TSTP Solution File: GRP470-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP470-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:18:34 EDT 2023
% Result : Unsatisfiable 0.21s 0.51s
% Output : Proof 1.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP470-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.35 % Computer : n009.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon Aug 28 19:43:35 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.21/0.51 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.51
% 0.21/0.51 % SZS status Unsatisfiable
% 0.21/0.51
% 0.21/0.58 % SZS output start Proof
% 0.21/0.58 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.21/0.58 Axiom 2 (single_axiom): divide(inverse(divide(X, divide(Y, divide(Z, W)))), divide(divide(W, Z), X)) = Y.
% 0.21/0.58
% 0.21/0.58 Lemma 3: divide(inverse(divide(X, divide(Y, multiply(inverse(Z), W)))), divide(multiply(inverse(W), Z), X)) = Y.
% 0.21/0.58 Proof:
% 0.21/0.58 divide(inverse(divide(X, divide(Y, multiply(inverse(Z), W)))), divide(multiply(inverse(W), Z), X))
% 0.21/0.58 = { by axiom 1 (multiply) }
% 0.21/0.58 divide(inverse(divide(X, divide(Y, multiply(inverse(Z), W)))), divide(divide(inverse(W), inverse(Z)), X))
% 0.21/0.58 = { by axiom 1 (multiply) }
% 0.21/0.58 divide(inverse(divide(X, divide(Y, divide(inverse(Z), inverse(W))))), divide(divide(inverse(W), inverse(Z)), X))
% 0.21/0.58 = { by axiom 2 (single_axiom) }
% 0.21/0.58 Y
% 0.21/0.58
% 0.21/0.58 Lemma 4: divide(inverse(X), multiply(multiply(inverse(Y), Z), divide(multiply(inverse(Z), Y), divide(X, divide(W, V))))) = divide(V, W).
% 0.21/0.58 Proof:
% 0.21/0.58 divide(inverse(X), multiply(multiply(inverse(Y), Z), divide(multiply(inverse(Z), Y), divide(X, divide(W, V)))))
% 0.21/0.58 = { by axiom 1 (multiply) }
% 0.21/0.58 divide(inverse(X), divide(multiply(inverse(Y), Z), inverse(divide(multiply(inverse(Z), Y), divide(X, divide(W, V))))))
% 0.21/0.58 = { by axiom 2 (single_axiom) R->L }
% 0.21/0.58 divide(inverse(divide(inverse(divide(multiply(inverse(Z), Y), divide(X, divide(W, V)))), divide(divide(V, W), multiply(inverse(Z), Y)))), divide(multiply(inverse(Y), Z), inverse(divide(multiply(inverse(Z), Y), divide(X, divide(W, V))))))
% 0.21/0.58 = { by lemma 3 }
% 0.21/0.58 divide(V, W)
% 0.21/0.58
% 0.21/0.58 Lemma 5: divide(inverse(divide(X, Y)), divide(divide(Z, multiply(inverse(W), V)), X)) = inverse(divide(Z, divide(Y, multiply(inverse(V), W)))).
% 0.21/0.58 Proof:
% 0.21/0.58 divide(inverse(divide(X, Y)), divide(divide(Z, multiply(inverse(W), V)), X))
% 0.21/0.58 = { by lemma 3 R->L }
% 0.21/0.58 divide(inverse(divide(X, divide(inverse(divide(Z, divide(Y, multiply(inverse(V), W)))), divide(multiply(inverse(W), V), Z)))), divide(divide(Z, multiply(inverse(W), V)), X))
% 0.21/0.58 = { by axiom 2 (single_axiom) }
% 0.21/0.58 inverse(divide(Z, divide(Y, multiply(inverse(V), W))))
% 0.21/0.58
% 0.21/0.58 Lemma 6: inverse(divide(X, divide(divide(Y, divide(multiply(inverse(Z), W), X)), multiply(inverse(W), Z)))) = Y.
% 0.21/0.58 Proof:
% 0.21/0.58 inverse(divide(X, divide(divide(Y, divide(multiply(inverse(Z), W), X)), multiply(inverse(W), Z))))
% 0.21/0.58 = { by lemma 5 R->L }
% 0.21/0.58 divide(inverse(divide(V, divide(Y, divide(multiply(inverse(Z), W), X)))), divide(divide(X, multiply(inverse(Z), W)), V))
% 0.21/0.58 = { by axiom 2 (single_axiom) }
% 0.21/0.58 Y
% 0.21/0.58
% 0.21/0.58 Lemma 7: inverse(divide(inverse(X), divide(divide(Y, multiply(multiply(inverse(Z), W), X)), multiply(inverse(W), Z)))) = Y.
% 0.21/0.58 Proof:
% 0.21/0.58 inverse(divide(inverse(X), divide(divide(Y, multiply(multiply(inverse(Z), W), X)), multiply(inverse(W), Z))))
% 0.21/0.58 = { by axiom 1 (multiply) }
% 0.21/0.58 inverse(divide(inverse(X), divide(divide(Y, divide(multiply(inverse(Z), W), inverse(X))), multiply(inverse(W), Z))))
% 0.21/0.58 = { by lemma 6 }
% 0.21/0.58 Y
% 0.21/0.58
% 0.21/0.58 Lemma 8: multiply(X, divide(inverse(Y), divide(divide(Z, multiply(multiply(inverse(W), V), Y)), multiply(inverse(V), W)))) = divide(X, Z).
% 0.21/0.58 Proof:
% 0.21/0.58 multiply(X, divide(inverse(Y), divide(divide(Z, multiply(multiply(inverse(W), V), Y)), multiply(inverse(V), W))))
% 0.21/0.58 = { by axiom 1 (multiply) }
% 0.21/0.58 divide(X, inverse(divide(inverse(Y), divide(divide(Z, multiply(multiply(inverse(W), V), Y)), multiply(inverse(V), W)))))
% 0.21/0.58 = { by lemma 7 }
% 0.21/0.58 divide(X, Z)
% 0.21/0.58
% 0.21/0.58 Lemma 9: divide(inverse(divide(inverse(X), divide(Y, multiply(inverse(Z), W)))), multiply(multiply(inverse(W), Z), X)) = Y.
% 0.21/0.58 Proof:
% 0.21/0.59 divide(inverse(divide(inverse(X), divide(Y, multiply(inverse(Z), W)))), multiply(multiply(inverse(W), Z), X))
% 0.21/0.59 = { by axiom 1 (multiply) }
% 0.21/0.59 divide(inverse(divide(inverse(X), divide(Y, multiply(inverse(Z), W)))), divide(multiply(inverse(W), Z), inverse(X)))
% 0.21/0.59 = { by lemma 3 }
% 0.21/0.59 Y
% 0.21/0.59
% 0.21/0.59 Lemma 10: divide(inverse(divide(X, Y)), divide(divide(Z, divide(W, V)), X)) = inverse(divide(Z, divide(Y, divide(V, W)))).
% 0.21/0.59 Proof:
% 0.21/0.59 divide(inverse(divide(X, Y)), divide(divide(Z, divide(W, V)), X))
% 0.21/0.59 = { by axiom 2 (single_axiom) R->L }
% 0.21/0.59 divide(inverse(divide(X, divide(inverse(divide(Z, divide(Y, divide(V, W)))), divide(divide(W, V), Z)))), divide(divide(Z, divide(W, V)), X))
% 0.21/0.59 = { by axiom 2 (single_axiom) }
% 0.21/0.59 inverse(divide(Z, divide(Y, divide(V, W))))
% 0.21/0.59
% 0.21/0.59 Lemma 11: divide(inverse(divide(X, Y)), divide(divide(Z, multiply(W, V)), X)) = inverse(divide(Z, divide(Y, divide(inverse(V), W)))).
% 0.21/0.59 Proof:
% 0.21/0.59 divide(inverse(divide(X, Y)), divide(divide(Z, multiply(W, V)), X))
% 0.21/0.59 = { by axiom 1 (multiply) }
% 0.21/0.59 divide(inverse(divide(X, Y)), divide(divide(Z, divide(W, inverse(V))), X))
% 0.21/0.59 = { by lemma 10 }
% 0.21/0.59 inverse(divide(Z, divide(Y, divide(inverse(V), W))))
% 0.21/0.59
% 0.21/0.59 Lemma 12: divide(inverse(multiply(W, Y)), divide(Z, W)) = divide(inverse(multiply(X, Y)), divide(Z, X)).
% 0.21/0.59 Proof:
% 0.21/0.59 divide(inverse(multiply(W, Y)), divide(Z, W))
% 0.21/0.59 = { by lemma 9 R->L }
% 0.21/0.59 divide(inverse(multiply(W, Y)), divide(divide(inverse(divide(inverse(V), divide(Z, multiply(inverse(U), T)))), multiply(multiply(inverse(T), U), V)), W))
% 0.21/0.59 = { by axiom 1 (multiply) }
% 0.21/0.59 divide(inverse(divide(W, inverse(Y))), divide(divide(inverse(divide(inverse(V), divide(Z, multiply(inverse(U), T)))), multiply(multiply(inverse(T), U), V)), W))
% 0.21/0.59 = { by lemma 11 }
% 0.21/0.59 inverse(divide(inverse(divide(inverse(V), divide(Z, multiply(inverse(U), T)))), divide(inverse(Y), divide(inverse(V), multiply(inverse(T), U)))))
% 0.21/0.59 = { by lemma 11 R->L }
% 0.21/0.59 divide(inverse(divide(X, inverse(Y))), divide(divide(inverse(divide(inverse(V), divide(Z, multiply(inverse(U), T)))), multiply(multiply(inverse(T), U), V)), X))
% 0.21/0.59 = { by axiom 1 (multiply) R->L }
% 0.21/0.59 divide(inverse(multiply(X, Y)), divide(divide(inverse(divide(inverse(V), divide(Z, multiply(inverse(U), T)))), multiply(multiply(inverse(T), U), V)), X))
% 0.21/0.59 = { by lemma 9 }
% 0.21/0.59 divide(inverse(multiply(X, Y)), divide(Z, X))
% 0.21/0.59
% 0.21/0.59 Lemma 13: divide(inverse(multiply(inverse(X), Y)), multiply(Z, X)) = divide(inverse(multiply(W, Y)), divide(Z, W)).
% 0.21/0.59 Proof:
% 0.21/0.59 divide(inverse(multiply(inverse(X), Y)), multiply(Z, X))
% 0.21/0.59 = { by axiom 1 (multiply) }
% 0.21/0.59 divide(inverse(multiply(inverse(X), Y)), divide(Z, inverse(X)))
% 0.21/0.59 = { by lemma 12 R->L }
% 0.21/0.59 divide(inverse(multiply(W, Y)), divide(Z, W))
% 0.21/0.59
% 0.21/0.59 Lemma 14: divide(inverse(divide(inverse(W), Y)), multiply(Z, W)) = divide(inverse(divide(X, Y)), divide(Z, X)).
% 0.21/0.59 Proof:
% 0.21/0.59 divide(inverse(divide(inverse(W), Y)), multiply(Z, W))
% 0.21/0.59 = { by lemma 8 R->L }
% 0.21/0.59 divide(inverse(multiply(inverse(W), divide(inverse(V), divide(divide(Y, multiply(multiply(inverse(U), T), V)), multiply(inverse(T), U))))), multiply(Z, W))
% 0.21/0.59 = { by lemma 13 }
% 0.21/0.59 divide(inverse(multiply(X, divide(inverse(V), divide(divide(Y, multiply(multiply(inverse(U), T), V)), multiply(inverse(T), U))))), divide(Z, X))
% 0.21/0.59 = { by lemma 8 }
% 0.21/0.59 divide(inverse(divide(X, Y)), divide(Z, X))
% 0.21/0.59
% 0.21/0.59 Lemma 15: multiply(multiply(X, W), divide(inverse(W), Z)) = multiply(divide(X, Y), divide(Y, Z)).
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(multiply(X, W), divide(inverse(W), Z))
% 0.21/0.59 = { by axiom 1 (multiply) }
% 0.21/0.59 divide(multiply(X, W), inverse(divide(inverse(W), Z)))
% 0.21/0.59 = { by lemma 4 R->L }
% 0.21/0.59 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(inverse(divide(inverse(W), Z)), multiply(X, W))))))
% 0.21/0.59 = { by lemma 14 }
% 0.21/0.59 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(inverse(divide(Y, Z)), divide(X, Y))))))
% 0.21/0.59 = { by lemma 4 }
% 0.21/0.59 divide(divide(X, Y), inverse(divide(Y, Z)))
% 0.21/0.59 = { by axiom 1 (multiply) R->L }
% 0.21/0.59 multiply(divide(X, Y), divide(Y, Z))
% 0.21/0.59
% 0.21/0.59 Lemma 16: multiply(multiply(multiply(inverse(V), U), T), divide(inverse(T), divide(W, multiply(inverse(U), V)))) = divide(inverse(X), multiply(multiply(inverse(Y), Z), divide(multiply(inverse(Z), Y), divide(X, W)))).
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(multiply(multiply(inverse(V), U), T), divide(inverse(T), divide(W, multiply(inverse(U), V))))
% 0.21/0.59 = { by lemma 15 }
% 0.21/0.59 multiply(divide(multiply(inverse(V), U), S), divide(S, divide(W, multiply(inverse(U), V))))
% 0.21/0.59 = { by axiom 1 (multiply) }
% 0.21/0.59 divide(divide(multiply(inverse(V), U), S), inverse(divide(S, divide(W, multiply(inverse(U), V)))))
% 0.21/0.59 = { by lemma 4 R->L }
% 0.21/0.59 divide(inverse(X), multiply(multiply(inverse(Y), Z), divide(multiply(inverse(Z), Y), divide(X, divide(inverse(divide(S, divide(W, multiply(inverse(U), V)))), divide(multiply(inverse(V), U), S))))))
% 0.21/0.59 = { by lemma 3 }
% 0.21/0.59 divide(inverse(X), multiply(multiply(inverse(Y), Z), divide(multiply(inverse(Z), Y), divide(X, W))))
% 0.21/0.59
% 0.21/0.59 Lemma 17: multiply(multiply(multiply(inverse(X), Y), Z), divide(inverse(Z), divide(divide(W, V), multiply(inverse(Y), X)))) = divide(V, W).
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(multiply(multiply(inverse(X), Y), Z), divide(inverse(Z), divide(divide(W, V), multiply(inverse(Y), X))))
% 0.21/0.59 = { by lemma 16 }
% 0.21/0.59 divide(inverse(U), multiply(multiply(inverse(T), S), divide(multiply(inverse(S), T), divide(U, divide(W, V)))))
% 0.21/0.59 = { by lemma 4 }
% 0.21/0.59 divide(V, W)
% 0.21/0.59
% 0.21/0.59 Lemma 18: multiply(multiply(multiply(inverse(X), Y), Z), divide(inverse(Z), divide(multiply(W, V), multiply(inverse(Y), X)))) = divide(inverse(V), W).
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(multiply(multiply(inverse(X), Y), Z), divide(inverse(Z), divide(multiply(W, V), multiply(inverse(Y), X))))
% 0.21/0.59 = { by axiom 1 (multiply) }
% 0.21/0.59 multiply(multiply(multiply(inverse(X), Y), Z), divide(inverse(Z), divide(divide(W, inverse(V)), multiply(inverse(Y), X))))
% 0.21/0.59 = { by lemma 17 }
% 0.21/0.59 divide(inverse(V), W)
% 0.21/0.59
% 0.21/0.59 Lemma 19: divide(inverse(X), multiply(multiply(inverse(Y), Z), divide(multiply(inverse(Z), Y), divide(X, multiply(inverse(W), V))))) = multiply(inverse(V), W).
% 0.21/0.59 Proof:
% 0.21/0.59 divide(inverse(X), multiply(multiply(inverse(Y), Z), divide(multiply(inverse(Z), Y), divide(X, multiply(inverse(W), V)))))
% 0.21/0.59 = { by axiom 1 (multiply) }
% 0.21/0.59 divide(inverse(X), divide(multiply(inverse(Y), Z), inverse(divide(multiply(inverse(Z), Y), divide(X, multiply(inverse(W), V))))))
% 0.21/0.59 = { by lemma 3 R->L }
% 0.21/0.59 divide(inverse(divide(inverse(divide(multiply(inverse(Z), Y), divide(X, multiply(inverse(W), V)))), divide(multiply(inverse(V), W), multiply(inverse(Z), Y)))), divide(multiply(inverse(Y), Z), inverse(divide(multiply(inverse(Z), Y), divide(X, multiply(inverse(W), V))))))
% 0.21/0.59 = { by lemma 3 }
% 0.21/0.59 multiply(inverse(V), W)
% 0.21/0.59
% 0.21/0.59 Lemma 20: multiply(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, multiply(inverse(W), V)))), Z) = multiply(inverse(W), V).
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, multiply(inverse(W), V)))), Z)
% 0.21/0.59 = { by axiom 1 (multiply) }
% 0.21/0.59 divide(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, multiply(inverse(W), V)))), inverse(Z))
% 0.21/0.59 = { by lemma 4 R->L }
% 0.21/0.59 divide(inverse(U), multiply(multiply(inverse(T), S), divide(multiply(inverse(S), T), divide(U, divide(inverse(Z), multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(Z, multiply(inverse(W), V)))))))))
% 0.21/0.59 = { by lemma 19 }
% 0.21/0.59 divide(inverse(U), multiply(multiply(inverse(T), S), divide(multiply(inverse(S), T), divide(U, multiply(inverse(V), W)))))
% 0.21/0.59 = { by lemma 19 }
% 0.21/0.59 multiply(inverse(W), V)
% 0.21/0.59
% 0.21/0.59 Lemma 21: multiply(X, divide(Y, divide(divide(Z, divide(multiply(inverse(W), V), Y)), multiply(inverse(V), W)))) = divide(X, Z).
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(X, divide(Y, divide(divide(Z, divide(multiply(inverse(W), V), Y)), multiply(inverse(V), W))))
% 0.21/0.59 = { by axiom 1 (multiply) }
% 0.21/0.59 divide(X, inverse(divide(Y, divide(divide(Z, divide(multiply(inverse(W), V), Y)), multiply(inverse(V), W)))))
% 0.21/0.59 = { by lemma 6 }
% 0.21/0.59 divide(X, Z)
% 0.21/0.59
% 0.21/0.59 Lemma 22: multiply(multiply(X, divide(Y, divide(Z, multiply(inverse(W), V)))), Z) = multiply(divide(X, U), divide(U, divide(multiply(inverse(V), W), Y))).
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(multiply(X, divide(Y, divide(Z, multiply(inverse(W), V)))), Z)
% 0.21/0.59 = { by axiom 1 (multiply) }
% 0.21/0.59 multiply(divide(X, inverse(divide(Y, divide(Z, multiply(inverse(W), V))))), Z)
% 0.21/0.59 = { by lemma 3 R->L }
% 0.21/0.59 multiply(divide(X, inverse(divide(Y, divide(Z, multiply(inverse(W), V))))), divide(inverse(divide(Y, divide(Z, multiply(inverse(W), V)))), divide(multiply(inverse(V), W), Y)))
% 0.21/0.59 = { by axiom 1 (multiply) }
% 0.21/0.59 divide(divide(X, inverse(divide(Y, divide(Z, multiply(inverse(W), V))))), inverse(divide(inverse(divide(Y, divide(Z, multiply(inverse(W), V)))), divide(multiply(inverse(V), W), Y))))
% 0.21/0.59 = { by lemma 4 R->L }
% 0.21/0.59 divide(inverse(T), multiply(multiply(inverse(S), X2), divide(multiply(inverse(X2), S), divide(T, divide(inverse(divide(inverse(divide(Y, divide(Z, multiply(inverse(W), V)))), divide(multiply(inverse(V), W), Y))), divide(X, inverse(divide(Y, divide(Z, multiply(inverse(W), V))))))))))
% 0.21/0.59 = { by lemma 21 R->L }
% 0.21/0.59 divide(inverse(T), multiply(multiply(inverse(S), X2), divide(multiply(inverse(X2), S), divide(T, divide(inverse(multiply(inverse(divide(Y, divide(Z, multiply(inverse(W), V)))), divide(Y2, divide(divide(divide(multiply(inverse(V), W), Y), divide(multiply(inverse(Z2), W2), Y2)), multiply(inverse(W2), Z2))))), divide(X, inverse(divide(Y, divide(Z, multiply(inverse(W), V))))))))))
% 0.21/0.59 = { by lemma 12 R->L }
% 0.21/0.59 divide(inverse(T), multiply(multiply(inverse(S), X2), divide(multiply(inverse(X2), S), divide(T, divide(inverse(multiply(U, divide(Y2, divide(divide(divide(multiply(inverse(V), W), Y), divide(multiply(inverse(Z2), W2), Y2)), multiply(inverse(W2), Z2))))), divide(X, U))))))
% 0.21/0.59 = { by lemma 21 }
% 0.21/0.59 divide(inverse(T), multiply(multiply(inverse(S), X2), divide(multiply(inverse(X2), S), divide(T, divide(inverse(divide(U, divide(multiply(inverse(V), W), Y))), divide(X, U))))))
% 0.21/0.59 = { by lemma 4 }
% 0.21/0.59 divide(divide(X, U), inverse(divide(U, divide(multiply(inverse(V), W), Y))))
% 0.21/0.59 = { by axiom 1 (multiply) R->L }
% 0.21/0.59 multiply(divide(X, U), divide(U, divide(multiply(inverse(V), W), Y)))
% 0.21/0.59
% 0.21/0.59 Lemma 23: multiply(multiply(inverse(Z), W), multiply(inverse(W), Z)) = multiply(divide(X, Y), divide(Y, X)).
% 0.21/0.59 Proof:
% 0.21/0.59 multiply(multiply(inverse(Z), W), multiply(inverse(W), Z))
% 0.21/0.59 = { by lemma 20 R->L }
% 0.21/0.59 multiply(multiply(multiply(multiply(inverse(V), U), divide(multiply(inverse(U), V), divide(divide(X2, divide(multiply(inverse(W), Z), multiply(inverse(U), V))), multiply(inverse(Z), W)))), divide(X2, divide(multiply(inverse(W), Z), multiply(inverse(U), V)))), multiply(inverse(W), Z))
% 0.21/0.59 = { by lemma 21 }
% 0.21/0.59 multiply(multiply(divide(multiply(inverse(V), U), X2), divide(X2, divide(multiply(inverse(W), Z), multiply(inverse(U), V)))), multiply(inverse(W), Z))
% 0.21/0.59 = { by lemma 15 R->L }
% 0.21/0.59 multiply(multiply(multiply(multiply(inverse(V), U), T), divide(inverse(T), divide(multiply(inverse(W), Z), multiply(inverse(U), V)))), multiply(inverse(W), Z))
% 0.21/0.59 = { by lemma 22 }
% 0.21/0.59 multiply(divide(multiply(multiply(inverse(V), U), T), S), divide(S, divide(multiply(inverse(V), U), inverse(T))))
% 0.21/0.59 = { by lemma 22 R->L }
% 0.21/0.59 multiply(multiply(multiply(multiply(inverse(V), U), T), divide(inverse(T), divide(divide(Y, X), multiply(inverse(U), V)))), divide(Y, X))
% 0.21/0.59 = { by lemma 17 }
% 0.21/0.59 multiply(divide(X, Y), divide(Y, X))
% 0.21/0.59
% 0.21/0.59 Lemma 24: divide(inverse(multiply(inverse(Z), W)), multiply(inverse(W), Z)) = divide(inverse(divide(inverse(X), Y)), multiply(Y, X)).
% 0.21/0.59 Proof:
% 0.21/0.59 divide(inverse(multiply(inverse(Z), W)), multiply(inverse(W), Z))
% 0.21/0.59 = { by lemma 18 R->L }
% 0.21/0.59 multiply(multiply(multiply(inverse(V), U), T), divide(inverse(T), divide(multiply(multiply(inverse(W), Z), multiply(inverse(Z), W)), multiply(inverse(U), V))))
% 0.21/0.59 = { by lemma 23 }
% 0.21/0.59 multiply(multiply(multiply(inverse(V), U), T), divide(inverse(T), divide(multiply(divide(Y, S), divide(S, Y)), multiply(inverse(U), V))))
% 0.21/0.59 = { by lemma 15 R->L }
% 0.21/0.59 multiply(multiply(multiply(inverse(V), U), T), divide(inverse(T), divide(multiply(multiply(Y, X), divide(inverse(X), Y)), multiply(inverse(U), V))))
% 0.21/0.59 = { by lemma 18 }
% 0.21/0.60 divide(inverse(divide(inverse(X), Y)), multiply(Y, X))
% 0.21/0.60
% 0.21/0.60 Lemma 25: divide(divide(X, multiply(divide(inverse(Y), multiply(inverse(Z), W)), V)), multiply(multiply(inverse(Z), W), Y)) = divide(divide(X, multiply(multiply(inverse(U), T), V)), multiply(inverse(T), U)).
% 0.21/0.60 Proof:
% 0.21/0.60 divide(divide(X, multiply(divide(inverse(Y), multiply(inverse(Z), W)), V)), multiply(multiply(inverse(Z), W), Y))
% 0.21/0.60 = { by axiom 1 (multiply) }
% 0.21/0.60 divide(divide(X, divide(divide(inverse(Y), multiply(inverse(Z), W)), inverse(V))), multiply(multiply(inverse(Z), W), Y))
% 0.21/0.60 = { by lemma 7 R->L }
% 0.21/0.60 divide(divide(inverse(divide(inverse(V), divide(divide(X, multiply(multiply(inverse(U), T), V)), multiply(inverse(T), U)))), divide(divide(inverse(Y), multiply(inverse(Z), W)), inverse(V))), multiply(multiply(inverse(Z), W), Y))
% 0.21/0.60 = { by lemma 5 }
% 0.21/0.60 divide(inverse(divide(inverse(Y), divide(divide(divide(X, multiply(multiply(inverse(U), T), V)), multiply(inverse(T), U)), multiply(inverse(W), Z)))), multiply(multiply(inverse(Z), W), Y))
% 0.21/0.60 = { by lemma 9 }
% 0.21/0.60 divide(divide(X, multiply(multiply(inverse(U), T), V)), multiply(inverse(T), U))
% 0.21/0.60
% 0.21/0.60 Lemma 26: divide(divide(inverse(multiply(inverse(X), Y)), multiply(inverse(Y), X)), multiply(inverse(Z), W)) = multiply(inverse(W), Z).
% 0.21/0.60 Proof:
% 0.21/0.60 divide(divide(inverse(multiply(inverse(X), Y)), multiply(inverse(Y), X)), multiply(inverse(Z), W))
% 0.21/0.60 = { by lemma 24 }
% 0.21/0.60 divide(divide(inverse(divide(inverse(V), multiply(inverse(W), Z))), multiply(multiply(inverse(W), Z), V)), multiply(inverse(Z), W))
% 0.21/0.60 = { by lemma 25 R->L }
% 0.21/0.60 divide(divide(inverse(divide(inverse(V), multiply(inverse(W), Z))), multiply(divide(inverse(U), multiply(inverse(T), S)), V)), multiply(multiply(inverse(T), S), U))
% 0.21/0.60 = { by axiom 1 (multiply) }
% 0.21/0.60 divide(divide(inverse(divide(inverse(V), multiply(inverse(W), Z))), divide(divide(inverse(U), multiply(inverse(T), S)), inverse(V))), multiply(multiply(inverse(T), S), U))
% 0.21/0.60 = { by lemma 5 }
% 0.21/0.60 divide(inverse(divide(inverse(U), divide(multiply(inverse(W), Z), multiply(inverse(S), T)))), multiply(multiply(inverse(T), S), U))
% 0.21/0.60 = { by lemma 9 }
% 0.21/0.60 multiply(inverse(W), Z)
% 0.21/0.60
% 0.21/0.60 Lemma 27: divide(multiply(inverse(X), Y), divide(inverse(multiply(inverse(Z), W)), multiply(inverse(W), Z))) = multiply(inverse(X), Y).
% 0.21/0.60 Proof:
% 0.21/0.60 divide(multiply(inverse(X), Y), divide(inverse(multiply(inverse(Z), W)), multiply(inverse(W), Z)))
% 0.21/0.60 = { by lemma 4 R->L }
% 0.21/0.60 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, divide(divide(inverse(multiply(inverse(Z), W)), multiply(inverse(W), Z)), multiply(inverse(X), Y))))))
% 0.21/0.60 = { by lemma 26 }
% 0.21/0.60 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, multiply(inverse(Y), X)))))
% 0.21/0.60 = { by lemma 19 }
% 0.21/0.60 multiply(inverse(X), Y)
% 0.21/0.60
% 0.21/0.60 Lemma 28: inverse(divide(inverse(multiply(inverse(X), Y)), divide(Z, multiply(inverse(X), Y)))) = divide(inverse(divide(multiply(inverse(W), V), Z)), multiply(inverse(V), W)).
% 0.21/0.60 Proof:
% 0.21/0.60 inverse(divide(inverse(multiply(inverse(X), Y)), divide(Z, multiply(inverse(X), Y))))
% 0.21/0.60 = { by lemma 5 R->L }
% 0.21/0.60 divide(inverse(divide(multiply(inverse(W), V), Z)), divide(divide(inverse(multiply(inverse(X), Y)), multiply(inverse(Y), X)), multiply(inverse(W), V)))
% 0.21/0.60 = { by lemma 26 }
% 0.21/0.60 divide(inverse(divide(multiply(inverse(W), V), Z)), multiply(inverse(V), W))
% 0.21/0.60
% 0.21/0.60 Lemma 29: divide(inverse(divide(multiply(inverse(X), Y), multiply(inverse(Z), W))), multiply(inverse(Y), X)) = inverse(inverse(multiply(inverse(Z), W))).
% 0.21/0.60 Proof:
% 0.21/0.60 divide(inverse(divide(multiply(inverse(X), Y), multiply(inverse(Z), W))), multiply(inverse(Y), X))
% 0.21/0.60 = { by lemma 28 R->L }
% 0.21/0.60 inverse(divide(inverse(multiply(inverse(V), U)), divide(multiply(inverse(Z), W), multiply(inverse(V), U))))
% 0.21/0.60 = { by lemma 27 R->L }
% 0.21/0.60 inverse(divide(inverse(divide(multiply(inverse(V), U), divide(inverse(multiply(inverse(Z), W)), multiply(inverse(W), Z)))), divide(multiply(inverse(Z), W), multiply(inverse(V), U))))
% 0.21/0.60 = { by lemma 3 }
% 0.21/0.60 inverse(inverse(multiply(inverse(Z), W)))
% 0.21/0.60
% 0.21/0.60 Lemma 30: inverse(divide(X, divide(divide(X, multiply(inverse(Y), Z)), multiply(inverse(Z), Y)))) = divide(inverse(multiply(inverse(W), V)), multiply(inverse(V), W)).
% 0.21/0.60 Proof:
% 0.21/0.60 inverse(divide(X, divide(divide(X, multiply(inverse(Y), Z)), multiply(inverse(Z), Y))))
% 0.21/0.60 = { by lemma 5 R->L }
% 0.21/0.60 divide(inverse(divide(U, divide(X, multiply(inverse(Y), Z)))), divide(divide(X, multiply(inverse(Y), Z)), U))
% 0.21/0.60 = { by lemma 18 R->L }
% 0.21/0.60 multiply(multiply(multiply(inverse(T), S), X2), divide(inverse(X2), divide(multiply(divide(divide(X, multiply(inverse(Y), Z)), U), divide(U, divide(X, multiply(inverse(Y), Z)))), multiply(inverse(S), T))))
% 0.21/0.60 = { by lemma 23 R->L }
% 0.21/0.60 multiply(multiply(multiply(inverse(T), S), X2), divide(inverse(X2), divide(multiply(multiply(inverse(V), W), multiply(inverse(W), V)), multiply(inverse(S), T))))
% 0.21/0.60 = { by lemma 18 }
% 0.21/0.60 divide(inverse(multiply(inverse(W), V)), multiply(inverse(V), W))
% 0.21/0.60
% 0.21/0.60 Lemma 31: divide(divide(inverse(multiply(inverse(X), Y)), multiply(inverse(Y), X)), divide(multiply(inverse(Z), W), V)) = divide(V, multiply(inverse(Z), W)).
% 0.21/0.60 Proof:
% 0.21/0.60 divide(divide(inverse(multiply(inverse(X), Y)), multiply(inverse(Y), X)), divide(multiply(inverse(Z), W), V))
% 0.21/0.60 = { by lemma 30 R->L }
% 0.21/0.60 divide(inverse(divide(V, divide(divide(V, multiply(inverse(Z), W)), multiply(inverse(W), Z)))), divide(multiply(inverse(Z), W), V))
% 0.21/0.60 = { by lemma 3 }
% 0.21/0.60 divide(V, multiply(inverse(Z), W))
% 0.21/0.60
% 0.21/0.60 Lemma 32: inverse(inverse(multiply(inverse(X), Y))) = multiply(inverse(X), Y).
% 0.21/0.60 Proof:
% 0.21/0.60 inverse(inverse(multiply(inverse(X), Y)))
% 0.21/0.60 = { by lemma 29 R->L }
% 0.21/0.60 divide(inverse(divide(multiply(inverse(Z), W), multiply(inverse(X), Y))), multiply(inverse(W), Z))
% 0.21/0.60 = { by lemma 27 R->L }
% 0.21/0.60 divide(inverse(divide(multiply(inverse(Z), W), multiply(inverse(X), Y))), divide(multiply(inverse(W), Z), divide(inverse(multiply(inverse(V), U)), multiply(inverse(U), V))))
% 0.21/0.60 = { by lemma 31 R->L }
% 0.21/0.60 divide(inverse(divide(divide(inverse(multiply(inverse(V), U)), multiply(inverse(U), V)), divide(multiply(inverse(X), Y), multiply(inverse(Z), W)))), divide(multiply(inverse(W), Z), divide(inverse(multiply(inverse(V), U)), multiply(inverse(U), V))))
% 0.21/0.60 = { by lemma 3 }
% 0.21/0.60 multiply(inverse(X), Y)
% 0.21/0.60
% 0.21/0.60 Lemma 33: multiply(X, inverse(multiply(inverse(Y), Z))) = divide(X, multiply(inverse(Y), Z)).
% 0.21/0.60 Proof:
% 0.21/0.60 multiply(X, inverse(multiply(inverse(Y), Z)))
% 0.21/0.60 = { by axiom 1 (multiply) }
% 0.21/0.60 divide(X, inverse(inverse(multiply(inverse(Y), Z))))
% 0.21/0.60 = { by lemma 32 }
% 0.21/0.60 divide(X, multiply(inverse(Y), Z))
% 0.21/0.60
% 0.21/0.60 Lemma 34: divide(multiply(multiply(inverse(X), Y), multiply(inverse(Y), X)), multiply(inverse(Z), W)) = multiply(inverse(W), Z).
% 0.21/0.60 Proof:
% 0.21/0.60 divide(multiply(multiply(inverse(X), Y), multiply(inverse(Y), X)), multiply(inverse(Z), W))
% 0.21/0.60 = { by lemma 27 R->L }
% 0.21/0.60 divide(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(inverse(multiply(inverse(Z), W)), multiply(inverse(W), Z)))), multiply(inverse(Z), W))
% 0.21/0.60 = { by lemma 33 R->L }
% 0.21/0.60 multiply(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), divide(inverse(multiply(inverse(Z), W)), multiply(inverse(W), Z)))), inverse(multiply(inverse(Z), W)))
% 0.21/0.60 = { by lemma 20 }
% 0.21/0.60 multiply(inverse(W), Z)
% 0.21/0.60
% 0.21/0.60 Lemma 35: divide(inverse(multiply(inverse(X), Y)), multiply(inverse(Y), X)) = multiply(multiply(inverse(Z), W), multiply(inverse(W), Z)).
% 0.21/0.60 Proof:
% 0.21/0.60 divide(inverse(multiply(inverse(X), Y)), multiply(inverse(Y), X))
% 0.21/0.60 = { by lemma 24 }
% 0.21/0.60 divide(inverse(divide(inverse(V), multiply(inverse(U), T))), multiply(multiply(inverse(U), T), V))
% 0.21/0.60 = { by lemma 14 }
% 0.21/0.60 divide(inverse(divide(S, multiply(inverse(U), T))), divide(multiply(inverse(U), T), S))
% 0.21/0.60 = { by lemma 34 R->L }
% 0.21/0.60 divide(inverse(divide(S, divide(multiply(multiply(inverse(Z), W), multiply(inverse(W), Z)), multiply(inverse(T), U)))), divide(multiply(inverse(U), T), S))
% 0.21/0.60 = { by lemma 3 }
% 0.21/0.60 multiply(multiply(inverse(Z), W), multiply(inverse(W), Z))
% 0.21/0.60
% 0.21/0.60 Lemma 36: inverse(divide(inverse(multiply(inverse(X), Y)), multiply(inverse(Y), X))) = divide(inverse(multiply(inverse(Z), W)), multiply(inverse(W), Z)).
% 0.21/0.60 Proof:
% 0.21/0.60 inverse(divide(inverse(multiply(inverse(X), Y)), multiply(inverse(Y), X)))
% 0.21/0.60 = { by lemma 26 R->L }
% 0.21/0.60 inverse(divide(inverse(multiply(inverse(X), Y)), divide(divide(inverse(multiply(inverse(V), U)), multiply(inverse(U), V)), multiply(inverse(X), Y))))
% 0.21/0.60 = { by lemma 28 }
% 0.21/0.60 divide(inverse(divide(multiply(inverse(Z), W), divide(inverse(multiply(inverse(V), U)), multiply(inverse(U), V)))), multiply(inverse(W), Z))
% 0.21/0.60 = { by lemma 27 }
% 0.21/0.60 divide(inverse(multiply(inverse(Z), W)), multiply(inverse(W), Z))
% 0.21/0.60
% 0.21/0.60 Lemma 37: multiply(X, multiply(multiply(inverse(Y), Z), multiply(inverse(Z), Y))) = divide(X, multiply(multiply(inverse(W), V), multiply(inverse(V), W))).
% 0.21/0.60 Proof:
% 0.21/0.60 multiply(X, multiply(multiply(inverse(Y), Z), multiply(inverse(Z), Y)))
% 0.21/0.60 = { by lemma 35 R->L }
% 0.21/0.60 multiply(X, divide(inverse(multiply(inverse(U), T)), multiply(inverse(T), U)))
% 0.21/0.60 = { by axiom 1 (multiply) }
% 0.21/0.60 divide(X, inverse(divide(inverse(multiply(inverse(U), T)), multiply(inverse(T), U))))
% 0.21/0.60 = { by lemma 36 }
% 0.21/0.60 divide(X, divide(inverse(multiply(inverse(S), X2)), multiply(inverse(X2), S)))
% 0.21/0.60 = { by lemma 35 }
% 0.21/0.60 divide(X, multiply(multiply(inverse(W), V), multiply(inverse(V), W)))
% 0.21/0.60
% 0.21/0.60 Lemma 38: inverse(inverse(divide(X, multiply(multiply(inverse(Y), Z), multiply(inverse(Z), Y))))) = X.
% 0.21/0.60 Proof:
% 0.21/0.60 inverse(inverse(divide(X, multiply(multiply(inverse(Y), Z), multiply(inverse(Z), Y)))))
% 0.21/0.60 = { by lemma 35 R->L }
% 0.21/0.60 inverse(inverse(divide(X, divide(inverse(multiply(inverse(W), V)), multiply(inverse(V), W)))))
% 0.21/0.60 = { by lemma 34 R->L }
% 0.21/0.60 inverse(inverse(divide(X, divide(inverse(multiply(inverse(W), V)), divide(multiply(multiply(inverse(U), T), multiply(inverse(T), U)), multiply(inverse(W), V))))))
% 0.21/0.60 = { by lemma 10 R->L }
% 0.21/0.60 inverse(divide(inverse(divide(multiply(inverse(V), W), inverse(multiply(inverse(W), V)))), divide(divide(X, divide(multiply(inverse(W), V), multiply(multiply(inverse(U), T), multiply(inverse(T), U)))), multiply(inverse(V), W))))
% 0.21/0.60 = { by axiom 1 (multiply) R->L }
% 0.21/0.60 inverse(divide(inverse(multiply(multiply(inverse(V), W), multiply(inverse(W), V))), divide(divide(X, divide(multiply(inverse(W), V), multiply(multiply(inverse(U), T), multiply(inverse(T), U)))), multiply(inverse(V), W))))
% 0.21/0.60 = { by lemma 37 R->L }
% 0.21/0.60 inverse(divide(inverse(multiply(multiply(inverse(V), W), multiply(inverse(W), V))), divide(divide(X, multiply(multiply(inverse(W), V), multiply(multiply(inverse(V), W), multiply(inverse(W), V)))), multiply(inverse(V), W))))
% 0.21/0.60 = { by lemma 7 }
% 0.21/0.60 X
% 0.21/0.60
% 0.21/0.60 Lemma 39: divide(multiply(multiply(inverse(X), Y), multiply(inverse(Y), X)), multiply(multiply(inverse(Z), W), V)) = divide(inverse(V), multiply(inverse(Z), W)).
% 0.21/0.60 Proof:
% 0.21/0.60 divide(multiply(multiply(inverse(X), Y), multiply(inverse(Y), X)), multiply(multiply(inverse(Z), W), V))
% 0.21/0.60 = { by lemma 35 R->L }
% 0.21/0.60 divide(divide(inverse(multiply(inverse(U), T)), multiply(inverse(T), U)), multiply(multiply(inverse(Z), W), V))
% 0.21/0.60 = { by lemma 30 R->L }
% 0.21/0.60 divide(inverse(divide(inverse(V), divide(divide(inverse(V), multiply(inverse(Z), W)), multiply(inverse(W), Z)))), multiply(multiply(inverse(Z), W), V))
% 0.21/0.60 = { by lemma 9 }
% 0.21/0.60 divide(inverse(V), multiply(inverse(Z), W))
% 0.21/0.60
% 0.21/0.60 Lemma 40: multiply(multiply(multiply(inverse(X), Y), Z), divide(inverse(Z), divide(inverse(W), multiply(inverse(Y), X)))) = divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), multiply(V, W)))).
% 0.21/0.60 Proof:
% 0.21/0.60 multiply(multiply(multiply(inverse(X), Y), Z), divide(inverse(Z), divide(inverse(W), multiply(inverse(Y), X))))
% 0.21/0.60 = { by lemma 16 }
% 0.21/0.60 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), divide(V, inverse(W)))))
% 0.21/0.60 = { by axiom 1 (multiply) R->L }
% 1.57/0.60 divide(inverse(V), multiply(multiply(inverse(U), T), divide(multiply(inverse(T), U), multiply(V, W))))
% 1.57/0.60
% 1.57/0.60 Lemma 41: inverse(inverse(divide(multiply(inverse(X), Y), Z))) = divide(multiply(inverse(X), Y), Z).
% 1.57/0.60 Proof:
% 1.57/0.60 inverse(inverse(divide(multiply(inverse(X), Y), Z)))
% 1.57/0.61 = { by lemma 4 R->L }
% 1.57/0.61 inverse(inverse(divide(inverse(W), multiply(multiply(inverse(V), U), divide(multiply(inverse(U), V), divide(W, divide(Z, multiply(inverse(X), Y))))))))
% 1.57/0.61 = { by lemma 7 R->L }
% 1.57/0.61 inverse(inverse(divide(inverse(W), multiply(multiply(inverse(V), U), divide(multiply(inverse(U), V), divide(W, divide(inverse(divide(inverse(T), divide(divide(Z, multiply(multiply(inverse(S), X2), T)), multiply(inverse(X2), S)))), multiply(inverse(X), Y))))))))
% 1.57/0.61 = { by lemma 39 R->L }
% 1.57/0.61 inverse(inverse(divide(inverse(W), multiply(multiply(inverse(V), U), divide(multiply(inverse(U), V), divide(W, divide(multiply(multiply(inverse(Y2), Z2), multiply(inverse(Z2), Y2)), multiply(multiply(inverse(X), Y), divide(inverse(T), divide(divide(Z, multiply(multiply(inverse(S), X2), T)), multiply(inverse(X2), S)))))))))))
% 1.57/0.61 = { by lemma 8 }
% 1.57/0.61 inverse(inverse(divide(inverse(W), multiply(multiply(inverse(V), U), divide(multiply(inverse(U), V), divide(W, divide(multiply(multiply(inverse(Y2), Z2), multiply(inverse(Z2), Y2)), divide(multiply(inverse(X), Y), Z))))))))
% 1.57/0.61 = { by lemma 4 }
% 1.57/0.61 inverse(inverse(divide(divide(multiply(inverse(X), Y), Z), multiply(multiply(inverse(Y2), Z2), multiply(inverse(Z2), Y2)))))
% 1.57/0.61 = { by lemma 38 }
% 1.57/0.61 divide(multiply(inverse(X), Y), Z)
% 1.57/0.61
% 1.57/0.61 Lemma 42: inverse(divide(inverse(multiply(inverse(X), Y)), divide(Z, multiply(inverse(X), Y)))) = inverse(inverse(Z)).
% 1.57/0.61 Proof:
% 1.57/0.61 inverse(divide(inverse(multiply(inverse(X), Y)), divide(Z, multiply(inverse(X), Y))))
% 1.57/0.61 = { by lemma 38 R->L }
% 1.57/0.61 inverse(inverse(divide(inverse(divide(inverse(multiply(inverse(X), Y)), divide(Z, multiply(inverse(X), Y)))), multiply(multiply(inverse(Y), X), multiply(inverse(X), Y)))))
% 1.57/0.61 = { by lemma 9 }
% 1.57/0.61 inverse(inverse(Z))
% 1.57/0.61
% 1.57/0.61 Lemma 43: inverse(divide(multiply(inverse(X), Y), multiply(inverse(X), Y))) = multiply(multiply(inverse(Z), W), multiply(inverse(W), Z)).
% 1.57/0.61 Proof:
% 1.57/0.61 inverse(divide(multiply(inverse(X), Y), multiply(inverse(X), Y)))
% 1.57/0.61 = { by lemma 41 R->L }
% 1.57/0.61 inverse(inverse(inverse(divide(multiply(inverse(X), Y), multiply(inverse(X), Y)))))
% 1.57/0.61 = { by lemma 42 R->L }
% 1.57/0.61 inverse(divide(inverse(multiply(inverse(Y), X)), divide(inverse(divide(multiply(inverse(X), Y), multiply(inverse(X), Y))), multiply(inverse(Y), X))))
% 1.57/0.61 = { by lemma 29 }
% 1.57/0.61 inverse(divide(inverse(multiply(inverse(Y), X)), inverse(inverse(multiply(inverse(X), Y)))))
% 1.57/0.61 = { by axiom 1 (multiply) R->L }
% 1.57/0.61 inverse(multiply(inverse(multiply(inverse(Y), X)), inverse(multiply(inverse(X), Y))))
% 1.57/0.61 = { by lemma 33 }
% 1.57/0.61 inverse(divide(inverse(multiply(inverse(Y), X)), multiply(inverse(X), Y)))
% 1.57/0.61 = { by lemma 36 }
% 1.57/0.61 divide(inverse(multiply(inverse(V), U)), multiply(inverse(U), V))
% 1.57/0.61 = { by lemma 35 }
% 1.57/0.61 multiply(multiply(inverse(Z), W), multiply(inverse(W), Z))
% 1.57/0.61
% 1.57/0.61 Lemma 44: multiply(multiply(inverse(X), Y), multiply(inverse(Y), X)) = divide(multiply(inverse(Z), W), multiply(inverse(Z), W)).
% 1.57/0.61 Proof:
% 1.57/0.61 multiply(multiply(inverse(X), Y), multiply(inverse(Y), X))
% 1.57/0.61 = { by lemma 35 R->L }
% 1.57/0.61 divide(inverse(multiply(inverse(V), U)), multiply(inverse(U), V))
% 1.57/0.61 = { by lemma 18 R->L }
% 1.57/0.61 multiply(multiply(multiply(inverse(T), S), X2), divide(inverse(X2), divide(multiply(multiply(inverse(U), V), multiply(inverse(V), U)), multiply(inverse(S), T))))
% 1.57/0.61 = { by lemma 16 }
% 1.57/0.61 divide(inverse(Y2), multiply(multiply(inverse(Z2), W2), divide(multiply(inverse(W2), Z2), divide(Y2, multiply(multiply(inverse(U), V), multiply(inverse(V), U))))))
% 1.57/0.61 = { by lemma 37 R->L }
% 1.57/0.61 divide(inverse(Y2), multiply(multiply(inverse(Z2), W2), divide(multiply(inverse(W2), Z2), multiply(Y2, multiply(multiply(inverse(V2), U2), multiply(inverse(U2), V2))))))
% 1.57/0.61 = { by lemma 40 R->L }
% 1.57/0.61 multiply(multiply(multiply(inverse(T2), S2), X3), divide(inverse(X3), divide(inverse(multiply(multiply(inverse(V2), U2), multiply(inverse(U2), V2))), multiply(inverse(S2), T2))))
% 1.57/0.61 = { by lemma 43 R->L }
% 1.57/0.61 multiply(multiply(multiply(inverse(T2), S2), X3), divide(inverse(X3), divide(inverse(inverse(divide(multiply(inverse(Z), W), multiply(inverse(Z), W)))), multiply(inverse(S2), T2))))
% 1.57/0.61 = { by lemma 41 }
% 1.57/0.61 multiply(multiply(multiply(inverse(T2), S2), X3), divide(inverse(X3), divide(divide(multiply(inverse(Z), W), multiply(inverse(Z), W)), multiply(inverse(S2), T2))))
% 1.57/0.61 = { by lemma 17 }
% 1.57/0.61 divide(multiply(inverse(Z), W), multiply(inverse(Z), W))
% 1.57/0.61
% 1.57/0.61 Lemma 45: divide(multiply(inverse(X), Y), divide(multiply(inverse(Z), W), multiply(inverse(Z), W))) = multiply(inverse(X), Y).
% 1.57/0.61 Proof:
% 1.57/0.61 divide(multiply(inverse(X), Y), divide(multiply(inverse(Z), W), multiply(inverse(Z), W)))
% 1.57/0.61 = { by lemma 32 R->L }
% 1.57/0.61 divide(inverse(inverse(multiply(inverse(X), Y))), divide(multiply(inverse(Z), W), multiply(inverse(Z), W)))
% 1.57/0.61 = { by lemma 44 R->L }
% 1.57/0.61 divide(inverse(inverse(multiply(inverse(X), Y))), multiply(multiply(inverse(V), U), multiply(inverse(U), V)))
% 1.57/0.61 = { by lemma 27 R->L }
% 1.57/0.61 divide(inverse(inverse(multiply(inverse(X), Y))), multiply(multiply(inverse(V), U), divide(multiply(inverse(U), V), divide(inverse(multiply(inverse(X), Y)), multiply(inverse(Y), X)))))
% 1.57/0.61 = { by lemma 19 }
% 1.57/0.61 multiply(inverse(X), Y)
% 1.57/0.61
% 1.57/0.61 Lemma 46: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
% 1.57/0.61 Proof:
% 1.57/0.61 inverse(multiply(inverse(X), Y))
% 1.57/0.61 = { by lemma 45 R->L }
% 1.57/0.61 inverse(divide(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), multiply(inverse(Y), X))))
% 1.57/0.61 = { by lemma 5 R->L }
% 1.57/0.61 divide(inverse(divide(Z, multiply(inverse(Y), X))), divide(divide(multiply(inverse(X), Y), multiply(inverse(X), Y)), Z))
% 1.57/0.61 = { by lemma 45 R->L }
% 1.57/0.61 divide(inverse(divide(Z, divide(multiply(inverse(Y), X), divide(multiply(inverse(X), Y), multiply(inverse(X), Y))))), divide(divide(multiply(inverse(X), Y), multiply(inverse(X), Y)), Z))
% 1.57/0.61 = { by axiom 2 (single_axiom) }
% 1.57/0.61 multiply(inverse(Y), X)
% 1.57/0.61
% 1.57/0.61 Lemma 47: divide(inverse(divide(multiply(inverse(X), Y), Z)), multiply(inverse(Y), X)) = inverse(inverse(Z)).
% 1.57/0.61 Proof:
% 1.57/0.61 divide(inverse(divide(multiply(inverse(X), Y), Z)), multiply(inverse(Y), X))
% 1.57/0.61 = { by lemma 28 R->L }
% 1.57/0.61 inverse(divide(inverse(multiply(inverse(W), V)), divide(Z, multiply(inverse(W), V))))
% 1.57/0.61 = { by lemma 42 }
% 1.57/0.61 inverse(inverse(Z))
% 1.57/0.61
% 1.57/0.61 Lemma 48: multiply(multiply(inverse(X), Y), inverse(Z)) = divide(multiply(inverse(X), Y), Z).
% 1.57/0.61 Proof:
% 1.57/0.61 multiply(multiply(inverse(X), Y), inverse(Z))
% 1.57/0.61 = { by lemma 38 R->L }
% 1.57/0.61 inverse(inverse(divide(multiply(multiply(inverse(X), Y), inverse(Z)), multiply(multiply(inverse(W), V), multiply(inverse(V), W)))))
% 1.57/0.61 = { by lemma 4 R->L }
% 1.57/0.61 inverse(inverse(divide(inverse(U), multiply(multiply(inverse(T), S), divide(multiply(inverse(S), T), divide(U, divide(multiply(multiply(inverse(W), V), multiply(inverse(V), W)), multiply(multiply(inverse(X), Y), inverse(Z)))))))))
% 1.57/0.61 = { by lemma 39 }
% 1.57/0.61 inverse(inverse(divide(inverse(U), multiply(multiply(inverse(T), S), divide(multiply(inverse(S), T), divide(U, divide(inverse(inverse(Z)), multiply(inverse(X), Y))))))))
% 1.57/0.61 = { by lemma 4 }
% 1.57/0.61 inverse(inverse(divide(multiply(inverse(X), Y), inverse(inverse(Z)))))
% 1.57/0.61 = { by axiom 1 (multiply) R->L }
% 1.57/0.61 inverse(inverse(multiply(multiply(inverse(X), Y), inverse(Z))))
% 1.57/0.61 = { by lemma 46 R->L }
% 1.57/0.61 inverse(inverse(multiply(inverse(multiply(inverse(Y), X)), inverse(Z))))
% 1.57/0.61 = { by axiom 1 (multiply) }
% 1.57/0.61 inverse(inverse(divide(inverse(multiply(inverse(Y), X)), inverse(inverse(Z)))))
% 1.57/0.61 = { by lemma 47 R->L }
% 1.57/0.61 inverse(inverse(divide(inverse(multiply(inverse(Y), X)), divide(inverse(divide(multiply(inverse(X), Y), Z)), multiply(inverse(Y), X)))))
% 1.57/0.61 = { by lemma 28 }
% 1.57/0.61 inverse(divide(inverse(divide(multiply(inverse(X2), Y2), inverse(divide(multiply(inverse(X), Y), Z)))), multiply(inverse(Y2), X2)))
% 1.57/0.61 = { by lemma 47 }
% 1.57/0.61 inverse(inverse(inverse(inverse(divide(multiply(inverse(X), Y), Z)))))
% 1.57/0.61 = { by lemma 41 }
% 1.57/0.61 inverse(inverse(divide(multiply(inverse(X), Y), Z)))
% 1.57/0.61 = { by lemma 41 }
% 1.57/0.61 divide(multiply(inverse(X), Y), Z)
% 1.57/0.61
% 1.57/0.61 Lemma 49: divide(inverse(inverse(X)), multiply(inverse(Y), Z)) = divide(X, multiply(inverse(Y), Z)).
% 1.57/0.61 Proof:
% 1.57/0.61 divide(inverse(inverse(X)), multiply(inverse(Y), Z))
% 1.57/0.61 = { by lemma 18 R->L }
% 1.57/0.61 multiply(multiply(multiply(inverse(W), V), U), divide(inverse(U), divide(multiply(multiply(inverse(Y), Z), inverse(X)), multiply(inverse(V), W))))
% 1.57/0.61 = { by lemma 48 }
% 1.57/0.61 multiply(multiply(multiply(inverse(W), V), U), divide(inverse(U), divide(divide(multiply(inverse(Y), Z), X), multiply(inverse(V), W))))
% 1.57/0.61 = { by lemma 17 }
% 1.57/0.61 divide(X, multiply(inverse(Y), Z))
% 1.57/0.61
% 1.57/0.61 Lemma 50: inverse(inverse(X)) = X.
% 1.57/0.61 Proof:
% 1.57/0.61 inverse(inverse(X))
% 1.57/0.61 = { by lemma 3 R->L }
% 1.57/0.61 divide(inverse(divide(Y, divide(inverse(inverse(X)), multiply(inverse(Z), W)))), divide(multiply(inverse(W), Z), Y))
% 1.57/0.61 = { by lemma 49 }
% 1.57/0.61 divide(inverse(divide(Y, divide(X, multiply(inverse(Z), W)))), divide(multiply(inverse(W), Z), Y))
% 1.57/0.61 = { by lemma 3 }
% 1.57/0.61 X
% 1.57/0.61
% 1.57/0.61 Lemma 51: divide(multiply(inverse(X), Y), Y) = inverse(X).
% 1.57/0.61 Proof:
% 1.57/0.61 divide(multiply(inverse(X), Y), Y)
% 1.57/0.61 = { by lemma 45 R->L }
% 1.57/0.61 divide(divide(multiply(inverse(X), Y), divide(multiply(inverse(Z), W), multiply(inverse(Z), W))), Y)
% 1.57/0.61 = { by lemma 44 R->L }
% 1.57/0.61 divide(divide(multiply(inverse(X), Y), multiply(multiply(inverse(V), U), multiply(inverse(U), V))), Y)
% 1.57/0.61 = { by lemma 43 R->L }
% 1.57/0.61 divide(divide(multiply(inverse(X), Y), inverse(divide(multiply(inverse(Y), X), multiply(inverse(Y), X)))), Y)
% 1.57/0.61 = { by axiom 1 (multiply) R->L }
% 1.57/0.61 divide(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), multiply(inverse(Y), X))), Y)
% 1.57/0.61 = { by lemma 50 R->L }
% 1.57/0.61 divide(multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), multiply(inverse(Y), X))), inverse(inverse(Y)))
% 1.57/0.61 = { by lemma 17 R->L }
% 1.57/0.61 multiply(multiply(multiply(inverse(T), S), X2), divide(inverse(X2), divide(divide(inverse(inverse(Y)), multiply(multiply(inverse(X), Y), divide(multiply(inverse(Y), X), multiply(inverse(Y), X)))), multiply(inverse(S), T))))
% 1.57/0.61 = { by lemma 40 R->L }
% 1.57/0.61 multiply(multiply(multiply(inverse(T), S), X2), divide(inverse(X2), divide(multiply(multiply(multiply(inverse(Y2), Z2), W2), divide(inverse(W2), divide(inverse(X), multiply(inverse(Z2), Y2)))), multiply(inverse(S), T))))
% 1.57/0.61 = { by lemma 18 }
% 1.57/0.61 divide(inverse(divide(inverse(W2), divide(inverse(X), multiply(inverse(Z2), Y2)))), multiply(multiply(inverse(Y2), Z2), W2))
% 1.57/0.61 = { by lemma 9 }
% 1.57/0.61 inverse(X)
% 1.57/0.61
% 1.57/0.61 Lemma 52: divide(divide(inverse(multiply(X, Y)), divide(multiply(inverse(Z), W), X)), multiply(inverse(W), Z)) = inverse(Y).
% 1.57/0.61 Proof:
% 1.57/0.61 divide(divide(inverse(multiply(X, Y)), divide(multiply(inverse(Z), W), X)), multiply(inverse(W), Z))
% 1.57/0.61 = { by lemma 13 R->L }
% 1.57/0.61 divide(divide(inverse(multiply(inverse(V), Y)), multiply(multiply(inverse(Z), W), V)), multiply(inverse(W), Z))
% 1.57/0.61 = { by lemma 25 R->L }
% 1.57/0.61 divide(divide(inverse(multiply(inverse(V), Y)), multiply(divide(inverse(U), multiply(inverse(T), S)), V)), multiply(multiply(inverse(T), S), U))
% 1.57/0.61 = { by lemma 13 }
% 1.57/0.61 divide(divide(inverse(multiply(X2, Y)), divide(divide(inverse(U), multiply(inverse(T), S)), X2)), multiply(multiply(inverse(T), S), U))
% 1.57/0.61 = { by axiom 1 (multiply) }
% 1.57/0.61 divide(divide(inverse(divide(X2, inverse(Y))), divide(divide(inverse(U), multiply(inverse(T), S)), X2)), multiply(multiply(inverse(T), S), U))
% 1.57/0.61 = { by lemma 5 }
% 1.57/0.61 divide(inverse(divide(inverse(U), divide(inverse(Y), multiply(inverse(S), T)))), multiply(multiply(inverse(T), S), U))
% 1.57/0.61 = { by lemma 9 }
% 1.57/0.61 inverse(Y)
% 1.57/0.61
% 1.57/0.61 Lemma 53: inverse(divide(inverse(multiply(multiply(inverse(X), Y), Z)), divide(multiply(inverse(W), V), multiply(inverse(X), Y)))) = multiply(inverse(multiply(inverse(V), W)), Z).
% 1.57/0.61 Proof:
% 1.57/0.61 inverse(divide(inverse(multiply(multiply(inverse(X), Y), Z)), divide(multiply(inverse(W), V), multiply(inverse(X), Y))))
% 1.57/0.61 = { by lemma 31 R->L }
% 1.57/0.61 inverse(divide(inverse(multiply(multiply(inverse(X), Y), Z)), divide(divide(inverse(multiply(inverse(U), T)), multiply(inverse(T), U)), divide(multiply(inverse(X), Y), multiply(inverse(W), V)))))
% 1.57/0.61 = { by lemma 10 R->L }
% 1.57/0.61 divide(inverse(divide(multiply(inverse(V), W), divide(inverse(multiply(inverse(U), T)), multiply(inverse(T), U)))), divide(divide(inverse(multiply(multiply(inverse(X), Y), Z)), divide(multiply(inverse(W), V), multiply(inverse(X), Y))), multiply(inverse(V), W)))
% 1.57/0.61 = { by lemma 52 }
% 1.57/0.61 divide(inverse(divide(multiply(inverse(V), W), divide(inverse(multiply(inverse(U), T)), multiply(inverse(T), U)))), inverse(Z))
% 1.57/0.61 = { by axiom 1 (multiply) R->L }
% 1.57/0.61 multiply(inverse(divide(multiply(inverse(V), W), divide(inverse(multiply(inverse(U), T)), multiply(inverse(T), U)))), Z)
% 1.57/0.61 = { by lemma 27 }
% 1.57/0.61 multiply(inverse(multiply(inverse(V), W)), Z)
% 1.57/0.61
% 1.57/0.61 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 1.57/0.61 Proof:
% 1.57/0.61 multiply(multiply(inverse(b2), b2), a2)
% 1.57/0.61 = { by lemma 46 R->L }
% 1.57/0.61 multiply(inverse(multiply(inverse(b2), b2)), a2)
% 1.57/0.62 = { by lemma 53 R->L }
% 1.57/0.62 inverse(divide(inverse(multiply(multiply(inverse(b2), b2), a2)), divide(multiply(inverse(b2), b2), multiply(inverse(b2), b2))))
% 1.57/0.62 = { by lemma 17 R->L }
% 1.57/0.62 inverse(divide(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(multiply(multiply(inverse(X), Y), Z), divide(inverse(Z), divide(divide(multiply(inverse(b2), b2), multiply(inverse(b2), b2)), multiply(inverse(Y), X))))))
% 1.57/0.62 = { by lemma 16 }
% 1.57/0.62 inverse(divide(inverse(multiply(multiply(inverse(b2), b2), a2)), divide(inverse(b2), multiply(multiply(inverse(b2), W), divide(multiply(inverse(W), b2), divide(b2, divide(multiply(inverse(b2), b2), multiply(inverse(b2), b2))))))))
% 1.57/0.62 = { by lemma 44 R->L }
% 1.57/0.62 inverse(divide(inverse(multiply(multiply(inverse(b2), b2), a2)), divide(inverse(b2), multiply(multiply(inverse(b2), W), divide(multiply(inverse(W), b2), divide(b2, multiply(multiply(inverse(V), U), multiply(inverse(U), V))))))))
% 1.57/0.62 = { by lemma 50 R->L }
% 1.57/0.62 inverse(divide(inverse(multiply(multiply(inverse(b2), b2), a2)), divide(inverse(b2), multiply(multiply(inverse(b2), W), divide(multiply(inverse(W), b2), inverse(inverse(divide(b2, multiply(multiply(inverse(V), U), multiply(inverse(U), V))))))))))
% 1.57/0.62 = { by lemma 38 }
% 1.57/0.62 inverse(divide(inverse(multiply(multiply(inverse(b2), b2), a2)), divide(inverse(b2), multiply(multiply(inverse(b2), W), divide(multiply(inverse(W), b2), b2)))))
% 1.57/0.62 = { by lemma 51 }
% 1.57/0.62 inverse(divide(inverse(multiply(multiply(inverse(b2), b2), a2)), divide(inverse(b2), multiply(multiply(inverse(b2), W), inverse(W)))))
% 1.57/0.62 = { by lemma 48 }
% 1.57/0.62 inverse(divide(inverse(multiply(multiply(inverse(b2), b2), a2)), divide(inverse(b2), divide(multiply(inverse(b2), W), W))))
% 1.57/0.62 = { by lemma 51 }
% 1.57/0.62 inverse(divide(inverse(multiply(multiply(inverse(b2), b2), a2)), divide(inverse(b2), inverse(b2))))
% 1.57/0.62 = { by axiom 1 (multiply) R->L }
% 1.57/0.62 inverse(divide(inverse(multiply(multiply(inverse(b2), b2), a2)), multiply(inverse(b2), b2)))
% 1.57/0.62 = { by lemma 46 R->L }
% 1.57/0.62 inverse(divide(inverse(multiply(inverse(multiply(inverse(b2), b2)), a2)), multiply(inverse(b2), b2)))
% 1.57/0.62 = { by lemma 53 R->L }
% 1.57/0.62 inverse(divide(inverse(inverse(divide(inverse(multiply(multiply(inverse(T), S), a2)), divide(multiply(inverse(b2), b2), multiply(inverse(T), S))))), multiply(inverse(b2), b2)))
% 1.57/0.62 = { by lemma 49 }
% 1.57/0.62 inverse(divide(divide(inverse(multiply(multiply(inverse(T), S), a2)), divide(multiply(inverse(b2), b2), multiply(inverse(T), S))), multiply(inverse(b2), b2)))
% 1.57/0.62 = { by lemma 52 }
% 1.57/0.62 inverse(inverse(a2))
% 1.57/0.62 = { by lemma 50 }
% 1.57/0.62 a2
% 1.57/0.62 % SZS output end Proof
% 1.57/0.62
% 1.57/0.62 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------