TSTP Solution File: GRP501-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP501-1 : 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 01:18:41 EDT 2023
% Result : Unsatisfiable 0.19s 0.56s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP501-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 23:59:55 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.56 Command-line arguments: --no-flatten-goal
% 0.19/0.56
% 0.19/0.56 % SZS status Unsatisfiable
% 0.19/0.56
% 0.19/0.63 % SZS output start Proof
% 0.19/0.63 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.19/0.63 Axiom 2 (single_axiom): double_divide(inverse(X), inverse(double_divide(inverse(double_divide(X, double_divide(Y, Z))), double_divide(W, double_divide(Y, W))))) = Z.
% 0.19/0.63
% 0.19/0.63 Lemma 3: double_divide(inverse(X), multiply(double_divide(Y, double_divide(Z, Y)), multiply(double_divide(Z, W), X))) = W.
% 0.19/0.63 Proof:
% 0.19/0.63 double_divide(inverse(X), multiply(double_divide(Y, double_divide(Z, Y)), multiply(double_divide(Z, W), X)))
% 0.19/0.63 = { by axiom 1 (multiply) }
% 0.19/0.63 double_divide(inverse(X), multiply(double_divide(Y, double_divide(Z, Y)), inverse(double_divide(X, double_divide(Z, W)))))
% 0.19/0.63 = { by axiom 1 (multiply) }
% 0.19/0.63 double_divide(inverse(X), inverse(double_divide(inverse(double_divide(X, double_divide(Z, W))), double_divide(Y, double_divide(Z, Y)))))
% 0.19/0.63 = { by axiom 2 (single_axiom) }
% 0.19/0.63 W
% 0.19/0.63
% 0.19/0.63 Lemma 4: double_divide(inverse(X), multiply(double_divide(Y, double_divide(inverse(Z), Y)), multiply(W, X))) = multiply(double_divide(V, double_divide(U, V)), multiply(double_divide(U, W), Z)).
% 0.19/0.63 Proof:
% 0.19/0.63 double_divide(inverse(X), multiply(double_divide(Y, double_divide(inverse(Z), Y)), multiply(W, X)))
% 0.19/0.63 = { by lemma 3 R->L }
% 0.19/0.63 double_divide(inverse(X), multiply(double_divide(Y, double_divide(inverse(Z), Y)), multiply(double_divide(inverse(Z), multiply(double_divide(V, double_divide(U, V)), multiply(double_divide(U, W), Z))), X)))
% 0.19/0.63 = { by lemma 3 }
% 0.19/0.63 multiply(double_divide(V, double_divide(U, V)), multiply(double_divide(U, W), Z))
% 0.19/0.63
% 0.19/0.63 Lemma 5: multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(inverse(Z), W)), Z)) = W.
% 0.19/0.63 Proof:
% 0.19/0.63 multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(inverse(Z), W)), Z))
% 0.19/0.63 = { by lemma 4 R->L }
% 0.19/0.63 double_divide(inverse(V), multiply(double_divide(U, double_divide(inverse(Z), U)), multiply(double_divide(inverse(Z), W), V)))
% 0.19/0.63 = { by lemma 3 }
% 0.19/0.63 W
% 0.19/0.63
% 0.19/0.63 Lemma 6: multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(Z, double_divide(W, Z))), V)) = double_divide(W, inverse(V)).
% 0.19/0.63 Proof:
% 0.19/0.63 multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(Z, double_divide(W, Z))), V))
% 0.19/0.63 = { by lemma 4 R->L }
% 0.19/0.63 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), multiply(double_divide(Z, double_divide(W, Z)), U)))
% 0.19/0.63 = { by lemma 5 R->L }
% 0.19/0.63 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), multiply(double_divide(Z, double_divide(W, Z)), multiply(double_divide(W, double_divide(S, W)), multiply(double_divide(S, double_divide(inverse(X2), U)), X2)))))
% 0.19/0.63 = { by lemma 3 R->L }
% 0.19/0.63 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), double_divide(inverse(Y2), multiply(double_divide(Z2, double_divide(inverse(multiply(double_divide(S, double_divide(inverse(X2), U)), X2)), Z2)), multiply(double_divide(inverse(multiply(double_divide(S, double_divide(inverse(X2), U)), X2)), multiply(double_divide(Z, double_divide(W, Z)), multiply(double_divide(W, double_divide(S, W)), multiply(double_divide(S, double_divide(inverse(X2), U)), X2)))), Y2)))))
% 0.19/0.63 = { by lemma 3 }
% 0.19/0.63 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), double_divide(inverse(Y2), multiply(double_divide(Z2, double_divide(inverse(multiply(double_divide(S, double_divide(inverse(X2), U)), X2)), Z2)), multiply(double_divide(S, W), Y2)))))
% 0.19/0.63 = { by lemma 3 R->L }
% 0.19/0.63 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), double_divide(inverse(Y2), multiply(double_divide(Z2, double_divide(inverse(multiply(double_divide(S, double_divide(inverse(X2), U)), X2)), Z2)), multiply(double_divide(inverse(multiply(double_divide(S, double_divide(inverse(X2), U)), X2)), multiply(double_divide(inverse(V), double_divide(W, inverse(V))), multiply(double_divide(W, double_divide(S, W)), multiply(double_divide(S, double_divide(inverse(X2), U)), X2)))), Y2)))))
% 0.19/0.63 = { by lemma 3 }
% 0.19/0.63 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), multiply(double_divide(inverse(V), double_divide(W, inverse(V))), multiply(double_divide(W, double_divide(S, W)), multiply(double_divide(S, double_divide(inverse(X2), U)), X2)))))
% 0.19/0.63 = { by lemma 5 }
% 0.19/0.63 double_divide(inverse(U), multiply(double_divide(T, double_divide(inverse(V), T)), multiply(double_divide(inverse(V), double_divide(W, inverse(V))), U)))
% 0.19/0.63 = { by lemma 3 }
% 0.19/0.63 double_divide(W, inverse(V))
% 0.19/0.63
% 0.19/0.63 Lemma 7: double_divide(multiply(X, Y), double_divide(Z, multiply(X, Y))) = double_divide(W, double_divide(Z, W)).
% 0.19/0.63 Proof:
% 0.19/0.63 double_divide(multiply(X, Y), double_divide(Z, multiply(X, Y)))
% 0.19/0.63 = { by axiom 1 (multiply) }
% 0.19/0.63 double_divide(multiply(X, Y), double_divide(Z, inverse(double_divide(Y, X))))
% 0.19/0.63 = { by lemma 6 R->L }
% 0.19/0.63 double_divide(multiply(X, Y), multiply(double_divide(V, double_divide(U, V)), multiply(double_divide(U, double_divide(W, double_divide(Z, W))), double_divide(Y, X))))
% 0.19/0.63 = { by axiom 1 (multiply) }
% 0.19/0.63 double_divide(inverse(double_divide(Y, X)), multiply(double_divide(V, double_divide(U, V)), multiply(double_divide(U, double_divide(W, double_divide(Z, W))), double_divide(Y, X))))
% 0.19/0.63 = { by lemma 3 }
% 0.19/0.63 double_divide(W, double_divide(Z, W))
% 0.19/0.63
% 0.19/0.63 Lemma 8: double_divide(Z, double_divide(Y, Z)) = double_divide(X, double_divide(Y, X)).
% 0.19/0.63 Proof:
% 0.19/0.63 double_divide(Z, double_divide(Y, Z))
% 0.19/0.63 = { by lemma 5 R->L }
% 0.19/0.63 double_divide(Z, double_divide(Y, multiply(double_divide(T, double_divide(S, T)), multiply(double_divide(S, double_divide(inverse(X2), Z)), X2))))
% 0.19/0.63 = { by lemma 5 R->L }
% 0.19/0.63 double_divide(multiply(double_divide(T, double_divide(S, T)), multiply(double_divide(S, double_divide(inverse(X2), Z)), X2)), double_divide(Y, multiply(double_divide(T, double_divide(S, T)), multiply(double_divide(S, double_divide(inverse(X2), Z)), X2))))
% 0.19/0.63 = { by lemma 7 }
% 0.19/0.63 double_divide(multiply(double_divide(W, double_divide(V, W)), multiply(double_divide(V, double_divide(inverse(U), X)), U)), double_divide(Y, multiply(double_divide(W, double_divide(V, W)), multiply(double_divide(V, double_divide(inverse(U), X)), U))))
% 0.19/0.63 = { by lemma 5 }
% 0.19/0.63 double_divide(X, double_divide(Y, multiply(double_divide(W, double_divide(V, W)), multiply(double_divide(V, double_divide(inverse(U), X)), U))))
% 0.19/0.63 = { by lemma 5 }
% 0.19/0.63 double_divide(X, double_divide(Y, X))
% 0.19/0.63
% 0.19/0.63 Lemma 9: multiply(double_divide(X, Z), Z) = multiply(double_divide(X, Y), Y).
% 0.19/0.63 Proof:
% 0.19/0.63 multiply(double_divide(X, Z), Z)
% 0.19/0.63 = { by axiom 1 (multiply) }
% 0.19/0.63 inverse(double_divide(Z, double_divide(X, Z)))
% 0.19/0.63 = { by lemma 8 }
% 0.19/0.63 inverse(double_divide(Y, double_divide(X, Y)))
% 0.19/0.63 = { by axiom 1 (multiply) R->L }
% 0.19/0.63 multiply(double_divide(X, Y), Y)
% 0.19/0.63
% 0.19/0.63 Lemma 10: double_divide(inverse(X), double_divide(Y, multiply(double_divide(Y, Z), Z))) = X.
% 0.19/0.63 Proof:
% 0.19/0.63 double_divide(inverse(X), double_divide(Y, multiply(double_divide(Y, Z), Z)))
% 0.19/0.63 = { by axiom 1 (multiply) }
% 0.19/0.63 double_divide(inverse(X), double_divide(Y, inverse(double_divide(Z, double_divide(Y, Z)))))
% 0.19/0.63 = { by lemma 6 R->L }
% 0.19/0.63 double_divide(inverse(X), multiply(double_divide(W, double_divide(V, W)), multiply(double_divide(V, double_divide(Z, double_divide(Y, Z))), double_divide(Z, double_divide(Y, Z)))))
% 0.19/0.63 = { by lemma 9 R->L }
% 0.19/0.63 double_divide(inverse(X), multiply(double_divide(W, double_divide(V, W)), multiply(double_divide(V, X), X)))
% 0.19/0.63 = { by lemma 3 }
% 0.19/0.63 X
% 0.19/0.63
% 0.19/0.63 Lemma 11: multiply(double_divide(X, multiply(double_divide(X, Y), Y)), inverse(Z)) = inverse(Z).
% 0.19/0.63 Proof:
% 0.19/0.63 multiply(double_divide(X, multiply(double_divide(X, Y), Y)), inverse(Z))
% 0.19/0.63 = { by axiom 1 (multiply) }
% 0.19/0.64 inverse(double_divide(inverse(Z), double_divide(X, multiply(double_divide(X, Y), Y))))
% 0.19/0.64 = { by lemma 10 }
% 0.19/0.64 inverse(Z)
% 0.19/0.64
% 0.19/0.64 Lemma 12: multiply(double_divide(X, multiply(double_divide(X, Y), Y)), Z) = Z.
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(double_divide(X, multiply(double_divide(X, Y), Y)), Z)
% 0.19/0.64 = { by lemma 5 R->L }
% 0.19/0.64 multiply(double_divide(X, multiply(double_divide(X, Y), Y)), multiply(double_divide(W, double_divide(V, W)), multiply(double_divide(V, double_divide(inverse(U), Z)), U)))
% 0.19/0.64 = { by axiom 1 (multiply) }
% 0.19/0.64 multiply(double_divide(X, multiply(double_divide(X, Y), Y)), inverse(double_divide(multiply(double_divide(V, double_divide(inverse(U), Z)), U), double_divide(W, double_divide(V, W)))))
% 0.19/0.64 = { by lemma 11 }
% 0.19/0.64 inverse(double_divide(multiply(double_divide(V, double_divide(inverse(U), Z)), U), double_divide(W, double_divide(V, W))))
% 0.19/0.64 = { by axiom 1 (multiply) R->L }
% 0.19/0.64 multiply(double_divide(W, double_divide(V, W)), multiply(double_divide(V, double_divide(inverse(U), Z)), U))
% 0.19/0.64 = { by lemma 5 }
% 0.19/0.64 Z
% 0.19/0.64
% 0.19/0.64 Lemma 13: double_divide(inverse(X), multiply(double_divide(Y, double_divide(Z, Y)), X)) = multiply(double_divide(Z, W), W).
% 0.19/0.64 Proof:
% 0.19/0.64 double_divide(inverse(X), multiply(double_divide(Y, double_divide(Z, Y)), X))
% 0.19/0.64 = { by lemma 12 R->L }
% 0.19/0.64 double_divide(inverse(X), multiply(double_divide(Y, double_divide(Z, Y)), multiply(double_divide(Z, multiply(double_divide(Z, W), W)), X)))
% 0.19/0.64 = { by lemma 3 }
% 0.19/0.64 multiply(double_divide(Z, W), W)
% 0.19/0.64
% 0.19/0.64 Lemma 14: double_divide(inverse(multiply(double_divide(X, double_divide(inverse(Y), Z)), Y)), Z) = multiply(double_divide(X, W), W).
% 0.19/0.64 Proof:
% 0.19/0.64 double_divide(inverse(multiply(double_divide(X, double_divide(inverse(Y), Z)), Y)), Z)
% 0.19/0.64 = { by lemma 5 R->L }
% 0.19/0.64 double_divide(inverse(multiply(double_divide(X, double_divide(inverse(Y), Z)), Y)), multiply(double_divide(V, double_divide(X, V)), multiply(double_divide(X, double_divide(inverse(Y), Z)), Y)))
% 0.19/0.64 = { by lemma 13 }
% 0.19/0.64 multiply(double_divide(X, W), W)
% 0.19/0.64
% 0.19/0.64 Lemma 15: double_divide(inverse(Y), Y) = double_divide(inverse(X), X).
% 0.19/0.64 Proof:
% 0.19/0.64 double_divide(inverse(Y), Y)
% 0.19/0.64 = { by lemma 12 R->L }
% 0.19/0.64 double_divide(inverse(Y), multiply(double_divide(Z, multiply(double_divide(Z, T), T)), Y))
% 0.19/0.64 = { by lemma 14 R->L }
% 0.19/0.64 double_divide(inverse(Y), multiply(double_divide(Z, double_divide(inverse(multiply(double_divide(Z, double_divide(inverse(V), Z)), V)), Z)), Y))
% 0.19/0.64 = { by lemma 13 }
% 0.19/0.64 multiply(double_divide(inverse(multiply(double_divide(Z, double_divide(inverse(V), Z)), V)), U), U)
% 0.19/0.64 = { by lemma 13 R->L }
% 0.19/0.64 double_divide(inverse(X), multiply(double_divide(Z, double_divide(inverse(multiply(double_divide(Z, double_divide(inverse(V), Z)), V)), Z)), X))
% 0.19/0.64 = { by lemma 14 }
% 0.19/0.64 double_divide(inverse(X), multiply(double_divide(Z, multiply(double_divide(Z, W), W)), X))
% 0.19/0.64 = { by lemma 12 }
% 0.19/0.64 double_divide(inverse(X), X)
% 0.19/0.64
% 0.19/0.64 Lemma 16: multiply(multiply(double_divide(X, Y), Y), X) = double_divide(inverse(Z), Z).
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(multiply(double_divide(X, Y), Y), X)
% 0.19/0.64 = { by lemma 14 R->L }
% 0.19/0.64 multiply(double_divide(inverse(multiply(double_divide(X, double_divide(inverse(W), X)), W)), X), X)
% 0.19/0.64 = { by lemma 13 R->L }
% 0.19/0.64 double_divide(inverse(Z), multiply(double_divide(X, double_divide(inverse(multiply(double_divide(X, double_divide(inverse(W), X)), W)), X)), Z))
% 0.19/0.64 = { by lemma 14 }
% 0.19/0.64 double_divide(inverse(Z), multiply(double_divide(X, multiply(double_divide(X, V), V)), Z))
% 0.19/0.64 = { by lemma 12 }
% 0.19/0.64 double_divide(inverse(Z), Z)
% 0.19/0.64
% 0.19/0.64 Lemma 17: double_divide(inverse(X), X) = multiply(Y, inverse(Y)).
% 0.19/0.64 Proof:
% 0.19/0.64 double_divide(inverse(X), X)
% 0.19/0.64 = { by lemma 16 R->L }
% 0.19/0.64 multiply(multiply(double_divide(Z, W), W), Z)
% 0.19/0.64 = { by axiom 1 (multiply) }
% 0.19/0.64 inverse(double_divide(Z, multiply(double_divide(Z, W), W)))
% 0.19/0.64 = { by lemma 11 R->L }
% 0.19/0.64 multiply(double_divide(Z, multiply(double_divide(Z, W), W)), inverse(double_divide(Z, multiply(double_divide(Z, W), W))))
% 0.19/0.64 = { by axiom 1 (multiply) }
% 0.19/0.64 inverse(double_divide(inverse(double_divide(Z, multiply(double_divide(Z, W), W))), double_divide(Z, multiply(double_divide(Z, W), W))))
% 0.19/0.64 = { by lemma 15 R->L }
% 0.19/0.64 inverse(double_divide(inverse(Y), Y))
% 0.19/0.64 = { by axiom 1 (multiply) R->L }
% 0.19/0.64 multiply(Y, inverse(Y))
% 0.19/0.64
% 0.19/0.64 Lemma 18: double_divide(X, double_divide(inverse(Y), X)) = double_divide(Y, multiply(Z, inverse(Z))).
% 0.19/0.64 Proof:
% 0.19/0.64 double_divide(X, double_divide(inverse(Y), X))
% 0.19/0.64 = { by lemma 8 }
% 0.19/0.64 double_divide(Y, double_divide(inverse(Y), Y))
% 0.19/0.64 = { by lemma 15 R->L }
% 0.19/0.64 double_divide(Y, double_divide(inverse(W), W))
% 0.19/0.64 = { by lemma 17 }
% 0.19/0.64 double_divide(Y, multiply(Z, inverse(Z)))
% 0.19/0.64
% 0.19/0.64 Lemma 19: multiply(double_divide(inverse(X), Y), Y) = multiply(multiply(Z, inverse(Z)), X).
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(double_divide(inverse(X), Y), Y)
% 0.19/0.64 = { by lemma 9 }
% 0.19/0.64 multiply(double_divide(inverse(X), X), X)
% 0.19/0.64 = { by lemma 15 R->L }
% 0.19/0.64 multiply(double_divide(inverse(W), W), X)
% 0.19/0.64 = { by lemma 17 }
% 0.19/0.64 multiply(multiply(Z, inverse(Z)), X)
% 0.19/0.64
% 0.19/0.64 Lemma 20: multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(Z, multiply(double_divide(Z, W), W))), V)) = multiply(multiply(U, inverse(U)), V).
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(Z, multiply(double_divide(Z, W), W))), V))
% 0.19/0.64 = { by axiom 1 (multiply) }
% 0.19/0.64 multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(Z, inverse(double_divide(W, double_divide(Z, W))))), V))
% 0.19/0.64 = { by lemma 6 R->L }
% 0.19/0.64 multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, multiply(double_divide(T, double_divide(S, T)), multiply(double_divide(S, double_divide(W, double_divide(Z, W))), double_divide(W, double_divide(Z, W))))), V))
% 0.19/0.64 = { by lemma 9 R->L }
% 0.19/0.64 multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, multiply(double_divide(T, double_divide(S, T)), multiply(double_divide(S, double_divide(X2, double_divide(inverse(V), X2))), double_divide(X2, double_divide(inverse(V), X2))))), V))
% 0.19/0.64 = { by lemma 6 }
% 0.19/0.64 multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(inverse(V), inverse(double_divide(X2, double_divide(inverse(V), X2))))), V))
% 0.19/0.64 = { by axiom 1 (multiply) R->L }
% 0.19/0.64 multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, double_divide(inverse(V), multiply(double_divide(inverse(V), X2), X2))), V))
% 0.19/0.64 = { by lemma 5 }
% 0.19/0.64 multiply(double_divide(inverse(V), X2), X2)
% 0.19/0.64 = { by lemma 19 }
% 0.19/0.64 multiply(multiply(U, inverse(U)), V)
% 0.19/0.64
% 0.19/0.64 Lemma 21: double_divide(multiply(X, Y), double_divide(Z, multiply(double_divide(Z, W), W))) = double_divide(Y, X).
% 0.19/0.64 Proof:
% 0.19/0.64 double_divide(multiply(X, Y), double_divide(Z, multiply(double_divide(Z, W), W)))
% 0.19/0.64 = { by axiom 1 (multiply) }
% 0.19/0.64 double_divide(inverse(double_divide(Y, X)), double_divide(Z, multiply(double_divide(Z, W), W)))
% 0.19/0.64 = { by lemma 10 }
% 0.19/0.64 double_divide(Y, X)
% 0.19/0.64
% 0.19/0.64 Lemma 22: multiply(multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, Z), W)), inverse(W)) = inverse(Z).
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, Z), W)), inverse(W))
% 0.19/0.64 = { by axiom 1 (multiply) }
% 0.19/0.64 inverse(double_divide(inverse(W), multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, Z), W))))
% 0.19/0.64 = { by lemma 3 }
% 0.19/0.64 inverse(Z)
% 0.19/0.64
% 0.19/0.64 Lemma 23: multiply(multiply(multiply(X, inverse(X)), Y), inverse(Y)) = multiply(Z, inverse(Z)).
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(multiply(multiply(X, inverse(X)), Y), inverse(Y))
% 0.19/0.64 = { by lemma 20 R->L }
% 0.19/0.64 multiply(multiply(double_divide(W, double_divide(V, W)), multiply(double_divide(V, double_divide(U, multiply(double_divide(U, T), T))), Y)), inverse(Y))
% 0.19/0.64 = { by lemma 22 }
% 0.19/0.64 inverse(double_divide(U, multiply(double_divide(U, T), T)))
% 0.19/0.64 = { by axiom 1 (multiply) R->L }
% 0.19/0.64 multiply(multiply(double_divide(U, T), T), U)
% 0.19/0.64 = { by lemma 16 }
% 0.19/0.64 double_divide(inverse(S), S)
% 0.19/0.64 = { by lemma 17 }
% 0.19/0.64 multiply(Z, inverse(Z))
% 0.19/0.64
% 0.19/0.64 Lemma 24: double_divide(inverse(X), multiply(multiply(Y, inverse(Y)), X)) = multiply(Z, inverse(Z)).
% 0.19/0.64 Proof:
% 0.19/0.64 double_divide(inverse(X), multiply(multiply(Y, inverse(Y)), X))
% 0.19/0.64 = { by lemma 21 R->L }
% 0.19/0.64 double_divide(multiply(multiply(multiply(Y, inverse(Y)), X), inverse(X)), double_divide(W, multiply(double_divide(W, V), V)))
% 0.19/0.64 = { by lemma 23 }
% 0.19/0.64 double_divide(multiply(U, inverse(U)), double_divide(W, multiply(double_divide(W, V), V)))
% 0.19/0.64 = { by lemma 21 }
% 0.19/0.64 double_divide(inverse(U), U)
% 0.19/0.64 = { by lemma 17 }
% 0.19/0.64 multiply(Z, inverse(Z))
% 0.19/0.64
% 0.19/0.64 Lemma 25: double_divide(X, multiply(double_divide(X, Y), Y)) = multiply(Z, inverse(Z)).
% 0.19/0.64 Proof:
% 0.19/0.64 double_divide(X, multiply(double_divide(X, Y), Y))
% 0.19/0.64 = { by lemma 3 R->L }
% 0.19/0.64 double_divide(inverse(W), multiply(double_divide(V, double_divide(U, V)), multiply(double_divide(U, double_divide(X, multiply(double_divide(X, Y), Y))), W)))
% 0.19/0.64 = { by lemma 20 }
% 0.19/0.64 double_divide(inverse(W), multiply(multiply(T, inverse(T)), W))
% 0.19/0.64 = { by lemma 24 }
% 0.19/0.64 multiply(Z, inverse(Z))
% 0.19/0.64
% 0.19/0.64 Lemma 26: double_divide(X, double_divide(inverse(inverse(Y)), X)) = Y.
% 0.19/0.64 Proof:
% 0.19/0.64 double_divide(X, double_divide(inverse(inverse(Y)), X))
% 0.19/0.64 = { by lemma 18 }
% 0.19/0.64 double_divide(inverse(Y), multiply(Z, inverse(Z)))
% 0.19/0.64 = { by lemma 25 R->L }
% 0.19/0.64 double_divide(inverse(Y), double_divide(W, multiply(double_divide(W, V), V)))
% 0.19/0.64 = { by lemma 10 }
% 0.19/0.64 Y
% 0.19/0.64
% 0.19/0.64 Lemma 27: multiply(multiply(double_divide(X, double_divide(Y, X)), Z), inverse(Z)) = inverse(multiply(double_divide(Y, W), W)).
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(multiply(double_divide(X, double_divide(Y, X)), Z), inverse(Z))
% 0.19/0.64 = { by lemma 12 R->L }
% 0.19/0.64 multiply(multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, multiply(double_divide(Y, W), W)), Z)), inverse(Z))
% 0.19/0.64 = { by lemma 22 }
% 0.19/0.64 inverse(multiply(double_divide(Y, W), W))
% 0.19/0.64
% 0.19/0.64 Lemma 28: multiply(multiply(X, inverse(X)), Y) = Y.
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(multiply(X, inverse(X)), Y)
% 0.19/0.64 = { by lemma 25 R->L }
% 0.19/0.64 multiply(double_divide(Z, multiply(double_divide(Z, W), W)), Y)
% 0.19/0.64 = { by lemma 12 }
% 0.19/0.64 Y
% 0.19/0.64
% 0.19/0.64 Lemma 29: multiply(multiply(X, Y), inverse(Y)) = inverse(inverse(X)).
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(multiply(X, Y), inverse(Y))
% 0.19/0.64 = { by lemma 26 R->L }
% 0.19/0.64 multiply(multiply(double_divide(Z, double_divide(inverse(inverse(X)), Z)), Y), inverse(Y))
% 0.19/0.64 = { by lemma 27 }
% 0.19/0.64 inverse(multiply(double_divide(inverse(inverse(X)), W), W))
% 0.19/0.64 = { by lemma 19 }
% 0.19/0.64 inverse(multiply(multiply(V, inverse(V)), inverse(X)))
% 0.19/0.64 = { by lemma 28 }
% 0.19/0.64 inverse(inverse(X))
% 0.19/0.64
% 0.19/0.64 Lemma 30: multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, multiply(double_divide(Z, double_divide(W, Z)), multiply(double_divide(W, V), U))), T)) = multiply(double_divide(S, double_divide(inverse(U), S)), multiply(V, T)).
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(double_divide(X, double_divide(Y, X)), multiply(double_divide(Y, multiply(double_divide(Z, double_divide(W, Z)), multiply(double_divide(W, V), U))), T))
% 0.19/0.64 = { by lemma 4 R->L }
% 0.19/0.64 double_divide(inverse(X2), multiply(double_divide(Y2, double_divide(inverse(T), Y2)), multiply(multiply(double_divide(Z, double_divide(W, Z)), multiply(double_divide(W, V), U)), X2)))
% 0.19/0.64 = { by lemma 4 R->L }
% 0.19/0.64 double_divide(inverse(X2), multiply(double_divide(Y2, double_divide(inverse(T), Y2)), multiply(double_divide(inverse(T), multiply(double_divide(S, double_divide(inverse(U), S)), multiply(V, T))), X2)))
% 0.19/0.64 = { by lemma 3 }
% 0.19/0.64 multiply(double_divide(S, double_divide(inverse(U), S)), multiply(V, T))
% 0.19/0.64
% 0.19/0.64 Lemma 31: multiply(double_divide(X, Y), Y) = inverse(X).
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(double_divide(X, Y), Y)
% 0.19/0.64 = { by lemma 9 }
% 0.19/0.64 multiply(double_divide(X, multiply(X, inverse(X))), multiply(X, inverse(X)))
% 0.19/0.64 = { by lemma 17 R->L }
% 0.19/0.64 multiply(double_divide(X, double_divide(inverse(X), X)), multiply(X, inverse(X)))
% 0.19/0.64 = { by lemma 30 R->L }
% 0.19/0.64 multiply(double_divide(Z, double_divide(W, Z)), multiply(double_divide(W, multiply(double_divide(V, double_divide(U, V)), multiply(double_divide(U, X), X))), inverse(X)))
% 0.19/0.64 = { by lemma 9 }
% 0.19/0.64 multiply(double_divide(Z, double_divide(W, Z)), multiply(double_divide(W, multiply(double_divide(V, double_divide(U, V)), multiply(double_divide(U, multiply(T, inverse(T))), multiply(T, inverse(T))))), inverse(X)))
% 0.19/0.64 = { by lemma 30 }
% 0.19/0.64 multiply(double_divide(S, double_divide(inverse(multiply(T, inverse(T))), S)), multiply(multiply(T, inverse(T)), inverse(X)))
% 0.19/0.64 = { by lemma 28 }
% 0.19/0.64 multiply(double_divide(S, double_divide(inverse(multiply(T, inverse(T))), S)), inverse(X))
% 0.19/0.64 = { by lemma 18 }
% 0.19/0.64 multiply(double_divide(multiply(T, inverse(T)), multiply(X2, inverse(X2))), inverse(X))
% 0.19/0.64 = { by lemma 23 R->L }
% 0.19/0.64 multiply(double_divide(multiply(multiply(multiply(Y2, inverse(Y2)), Z2), inverse(Z2)), multiply(X2, inverse(X2))), inverse(X))
% 0.19/0.64 = { by lemma 24 R->L }
% 0.19/0.64 multiply(double_divide(multiply(multiply(multiply(Y2, inverse(Y2)), Z2), inverse(Z2)), double_divide(inverse(Z2), multiply(multiply(Y2, inverse(Y2)), Z2))), inverse(X))
% 0.19/0.64 = { by axiom 1 (multiply) }
% 0.19/0.64 multiply(double_divide(inverse(double_divide(inverse(Z2), multiply(multiply(Y2, inverse(Y2)), Z2))), double_divide(inverse(Z2), multiply(multiply(Y2, inverse(Y2)), Z2))), inverse(X))
% 0.19/0.64 = { by lemma 17 }
% 0.19/0.64 multiply(multiply(W2, inverse(W2)), inverse(X))
% 0.19/0.64 = { by lemma 28 }
% 0.19/0.64 inverse(X)
% 0.19/0.64
% 0.19/0.64 Lemma 32: double_divide(X, double_divide(Y, X)) = Y.
% 0.19/0.64 Proof:
% 0.19/0.64 double_divide(X, double_divide(Y, X))
% 0.19/0.64 = { by lemma 7 R->L }
% 0.19/0.64 double_divide(multiply(double_divide(Y, Z), Z), double_divide(Y, multiply(double_divide(Y, Z), Z)))
% 0.19/0.64 = { by lemma 31 }
% 0.19/0.64 double_divide(inverse(Y), double_divide(Y, multiply(double_divide(Y, Z), Z)))
% 0.19/0.64 = { by lemma 10 }
% 0.19/0.64 Y
% 0.19/0.64
% 0.19/0.64 Lemma 33: multiply(X, multiply(Y, inverse(Y))) = X.
% 0.19/0.64 Proof:
% 0.19/0.64 multiply(X, multiply(Y, inverse(Y)))
% 0.19/0.64 = { by lemma 32 R->L }
% 0.19/0.64 multiply(double_divide(Z, double_divide(X, Z)), multiply(Y, inverse(Y)))
% 0.19/0.64 = { by lemma 26 R->L }
% 0.19/0.64 multiply(double_divide(Z, double_divide(X, Z)), multiply(double_divide(X, double_divide(inverse(inverse(Y)), X)), inverse(Y)))
% 0.19/0.64 = { by lemma 5 }
% 0.19/0.64 X
% 0.19/0.64
% 0.19/0.64 Lemma 34: inverse(inverse(X)) = X.
% 0.19/0.64 Proof:
% 0.19/0.64 inverse(inverse(X))
% 0.19/0.65 = { by lemma 29 R->L }
% 0.19/0.65 multiply(multiply(X, multiply(Y, inverse(Y))), inverse(multiply(Y, inverse(Y))))
% 0.19/0.65 = { by lemma 33 }
% 0.19/0.65 multiply(X, inverse(multiply(Y, inverse(Y))))
% 0.19/0.65 = { by lemma 17 R->L }
% 0.19/0.65 multiply(X, inverse(double_divide(inverse(Z), Z)))
% 0.19/0.65 = { by axiom 1 (multiply) R->L }
% 0.19/0.65 multiply(X, multiply(Z, inverse(Z)))
% 0.19/0.65 = { by lemma 33 }
% 0.19/0.65 X
% 0.19/0.65
% 0.19/0.65 Lemma 35: inverse(multiply(X, Y)) = double_divide(Y, X).
% 0.19/0.65 Proof:
% 0.19/0.65 inverse(multiply(X, Y))
% 0.19/0.65 = { by axiom 1 (multiply) }
% 0.19/0.65 inverse(inverse(double_divide(Y, X)))
% 0.19/0.65 = { by lemma 34 }
% 0.19/0.65 double_divide(Y, X)
% 0.19/0.65
% 0.19/0.65 Lemma 36: double_divide(X, inverse(Y)) = multiply(inverse(X), Y).
% 0.19/0.65 Proof:
% 0.19/0.65 double_divide(X, inverse(Y))
% 0.19/0.65 = { by lemma 34 R->L }
% 0.19/0.65 inverse(inverse(double_divide(X, inverse(Y))))
% 0.19/0.65 = { by lemma 29 R->L }
% 0.19/0.65 multiply(multiply(double_divide(X, inverse(Y)), inverse(Y)), inverse(inverse(Y)))
% 0.19/0.65 = { by lemma 34 }
% 0.19/0.65 multiply(multiply(double_divide(X, inverse(Y)), inverse(Y)), Y)
% 0.19/0.65 = { by lemma 31 }
% 0.19/0.65 multiply(inverse(X), Y)
% 0.19/0.65
% 0.19/0.65 Lemma 37: multiply(inverse(X), inverse(Y)) = double_divide(X, Y).
% 0.19/0.65 Proof:
% 0.19/0.65 multiply(inverse(X), inverse(Y))
% 0.19/0.65 = { by lemma 31 R->L }
% 0.19/0.65 multiply(multiply(double_divide(X, Y), Y), inverse(Y))
% 0.19/0.65 = { by lemma 29 }
% 0.19/0.65 inverse(inverse(double_divide(X, Y)))
% 0.19/0.65 = { by lemma 34 }
% 0.19/0.65 double_divide(X, Y)
% 0.19/0.65
% 0.19/0.65 Lemma 38: double_divide(inverse(X), multiply(Y, X)) = inverse(Y).
% 0.19/0.65 Proof:
% 0.19/0.65 double_divide(inverse(X), multiply(Y, X))
% 0.19/0.65 = { by lemma 26 R->L }
% 0.19/0.65 double_divide(inverse(X), multiply(double_divide(Z, double_divide(inverse(inverse(Y)), Z)), X))
% 0.19/0.65 = { by lemma 13 }
% 0.19/0.65 multiply(double_divide(inverse(inverse(Y)), W), W)
% 0.19/0.65 = { by lemma 19 }
% 0.19/0.65 multiply(multiply(V, inverse(V)), inverse(Y))
% 0.19/0.65 = { by lemma 28 }
% 0.19/0.65 inverse(Y)
% 0.19/0.65
% 0.19/0.65 Lemma 39: multiply(X, multiply(double_divide(X, Y), Z)) = multiply(inverse(Y), Z).
% 0.19/0.65 Proof:
% 0.19/0.65 multiply(X, multiply(double_divide(X, Y), Z))
% 0.19/0.65 = { by lemma 32 R->L }
% 0.19/0.65 multiply(double_divide(W, double_divide(X, W)), multiply(double_divide(X, Y), Z))
% 0.19/0.65 = { by lemma 26 R->L }
% 0.19/0.65 multiply(double_divide(W, double_divide(X, W)), multiply(double_divide(X, double_divide(V, double_divide(inverse(inverse(Y)), V))), Z))
% 0.19/0.65 = { by lemma 6 }
% 0.19/0.65 double_divide(inverse(inverse(Y)), inverse(Z))
% 0.19/0.65 = { by lemma 32 R->L }
% 0.19/0.65 double_divide(inverse(inverse(Y)), double_divide(inverse(U), double_divide(inverse(Z), inverse(U))))
% 0.19/0.65 = { by lemma 36 }
% 0.19/0.65 double_divide(inverse(inverse(Y)), double_divide(inverse(U), multiply(inverse(inverse(Z)), U)))
% 0.19/0.65 = { by lemma 38 }
% 0.19/0.65 double_divide(inverse(inverse(Y)), inverse(inverse(inverse(Z))))
% 0.19/0.65 = { by lemma 36 }
% 0.19/0.65 multiply(inverse(inverse(inverse(Y))), inverse(inverse(Z)))
% 0.19/0.65 = { by lemma 34 }
% 0.19/0.65 multiply(inverse(Y), inverse(inverse(Z)))
% 0.19/0.65 = { by lemma 37 }
% 0.19/0.65 double_divide(Y, inverse(Z))
% 0.19/0.65 = { by lemma 36 }
% 0.19/0.65 multiply(inverse(Y), Z)
% 0.19/0.65
% 0.19/0.65 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.19/0.65 Proof:
% 0.19/0.65 multiply(multiply(a3, b3), c3)
% 0.19/0.65 = { by lemma 10 R->L }
% 0.19/0.65 multiply(double_divide(inverse(multiply(a3, b3)), double_divide(X, multiply(double_divide(X, Y), Y))), c3)
% 0.19/0.65 = { by lemma 28 R->L }
% 0.19/0.65 multiply(double_divide(multiply(multiply(Z, inverse(Z)), inverse(multiply(a3, b3))), double_divide(X, multiply(double_divide(X, Y), Y))), c3)
% 0.19/0.65 = { by lemma 19 R->L }
% 0.19/0.65 multiply(double_divide(multiply(double_divide(inverse(inverse(multiply(a3, b3))), multiply(inverse(W), inverse(multiply(a3, b3)))), multiply(inverse(W), inverse(multiply(a3, b3)))), double_divide(X, multiply(double_divide(X, Y), Y))), c3)
% 0.19/0.65 = { by lemma 38 }
% 0.19/0.65 multiply(double_divide(multiply(inverse(inverse(W)), multiply(inverse(W), inverse(multiply(a3, b3)))), double_divide(X, multiply(double_divide(X, Y), Y))), c3)
% 0.19/0.65 = { by lemma 37 }
% 0.19/0.65 multiply(double_divide(multiply(inverse(inverse(W)), double_divide(W, multiply(a3, b3))), double_divide(X, multiply(double_divide(X, Y), Y))), c3)
% 0.19/0.65 = { by lemma 34 }
% 0.19/0.65 multiply(double_divide(multiply(W, double_divide(W, multiply(a3, b3))), double_divide(X, multiply(double_divide(X, Y), Y))), c3)
% 0.19/0.65 = { by lemma 21 }
% 0.19/0.65 multiply(double_divide(double_divide(W, multiply(a3, b3)), W), c3)
% 0.19/0.65 = { by lemma 35 R->L }
% 0.19/0.65 multiply(inverse(multiply(W, double_divide(W, multiply(a3, b3)))), c3)
% 0.19/0.65 = { by lemma 39 R->L }
% 0.19/0.65 multiply(V, multiply(double_divide(V, multiply(W, double_divide(W, multiply(a3, b3)))), c3))
% 0.19/0.65 = { by lemma 32 R->L }
% 0.19/0.65 multiply(double_divide(U, double_divide(V, U)), multiply(double_divide(V, multiply(W, double_divide(W, multiply(a3, b3)))), c3))
% 0.19/0.65 = { by lemma 32 R->L }
% 0.19/0.65 multiply(double_divide(U, double_divide(V, U)), multiply(double_divide(V, multiply(double_divide(T, double_divide(W, T)), double_divide(W, multiply(a3, b3)))), c3))
% 0.19/0.65 = { by lemma 34 R->L }
% 0.19/0.65 multiply(double_divide(U, double_divide(V, U)), multiply(double_divide(V, multiply(double_divide(T, double_divide(W, T)), double_divide(W, multiply(inverse(inverse(a3)), b3)))), c3))
% 0.19/0.65 = { by lemma 36 R->L }
% 0.19/0.65 multiply(double_divide(U, double_divide(V, U)), multiply(double_divide(V, multiply(double_divide(T, double_divide(W, T)), double_divide(W, double_divide(inverse(a3), inverse(b3))))), c3))
% 0.19/0.65 = { by lemma 37 R->L }
% 0.19/0.65 multiply(double_divide(U, double_divide(V, U)), multiply(double_divide(V, multiply(double_divide(T, double_divide(W, T)), multiply(inverse(W), inverse(double_divide(inverse(a3), inverse(b3)))))), c3))
% 0.19/0.65 = { by axiom 1 (multiply) R->L }
% 0.19/0.65 multiply(double_divide(U, double_divide(V, U)), multiply(double_divide(V, multiply(double_divide(T, double_divide(W, T)), multiply(inverse(W), multiply(inverse(b3), inverse(a3))))), c3))
% 0.19/0.65 = { by lemma 31 R->L }
% 0.19/0.65 multiply(double_divide(U, double_divide(V, U)), multiply(double_divide(V, multiply(double_divide(T, double_divide(W, T)), multiply(multiply(double_divide(W, double_divide(multiply(double_divide(W, b3), inverse(a3)), W)), double_divide(multiply(double_divide(W, b3), inverse(a3)), W)), multiply(inverse(b3), inverse(a3))))), c3))
% 0.19/0.65 = { by lemma 39 R->L }
% 0.19/0.65 multiply(double_divide(U, double_divide(V, U)), multiply(double_divide(V, multiply(double_divide(T, double_divide(W, T)), multiply(multiply(double_divide(W, double_divide(multiply(double_divide(W, b3), inverse(a3)), W)), double_divide(multiply(double_divide(W, b3), inverse(a3)), W)), multiply(W, multiply(double_divide(W, b3), inverse(a3)))))), c3))
% 0.19/0.65 = { by axiom 1 (multiply) }
% 0.19/0.65 multiply(double_divide(U, double_divide(V, U)), multiply(double_divide(V, multiply(double_divide(T, double_divide(W, T)), multiply(multiply(double_divide(W, double_divide(multiply(double_divide(W, b3), inverse(a3)), W)), double_divide(multiply(double_divide(W, b3), inverse(a3)), W)), inverse(double_divide(multiply(double_divide(W, b3), inverse(a3)), W))))), c3))
% 0.19/0.65 = { by lemma 27 }
% 0.19/0.65 multiply(double_divide(U, double_divide(V, U)), multiply(double_divide(V, multiply(double_divide(T, double_divide(W, T)), inverse(multiply(double_divide(multiply(double_divide(W, b3), inverse(a3)), S), S)))), c3))
% 0.19/0.65 = { by lemma 35 }
% 0.19/0.65 multiply(double_divide(U, double_divide(V, U)), multiply(double_divide(V, multiply(double_divide(T, double_divide(W, T)), double_divide(S, double_divide(multiply(double_divide(W, b3), inverse(a3)), S)))), c3))
% 0.19/0.65 = { by lemma 32 }
% 0.19/0.65 multiply(double_divide(U, double_divide(V, U)), multiply(double_divide(V, multiply(double_divide(T, double_divide(W, T)), multiply(double_divide(W, b3), inverse(a3)))), c3))
% 0.19/0.65 = { by lemma 30 }
% 0.19/0.65 multiply(double_divide(X2, double_divide(inverse(inverse(a3)), X2)), multiply(b3, c3))
% 0.19/0.65 = { by lemma 26 }
% 0.19/0.65 multiply(a3, multiply(b3, c3))
% 0.19/0.65 % SZS output end Proof
% 0.19/0.65
% 0.19/0.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------