TSTP Solution File: GRP476-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP476-1 : 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 : n015.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 01:18:35 EDT 2023
% Result : Unsatisfiable 0.21s 0.59s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP476-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 22:49:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.59 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.21/0.59
% 0.21/0.59 % SZS status Unsatisfiable
% 0.21/0.59
% 0.21/0.67 % SZS output start Proof
% 0.21/0.67 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.21/0.67 Axiom 2 (single_axiom): divide(inverse(divide(divide(divide(X, Y), Z), divide(W, Z))), divide(Y, X)) = W.
% 0.21/0.67
% 0.21/0.67 Lemma 3: divide(inverse(divide(divide(multiply(inverse(X), Y), Z), divide(W, Z))), multiply(inverse(Y), X)) = W.
% 0.21/0.67 Proof:
% 0.21/0.67 divide(inverse(divide(divide(multiply(inverse(X), Y), Z), divide(W, Z))), multiply(inverse(Y), X))
% 0.21/0.67 = { by axiom 1 (multiply) }
% 0.21/0.67 divide(inverse(divide(divide(multiply(inverse(X), Y), Z), divide(W, Z))), divide(inverse(Y), inverse(X)))
% 0.21/0.67 = { by axiom 1 (multiply) }
% 0.21/0.67 divide(inverse(divide(divide(divide(inverse(X), inverse(Y)), Z), divide(W, Z))), divide(inverse(Y), inverse(X)))
% 0.21/0.67 = { by axiom 2 (single_axiom) }
% 0.21/0.67 W
% 0.21/0.67
% 0.21/0.67 Lemma 4: divide(inverse(divide(multiply(multiply(inverse(X), Y), Z), multiply(W, Z))), multiply(inverse(Y), X)) = W.
% 0.21/0.67 Proof:
% 0.21/0.67 divide(inverse(divide(multiply(multiply(inverse(X), Y), Z), multiply(W, Z))), multiply(inverse(Y), X))
% 0.21/0.67 = { by axiom 1 (multiply) }
% 0.21/0.67 divide(inverse(divide(multiply(multiply(inverse(X), Y), Z), divide(W, inverse(Z)))), multiply(inverse(Y), X))
% 0.21/0.67 = { by axiom 1 (multiply) }
% 0.21/0.67 divide(inverse(divide(divide(multiply(inverse(X), Y), inverse(Z)), divide(W, inverse(Z)))), multiply(inverse(Y), X))
% 0.21/0.67 = { by lemma 3 }
% 0.21/0.67 W
% 0.21/0.67
% 0.21/0.67 Lemma 5: divide(inverse(divide(divide(multiply(inverse(X), Y), multiply(inverse(Z), W)), V)), multiply(inverse(Y), X)) = inverse(divide(multiply(multiply(inverse(W), Z), U), multiply(V, U))).
% 0.21/0.67 Proof:
% 0.21/0.67 divide(inverse(divide(divide(multiply(inverse(X), Y), multiply(inverse(Z), W)), V)), multiply(inverse(Y), X))
% 0.21/0.67 = { by lemma 4 R->L }
% 0.21/0.67 divide(inverse(divide(divide(multiply(inverse(X), Y), multiply(inverse(Z), W)), divide(inverse(divide(multiply(multiply(inverse(W), Z), U), multiply(V, U))), multiply(inverse(Z), W)))), multiply(inverse(Y), X))
% 0.21/0.67 = { by lemma 3 }
% 0.21/0.67 inverse(divide(multiply(multiply(inverse(W), Z), U), multiply(V, U)))
% 0.21/0.67
% 0.21/0.67 Lemma 6: inverse(divide(multiply(multiply(inverse(X), Y), Z), multiply(divide(W, multiply(inverse(Y), X)), Z))) = W.
% 0.21/0.67 Proof:
% 0.21/0.67 inverse(divide(multiply(multiply(inverse(X), Y), Z), multiply(divide(W, multiply(inverse(Y), X)), Z)))
% 0.21/0.67 = { by lemma 5 R->L }
% 0.21/0.67 divide(inverse(divide(divide(multiply(inverse(V), U), multiply(inverse(Y), X)), divide(W, multiply(inverse(Y), X)))), multiply(inverse(U), V))
% 0.21/0.67 = { by lemma 3 }
% 0.21/0.67 W
% 0.21/0.67
% 0.21/0.67 Lemma 7: multiply(X, divide(multiply(multiply(inverse(Y), Z), W), multiply(divide(V, multiply(inverse(Z), Y)), W))) = divide(X, V).
% 0.21/0.67 Proof:
% 0.21/0.67 multiply(X, divide(multiply(multiply(inverse(Y), Z), W), multiply(divide(V, multiply(inverse(Z), Y)), W)))
% 0.21/0.67 = { by axiom 1 (multiply) }
% 0.21/0.67 divide(X, inverse(divide(multiply(multiply(inverse(Y), Z), W), multiply(divide(V, multiply(inverse(Z), Y)), W))))
% 0.21/0.67 = { by lemma 6 }
% 0.21/0.67 divide(X, V)
% 0.21/0.67
% 0.21/0.68 Lemma 8: divide(inverse(divide(multiply(divide(X, Y), Z), multiply(W, Z))), divide(Y, X)) = W.
% 0.21/0.68 Proof:
% 0.21/0.68 divide(inverse(divide(multiply(divide(X, Y), Z), multiply(W, Z))), divide(Y, X))
% 0.21/0.68 = { by axiom 1 (multiply) }
% 0.21/0.68 divide(inverse(divide(multiply(divide(X, Y), Z), divide(W, inverse(Z)))), divide(Y, X))
% 0.21/0.68 = { by axiom 1 (multiply) }
% 0.21/0.68 divide(inverse(divide(divide(divide(X, Y), inverse(Z)), divide(W, inverse(Z)))), divide(Y, X))
% 0.21/0.68 = { by axiom 2 (single_axiom) }
% 0.21/0.68 W
% 0.21/0.68
% 0.21/0.68 Lemma 9: divide(X, multiply(divide(Y, Z), divide(multiply(divide(Z, Y), W), multiply(multiply(inverse(V), U), W)))) = divide(X, multiply(inverse(U), V)).
% 0.21/0.68 Proof:
% 0.21/0.68 divide(X, multiply(divide(Y, Z), divide(multiply(divide(Z, Y), W), multiply(multiply(inverse(V), U), W))))
% 0.21/0.68 = { by lemma 6 R->L }
% 0.21/0.68 divide(inverse(divide(multiply(multiply(inverse(V), U), T), multiply(divide(X, multiply(inverse(U), V)), T))), multiply(divide(Y, Z), divide(multiply(divide(Z, Y), W), multiply(multiply(inverse(V), U), W))))
% 0.21/0.68 = { by lemma 8 R->L }
% 0.21/0.68 divide(inverse(divide(multiply(divide(inverse(divide(multiply(divide(Z, Y), W), multiply(multiply(inverse(V), U), W))), divide(Y, Z)), T), multiply(divide(X, multiply(inverse(U), V)), T))), multiply(divide(Y, Z), divide(multiply(divide(Z, Y), W), multiply(multiply(inverse(V), U), W))))
% 0.21/0.68 = { by axiom 1 (multiply) }
% 0.21/0.68 divide(inverse(divide(multiply(divide(inverse(divide(multiply(divide(Z, Y), W), multiply(multiply(inverse(V), U), W))), divide(Y, Z)), T), multiply(divide(X, multiply(inverse(U), V)), T))), divide(divide(Y, Z), inverse(divide(multiply(divide(Z, Y), W), multiply(multiply(inverse(V), U), W)))))
% 0.21/0.68 = { by lemma 8 }
% 0.21/0.68 divide(X, multiply(inverse(U), V))
% 0.21/0.68
% 0.21/0.68 Lemma 10: divide(divide(inverse(divide(divide(multiply(inverse(X), Y), multiply(inverse(Z), W)), V)), multiply(inverse(Y), X)), multiply(inverse(Z), W)) = V.
% 0.21/0.68 Proof:
% 0.21/0.68 divide(divide(inverse(divide(divide(multiply(inverse(X), Y), multiply(inverse(Z), W)), V)), multiply(inverse(Y), X)), multiply(inverse(Z), W))
% 0.21/0.68 = { by lemma 5 }
% 0.21/0.68 divide(inverse(divide(multiply(multiply(inverse(W), Z), U), multiply(V, U))), multiply(inverse(Z), W))
% 0.21/0.68 = { by lemma 4 }
% 0.21/0.68 V
% 0.21/0.68
% 0.21/0.68 Lemma 11: multiply(divide(X, Y), divide(multiply(divide(Y, X), Z), multiply(multiply(inverse(W), V), Z))) = multiply(inverse(V), W).
% 0.21/0.68 Proof:
% 0.21/0.68 multiply(divide(X, Y), divide(multiply(divide(Y, X), Z), multiply(multiply(inverse(W), V), Z)))
% 0.21/0.68 = { by lemma 10 R->L }
% 0.21/0.68 divide(divide(inverse(divide(divide(multiply(inverse(U), T), multiply(inverse(S), X2)), multiply(divide(X, Y), divide(multiply(divide(Y, X), Z), multiply(multiply(inverse(W), V), Z))))), multiply(inverse(T), U)), multiply(inverse(S), X2))
% 0.21/0.68 = { by lemma 9 }
% 0.21/0.68 divide(divide(inverse(divide(divide(multiply(inverse(U), T), multiply(inverse(S), X2)), multiply(inverse(V), W))), multiply(inverse(T), U)), multiply(inverse(S), X2))
% 0.21/0.68 = { by lemma 10 }
% 0.21/0.68 multiply(inverse(V), W)
% 0.21/0.68
% 0.21/0.68 Lemma 12: divide(inverse(divide(multiply(inverse(X), Y), multiply(inverse(X), Y))), divide(Z, W)) = divide(W, Z).
% 0.21/0.68 Proof:
% 0.21/0.68 divide(inverse(divide(multiply(inverse(X), Y), multiply(inverse(X), Y))), divide(Z, W))
% 0.21/0.68 = { by lemma 9 R->L }
% 0.21/0.68 divide(inverse(divide(multiply(inverse(X), Y), multiply(divide(W, Z), divide(multiply(divide(Z, W), V), multiply(multiply(inverse(Y), X), V))))), divide(Z, W))
% 0.21/0.68 = { by lemma 4 R->L }
% 0.21/0.68 divide(inverse(divide(multiply(inverse(X), Y), multiply(divide(W, Z), divide(multiply(divide(inverse(divide(multiply(multiply(inverse(U), T), S), multiply(divide(Z, W), S))), multiply(inverse(T), U)), V), multiply(multiply(inverse(Y), X), V))))), divide(Z, W))
% 0.21/0.68 = { by lemma 11 R->L }
% 0.21/0.68 divide(inverse(divide(multiply(divide(multiply(inverse(T), U), inverse(divide(multiply(multiply(inverse(U), T), S), multiply(divide(Z, W), S)))), divide(multiply(divide(inverse(divide(multiply(multiply(inverse(U), T), S), multiply(divide(Z, W), S))), multiply(inverse(T), U)), V), multiply(multiply(inverse(Y), X), V))), multiply(divide(W, Z), divide(multiply(divide(inverse(divide(multiply(multiply(inverse(U), T), S), multiply(divide(Z, W), S))), multiply(inverse(T), U)), V), multiply(multiply(inverse(Y), X), V))))), divide(Z, W))
% 0.21/0.68 = { by lemma 4 R->L }
% 0.21/0.68 divide(inverse(divide(multiply(divide(multiply(inverse(T), U), inverse(divide(multiply(multiply(inverse(U), T), S), multiply(divide(Z, W), S)))), divide(multiply(divide(inverse(divide(multiply(multiply(inverse(U), T), S), multiply(divide(Z, W), S))), multiply(inverse(T), U)), V), multiply(multiply(inverse(Y), X), V))), multiply(divide(W, Z), divide(multiply(divide(inverse(divide(multiply(multiply(inverse(U), T), S), multiply(divide(Z, W), S))), multiply(inverse(T), U)), V), multiply(multiply(inverse(Y), X), V))))), divide(inverse(divide(multiply(multiply(inverse(U), T), S), multiply(divide(Z, W), S))), multiply(inverse(T), U)))
% 0.21/0.68 = { by lemma 8 }
% 0.21/0.68 divide(W, Z)
% 0.21/0.68
% 0.21/0.68 Lemma 13: multiply(divide(X, Y), divide(multiply(inverse(Z), W), multiply(inverse(Z), W))) = divide(X, Y).
% 0.21/0.68 Proof:
% 0.21/0.68 multiply(divide(X, Y), divide(multiply(inverse(Z), W), multiply(inverse(Z), W)))
% 0.21/0.68 = { by axiom 1 (multiply) }
% 0.21/0.68 divide(divide(X, Y), inverse(divide(multiply(inverse(Z), W), multiply(inverse(Z), W))))
% 0.21/0.68 = { by lemma 12 R->L }
% 0.21/0.68 divide(inverse(divide(multiply(inverse(V), U), multiply(inverse(V), U))), divide(inverse(divide(multiply(inverse(Z), W), multiply(inverse(Z), W))), divide(X, Y)))
% 0.21/0.68 = { by lemma 12 }
% 0.21/0.68 divide(inverse(divide(multiply(inverse(V), U), multiply(inverse(V), U))), divide(Y, X))
% 0.21/0.68 = { by lemma 12 }
% 0.21/0.68 divide(X, Y)
% 0.21/0.68
% 0.21/0.68 Lemma 14: multiply(X, divide(multiply(inverse(Y), Z), multiply(inverse(Y), Z))) = X.
% 0.21/0.68 Proof:
% 0.21/0.68 multiply(X, divide(multiply(inverse(Y), Z), multiply(inverse(Y), Z)))
% 0.21/0.68 = { by axiom 2 (single_axiom) R->L }
% 0.21/0.68 multiply(divide(inverse(divide(divide(divide(W, V), U), divide(X, U))), divide(V, W)), divide(multiply(inverse(Y), Z), multiply(inverse(Y), Z)))
% 0.21/0.68 = { by lemma 13 }
% 0.21/0.68 divide(inverse(divide(divide(divide(W, V), U), divide(X, U))), divide(V, W))
% 0.21/0.68 = { by axiom 2 (single_axiom) }
% 0.21/0.68 X
% 0.21/0.68
% 0.21/0.68 Lemma 15: divide(X, multiply(multiply(inverse(Y), Z), divide(multiply(multiply(inverse(Z), Y), W), multiply(multiply(inverse(V), U), W)))) = divide(X, multiply(inverse(U), V)).
% 0.21/0.68 Proof:
% 0.21/0.68 divide(X, multiply(multiply(inverse(Y), Z), divide(multiply(multiply(inverse(Z), Y), W), multiply(multiply(inverse(V), U), W))))
% 0.21/0.68 = { by lemma 3 R->L }
% 0.21/0.68 divide(divide(inverse(divide(divide(multiply(inverse(T), S), multiply(inverse(U), V)), divide(X, multiply(inverse(U), V)))), multiply(inverse(S), T)), multiply(multiply(inverse(Y), Z), divide(multiply(multiply(inverse(Z), Y), W), multiply(multiply(inverse(V), U), W))))
% 0.21/0.68 = { by lemma 5 }
% 0.21/0.68 divide(inverse(divide(multiply(multiply(inverse(V), U), X2), multiply(divide(X, multiply(inverse(U), V)), X2))), multiply(multiply(inverse(Y), Z), divide(multiply(multiply(inverse(Z), Y), W), multiply(multiply(inverse(V), U), W))))
% 0.21/0.68 = { by axiom 1 (multiply) }
% 0.21/0.68 divide(inverse(divide(multiply(multiply(inverse(V), U), X2), multiply(divide(X, multiply(inverse(U), V)), X2))), divide(multiply(inverse(Y), Z), inverse(divide(multiply(multiply(inverse(Z), Y), W), multiply(multiply(inverse(V), U), W)))))
% 0.21/0.68 = { by lemma 4 R->L }
% 0.21/0.68 divide(inverse(divide(multiply(divide(inverse(divide(multiply(multiply(inverse(Z), Y), W), multiply(multiply(inverse(V), U), W))), multiply(inverse(Y), Z)), X2), multiply(divide(X, multiply(inverse(U), V)), X2))), divide(multiply(inverse(Y), Z), inverse(divide(multiply(multiply(inverse(Z), Y), W), multiply(multiply(inverse(V), U), W)))))
% 0.21/0.68 = { by lemma 8 }
% 0.21/0.68 divide(X, multiply(inverse(U), V))
% 0.21/0.68
% 0.21/0.68 Lemma 16: multiply(multiply(inverse(X), Y), divide(multiply(multiply(inverse(Y), X), Z), multiply(multiply(inverse(W), V), Z))) = multiply(inverse(V), W).
% 0.21/0.68 Proof:
% 0.21/0.68 multiply(multiply(inverse(X), Y), divide(multiply(multiply(inverse(Y), X), Z), multiply(multiply(inverse(W), V), Z)))
% 0.21/0.68 = { by lemma 10 R->L }
% 0.21/0.68 divide(divide(inverse(divide(divide(multiply(inverse(U), T), multiply(inverse(S), X2)), multiply(multiply(inverse(X), Y), divide(multiply(multiply(inverse(Y), X), Z), multiply(multiply(inverse(W), V), Z))))), multiply(inverse(T), U)), multiply(inverse(S), X2))
% 0.21/0.68 = { by lemma 15 }
% 0.21/0.68 divide(divide(inverse(divide(divide(multiply(inverse(U), T), multiply(inverse(S), X2)), multiply(inverse(V), W))), multiply(inverse(T), U)), multiply(inverse(S), X2))
% 0.21/0.68 = { by lemma 10 }
% 0.21/0.68 multiply(inverse(V), W)
% 0.21/0.68
% 0.21/0.68 Lemma 17: multiply(X, divide(multiply(multiply(inverse(Y), Z), W), multiply(multiply(inverse(Y), Z), W))) = multiply(X, divide(multiply(inverse(V), U), multiply(inverse(V), U))).
% 0.21/0.68 Proof:
% 0.21/0.68 multiply(X, divide(multiply(multiply(inverse(Y), Z), W), multiply(multiply(inverse(Y), Z), W)))
% 0.21/0.68 = { by axiom 1 (multiply) }
% 0.21/0.68 divide(X, inverse(divide(multiply(multiply(inverse(Y), Z), W), multiply(multiply(inverse(Y), Z), W))))
% 0.21/0.68 = { by lemma 5 R->L }
% 0.21/0.68 divide(X, divide(inverse(divide(divide(multiply(inverse(T), S), multiply(inverse(Z), Y)), multiply(inverse(Y), Z))), multiply(inverse(S), T)))
% 0.21/0.68 = { by lemma 5 }
% 0.21/0.68 divide(X, inverse(divide(multiply(multiply(inverse(Y), Z), divide(multiply(multiply(inverse(Z), Y), X2), multiply(multiply(inverse(U), V), X2))), multiply(multiply(inverse(Y), Z), divide(multiply(multiply(inverse(Z), Y), X2), multiply(multiply(inverse(U), V), X2))))))
% 0.21/0.68 = { by lemma 16 }
% 0.21/0.68 divide(X, inverse(divide(multiply(multiply(inverse(Y), Z), divide(multiply(multiply(inverse(Z), Y), X2), multiply(multiply(inverse(U), V), X2))), multiply(inverse(V), U))))
% 0.21/0.68 = { by lemma 16 }
% 0.21/0.68 divide(X, inverse(divide(multiply(inverse(V), U), multiply(inverse(V), U))))
% 0.21/0.68 = { by axiom 1 (multiply) R->L }
% 0.21/0.68 multiply(X, divide(multiply(inverse(V), U), multiply(inverse(V), U)))
% 0.21/0.68
% 0.21/0.68 Lemma 18: inverse(divide(multiply(inverse(X), Y), multiply(inverse(X), Y))) = divide(multiply(inverse(Z), W), multiply(inverse(Z), W)).
% 0.21/0.68 Proof:
% 0.21/0.68 inverse(divide(multiply(inverse(X), Y), multiply(inverse(X), Y)))
% 0.21/0.68 = { by lemma 10 R->L }
% 0.21/0.68 divide(divide(inverse(divide(divide(multiply(inverse(Z), W), multiply(inverse(Z), W)), inverse(divide(multiply(inverse(X), Y), multiply(inverse(X), Y))))), multiply(inverse(W), Z)), multiply(inverse(Z), W))
% 0.21/0.68 = { by axiom 1 (multiply) R->L }
% 0.21/0.68 divide(divide(inverse(multiply(divide(multiply(inverse(Z), W), multiply(inverse(Z), W)), divide(multiply(inverse(X), Y), multiply(inverse(X), Y)))), multiply(inverse(W), Z)), multiply(inverse(Z), W))
% 0.21/0.68 = { by lemma 13 }
% 0.21/0.68 divide(divide(inverse(divide(multiply(inverse(Z), W), multiply(inverse(Z), W))), multiply(inverse(W), Z)), multiply(inverse(Z), W))
% 0.21/0.68 = { by lemma 16 R->L }
% 0.21/0.68 divide(divide(inverse(divide(multiply(multiply(inverse(Z), W), divide(multiply(multiply(inverse(W), Z), V), multiply(multiply(inverse(W), Z), V))), multiply(inverse(Z), W))), multiply(inverse(W), Z)), multiply(inverse(Z), W))
% 0.21/0.68 = { by lemma 16 R->L }
% 0.21/0.68 divide(divide(inverse(divide(multiply(multiply(inverse(Z), W), divide(multiply(multiply(inverse(W), Z), V), multiply(multiply(inverse(W), Z), V))), multiply(multiply(inverse(Z), W), divide(multiply(multiply(inverse(W), Z), V), multiply(multiply(inverse(W), Z), V))))), multiply(inverse(W), Z)), multiply(inverse(Z), W))
% 0.21/0.68 = { by lemma 4 }
% 0.21/0.68 divide(multiply(inverse(Z), W), multiply(inverse(Z), W))
% 0.21/0.68
% 0.21/0.68 Lemma 19: divide(X, divide(multiply(inverse(Y), Z), multiply(inverse(Y), Z))) = X.
% 0.21/0.68 Proof:
% 0.21/0.68 divide(X, divide(multiply(inverse(Y), Z), multiply(inverse(Y), Z)))
% 0.21/0.68 = { by lemma 18 R->L }
% 0.21/0.68 divide(X, inverse(divide(multiply(inverse(W), V), multiply(inverse(W), V))))
% 0.21/0.68 = { by axiom 1 (multiply) R->L }
% 0.21/0.68 multiply(X, divide(multiply(inverse(W), V), multiply(inverse(W), V)))
% 0.21/0.68 = { by lemma 14 }
% 0.21/0.68 X
% 0.21/0.68
% 0.21/0.68 Lemma 20: divide(inverse(X), multiply(multiply(inverse(Y), Z), multiply(divide(multiply(inverse(Z), Y), multiply(inverse(W), V)), divide(multiply(divide(multiply(inverse(W), V), U), T), multiply(X, T))))) = U.
% 0.21/0.68 Proof:
% 0.21/0.68 divide(inverse(X), multiply(multiply(inverse(Y), Z), multiply(divide(multiply(inverse(Z), Y), multiply(inverse(W), V)), divide(multiply(divide(multiply(inverse(W), V), U), T), multiply(X, T)))))
% 0.21/0.68 = { by axiom 1 (multiply) }
% 0.21/0.68 divide(inverse(X), multiply(multiply(inverse(Y), Z), divide(divide(multiply(inverse(Z), Y), multiply(inverse(W), V)), inverse(divide(multiply(divide(multiply(inverse(W), V), U), T), multiply(X, T))))))
% 0.21/0.68 = { by lemma 8 R->L }
% 0.21/0.68 divide(inverse(divide(inverse(divide(multiply(divide(multiply(inverse(W), V), U), T), multiply(X, T))), divide(U, multiply(inverse(W), V)))), multiply(multiply(inverse(Y), Z), divide(divide(multiply(inverse(Z), Y), multiply(inverse(W), V)), inverse(divide(multiply(divide(multiply(inverse(W), V), U), T), multiply(X, T))))))
% 0.21/0.68 = { by axiom 1 (multiply) }
% 0.21/0.68 divide(inverse(divide(inverse(divide(multiply(divide(multiply(inverse(W), V), U), T), multiply(X, T))), divide(U, multiply(inverse(W), V)))), divide(multiply(inverse(Y), Z), inverse(divide(divide(multiply(inverse(Z), Y), multiply(inverse(W), V)), inverse(divide(multiply(divide(multiply(inverse(W), V), U), T), multiply(X, T)))))))
% 0.21/0.68 = { by lemma 10 R->L }
% 0.21/0.69 divide(inverse(divide(divide(divide(inverse(divide(divide(multiply(inverse(Z), Y), multiply(inverse(W), V)), inverse(divide(multiply(divide(multiply(inverse(W), V), U), T), multiply(X, T))))), multiply(inverse(Y), Z)), multiply(inverse(W), V)), divide(U, multiply(inverse(W), V)))), divide(multiply(inverse(Y), Z), inverse(divide(divide(multiply(inverse(Z), Y), multiply(inverse(W), V)), inverse(divide(multiply(divide(multiply(inverse(W), V), U), T), multiply(X, T)))))))
% 0.21/0.69 = { by axiom 2 (single_axiom) }
% 0.21/0.69 U
% 0.21/0.69
% 0.21/0.69 Lemma 21: multiply(X, multiply(inverse(Y), Z)) = divide(X, multiply(inverse(Z), Y)).
% 0.21/0.69 Proof:
% 0.21/0.69 multiply(X, multiply(inverse(Y), Z))
% 0.21/0.69 = { by axiom 1 (multiply) }
% 0.21/0.69 divide(X, inverse(multiply(inverse(Y), Z)))
% 0.21/0.69 = { by lemma 7 R->L }
% 0.21/0.69 multiply(X, divide(multiply(multiply(inverse(Y), Z), W), multiply(divide(inverse(multiply(inverse(Y), Z)), multiply(inverse(Z), Y)), W)))
% 0.21/0.69 = { by lemma 14 R->L }
% 0.21/0.69 multiply(X, divide(multiply(multiply(inverse(Y), Z), W), multiply(divide(inverse(multiply(inverse(Y), Z)), multiply(multiply(inverse(Z), Y), divide(multiply(inverse(Y), Z), multiply(inverse(Y), Z)))), W)))
% 0.21/0.69 = { by lemma 13 R->L }
% 0.21/0.69 multiply(X, divide(multiply(multiply(inverse(Y), Z), W), multiply(divide(inverse(multiply(inverse(Y), Z)), multiply(multiply(inverse(Z), Y), multiply(divide(multiply(inverse(Y), Z), multiply(inverse(Y), Z)), divide(multiply(inverse(V), U), multiply(inverse(V), U))))), W)))
% 0.21/0.69 = { by lemma 17 R->L }
% 0.21/0.69 multiply(X, divide(multiply(multiply(inverse(Y), Z), W), multiply(divide(inverse(multiply(inverse(Y), Z)), multiply(multiply(inverse(Z), Y), multiply(divide(multiply(inverse(Y), Z), multiply(inverse(Y), Z)), divide(multiply(multiply(inverse(Y), Z), T), multiply(multiply(inverse(Y), Z), T))))), W)))
% 0.21/0.69 = { by lemma 19 R->L }
% 0.21/0.69 multiply(X, divide(multiply(multiply(inverse(Y), Z), W), multiply(divide(inverse(multiply(inverse(Y), Z)), multiply(multiply(inverse(Z), Y), multiply(divide(multiply(inverse(Y), Z), multiply(inverse(Y), Z)), divide(multiply(divide(multiply(inverse(Y), Z), divide(multiply(inverse(Z), Y), multiply(inverse(Z), Y))), T), multiply(multiply(inverse(Y), Z), T))))), W)))
% 0.21/0.69 = { by lemma 20 }
% 0.21/0.69 multiply(X, divide(multiply(multiply(inverse(Y), Z), W), multiply(divide(multiply(inverse(Z), Y), multiply(inverse(Z), Y)), W)))
% 0.21/0.69 = { by lemma 7 }
% 0.21/0.69 divide(X, multiply(inverse(Z), Y))
% 0.21/0.69
% 0.21/0.69 Lemma 22: divide(inverse(divide(multiply(inverse(X), Y), Z)), multiply(inverse(Y), X)) = Z.
% 0.21/0.69 Proof:
% 0.21/0.69 divide(inverse(divide(multiply(inverse(X), Y), Z)), multiply(inverse(Y), X))
% 0.21/0.69 = { by lemma 14 R->L }
% 0.21/0.69 divide(inverse(divide(multiply(multiply(inverse(X), Y), divide(multiply(inverse(W), V), multiply(inverse(W), V))), Z)), multiply(inverse(Y), X))
% 0.21/0.69 = { by lemma 14 R->L }
% 0.21/0.69 divide(inverse(divide(multiply(multiply(inverse(X), Y), divide(multiply(inverse(W), V), multiply(inverse(W), V))), multiply(Z, divide(multiply(inverse(W), V), multiply(inverse(W), V))))), multiply(inverse(Y), X))
% 0.21/0.69 = { by lemma 4 }
% 0.21/0.69 Z
% 0.21/0.69
% 0.21/0.69 Lemma 23: multiply(divide(multiply(inverse(X), Y), multiply(inverse(X), Y)), Z) = multiply(multiply(inverse(W), V), multiply(multiply(inverse(V), W), Z)).
% 0.21/0.69 Proof:
% 0.21/0.69 multiply(divide(multiply(inverse(X), Y), multiply(inverse(X), Y)), Z)
% 0.21/0.69 = { by lemma 18 R->L }
% 0.21/0.69 multiply(inverse(divide(multiply(inverse(U), T), multiply(inverse(U), T))), Z)
% 0.21/0.69 = { by axiom 1 (multiply) }
% 0.21/0.69 divide(inverse(divide(multiply(inverse(U), T), multiply(inverse(U), T))), inverse(Z))
% 0.21/0.69 = { by lemma 22 R->L }
% 0.21/0.69 divide(inverse(divide(multiply(inverse(U), T), multiply(inverse(U), T))), divide(inverse(divide(multiply(inverse(V), W), inverse(Z))), multiply(inverse(W), V)))
% 0.21/0.69 = { by axiom 1 (multiply) R->L }
% 0.21/0.69 divide(inverse(divide(multiply(inverse(U), T), multiply(inverse(U), T))), divide(inverse(multiply(multiply(inverse(V), W), Z)), multiply(inverse(W), V)))
% 0.21/0.69 = { by lemma 12 }
% 0.21/0.69 divide(multiply(inverse(W), V), inverse(multiply(multiply(inverse(V), W), Z)))
% 0.21/0.69 = { by axiom 1 (multiply) R->L }
% 0.21/0.69 multiply(multiply(inverse(W), V), multiply(multiply(inverse(V), W), Z))
% 0.21/0.69
% 0.21/0.69 Lemma 24: inverse(divide(multiply(divide(multiply(inverse(X), Y), multiply(inverse(X), Y)), Z), multiply(W, Z))) = W.
% 0.21/0.69 Proof:
% 0.21/0.69 inverse(divide(multiply(divide(multiply(inverse(X), Y), multiply(inverse(X), Y)), Z), multiply(W, Z)))
% 0.21/0.69 = { by lemma 19 R->L }
% 0.21/0.69 divide(inverse(divide(multiply(divide(multiply(inverse(X), Y), multiply(inverse(X), Y)), Z), multiply(W, Z))), divide(multiply(inverse(X), Y), multiply(inverse(X), Y)))
% 0.21/0.69 = { by lemma 8 }
% 0.21/0.69 W
% 0.21/0.69
% 0.21/0.69 Lemma 25: inverse(multiply(multiply(inverse(X), Y), multiply(multiply(inverse(Y), X), Z))) = inverse(Z).
% 0.21/0.69 Proof:
% 0.21/0.69 inverse(multiply(multiply(inverse(X), Y), multiply(multiply(inverse(Y), X), Z)))
% 0.21/0.69 = { by lemma 23 R->L }
% 0.21/0.69 inverse(multiply(divide(multiply(inverse(W), V), multiply(inverse(W), V)), Z))
% 0.21/0.69 = { by axiom 1 (multiply) }
% 0.21/0.69 inverse(divide(divide(multiply(inverse(W), V), multiply(inverse(W), V)), inverse(Z)))
% 0.21/0.69 = { by lemma 14 R->L }
% 0.21/0.69 inverse(divide(divide(multiply(inverse(W), V), multiply(inverse(W), V)), multiply(inverse(Z), divide(multiply(inverse(U), T), multiply(inverse(U), T)))))
% 0.21/0.69 = { by lemma 17 R->L }
% 0.21/0.69 inverse(divide(divide(multiply(inverse(W), V), multiply(inverse(W), V)), multiply(inverse(Z), divide(multiply(multiply(inverse(S), X2), Y2), multiply(multiply(inverse(S), X2), Y2)))))
% 0.21/0.69 = { by lemma 21 R->L }
% 0.21/0.69 inverse(divide(multiply(multiply(inverse(W), V), multiply(inverse(V), W)), multiply(inverse(Z), divide(multiply(multiply(inverse(S), X2), Y2), multiply(multiply(inverse(S), X2), Y2)))))
% 0.21/0.69 = { by lemma 14 R->L }
% 0.21/0.69 inverse(divide(multiply(multiply(inverse(W), V), multiply(multiply(inverse(V), W), divide(multiply(inverse(Z2), W2), multiply(inverse(Z2), W2)))), multiply(inverse(Z), divide(multiply(multiply(inverse(S), X2), Y2), multiply(multiply(inverse(S), X2), Y2)))))
% 0.21/0.69 = { by lemma 23 R->L }
% 0.21/0.69 inverse(divide(multiply(divide(multiply(inverse(V2), U2), multiply(inverse(V2), U2)), divide(multiply(inverse(Z2), W2), multiply(inverse(Z2), W2))), multiply(inverse(Z), divide(multiply(multiply(inverse(S), X2), Y2), multiply(multiply(inverse(S), X2), Y2)))))
% 0.21/0.69 = { by lemma 17 R->L }
% 0.21/0.69 inverse(divide(multiply(divide(multiply(inverse(V2), U2), multiply(inverse(V2), U2)), divide(multiply(multiply(inverse(S), X2), Y2), multiply(multiply(inverse(S), X2), Y2))), multiply(inverse(Z), divide(multiply(multiply(inverse(S), X2), Y2), multiply(multiply(inverse(S), X2), Y2)))))
% 0.21/0.69 = { by lemma 24 }
% 0.21/0.69 inverse(Z)
% 0.21/0.69
% 0.21/0.69 Lemma 26: inverse(divide(multiply(multiply(inverse(X), Y), multiply(multiply(inverse(Y), X), Z)), multiply(inverse(W), V))) = divide(multiply(inverse(W), V), Z).
% 0.21/0.69 Proof:
% 0.21/0.69 inverse(divide(multiply(multiply(inverse(X), Y), multiply(multiply(inverse(Y), X), Z)), multiply(inverse(W), V)))
% 0.21/0.69 = { by lemma 23 R->L }
% 0.21/0.69 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(inverse(W), V)))
% 0.21/0.69 = { by lemma 11 R->L }
% 0.21/0.69 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(divide(multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), inverse(divide(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))), multiply(inverse(V), W)))), divide(multiply(divide(inverse(divide(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))), multiply(inverse(V), W))), multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2)))))))), Y2), multiply(multiply(inverse(V), W), Y2)))))
% 0.21/0.69 = { by axiom 1 (multiply) }
% 0.21/0.69 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(divide(multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), inverse(divide(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))), multiply(inverse(V), W)))), divide(multiply(divide(inverse(divide(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))), multiply(inverse(V), W))), divide(multiply(inverse(W), V), inverse(divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))))), Y2), multiply(multiply(inverse(V), W), Y2)))))
% 0.21/0.70 = { by lemma 14 R->L }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(divide(multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), inverse(divide(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))), multiply(inverse(V), W)))), divide(multiply(divide(inverse(divide(multiply(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))), divide(multiply(inverse(Z2), W2), multiply(inverse(Z2), W2))), multiply(inverse(V), W))), divide(multiply(inverse(W), V), inverse(divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))))), Y2), multiply(multiply(inverse(V), W), Y2)))))
% 0.21/0.70 = { by lemma 22 R->L }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(divide(multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), inverse(divide(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))), multiply(inverse(V), W)))), divide(multiply(divide(inverse(divide(multiply(divide(inverse(divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), multiply(inverse(W), V)), divide(multiply(inverse(Z2), W2), multiply(inverse(Z2), W2))), multiply(inverse(V), W))), divide(multiply(inverse(W), V), inverse(divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))))), Y2), multiply(multiply(inverse(V), W), Y2)))))
% 0.21/0.70 = { by lemma 17 R->L }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(divide(multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), inverse(divide(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))), multiply(inverse(V), W)))), divide(multiply(divide(inverse(divide(multiply(divide(inverse(divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), multiply(inverse(W), V)), divide(multiply(multiply(inverse(W), V), V2), multiply(multiply(inverse(W), V), V2))), multiply(inverse(V), W))), divide(multiply(inverse(W), V), inverse(divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))))), Y2), multiply(multiply(inverse(V), W), Y2)))))
% 0.21/0.70 = { by lemma 15 R->L }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(divide(multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), inverse(divide(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))), multiply(inverse(V), W)))), divide(multiply(divide(inverse(divide(multiply(divide(inverse(divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), multiply(inverse(W), V)), divide(multiply(multiply(inverse(W), V), V2), multiply(multiply(inverse(W), V), V2))), multiply(multiply(inverse(V), W), divide(multiply(multiply(inverse(W), V), V2), multiply(multiply(inverse(W), V), V2))))), divide(multiply(inverse(W), V), inverse(divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))))), Y2), multiply(multiply(inverse(V), W), Y2)))))
% 0.21/0.70 = { by lemma 8 }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(divide(multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), inverse(divide(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))), multiply(inverse(V), W)))), divide(multiply(multiply(inverse(V), W), Y2), multiply(multiply(inverse(V), W), Y2)))))
% 0.21/0.70 = { by axiom 1 (multiply) R->L }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(multiply(multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), divide(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))), multiply(inverse(V), W))), divide(multiply(multiply(inverse(V), W), Y2), multiply(multiply(inverse(V), W), Y2)))))
% 0.21/0.70 = { by lemma 17 }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(multiply(multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), divide(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))), multiply(inverse(V), W))), divide(multiply(inverse(U2), T2), multiply(inverse(U2), T2)))))
% 0.21/0.70 = { by lemma 14 }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), divide(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))), multiply(inverse(V), W)))))
% 0.21/0.70 = { by lemma 17 R->L }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), divide(inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(multiply(inverse(V), W), S2), multiply(multiply(inverse(V), W), S2))))), multiply(inverse(V), W)))))
% 0.21/0.70 = { by lemma 16 R->L }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), divide(inverse(divide(multiply(multiply(inverse(W), V), divide(multiply(multiply(inverse(V), W), S2), multiply(multiply(inverse(V), W), S2))), multiply(Z, divide(multiply(multiply(inverse(V), W), S2), multiply(multiply(inverse(V), W), S2))))), multiply(inverse(V), W)))))
% 0.21/0.70 = { by lemma 4 }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(multiply(multiply(inverse(W), V), divide(multiply(inverse(V), W), inverse(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), Z)))
% 0.21/0.70 = { by axiom 1 (multiply) R->L }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(multiply(multiply(inverse(W), V), multiply(multiply(inverse(V), W), divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2)))))), Z)))
% 0.21/0.70 = { by axiom 1 (multiply) }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(divide(multiply(inverse(W), V), inverse(multiply(multiply(inverse(V), W), divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))))))), Z)))
% 0.21/0.70 = { by lemma 7 R->L }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(divide(multiply(inverse(W), V), inverse(multiply(multiply(inverse(V), W), multiply(multiply(inverse(W), V), divide(multiply(multiply(inverse(X3), Y3), Z3), multiply(divide(multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))), multiply(inverse(Y3), X3)), Z3)))))), Z)))
% 0.21/0.70 = { by lemma 25 }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(divide(multiply(inverse(W), V), inverse(divide(multiply(multiply(inverse(X3), Y3), Z3), multiply(divide(multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2))), multiply(inverse(Y3), X3)), Z3)))), Z)))
% 0.21/0.70 = { by lemma 6 }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(divide(multiply(inverse(W), V), multiply(Z, divide(multiply(inverse(S), X2), multiply(inverse(S), X2)))), Z)))
% 0.21/0.70 = { by lemma 14 }
% 0.21/0.70 inverse(divide(multiply(divide(multiply(inverse(U), T), multiply(inverse(U), T)), Z), multiply(divide(multiply(inverse(W), V), Z), Z)))
% 0.21/0.70 = { by lemma 24 }
% 0.21/0.70 divide(multiply(inverse(W), V), Z)
% 0.21/0.70
% 0.21/0.70 Lemma 27: multiply(multiply(inverse(X), Y), multiply(multiply(inverse(Y), X), Z)) = Z.
% 0.21/0.70 Proof:
% 0.21/0.70 multiply(multiply(inverse(X), Y), multiply(multiply(inverse(Y), X), Z))
% 0.21/0.70 = { by lemma 20 R->L }
% 0.21/0.70 divide(inverse(W), multiply(multiply(inverse(V), U), multiply(divide(multiply(inverse(U), V), multiply(inverse(T), S)), divide(multiply(divide(multiply(inverse(T), S), multiply(multiply(inverse(X), Y), multiply(multiply(inverse(Y), X), Z))), X2), multiply(W, X2)))))
% 0.21/0.70 = { by lemma 26 R->L }
% 0.21/0.70 divide(inverse(W), multiply(multiply(inverse(V), U), multiply(divide(multiply(inverse(U), V), multiply(inverse(T), S)), divide(multiply(inverse(divide(multiply(multiply(inverse(Y2), Z2), multiply(multiply(inverse(Z2), Y2), multiply(multiply(inverse(X), Y), multiply(multiply(inverse(Y), X), Z)))), multiply(inverse(T), S))), X2), multiply(W, X2)))))
% 0.21/0.70 = { by axiom 1 (multiply) }
% 0.21/0.70 divide(inverse(W), multiply(multiply(inverse(V), U), multiply(divide(multiply(inverse(U), V), multiply(inverse(T), S)), divide(multiply(inverse(divide(multiply(multiply(inverse(Y2), Z2), divide(multiply(inverse(Z2), Y2), inverse(multiply(multiply(inverse(X), Y), multiply(multiply(inverse(Y), X), Z))))), multiply(inverse(T), S))), X2), multiply(W, X2)))))
% 0.21/0.70 = { by lemma 25 }
% 0.21/0.70 divide(inverse(W), multiply(multiply(inverse(V), U), multiply(divide(multiply(inverse(U), V), multiply(inverse(T), S)), divide(multiply(inverse(divide(multiply(multiply(inverse(Y2), Z2), divide(multiply(inverse(Z2), Y2), inverse(Z))), multiply(inverse(T), S))), X2), multiply(W, X2)))))
% 0.21/0.70 = { by axiom 1 (multiply) R->L }
% 0.21/0.70 divide(inverse(W), multiply(multiply(inverse(V), U), multiply(divide(multiply(inverse(U), V), multiply(inverse(T), S)), divide(multiply(inverse(divide(multiply(multiply(inverse(Y2), Z2), multiply(multiply(inverse(Z2), Y2), Z)), multiply(inverse(T), S))), X2), multiply(W, X2)))))
% 0.21/0.70 = { by lemma 26 }
% 0.21/0.70 divide(inverse(W), multiply(multiply(inverse(V), U), multiply(divide(multiply(inverse(U), V), multiply(inverse(T), S)), divide(multiply(divide(multiply(inverse(T), S), Z), X2), multiply(W, X2)))))
% 0.21/0.70 = { by lemma 20 }
% 0.21/0.70 Z
% 0.21/0.70
% 0.21/0.70 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.21/0.70 Proof:
% 0.21/0.70 multiply(multiply(inverse(b2), b2), a2)
% 0.21/0.70 = { by lemma 14 R->L }
% 0.21/0.70 multiply(multiply(multiply(inverse(b2), b2), divide(multiply(inverse(X), Y), multiply(inverse(X), Y))), a2)
% 0.21/0.70 = { by lemma 17 R->L }
% 0.21/0.70 multiply(multiply(multiply(inverse(b2), b2), divide(multiply(multiply(inverse(Z), W), multiply(multiply(inverse(W), Z), inverse(b2))), multiply(multiply(inverse(Z), W), multiply(multiply(inverse(W), Z), inverse(b2))))), a2)
% 0.21/0.70 = { by lemma 27 }
% 0.21/0.70 multiply(multiply(multiply(inverse(b2), b2), divide(multiply(multiply(inverse(Z), W), multiply(multiply(inverse(W), Z), inverse(b2))), inverse(b2))), a2)
% 0.21/0.70 = { by lemma 27 }
% 0.21/0.70 multiply(multiply(multiply(inverse(b2), b2), divide(inverse(b2), inverse(b2))), a2)
% 0.21/0.70 = { by axiom 1 (multiply) R->L }
% 0.21/0.70 multiply(multiply(multiply(inverse(b2), b2), multiply(inverse(b2), b2)), a2)
% 0.21/0.70 = { by lemma 21 }
% 0.21/0.70 multiply(divide(multiply(inverse(b2), b2), multiply(inverse(b2), b2)), a2)
% 0.21/0.70 = { by lemma 23 }
% 0.21/0.70 multiply(multiply(inverse(V), U), multiply(multiply(inverse(U), V), a2))
% 0.21/0.70 = { by lemma 27 }
% 0.21/0.70 a2
% 0.21/0.70 % SZS output end Proof
% 0.21/0.70
% 0.21/0.70 RESULT: Unsatisfiable (the axioms are contradictory).
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