 14.20/2.25 multiply(multiply(inverse(Y), multiply(Y, multiply(Z, inverse(Z)))), inverse(multiply(Y, multiply(Z, inverse(Z)))))
% 14.20/2.25 = { by lemma 5 R->L }
% 14.20/2.25 multiply(multiply(inverse(Y), Y), inverse(Y))
% 14.20/2.25 = { by lemma 34 }
% 14.20/2.25 multiply(multiply(T, inverse(inverse(inverse(T)))), inverse(Y))
% 14.20/2.25 = { by lemma 38 R->L }
% 14.20/2.25 multiply(multiply(S, inverse(S)), inverse(Y))
% 14.20/2.25 = { by lemma 40 }
% 14.20/2.25 inverse(Y)
% 14.20/2.25
% 14.20/2.25 Lemma 48: multiply(inverse(X), inverse(multiply(Y, inverse(Y)))) = inverse(X).
% 14.20/2.25 Proof:
% 14.20/2.25 multiply(inverse(X), inverse(multiply(Y, inverse(Y))))
% 14.20/2.25 = { by lemma 38 }
% 14.20/2.25 multiply(inverse(X), inverse(multiply(Z, inverse(inverse(inverse(Z))))))
% 14.20/2.25 = { by lemma 34 R->L }
% 14.20/2.25 multiply(inverse(X), inverse(multiply(inverse(multiply(X, multiply(X, inverse(X)))), multiply(X, multiply(X, inverse(X))))))
% 14.20/2.25 = { by lemma 44 R->L }
% 14.20/2.25 multiply(multiply(inverse(X), multiply(inverse(X), inverse(inverse(X)))), inverse(multiply(inverse(multiply(X, multiply(X, inverse(X)))), multiply(X, multiply(X, inverse(X))))))
% 14.20/2.25 = { by lemma 46 R->L }
% 14.20/2.25 multiply(multiply(inverse(X), multiply(inverse(multiply(X, multiply(X, inverse(X)))), X)), inverse(multiply(inverse(multiply(X, multiply(X, inverse(X)))), multiply(X, multiply(X, inverse(X))))))
% 14.20/2.25 = { by lemma 17 }
% 14.20/2.25 multiply(multiply(inverse(multiply(X, multiply(X, inverse(X)))), multiply(X, multiply(X, inverse(X)))), inverse(multiply(X, multiply(X, inverse(X)))))
% 14.20/2.25 = { by lemma 34 }
% 14.20/2.25 multiply(multiply(W, inverse(inverse(inverse(W)))), inverse(multiply(X, multiply(X, inverse(X)))))
% 14.20/2.25 = { by lemma 38 R->L }
% 14.20/2.25 multiply(multiply(V, inverse(V)), inverse(multiply(X, multiply(X, inverse(X)))))
% 14.20/2.25 = { by lemma 47 }
% 14.20/2.25 inverse(X)
% 14.20/2.25
% 14.20/2.25 Lemma 49: multiply(multiply(Z, inverse(Z)), X) = multiply(multiply(X, Y), inverse(Y)).
% 14.20/2.25 Proof:
% 14.20/2.25 multiply(multiply(Z, inverse(Z)), X)
% 14.20/2.25 = { by lemma 38 }
% 14.20/2.25 multiply(multiply(V, inverse(inverse(inverse(V)))), X)
% 14.20/2.25 = { by lemma 34 R->L }
% 14.20/2.25 multiply(multiply(inverse(W), W), X)
% 14.20/2.25 = { by lemma 21 }
% 14.20/2.25 multiply(multiply(X, Y), inverse(Y))
% 14.20/2.25
% 14.20/2.25 Lemma 50: inverse(multiply(X, inverse(X))) = multiply(Y, inverse(Y)).
% 14.20/2.25 Proof:
% 14.20/2.25 inverse(multiply(X, inverse(X)))
% 14.20/2.25 = { by axiom 1 (single_axiom) R->L }
% 14.20/2.25 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(inverse(multiply(X, inverse(X))), inverse(T)), inverse(U))))))), T)
% 14.20/2.25 = { by lemma 38 }
% 14.20/2.25 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(inverse(multiply(S, inverse(inverse(inverse(S))))), inverse(T)), inverse(U))))))), T)
% 14.20/2.25 = { by lemma 34 R->L }
% 14.20/2.25 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(X2), X2)), inverse(T)), inverse(U))))))), T)
% 14.20/2.25 = { by lemma 48 R->L }
% 14.20/2.25 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(inverse(multiply(inverse(X2), X2)), multiply(inverse(T), inverse(multiply(Y2, inverse(Y2))))), inverse(U))))))), T)
% 14.20/2.25 = { by lemma 35 }
% 14.20/2.25 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(multiply(inverse(T), inverse(multiply(Y2, inverse(Y2)))), inverse(U))))))), T)
% 14.20/2.25 = { by lemma 48 }
% 14.20/2.25 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), multiply(W, Z))), multiply(inverse(multiply(V, U)), multiply(V, inverse(multiply(inverse(T), inverse(U))))))), T)
% 14.20/2.25 = { by lemma 43 }
% 14.20/2.25 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z2, Z2)), multiply(Z2, Z2))), multiply(inverse(multiply(W2, T)), multiply(W2, inverse(inverse(T)))))), multiply(inverse(multiply(inverse(multiply(Z2, Z2)), multiply(Z2, Z2))), multiply(inverse(multiply(W2, T)), multiply(W2, inverse(inverse(T)))))), inverse(multiply(inverse(multiply(inverse(multiply(Z2, Z2)), multiply(Z2, Z2))), multiply(inverse(multiply(W2, T)), multiply(W2, inverse(inverse(T)))))))
% 14.20/2.25 = { by lemma 34 }
% 14.20/2.25 multiply(multiply(V2, inverse(inverse(inverse(V2)))), inverse(multiply(inverse(multiply(inverse(multiply(Z2, Z2)), multiply(Z2, Z2))), multiply(inverse(multiply(W2, T)), multiply(W2, inverse(inverse(T)))))))
% 14.20/2.25 = { by lemma 38 R->L }
% 14.20/2.25 multiply(multiply(U2, inverse(U2)), inverse(multiply(inverse(multiply(inverse(multiply(Z2, Z2)), multiply(Z2, Z2))), multiply(inverse(multiply(W2, T)), multiply(W2, inverse(inverse(T)))))))
% 14.20/2.25 = { by lemma 34 }
% 14.20/2.25 multiply(multiply(U2, inverse(U2)), inverse(multiply(inverse(multiply(T2, inverse(inverse(inverse(T2))))), multiply(inverse(multiply(W2, T)), multiply(W2, inverse(inverse(T)))))))
% 14.20/2.25 = { by lemma 38 R->L }
% 14.20/2.25 multiply(multiply(U2, inverse(U2)), inverse(multiply(inverse(multiply(multiply(W2, T), inverse(multiply(W2, T)))), multiply(inverse(multiply(W2, T)), multiply(W2, inverse(inverse(T)))))))
% 14.20/2.25 = { by lemma 39 }
% 14.20/2.25 multiply(multiply(U2, inverse(U2)), inverse(multiply(inverse(multiply(multiply(W2, T), inverse(multiply(W2, T)))), multiply(inverse(multiply(W2, T)), multiply(W2, T)))))
% 14.20/2.25 = { by lemma 13 R->L }
% 14.20/2.25 multiply(multiply(U2, inverse(U2)), inverse(multiply(inverse(multiply(S2, S2)), multiply(S2, S2))))
% 14.20/2.25 = { by lemma 49 }
% 14.20/2.25 multiply(multiply(inverse(multiply(inverse(multiply(S2, S2)), multiply(S2, S2))), X3), inverse(X3))
% 14.20/2.25 = { by lemma 20 R->L }
% 14.20/2.25 multiply(multiply(inverse(multiply(S2, S2)), multiply(S2, S2)), inverse(multiply(inverse(multiply(S2, S2)), multiply(S2, S2))))
% 14.20/2.25 = { by lemma 30 R->L }
% 14.20/2.25 multiply(multiply(inverse(Y3), Y3), inverse(multiply(Z3, inverse(Z3))))
% 14.20/2.25 = { by lemma 31 }
% 14.20/2.25 multiply(inverse(W3), W3)
% 14.20/2.25 = { by lemma 34 }
% 14.20/2.25 multiply(V3, inverse(inverse(inverse(V3))))
% 14.20/2.25 = { by lemma 38 R->L }
% 14.20/2.25 multiply(Y, inverse(Y))
% 14.20/2.25
% 14.20/2.25 Lemma 51: multiply(multiply(X, inverse(X)), multiply(Y, Z)) = multiply(Y, inverse(inverse(Z))).
% 14.20/2.25 Proof:
% 14.20/2.25 multiply(multiply(X, inverse(X)), multiply(Y, Z))
% 14.20/2.25 = { by lemma 39 R->L }
% 14.20/2.25 multiply(multiply(X, inverse(X)), multiply(inverse(inverse(Y)), Z))
% 14.20/2.25 = { by lemma 38 }
% 14.20/2.25 multiply(multiply(W, inverse(inverse(inverse(W)))), multiply(inverse(inverse(Y)), Z))
% 14.20/2.25 = { by lemma 34 R->L }
% 14.20/2.25 multiply(multiply(inverse(V), V), multiply(inverse(inverse(Y)), Z))
% 14.20/2.25 = { by lemma 32 R->L }
% 14.20/2.25 multiply(multiply(multiply(inverse(U), U), inverse(inverse(Y))), inverse(inverse(Z)))
% 14.20/2.25 = { by lemma 33 }
% 14.20/2.25 multiply(Y, inverse(inverse(Z)))
% 14.20/2.25
% 14.20/2.25 Lemma 52: multiply(Z, multiply(Y, inverse(Z))) = multiply(X, inverse(inverse(multiply(Y, inverse(X))))).
% 14.20/2.25 Proof:
% 14.20/2.25 multiply(Z, multiply(Y, inverse(Z)))
% 14.20/2.25 = { by lemma 41 R->L }
% 14.20/2.25 multiply(inverse(multiply(V, inverse(V))), multiply(Y, multiply(V, inverse(V))))
% 14.20/2.25 = { by lemma 50 }
% 14.20/2.25 multiply(multiply(W, inverse(W)), multiply(Y, multiply(V, inverse(V))))
% 14.20/2.25 = { by lemma 42 R->L }
% 14.20/2.25 multiply(multiply(W, inverse(W)), multiply(X, multiply(Y, inverse(X))))
% 14.20/2.25 = { by lemma 51 }
% 14.20/2.25 multiply(X, inverse(inverse(multiply(Y, inverse(X)))))
% 14.20/2.25
% 14.20/2.25 Lemma 53: multiply(multiply(X, inverse(X)), Y) = Y.
% 14.20/2.25 Proof:
% 14.20/2.25 multiply(multiply(X, inverse(X)), Y)
% 14.20/2.25 = { by lemma 46 R->L }
% 14.20/2.25 multiply(multiply(inverse(multiply(Z, multiply(W, inverse(Z)))), W), Y)
% 14.20/2.25 = { by lemma 52 }
% 14.20/2.25 multiply(multiply(inverse(multiply(W, inverse(inverse(multiply(W, inverse(W)))))), W), Y)
% 14.20/2.26 = { by lemma 51 R->L }
% 14.20/2.26 multiply(multiply(inverse(multiply(multiply(V, inverse(V)), multiply(W, multiply(W, inverse(W))))), W), Y)
% 14.20/2.26 = { by lemma 39 R->L }
% 14.20/2.26 multiply(multiply(inverse(multiply(multiply(V, inverse(V)), inverse(inverse(multiply(W, multiply(W, inverse(W))))))), W), Y)
% 14.20/2.26 = { by lemma 38 }
% 14.20/2.26 multiply(multiply(inverse(multiply(multiply(U, inverse(inverse(inverse(U)))), inverse(inverse(multiply(W, multiply(W, inverse(W))))))), W), Y)
% 14.20/2.26 = { by lemma 34 R->L }
% 14.20/2.26 multiply(multiply(inverse(multiply(multiply(inverse(T), T), inverse(inverse(multiply(W, multiply(W, inverse(W))))))), W), Y)
% 14.20/2.26 = { by lemma 29 R->L }
% 14.20/2.26 multiply(multiply(inverse(multiply(multiply(inverse(S), multiply(multiply(S, X2), inverse(X2))), inverse(inverse(multiply(W, multiply(W, inverse(W))))))), W), Y)
% 14.20/2.26 = { by lemma 37 R->L }
% 14.20/2.26 multiply(multiply(inverse(multiply(multiply(multiply(multiply(multiply(W, multiply(W, inverse(W))), Y2), inverse(Y2)), inverse(multiply(W, multiply(W, inverse(W))))), inverse(inverse(multiply(W, multiply(W, inverse(W))))))), W), Y)
% 14.20/2.26 = { by lemma 49 R->L }
% 14.20/2.26 multiply(multiply(inverse(multiply(multiply(multiply(multiply(Z2, inverse(Z2)), multiply(W, multiply(W, inverse(W)))), inverse(multiply(W, multiply(W, inverse(W))))), inverse(inverse(multiply(W, multiply(W, inverse(W))))))), W), Y)
% 14.20/2.26 = { by lemma 21 R->L }
% 14.20/2.26 multiply(multiply(inverse(multiply(multiply(inverse(W2), W2), multiply(multiply(Z2, inverse(Z2)), multiply(W, multiply(W, inverse(W)))))), W), Y)
% 14.20/2.26 = { by lemma 34 }
% 14.20/2.26 multiply(multiply(inverse(multiply(multiply(V2, inverse(inverse(inverse(V2)))), multiply(multiply(Z2, inverse(Z2)), multiply(W, multiply(W, inverse(W)))))), W), Y)
% 14.20/2.26 = { by lemma 38 R->L }
% 14.20/2.26 multiply(multiply(inverse(multiply(multiply(U2, inverse(U2)), multiply(multiply(Z2, inverse(Z2)), multiply(W, multiply(W, inverse(W)))))), W), Y)
% 14.20/2.26 = { by lemma 50 R->L }
% 14.20/2.26 multiply(multiply(inverse(multiply(inverse(multiply(T2, inverse(T2))), multiply(multiply(Z2, inverse(Z2)), multiply(W, multiply(W, inverse(W)))))), W), Y)
% 14.20/2.26 = { by lemma 50 R->L }
% 14.20/2.26 multiply(multiply(inverse(multiply(inverse(multiply(T2, inverse(T2))), multiply(inverse(multiply(W, inverse(W))), multiply(W, multiply(W, inverse(W)))))), W), Y)
% 14.20/2.26 = { by lemma 50 R->L }
% 14.20/2.26 multiply(multiply(inverse(multiply(inverse(multiply(T2, inverse(T2))), multiply(inverse(multiply(W, inverse(W))), multiply(W, inverse(multiply(Y, inverse(Y))))))), W), Y)
% 14.20/2.26 = { by lemma 38 }
% 14.20/2.26 multiply(multiply(inverse(multiply(inverse(multiply(S2, inverse(inverse(inverse(S2))))), multiply(inverse(multiply(W, inverse(W))), multiply(W, inverse(multiply(Y, inverse(Y))))))), W), Y)
% 14.20/2.26 = { by lemma 34 R->L }
% 14.20/2.26 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X3, X3)), multiply(X3, X3))), multiply(inverse(multiply(W, inverse(W))), multiply(W, inverse(multiply(Y, inverse(Y))))))), W), Y)
% 14.20/2.26 = { by lemma 25 R->L }
% 14.20/2.26 multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y3, Z3)), multiply(Z3, Y3))), multiply(inverse(multiply(W3, V3)), multiply(W3, inverse(multiply(multiply(Y, inverse(Y)), inverse(V3))))))), Y)
% 14.20/2.26 = { by axiom 1 (single_axiom) }
% 14.20/2.26 Y
% 14.20/2.26
% 14.20/2.26 Lemma 54: multiply(X, Y) = multiply(Y, X).
% 14.20/2.26 Proof:
% 14.20/2.26 multiply(X, Y)
% 14.20/2.26 = { by lemma 45 R->L }
% 14.20/2.26 multiply(Y, multiply(multiply(X, Y), inverse(Y)))
% 14.20/2.26 = { by lemma 21 R->L }
% 14.20/2.26 multiply(Y, multiply(multiply(inverse(Z), Z), X))
% 14.20/2.26 = { by lemma 34 }
% 14.20/2.26 multiply(Y, multiply(multiply(W, inverse(inverse(inverse(W)))), X))
% 14.20/2.26 = { by lemma 38 R->L }
% 14.20/2.26 multiply(Y, multiply(multiply(V, inverse(V)), X))
% 14.20/2.26 = { by lemma 53 }
% 14.20/2.26 multiply(Y, X)
% 14.20/2.26
% 14.20/2.26 Lemma 55: inverse(multiply(X, Y)) = multiply(inverse(X), inverse(Y)).
% 14.20/2.26 Proof:
% 14.20/2.26 inverse(multiply(X, Y))
% 14.20/2.26 = { by lemma 7 R->L }
% 14.20/2.26 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))), multiply(inverse(multiply(X, Y)), multiply(X, inverse(inverse(multiply(X, Y))))))), multiply(inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))), multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, Y))))), inverse(multiply(inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))), multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, Y)))))), inverse(Y))
% 14.20/2.26 = { by lemma 39 }
% 14.20/2.26 multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))), multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, Y))))), multiply(inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))), multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, Y))))), inverse(multiply(inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))), multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, Y)))))), inverse(Y))
% 14.20/2.26 = { by lemma 34 }
% 14.20/2.26 multiply(multiply(multiply(W, inverse(inverse(inverse(W)))), inverse(multiply(inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))), multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, Y)))))), inverse(Y))
% 14.20/2.26 = { by lemma 38 R->L }
% 14.20/2.26 multiply(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(multiply(inverse(multiply(Z, Z)), multiply(Z, Z))), multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, Y)))))), inverse(Y))
% 14.20/2.26 = { by lemma 34 }
% 14.20/2.26 multiply(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(multiply(U, inverse(inverse(inverse(U))))), multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, Y)))))), inverse(Y))
% 14.20/2.26 = { by lemma 38 R->L }
% 14.20/2.26 multiply(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(multiply(T, inverse(T))), multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, Y)))))), inverse(Y))
% 14.20/2.26 = { by lemma 50 }
% 14.20/2.26 multiply(multiply(multiply(V, inverse(V)), inverse(multiply(multiply(S, inverse(S)), multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, Y)))))), inverse(Y))
% 14.20/2.26 = { by lemma 51 }
% 14.20/2.26 multiply(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(multiply(X, Y)), inverse(inverse(multiply(X, multiply(X, Y))))))), inverse(Y))
% 14.20/2.26 = { by lemma 39 }
% 14.20/2.26 multiply(multiply(multiply(V, inverse(V)), inverse(multiply(inverse(multiply(X, Y)), multiply(X, multiply(X, Y))))), inverse(Y))
% 14.20/2.26 = { by lemma 41 }
% 14.20/2.26 multiply(multiply(multiply(V, inverse(V)), inverse(multiply(X, multiply(X, inverse(X))))), inverse(Y))
% 14.20/2.26 = { by lemma 47 }
% 14.20/2.26 multiply(inverse(X), inverse(Y))
% 14.20/2.26
% 14.20/2.26 Lemma 56: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
% 14.20/2.26 Proof:
% 14.20/2.26 inverse(multiply(X, inverse(Y)))
% 14.20/2.26 = { by lemma 53 R->L }
% 14.20/2.26 multiply(multiply(Z, inverse(Z)), inverse(multiply(X, inverse(Y))))
% 14.20/2.26 = { by lemma 38 }
% 14.20/2.26 multiply(multiply(W, inverse(inverse(inverse(W)))), inverse(multiply(X, inverse(Y))))
% 14.20/2.26 = { by lemma 34 R->L }
% 14.20/2.26 multiply(multiply(inverse(multiply(X, inverse(Y))), multiply(X, inverse(Y))), inverse(multiply(X, inverse(Y))))
% 14.20/2.26 = { by lemma 17 R->L }
% 14.20/2.26 multiply(multiply(inverse(V), multiply(Y, V)), inverse(multiply(Y, multiply(X, inverse(Y)))))
% 14.20/2.26 = { by lemma 45 }
% 14.20/2.26 multiply(multiply(inverse(V), multiply(Y, V)), inverse(X))
% 14.20/2.26 = { by lemma 41 }
% 14.20/2.26 multiply(multiply(U, multiply(Y, inverse(U))), inverse(X))
% 14.20/2.26 = { by lemma 45 }
% 14.20/2.26 multiply(Y, inverse(X))
% 14.20/2.26
% 14.20/2.26 Lemma 57: multiply(multiply(X, inverse(Y)), multiply(Y, inverse(X))) = multiply(Z, inverse(Z)).
% 14.20/2.26 Proof:
% 14.20/2.26 multiply(multiply(X, inverse(Y)), multiply(Y, inverse(X)))
% 14.20/2.26 = { by lemma 54 R->L }
% 14.20/2.27 multiply(multiply(X, inverse(Y)), multiply(inverse(X), Y))
% 14.20/2.27 = { by axiom 1 (single_axiom) R->L }
% 14.20/2.27 multiply(multiply(X, multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(inverse(Y), inverse(inverse(X))), inverse(T))))))), inverse(X))), multiply(inverse(X), Y))
% 14.20/2.27 = { by lemma 52 }
% 14.20/2.27 multiply(multiply(X, inverse(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(inverse(Y), inverse(inverse(X))), inverse(T))))))), inverse(X))))), multiply(inverse(X), Y))
% 14.20/2.27 = { by axiom 1 (single_axiom) }
% 14.20/2.27 multiply(multiply(X, inverse(inverse(inverse(Y)))), multiply(inverse(X), Y))
% 14.20/2.27 = { by lemma 54 R->L }
% 14.20/2.27 multiply(multiply(inverse(inverse(inverse(Y))), X), multiply(inverse(X), Y))
% 14.20/2.27 = { by lemma 36 R->L }
% 14.20/2.27 multiply(multiply(inverse(inverse(inverse(Y))), multiply(multiply(X, inverse(Y)), inverse(inverse(Y)))), multiply(inverse(X), Y))
% 14.20/2.27 = { by lemma 41 }
% 14.20/2.27 multiply(multiply(multiply(X, inverse(Y)), multiply(multiply(X, inverse(Y)), inverse(multiply(X, inverse(Y))))), multiply(inverse(X), Y))
% 14.20/2.27 = { by lemma 38 }
% 14.20/2.27 multiply(multiply(multiply(X, inverse(Y)), multiply(S, inverse(inverse(inverse(S))))), multiply(inverse(X), Y))
% 14.20/2.27 = { by lemma 34 R->L }
% 14.20/2.27 multiply(multiply(multiply(X, inverse(Y)), multiply(inverse(X2), X2)), multiply(inverse(X), Y))
% 14.20/2.27 = { by lemma 39 R->L }
% 14.20/2.27 multiply(multiply(multiply(X, inverse(Y)), inverse(inverse(multiply(inverse(X2), X2)))), multiply(inverse(X), Y))
% 14.20/2.27 = { by lemma 39 R->L }
% 14.20/2.27 multiply(multiply(multiply(inverse(inverse(X)), inverse(Y)), inverse(inverse(multiply(inverse(X2), X2)))), multiply(inverse(X), Y))
% 14.20/2.27 = { by lemma 55 R->L }
% 14.20/2.27 multiply(multiply(inverse(multiply(inverse(X), Y)), inverse(inverse(multiply(inverse(X2), X2)))), multiply(inverse(X), Y))
% 14.20/2.27 = { by lemma 55 R->L }
% 14.20/2.27 multiply(inverse(multiply(multiply(inverse(X), Y), inverse(multiply(inverse(X2), X2)))), multiply(inverse(X), Y))
% 14.20/2.27 = { by lemma 35 R->L }
% 14.20/2.27 multiply(inverse(multiply(multiply(inverse(X), Y), inverse(multiply(inverse(X2), X2)))), multiply(inverse(multiply(inverse(X2), X2)), multiply(inverse(X), Y)))
% 14.20/2.27 = { by lemma 14 R->L }
% 14.20/2.27 multiply(inverse(multiply(Y2, Y2)), multiply(Y2, Y2))
% 14.20/2.27 = { by lemma 34 }
% 14.20/2.27 multiply(Z2, inverse(inverse(inverse(Z2))))
% 14.20/2.27 = { by lemma 38 R->L }
% 14.20/2.27 multiply(Z, inverse(Z))
% 14.20/2.27
% 14.20/2.27 Lemma 58: multiply(Y, multiply(X, Z)) = multiply(X, multiply(Y, Z)).
% 14.20/2.27 Proof:
% 14.20/2.27 multiply(Y, multiply(X, Z))
% 14.20/2.27 = { by lemma 45 R->L }
% 14.20/2.27 multiply(Y, multiply(multiply(W5, multiply(X, inverse(W5))), Z))
% 14.20/2.27 = { by lemma 45 R->L }
% 14.20/2.27 multiply(Y, multiply(multiply(W5, multiply(V5, multiply(multiply(X, inverse(W5)), inverse(V5)))), Z))
% 14.20/2.27 = { by lemma 42 }
% 14.20/2.27 multiply(Y, multiply(multiply(W5, multiply(multiply(X, inverse(W5)), multiply(W5, inverse(W5)))), Z))
% 14.20/2.27 = { by lemma 39 R->L }
% 14.20/2.27 multiply(Y, multiply(multiply(W5, multiply(multiply(X, inverse(W5)), inverse(inverse(multiply(W5, inverse(W5)))))), Z))
% 14.20/2.27 = { by lemma 56 R->L }
% 14.20/2.27 multiply(Y, multiply(multiply(W5, multiply(inverse(multiply(W5, inverse(X))), inverse(inverse(multiply(W5, inverse(W5)))))), Z))
% 14.20/2.27 = { by lemma 55 R->L }
% 14.20/2.27 multiply(Y, multiply(multiply(W5, inverse(multiply(multiply(W5, inverse(X)), inverse(multiply(W5, inverse(W5)))))), Z))
% 14.20/2.27 = { by lemma 54 R->L }
% 14.20/2.27 multiply(Y, multiply(multiply(inverse(multiply(multiply(W5, inverse(X)), inverse(multiply(W5, inverse(W5))))), W5), Z))
% 14.20/2.27 = { by lemma 45 R->L }
% 14.20/2.27 multiply(Y, multiply(multiply(W5, multiply(multiply(inverse(multiply(multiply(W5, inverse(X)), inverse(multiply(W5, inverse(W5))))), W5), inverse(W5))), Z))
% 14.20/2.27 = { by lemma 15 R->L }
% 14.20/2.27 multiply(Y, multiply(multiply(W5, multiply(multiply(inverse(multiply(Y5, Z5)), multiply(Z5, Y5)), inverse(multiply(inverse(multiply(W5, inverse(W5))), multiply(W5, inverse(X)))))), Z))
% 14.20/2.27 = { by lemma 39 R->L }
% 14.20/2.27 multiply(Y, multiply(multiply(W5, multiply(inverse(inverse(multiply(inverse(multiply(Y5, Z5)), multiply(Z5, Y5)))), inverse(multiply(inverse(multiply(W5, inverse(W5))), multiply(W5, inverse(X)))))), Z))
% 14.20/2.27 = { by lemma 55 R->L }
% 14.20/2.27 multiply(Y, multiply(multiply(W5, inverse(multiply(inverse(multiply(inverse(multiply(Y5, Z5)), multiply(Z5, Y5))), multiply(inverse(multiply(W5, inverse(W5))), multiply(W5, inverse(X)))))), Z))
% 14.20/2.27 = { by lemma 54 R->L }
% 14.20/2.27 multiply(Y, multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y5, Z5)), multiply(Z5, Y5))), multiply(inverse(multiply(W5, inverse(W5))), multiply(W5, inverse(X))))), W5), Z))
% 14.20/2.27 = { by lemma 25 R->L }
% 14.20/2.27 multiply(Y, multiply(inverse(multiply(inverse(multiply(inverse(multiply(U4, T4)), multiply(T4, U4))), multiply(inverse(multiply(S4, X5)), multiply(S4, inverse(multiply(X, inverse(X5))))))), Z))
% 14.20/2.27 = { by lemma 2 R->L }
% 14.20/2.27 multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))
% 14.20/2.27 = { by lemma 45 R->L }
% 14.20/2.27 multiply(Y, multiply(Y2, multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2))))
% 14.20/2.27 = { by lemma 8 R->L }
% 14.20/2.27 multiply(Y, multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))))
% 14.20/2.27 = { by lemma 56 R->L }
% 14.20/2.28 multiply(Y, inverse(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2))))
% 14.20/2.28 = { by lemma 56 R->L }
% 14.20/2.28 inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y)))
% 14.20/2.28 = { by lemma 53 R->L }
% 14.20/2.28 multiply(multiply(V4, inverse(V4)), inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))))
% 14.20/2.28 = { by lemma 38 }
% 14.20/2.28 multiply(multiply(W4, inverse(inverse(inverse(W4)))), inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))))
% 14.20/2.28 = { by lemma 34 R->L }
% 14.20/2.28 multiply(multiply(inverse(Z4), Z4), inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))))
% 14.20/2.29 = { by lemma 20 }
% 14.20/2.29 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))))
% 14.20/2.29 = { by lemma 54 R->L }
% 14.20/2.29 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))))
% 14.20/2.29 = { by lemma 56 R->L }
% 14.20/2.29 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(inverse(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3))))))))), inverse(Y))))
% 14.20/2.30 = { by lemma 55 R->L }
% 14.20/2.30 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y))))
% 14.20/2.30 = { by lemma 44 R->L }
% 14.20/2.30 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y)), multiply(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y)), inverse(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y)))))))
% 15.02/2.30 = { by lemma 53 R->L }
% 15.02/2.31 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(multiply(Y4, inverse(Y4)), multiply(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y)), multiply(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y)), inverse(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y))))))))
% 15.02/2.31 = { by lemma 38 }
% 15.02/2.31 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(multiply(X4, inverse(inverse(inverse(X4)))), multiply(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y)), multiply(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y)), inverse(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y))))))))
% 15.02/2.32 = { by lemma 34 R->L }
% 15.02/2.32 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(multiply(inverse(inverse(multiply(S3, S3))), inverse(multiply(S3, S3))), multiply(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y)), multiply(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y)), inverse(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y))))))))
% 15.02/2.32 = { by lemma 55 R->L }
% 15.02/2.32 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(inverse(multiply(inverse(multiply(S3, S3)), multiply(S3, S3))), multiply(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y)), multiply(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y)), inverse(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y))))))))
% 15.02/2.32 = { by lemma 57 R->L }
% 15.02/2.33 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(inverse(multiply(inverse(multiply(S3, S3)), multiply(S3, S3))), multiply(inverse(multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), Y)), multiply(multiply(Y2, inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))))))
% 15.02/2.33 = { by lemma 11 R->L }
% 15.02/2.33 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(inverse(multiply(inverse(multiply(T3, T3)), multiply(T3, T3))), multiply(inverse(multiply(Y2, Y)), multiply(Y2, multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))))))
% 15.02/2.33 = { by lemma 55 }
% 15.02/2.33 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(multiply(inverse(inverse(multiply(T3, T3))), inverse(multiply(T3, T3))), multiply(inverse(multiply(Y2, Y)), multiply(Y2, multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))))))
% 15.02/2.34 = { by lemma 34 }
% 15.02/2.34 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(multiply(U3, inverse(inverse(inverse(U3)))), multiply(inverse(multiply(Y2, Y)), multiply(Y2, multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))))))
% 15.02/2.34 = { by lemma 38 R->L }
% 15.02/2.34 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(multiply(V3, inverse(V3)), multiply(inverse(multiply(Y2, Y)), multiply(Y2, multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))))))
% 15.02/2.34 = { by lemma 53 }
% 15.02/2.34 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(inverse(multiply(Y2, Y)), multiply(Y2, multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2))))))
% 15.02/2.34 = { by lemma 55 }
% 15.02/2.35 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(multiply(inverse(Y2), inverse(Y)), multiply(Y2, multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2))))))
% 15.02/2.35 = { by lemma 45 }
% 15.02/2.35 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(multiply(inverse(Y2), inverse(Y)), multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))))
% 15.02/2.35 = { by lemma 54 }
% 15.02/2.35 multiply(multiply(inverse(multiply(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)), inverse(Y))), multiply(inverse(Y), multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), inverse(Y2)))), inverse(multiply(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))), multiply(inverse(Y2), inverse(Y)))))
% 15.02/2.35 = { by lemma 15 }
% 15.02/2.35 multiply(multiply(inverse(multiply(multiply(inverse(Y2), inverse(Y)), multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), multiply(multiply(inverse(Y2), inverse(Y)), multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))), inverse(multiply(multiply(inverse(Y2), inverse(Y)), multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))))
% 15.02/2.35 = { by lemma 34 }
% 15.02/2.35 multiply(multiply(W3, inverse(inverse(inverse(W3)))), inverse(multiply(multiply(inverse(Y2), inverse(Y)), multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))))
% 15.02/2.35 = { by lemma 38 R->L }
% 15.02/2.35 multiply(multiply(Z3, inverse(Z3)), inverse(multiply(multiply(inverse(Y2), inverse(Y)), multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3)))))))))
% 15.02/2.35 = { by lemma 53 }
% 15.02/2.35 inverse(multiply(multiply(inverse(Y2), inverse(Y)), multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3))))))))
% 15.02/2.35 = { by lemma 55 }
% 15.02/2.35 multiply(inverse(multiply(inverse(Y2), inverse(Y))), inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3))))))))
% 15.02/2.35 = { by lemma 55 R->L }
% 15.02/2.35 multiply(inverse(inverse(multiply(Y2, Y))), inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3))))))))
% 15.02/2.35 = { by lemma 39 }
% 15.02/2.35 multiply(multiply(Y2, Y), inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3))))))))
% 15.02/2.35 = { by lemma 54 }
% 15.02/2.35 multiply(inverse(multiply(inverse(multiply(inverse(multiply(U2, T2)), multiply(T2, U2))), multiply(inverse(multiply(S2, X3)), multiply(S2, inverse(multiply(multiply(multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), Y3), inverse(Y3)), inverse(X3))))))), multiply(Y2, Y))
% 15.02/2.35 = { by lemma 6 }
% 15.02/2.35 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), multiply(Y2, Y))
% 15.02/2.35 = { by lemma 39 R->L }
% 15.02/2.35 multiply(multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Y2)), inverse(inverse(multiply(Y2, Y))))
% 15.02/2.35 = { by lemma 56 R->L }
% 15.02/2.35 multiply(inverse(multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T)))))))))), inverse(inverse(multiply(Y2, Y))))
% 15.02/2.35 = { by lemma 55 R->L }
% 15.02/2.35 inverse(multiply(multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))), inverse(multiply(Y2, Y))))
% 15.02/2.36 = { by lemma 53 R->L }
% 15.02/2.36 multiply(multiply(V2, inverse(V2)), inverse(multiply(multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))), inverse(multiply(Y2, Y)))))
% 15.02/2.36 = { by lemma 38 }
% 15.02/2.36 multiply(multiply(W2, inverse(inverse(inverse(W2)))), inverse(multiply(multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))), inverse(multiply(Y2, Y)))))
% 15.02/2.36 = { by lemma 34 R->L }
% 15.02/2.36 multiply(multiply(inverse(Z2), Z2), inverse(multiply(multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))), inverse(multiply(Y2, Y)))))
% 15.02/2.36 = { by lemma 20 }
% 15.02/2.36 multiply(multiply(inverse(multiply(multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))), inverse(multiply(Y2, Y)))), multiply(inverse(multiply(Y2, Y)), multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))))), inverse(multiply(inverse(multiply(Y2, Y)), multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))))))
% 15.02/2.36 = { by lemma 39 R->L }
% 15.02/2.36 multiply(inverse(inverse(multiply(inverse(multiply(multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))), inverse(multiply(Y2, Y)))), multiply(inverse(multiply(Y2, Y)), multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))))))), inverse(multiply(inverse(multiply(Y2, Y)), multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))))))
% 15.02/2.36 = { by lemma 55 R->L }
% 15.02/2.36 inverse(multiply(inverse(multiply(inverse(multiply(multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))), inverse(multiply(Y2, Y)))), multiply(inverse(multiply(Y2, Y)), multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T)))))))))))), multiply(inverse(multiply(Y2, Y)), multiply(Y2, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))))))
% 15.02/2.36 = { by lemma 10 }
% 15.02/2.36 inverse(multiply(inverse(multiply(inverse(multiply(multiply(X2, inverse(S)), multiply(S, inverse(X2)))), multiply(multiply(S, inverse(X2)), multiply(X2, inverse(S))))), multiply(inverse(multiply(Z, Y)), multiply(Z, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))))))
% 15.02/2.36 = { by lemma 57 }
% 15.02/2.36 inverse(multiply(inverse(multiply(inverse(multiply(multiply(X2, inverse(S)), multiply(S, inverse(X2)))), multiply(inverse(multiply(multiply(X2, inverse(S)), multiply(S, inverse(X2)))), inverse(inverse(multiply(multiply(X2, inverse(S)), multiply(S, inverse(X2)))))))), multiply(inverse(multiply(Z, Y)), multiply(Z, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))))))
% 15.02/2.36 = { by lemma 55 }
% 15.02/2.36 multiply(inverse(inverse(multiply(inverse(multiply(multiply(X2, inverse(S)), multiply(S, inverse(X2)))), multiply(inverse(multiply(multiply(X2, inverse(S)), multiply(S, inverse(X2)))), inverse(inverse(multiply(multiply(X2, inverse(S)), multiply(S, inverse(X2))))))))), inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))))))
% 15.02/2.36 = { by lemma 39 }
% 15.02/2.36 multiply(multiply(inverse(multiply(multiply(X2, inverse(S)), multiply(S, inverse(X2)))), multiply(inverse(multiply(multiply(X2, inverse(S)), multiply(S, inverse(X2)))), inverse(inverse(multiply(multiply(X2, inverse(S)), multiply(S, inverse(X2))))))), inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))))))
% 15.02/2.36 = { by lemma 44 }
% 15.02/2.36 multiply(inverse(multiply(multiply(X2, inverse(S)), multiply(S, inverse(X2)))), inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))))))
% 15.02/2.36 = { by lemma 55 }
% 15.02/2.36 multiply(multiply(inverse(multiply(X2, inverse(S))), inverse(multiply(S, inverse(X2)))), inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))))))
% 15.02/2.36 = { by lemma 56 }
% 15.02/2.36 multiply(multiply(multiply(S, inverse(X2)), inverse(multiply(S, inverse(X2)))), inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))))))))
% 15.02/2.36 = { by lemma 53 }
% 15.02/2.36 inverse(multiply(inverse(multiply(Z, Y)), multiply(Z, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T)))))))))))
% 15.02/2.36 = { by lemma 55 }
% 15.02/2.36 multiply(inverse(inverse(multiply(Z, Y))), inverse(multiply(Z, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T)))))))))))
% 15.02/2.36 = { by lemma 39 }
% 15.02/2.36 multiply(multiply(Z, Y), inverse(multiply(Z, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T)))))))))))
% 15.02/2.36 = { by lemma 54 }
% 15.02/2.36 multiply(multiply(Y, Z), inverse(multiply(Z, inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T)))))))))))
% 15.02/2.36 = { by lemma 55 }
% 15.02/2.36 multiply(multiply(Y, Z), multiply(inverse(Z), inverse(inverse(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T)))))))))))
% 15.02/2.36 = { by lemma 39 }
% 15.02/2.36 multiply(multiply(Y, Z), multiply(inverse(Z), inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T)))))))))
% 15.02/2.36 = { by lemma 54 }
% 15.02/2.36 multiply(multiply(Y, Z), multiply(inverse(multiply(inverse(multiply(inverse(multiply(W, V)), multiply(V, W))), multiply(inverse(multiply(U, T)), multiply(U, inverse(multiply(multiply(X, inverse(inverse(Z))), inverse(T))))))), inverse(Z)))
% 15.02/2.36 = { by axiom 1 (single_axiom) }
% 15.02/2.36 multiply(multiply(Y, Z), X)
% 15.02/2.36 = { by lemma 54 }
% 15.02/2.36 multiply(X, multiply(Y, Z))
% 15.02/2.36
% 15.02/2.36 Goal 1 (prove_these_axioms): tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4)) = tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4)).
% 15.02/2.36 Proof:
% 15.02/2.36 tuple(multiply(multiply(inverse(b2), b2), a2), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 15.02/2.36 = { by lemma 54 }
% 15.02/2.36 tuple(multiply(a2, multiply(inverse(b2), b2)), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 15.02/2.36 = { by lemma 54 }
% 15.02/2.36 tuple(multiply(a2, multiply(b2, inverse(b2))), multiply(multiply(a3, b3), c3), multiply(inverse(a1), a1), multiply(a4, b4))
% 15.02/2.36 = { by lemma 54 }
% 15.02/2.36 tuple(multiply(a2, multiply(b2, inverse(b2))), multiply(c3, multiply(a3, b3)), multiply(inverse(a1), a1), multiply(a4, b4))
% 15.02/2.36 = { by lemma 54 }
% 15.02/2.36 tuple(multiply(a2, multiply(b2, inverse(b2))), multiply(c3, multiply(a3, b3)), multiply(a1, inverse(a1)), multiply(a4, b4))
% 15.02/2.36 = { by lemma 58 R->L }
% 15.02/2.36 tuple(multiply(b2, multiply(a2, inverse(b2))), multiply(c3, multiply(a3, b3)), multiply(a1, inverse(a1)), multiply(a4, b4))
% 15.02/2.37 = { by lemma 45 }
% 15.02/2.37 tuple(a2, multiply(c3, multiply(a3, b3)), multiply(a1, inverse(a1)), multiply(a4, b4))
% 15.02/2.37 = { by lemma 58 R->L }
% 15.02/2.37 tuple(a2, multiply(a3, multiply(c3, b3)), multiply(a1, inverse(a1)), multiply(a4, b4))
% 15.02/2.37 = { by lemma 54 }
% 15.02/2.37 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(a1, inverse(a1)), multiply(a4, b4))
% 15.02/2.37 = { by lemma 39 R->L }
% 15.02/2.37 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(inverse(a1)), inverse(a1)), multiply(a4, b4))
% 15.02/2.37 = { by lemma 19 R->L }
% 15.02/2.37 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(inverse(b1)), inverse(b1)), multiply(a4, b4))
% 15.02/2.37 = { by lemma 39 }
% 15.02/2.37 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(b1, inverse(b1)), multiply(a4, b4))
% 15.02/2.37 = { by lemma 54 R->L }
% 15.02/2.37 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(b1, inverse(b1)), multiply(b4, a4))
% 15.02/2.37 = { by lemma 54 R->L }
% 15.02/2.37 tuple(a2, multiply(a3, multiply(b3, c3)), multiply(inverse(b1), b1), multiply(b4, a4))
% 15.02/2.37 % SZS output end Proof
% 15.02/2.37
% 15.02/2.37 RESULT: Unsatisfiable (the axioms are contradictory).
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