TSTP Solution File: GRP504-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP504-1 : 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 : n001.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 0.18s 0.57s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP504-1 : 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
% 0.16/0.33 % Computer : n001.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon Aug 28 21:45:35 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.18/0.57 Command-line arguments: --no-flatten-goal
% 0.18/0.57
% 0.18/0.57 % SZS status Unsatisfiable
% 0.18/0.57
% 0.18/0.67 % SZS output start Proof
% 0.18/0.67 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.18/0.67 Axiom 2 (single_axiom): double_divide(double_divide(X, inverse(double_divide(Y, Z))), double_divide(inverse(Y), inverse(double_divide(W, double_divide(X, W))))) = Z.
% 0.18/0.67
% 0.18/0.67 Lemma 3: double_divide(double_divide(X, multiply(Y, Z)), double_divide(inverse(Z), multiply(double_divide(X, W), W))) = Y.
% 0.18/0.67 Proof:
% 0.18/0.67 double_divide(double_divide(X, multiply(Y, Z)), double_divide(inverse(Z), multiply(double_divide(X, W), W)))
% 0.18/0.67 = { by axiom 1 (multiply) }
% 0.18/0.67 double_divide(double_divide(X, multiply(Y, Z)), double_divide(inverse(Z), inverse(double_divide(W, double_divide(X, W)))))
% 0.18/0.67 = { by axiom 1 (multiply) }
% 0.18/0.67 double_divide(double_divide(X, inverse(double_divide(Z, Y))), double_divide(inverse(Z), inverse(double_divide(W, double_divide(X, W)))))
% 0.18/0.67 = { by axiom 2 (single_axiom) }
% 0.18/0.67 Y
% 0.18/0.67
% 0.18/0.67 Lemma 4: multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(W, X))) = inverse(W).
% 0.18/0.67 Proof:
% 0.18/0.67 multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(W, X)))
% 0.18/0.67 = { by axiom 1 (multiply) }
% 0.18/0.67 inverse(double_divide(double_divide(Y, multiply(W, X)), double_divide(inverse(X), multiply(double_divide(Y, Z), Z))))
% 0.18/0.67 = { by lemma 3 }
% 0.18/0.67 inverse(W)
% 0.18/0.67
% 0.18/0.67 Lemma 5: double_divide(inverse(X), multiply(double_divide(Y, W), W)) = double_divide(inverse(X), multiply(double_divide(Y, Z), Z)).
% 0.18/0.67 Proof:
% 0.18/0.67 double_divide(inverse(X), multiply(double_divide(Y, W), W))
% 0.18/0.67 = { by lemma 3 R->L }
% 0.18/0.67 double_divide(double_divide(V, multiply(double_divide(inverse(X), multiply(double_divide(Y, W), W)), double_divide(Y, multiply(U, X)))), double_divide(inverse(double_divide(Y, multiply(U, X))), multiply(double_divide(V, T), T)))
% 0.18/0.67 = { by lemma 4 }
% 0.18/0.67 double_divide(double_divide(V, inverse(U)), double_divide(inverse(double_divide(Y, multiply(U, X))), multiply(double_divide(V, T), T)))
% 0.18/0.67 = { by lemma 4 R->L }
% 0.18/0.67 double_divide(double_divide(V, multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(U, X)))), double_divide(inverse(double_divide(Y, multiply(U, X))), multiply(double_divide(V, T), T)))
% 0.18/0.67 = { by lemma 3 }
% 0.18/0.67 double_divide(inverse(X), multiply(double_divide(Y, Z), Z))
% 0.18/0.67
% 0.18/0.67 Lemma 6: multiply(double_divide(X, Z), Z) = multiply(double_divide(X, Y), Y).
% 0.18/0.67 Proof:
% 0.18/0.67 multiply(double_divide(X, Z), Z)
% 0.18/0.67 = { by lemma 3 R->L }
% 0.18/0.67 double_divide(double_divide(W, multiply(multiply(double_divide(X, Z), Z), inverse(V))), double_divide(inverse(inverse(V)), multiply(double_divide(W, U), U)))
% 0.18/0.67 = { by axiom 1 (multiply) }
% 0.18/0.67 double_divide(double_divide(W, inverse(double_divide(inverse(V), multiply(double_divide(X, Z), Z)))), double_divide(inverse(inverse(V)), multiply(double_divide(W, U), U)))
% 0.18/0.67 = { by lemma 5 }
% 0.18/0.67 double_divide(double_divide(W, inverse(double_divide(inverse(V), multiply(double_divide(X, Y), Y)))), double_divide(inverse(inverse(V)), multiply(double_divide(W, U), U)))
% 0.18/0.67 = { by axiom 1 (multiply) R->L }
% 0.18/0.67 double_divide(double_divide(W, multiply(multiply(double_divide(X, Y), Y), inverse(V))), double_divide(inverse(inverse(V)), multiply(double_divide(W, U), U)))
% 0.18/0.67 = { by lemma 3 }
% 0.18/0.67 multiply(double_divide(X, Y), Y)
% 0.18/0.67
% 0.18/0.67 Lemma 7: multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(double_divide(W, V), V))) = multiply(X, W).
% 0.18/0.67 Proof:
% 0.18/0.67 multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(double_divide(W, V), V)))
% 0.18/0.67 = { by lemma 6 }
% 0.18/0.67 multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(double_divide(W, X), X)))
% 0.18/0.67 = { by lemma 4 }
% 0.18/0.67 inverse(double_divide(W, X))
% 0.18/0.67 = { by axiom 1 (multiply) R->L }
% 0.18/0.67 multiply(X, W)
% 0.18/0.67
% 0.18/0.67 Lemma 8: multiply(X, double_divide(inverse(Y), multiply(double_divide(Z, W), W))) = multiply(double_divide(double_divide(Z, multiply(X, Y)), V), V).
% 0.18/0.67 Proof:
% 0.18/0.67 multiply(X, double_divide(inverse(Y), multiply(double_divide(Z, W), W)))
% 0.18/0.67 = { by lemma 3 R->L }
% 0.18/0.67 multiply(double_divide(double_divide(Z, multiply(X, Y)), double_divide(inverse(Y), multiply(double_divide(Z, W), W))), double_divide(inverse(Y), multiply(double_divide(Z, W), W)))
% 0.18/0.67 = { by lemma 6 R->L }
% 0.18/0.67 multiply(double_divide(double_divide(Z, multiply(X, Y)), V), V)
% 0.18/0.67
% 0.18/0.67 Lemma 9: multiply(double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), W), W)), Z)), V), V) = multiply(Y, X).
% 0.18/0.67 Proof:
% 0.18/0.67 multiply(double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), W), W)), Z)), V), V)
% 0.18/0.67 = { by lemma 8 R->L }
% 0.18/0.67 multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), W), W)), double_divide(inverse(Z), multiply(double_divide(X, Y), Y)))
% 0.18/0.67 = { by lemma 4 }
% 0.18/0.67 inverse(double_divide(X, Y))
% 0.18/0.67 = { by axiom 1 (multiply) R->L }
% 0.18/0.67 multiply(Y, X)
% 0.18/0.67
% 0.18/0.67 Lemma 10: double_divide(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(inverse(W), multiply(double_divide(inverse(X), V), V))) = double_divide(Y, W).
% 0.18/0.67 Proof:
% 0.18/0.67 double_divide(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(inverse(W), multiply(double_divide(inverse(X), V), V)))
% 0.18/0.67 = { by lemma 5 }
% 0.18/0.67 double_divide(double_divide(inverse(X), multiply(double_divide(Y, W), W)), double_divide(inverse(W), multiply(double_divide(inverse(X), V), V)))
% 0.18/0.67 = { by lemma 3 }
% 0.18/0.67 double_divide(Y, W)
% 0.18/0.67
% 0.18/0.67 Lemma 11: double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), W), W)), Z)), X) = Y.
% 0.18/0.67 Proof:
% 0.18/0.67 double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), W), W)), Z)), X)
% 0.18/0.67 = { by lemma 10 R->L }
% 0.18/0.67 double_divide(double_divide(inverse(V), multiply(double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), W), W)), Z)), U), U)), double_divide(inverse(X), multiply(double_divide(inverse(V), T), T)))
% 0.18/0.67 = { by lemma 9 }
% 0.18/0.67 double_divide(double_divide(inverse(V), multiply(Y, X)), double_divide(inverse(X), multiply(double_divide(inverse(V), T), T)))
% 0.18/0.67 = { by lemma 3 }
% 0.18/0.67 Y
% 0.18/0.67
% 0.18/0.67 Lemma 12: multiply(double_divide(inverse(X), multiply(Y, multiply(double_divide(Z, W), W))), Y) = multiply(X, Z).
% 0.18/0.67 Proof:
% 0.18/0.67 multiply(double_divide(inverse(X), multiply(Y, multiply(double_divide(Z, W), W))), Y)
% 0.18/0.67 = { by lemma 9 R->L }
% 0.18/0.67 multiply(double_divide(inverse(X), multiply(double_divide(double_divide(multiply(double_divide(Z, W), W), multiply(double_divide(inverse(Y), multiply(double_divide(inverse(V), U), U)), V)), T), T)), Y)
% 0.18/0.67 = { by lemma 11 R->L }
% 0.18/0.67 multiply(double_divide(inverse(X), multiply(double_divide(double_divide(multiply(double_divide(Z, W), W), multiply(double_divide(inverse(Y), multiply(double_divide(inverse(V), U), U)), V)), T), T)), double_divide(double_divide(multiply(double_divide(Z, W), W), multiply(double_divide(inverse(Y), multiply(double_divide(inverse(V), U), U)), V)), multiply(double_divide(Z, W), W)))
% 0.18/0.67 = { by lemma 7 }
% 0.18/0.68 multiply(X, Z)
% 0.18/0.68
% 0.18/0.68 Lemma 13: multiply(double_divide(inverse(X), multiply(Y, multiply(Z, X))), Y) = inverse(Z).
% 0.18/0.68 Proof:
% 0.18/0.68 multiply(double_divide(inverse(X), multiply(Y, multiply(Z, X))), Y)
% 0.18/0.68 = { by lemma 9 R->L }
% 0.18/0.68 multiply(double_divide(inverse(X), multiply(double_divide(double_divide(multiply(Z, X), multiply(double_divide(inverse(Y), multiply(double_divide(inverse(W), V), V)), W)), U), U)), Y)
% 0.18/0.68 = { by lemma 11 R->L }
% 0.18/0.68 multiply(double_divide(inverse(X), multiply(double_divide(double_divide(multiply(Z, X), multiply(double_divide(inverse(Y), multiply(double_divide(inverse(W), V), V)), W)), U), U)), double_divide(double_divide(multiply(Z, X), multiply(double_divide(inverse(Y), multiply(double_divide(inverse(W), V), V)), W)), multiply(Z, X)))
% 0.18/0.68 = { by lemma 4 }
% 0.18/0.68 inverse(Z)
% 0.18/0.68
% 0.18/0.68 Lemma 14: multiply(double_divide(inverse(X), multiply(Y, multiply(Z, W))), Y) = multiply(multiply(X, multiply(double_divide(W, V), V)), inverse(Z)).
% 0.18/0.68 Proof:
% 0.18/0.68 multiply(double_divide(inverse(X), multiply(Y, multiply(Z, W))), Y)
% 0.18/0.68 = { by lemma 12 R->L }
% 0.18/0.68 multiply(double_divide(inverse(X), multiply(Y, multiply(double_divide(inverse(Z), multiply(X, multiply(double_divide(W, V), V))), X))), Y)
% 0.18/0.68 = { by lemma 13 }
% 0.18/0.68 inverse(double_divide(inverse(Z), multiply(X, multiply(double_divide(W, V), V))))
% 0.18/0.68 = { by axiom 1 (multiply) R->L }
% 0.18/0.68 multiply(multiply(X, multiply(double_divide(W, V), V)), inverse(Z))
% 0.18/0.68
% 0.18/0.68 Lemma 15: multiply(multiply(X, multiply(double_divide(Y, Z), Z)), multiply(Y, W)) = multiply(X, W).
% 0.18/0.68 Proof:
% 0.18/0.68 multiply(multiply(X, multiply(double_divide(Y, Z), Z)), multiply(Y, W))
% 0.18/0.68 = { by axiom 1 (multiply) }
% 0.18/0.68 multiply(multiply(X, multiply(double_divide(Y, Z), Z)), inverse(double_divide(W, Y)))
% 0.18/0.68 = { by lemma 14 R->L }
% 0.18/0.68 multiply(double_divide(inverse(X), multiply(V, multiply(double_divide(W, Y), Y))), V)
% 0.18/0.68 = { by lemma 6 R->L }
% 0.18/0.68 multiply(double_divide(inverse(X), multiply(V, multiply(double_divide(W, U), U))), V)
% 0.18/0.68 = { by lemma 12 }
% 0.18/0.68 multiply(X, W)
% 0.18/0.68
% 0.18/0.68 Lemma 16: double_divide(X, double_divide(inverse(Y), multiply(X, multiply(Z, Y)))) = Z.
% 0.18/0.68 Proof:
% 0.18/0.68 double_divide(X, double_divide(inverse(Y), multiply(X, multiply(Z, Y))))
% 0.18/0.68 = { by lemma 9 R->L }
% 0.18/0.68 double_divide(X, double_divide(inverse(Y), multiply(double_divide(double_divide(multiply(Z, Y), multiply(double_divide(inverse(X), multiply(double_divide(inverse(W), V), V)), W)), U), U)))
% 0.18/0.68 = { by lemma 11 R->L }
% 0.18/0.68 double_divide(double_divide(double_divide(multiply(Z, Y), multiply(double_divide(inverse(X), multiply(double_divide(inverse(W), V), V)), W)), multiply(Z, Y)), double_divide(inverse(Y), multiply(double_divide(double_divide(multiply(Z, Y), multiply(double_divide(inverse(X), multiply(double_divide(inverse(W), V), V)), W)), U), U)))
% 0.18/0.68 = { by lemma 3 }
% 0.18/0.68 Z
% 0.18/0.68
% 0.18/0.68 Lemma 17: double_divide(inverse(W), multiply(Y, multiply(Z, W))) = double_divide(inverse(X), multiply(Y, multiply(Z, X))).
% 0.18/0.68 Proof:
% 0.18/0.68 double_divide(inverse(W), multiply(Y, multiply(Z, W)))
% 0.18/0.68 = { by lemma 16 R->L }
% 0.18/0.68 double_divide(V, double_divide(inverse(Y), multiply(V, multiply(double_divide(inverse(W), multiply(Y, multiply(Z, W))), Y))))
% 0.18/0.68 = { by lemma 13 }
% 0.18/0.68 double_divide(V, double_divide(inverse(Y), multiply(V, inverse(Z))))
% 0.18/0.68 = { by lemma 13 R->L }
% 0.18/0.68 double_divide(V, double_divide(inverse(Y), multiply(V, multiply(double_divide(inverse(X), multiply(Y, multiply(Z, X))), Y))))
% 0.18/0.68 = { by lemma 16 }
% 0.18/0.68 double_divide(inverse(X), multiply(Y, multiply(Z, X)))
% 0.18/0.68
% 0.18/0.68 Lemma 18: double_divide(inverse(Z), multiply(Y, Z)) = double_divide(inverse(X), multiply(Y, X)).
% 0.18/0.68 Proof:
% 0.18/0.68 double_divide(inverse(Z), multiply(Y, Z))
% 0.18/0.68 = { by lemma 15 R->L }
% 0.18/0.68 double_divide(inverse(Z), multiply(multiply(Y, multiply(double_divide(W, V), V)), multiply(W, Z)))
% 0.18/0.68 = { by lemma 17 }
% 0.18/0.68 double_divide(inverse(X), multiply(multiply(Y, multiply(double_divide(W, V), V)), multiply(W, X)))
% 0.18/0.68 = { by lemma 15 }
% 0.18/0.68 double_divide(inverse(X), multiply(Y, X))
% 0.18/0.68
% 0.18/0.68 Lemma 19: multiply(multiply(X, multiply(double_divide(X, Y), Y)), inverse(Z)) = inverse(Z).
% 0.18/0.68 Proof:
% 0.18/0.68 multiply(multiply(X, multiply(double_divide(X, Y), Y)), inverse(Z))
% 0.18/0.68 = { by lemma 14 R->L }
% 0.18/0.68 multiply(double_divide(inverse(X), multiply(double_divide(W, multiply(Z, X)), multiply(Z, X))), double_divide(W, multiply(Z, X)))
% 0.18/0.68 = { by lemma 4 }
% 0.18/0.68 inverse(Z)
% 0.18/0.68
% 0.18/0.68 Lemma 20: multiply(Z, multiply(double_divide(Z, W), W)) = multiply(X, multiply(double_divide(X, Y), Y)).
% 0.18/0.68 Proof:
% 0.18/0.68 multiply(Z, multiply(double_divide(Z, W), W))
% 0.18/0.68 = { by lemma 16 R->L }
% 0.18/0.68 double_divide(V, double_divide(inverse(inverse(U)), multiply(V, multiply(multiply(Z, multiply(double_divide(Z, W), W)), inverse(U)))))
% 0.18/0.68 = { by lemma 19 }
% 0.18/0.68 double_divide(V, double_divide(inverse(inverse(U)), multiply(V, inverse(U))))
% 0.18/0.68 = { by lemma 19 R->L }
% 0.18/0.68 double_divide(V, double_divide(inverse(inverse(U)), multiply(V, multiply(multiply(X, multiply(double_divide(X, Y), Y)), inverse(U)))))
% 0.18/0.68 = { by lemma 16 }
% 0.18/0.68 multiply(X, multiply(double_divide(X, Y), Y))
% 0.18/0.68
% 0.18/0.68 Lemma 21: double_divide(inverse(X), multiply(Y, X)) = multiply(double_divide(Y, Z), Z).
% 0.18/0.68 Proof:
% 0.18/0.68 double_divide(inverse(X), multiply(Y, X))
% 0.18/0.68 = { by lemma 18 }
% 0.18/0.68 double_divide(inverse(multiply(double_divide(Y, Z), Z)), multiply(Y, multiply(double_divide(Y, Z), Z)))
% 0.18/0.68 = { by lemma 20 R->L }
% 0.18/0.68 double_divide(inverse(multiply(double_divide(Y, Z), Z)), multiply(W, multiply(double_divide(W, V), V)))
% 0.18/0.68 = { by lemma 16 R->L }
% 0.18/0.68 double_divide(U, double_divide(inverse(W), multiply(U, multiply(double_divide(inverse(multiply(double_divide(Y, Z), Z)), multiply(W, multiply(double_divide(W, V), V))), W))))
% 0.18/0.68 = { by lemma 12 }
% 0.18/0.68 double_divide(U, double_divide(inverse(W), multiply(U, multiply(multiply(double_divide(Y, Z), Z), W))))
% 0.18/0.68 = { by lemma 16 }
% 0.18/0.68 multiply(double_divide(Y, Z), Z)
% 0.18/0.68
% 0.18/0.68 Lemma 22: double_divide(inverse(X), multiply(double_divide(Y, Z), Z)) = multiply(double_divide(double_divide(Y, X), W), W).
% 0.18/0.68 Proof:
% 0.18/0.68 double_divide(inverse(X), multiply(double_divide(Y, Z), Z))
% 0.18/0.68 = { by lemma 5 }
% 0.18/0.68 double_divide(inverse(X), multiply(double_divide(Y, X), X))
% 0.18/0.68 = { by lemma 18 R->L }
% 0.18/0.68 double_divide(inverse(V), multiply(double_divide(Y, X), V))
% 0.18/0.68 = { by lemma 21 }
% 0.18/0.68 multiply(double_divide(double_divide(Y, X), W), W)
% 0.18/0.68
% 0.18/0.68 Lemma 23: double_divide(double_divide(X, inverse(Y)), double_divide(multiply(multiply(Y, Z), W), multiply(double_divide(X, V), V))) = double_divide(inverse(Z), multiply(double_divide(W, U), U)).
% 0.18/0.68 Proof:
% 0.18/0.68 double_divide(double_divide(X, inverse(Y)), double_divide(multiply(multiply(Y, Z), W), multiply(double_divide(X, V), V)))
% 0.18/0.68 = { by axiom 1 (multiply) }
% 0.18/0.68 double_divide(double_divide(X, inverse(Y)), double_divide(inverse(double_divide(W, multiply(Y, Z))), multiply(double_divide(X, V), V)))
% 0.18/0.68 = { by lemma 4 R->L }
% 0.18/0.68 double_divide(double_divide(X, multiply(double_divide(inverse(Z), multiply(double_divide(W, U), U)), double_divide(W, multiply(Y, Z)))), double_divide(inverse(double_divide(W, multiply(Y, Z))), multiply(double_divide(X, V), V)))
% 0.18/0.68 = { by lemma 3 }
% 0.18/0.68 double_divide(inverse(Z), multiply(double_divide(W, U), U))
% 0.18/0.69
% 0.18/0.69 Lemma 24: multiply(double_divide(multiply(X, Y), multiply(double_divide(Z, W), W)), double_divide(Z, multiply(V, double_divide(Y, X)))) = inverse(V).
% 0.18/0.69 Proof:
% 0.18/0.69 multiply(double_divide(multiply(X, Y), multiply(double_divide(Z, W), W)), double_divide(Z, multiply(V, double_divide(Y, X))))
% 0.18/0.69 = { by axiom 1 (multiply) }
% 0.18/0.69 multiply(double_divide(inverse(double_divide(Y, X)), multiply(double_divide(Z, W), W)), double_divide(Z, multiply(V, double_divide(Y, X))))
% 0.18/0.69 = { by lemma 4 }
% 0.18/0.69 inverse(V)
% 0.18/0.69
% 0.18/0.69 Lemma 25: double_divide(double_divide(X, multiply(Y, double_divide(Z, W))), double_divide(multiply(W, Z), multiply(double_divide(X, V), V))) = Y.
% 0.18/0.69 Proof:
% 0.18/0.69 double_divide(double_divide(X, multiply(Y, double_divide(Z, W))), double_divide(multiply(W, Z), multiply(double_divide(X, V), V)))
% 0.18/0.69 = { by axiom 1 (multiply) }
% 0.18/0.69 double_divide(double_divide(X, multiply(Y, double_divide(Z, W))), double_divide(inverse(double_divide(Z, W)), multiply(double_divide(X, V), V)))
% 0.18/0.69 = { by lemma 3 }
% 0.18/0.69 Y
% 0.18/0.69
% 0.18/0.69 Lemma 26: double_divide(X, double_divide(inverse(Y), multiply(X, inverse(Z)))) = double_divide(inverse(W), multiply(Y, multiply(Z, W))).
% 0.18/0.69 Proof:
% 0.18/0.69 double_divide(X, double_divide(inverse(Y), multiply(X, inverse(Z))))
% 0.18/0.69 = { by lemma 13 R->L }
% 0.18/0.69 double_divide(X, double_divide(inverse(Y), multiply(X, multiply(double_divide(inverse(W), multiply(Y, multiply(Z, W))), Y))))
% 0.18/0.69 = { by lemma 16 }
% 0.18/0.69 double_divide(inverse(W), multiply(Y, multiply(Z, W)))
% 0.18/0.69
% 0.18/0.69 Lemma 27: multiply(double_divide(multiply(double_divide(X, Y), Y), Z), Z) = multiply(double_divide(inverse(X), W), W).
% 0.18/0.69 Proof:
% 0.18/0.69 multiply(double_divide(multiply(double_divide(X, Y), Y), Z), Z)
% 0.18/0.69 = { by lemma 21 R->L }
% 0.18/0.69 multiply(double_divide(double_divide(inverse(V), multiply(X, V)), Z), Z)
% 0.18/0.69 = { by lemma 22 R->L }
% 0.18/0.69 double_divide(inverse(multiply(X, V)), multiply(double_divide(inverse(V), U), U))
% 0.18/0.69 = { by lemma 23 R->L }
% 0.18/0.69 double_divide(double_divide(T, inverse(S)), double_divide(multiply(multiply(S, multiply(X, V)), inverse(V)), multiply(double_divide(T, X2), X2)))
% 0.18/0.69 = { by axiom 1 (multiply) }
% 0.18/0.69 double_divide(double_divide(T, inverse(S)), double_divide(inverse(double_divide(inverse(V), multiply(S, multiply(X, V)))), multiply(double_divide(T, X2), X2)))
% 0.18/0.69 = { by lemma 13 R->L }
% 0.18/0.69 double_divide(double_divide(T, inverse(S)), double_divide(multiply(double_divide(inverse(S), multiply(Y2, multiply(double_divide(inverse(V), multiply(S, multiply(X, V))), S))), Y2), multiply(double_divide(T, X2), X2)))
% 0.18/0.69 = { by lemma 13 }
% 0.18/0.69 double_divide(double_divide(T, inverse(S)), double_divide(multiply(double_divide(inverse(S), multiply(Y2, inverse(X))), Y2), multiply(double_divide(T, X2), X2)))
% 0.18/0.69 = { by lemma 24 R->L }
% 0.18/0.69 double_divide(double_divide(T, inverse(S)), double_divide(multiply(double_divide(inverse(S), multiply(Y2, multiply(double_divide(multiply(Z2, W2), multiply(double_divide(double_divide(multiply(X, double_divide(W2, Z2)), multiply(double_divide(inverse(S), multiply(double_divide(inverse(V2), U2), U2)), V2)), T2), T2)), double_divide(double_divide(multiply(X, double_divide(W2, Z2)), multiply(double_divide(inverse(S), multiply(double_divide(inverse(V2), U2), U2)), V2)), multiply(X, double_divide(W2, Z2)))))), Y2), multiply(double_divide(T, X2), X2)))
% 0.18/0.69 = { by lemma 11 }
% 0.18/0.69 double_divide(double_divide(T, inverse(S)), double_divide(multiply(double_divide(inverse(S), multiply(Y2, multiply(double_divide(multiply(Z2, W2), multiply(double_divide(double_divide(multiply(X, double_divide(W2, Z2)), multiply(double_divide(inverse(S), multiply(double_divide(inverse(V2), U2), U2)), V2)), T2), T2)), S))), Y2), multiply(double_divide(T, X2), X2)))
% 0.18/0.69 = { by lemma 9 }
% 0.18/0.69 double_divide(double_divide(T, inverse(S)), double_divide(multiply(double_divide(inverse(S), multiply(Y2, multiply(double_divide(multiply(Z2, W2), multiply(S, multiply(X, double_divide(W2, Z2)))), S))), Y2), multiply(double_divide(T, X2), X2)))
% 0.18/0.69 = { by lemma 13 }
% 0.18/0.69 double_divide(double_divide(T, inverse(S)), double_divide(inverse(double_divide(multiply(Z2, W2), multiply(S, multiply(X, double_divide(W2, Z2))))), multiply(double_divide(T, X2), X2)))
% 0.18/0.69 = { by axiom 1 (multiply) R->L }
% 0.18/0.69 double_divide(double_divide(T, inverse(S)), double_divide(multiply(multiply(S, multiply(X, double_divide(W2, Z2))), multiply(Z2, W2)), multiply(double_divide(T, X2), X2)))
% 0.18/0.69 = { by lemma 23 }
% 0.18/0.69 double_divide(inverse(multiply(X, double_divide(W2, Z2))), multiply(double_divide(multiply(Z2, W2), S2), S2))
% 0.18/0.69 = { by lemma 22 }
% 0.18/0.69 multiply(double_divide(double_divide(multiply(Z2, W2), multiply(X, double_divide(W2, Z2))), double_divide(multiply(Z2, W2), multiply(double_divide(multiply(Z2, W2), X3), X3))), double_divide(multiply(Z2, W2), multiply(double_divide(multiply(Z2, W2), X3), X3)))
% 0.18/0.69 = { by lemma 25 }
% 0.18/0.69 multiply(X, double_divide(multiply(Z2, W2), multiply(double_divide(multiply(Z2, W2), X3), X3)))
% 0.18/0.69 = { by lemma 21 R->L }
% 0.18/0.69 multiply(X, double_divide(multiply(Z2, W2), double_divide(inverse(inverse(X)), multiply(multiply(Z2, W2), inverse(X)))))
% 0.18/0.69 = { by lemma 26 }
% 0.18/0.69 multiply(X, double_divide(inverse(Y3), multiply(inverse(X), multiply(X, Y3))))
% 0.18/0.69 = { by lemma 16 R->L }
% 0.18/0.69 multiply(double_divide(inverse(X), double_divide(inverse(Y3), multiply(inverse(X), multiply(X, Y3)))), double_divide(inverse(Y3), multiply(inverse(X), multiply(X, Y3))))
% 0.18/0.69 = { by lemma 6 R->L }
% 0.18/0.69 multiply(double_divide(inverse(X), W), W)
% 0.18/0.69
% 0.18/0.69 Lemma 28: multiply(X, multiply(double_divide(Y, Z), Z)) = multiply(X, inverse(Y)).
% 0.18/0.69 Proof:
% 0.18/0.69 multiply(X, multiply(double_divide(Y, Z), Z))
% 0.18/0.69 = { by lemma 7 R->L }
% 0.18/0.69 multiply(double_divide(inverse(X), multiply(double_divide(W, V), V)), double_divide(W, multiply(double_divide(multiply(double_divide(Y, Z), Z), U), U)))
% 0.18/0.69 = { by lemma 27 }
% 0.18/0.69 multiply(double_divide(inverse(X), multiply(double_divide(W, V), V)), double_divide(W, multiply(double_divide(inverse(Y), T), T)))
% 0.18/0.69 = { by lemma 7 }
% 0.18/0.69 multiply(X, inverse(Y))
% 0.18/0.69
% 0.18/0.69 Lemma 29: multiply(multiply(X, inverse(X)), inverse(Y)) = inverse(Y).
% 0.18/0.69 Proof:
% 0.18/0.69 multiply(multiply(X, inverse(X)), inverse(Y))
% 0.18/0.69 = { by lemma 28 R->L }
% 0.18/0.69 multiply(multiply(X, multiply(double_divide(X, Z), Z)), inverse(Y))
% 0.18/0.69 = { by lemma 19 }
% 0.18/0.69 inverse(Y)
% 0.18/0.69
% 0.18/0.69 Lemma 30: inverse(multiply(X, inverse(X))) = multiply(Y, inverse(Y)).
% 0.18/0.69 Proof:
% 0.18/0.69 inverse(multiply(X, inverse(X)))
% 0.18/0.69 = { by lemma 29 R->L }
% 0.18/0.69 multiply(multiply(X, inverse(X)), inverse(multiply(X, inverse(X))))
% 0.18/0.69 = { by lemma 28 R->L }
% 0.18/0.69 multiply(multiply(X, inverse(X)), multiply(double_divide(multiply(X, inverse(X)), Z), Z))
% 0.18/0.69 = { by lemma 20 R->L }
% 0.18/0.69 multiply(Y, multiply(double_divide(Y, W), W))
% 0.18/0.69 = { by lemma 28 }
% 0.18/0.69 multiply(Y, inverse(Y))
% 0.18/0.69
% 0.18/0.69 Lemma 31: double_divide(multiply(double_divide(X, Y), Y), Z) = double_divide(inverse(X), Z).
% 0.18/0.69 Proof:
% 0.18/0.69 double_divide(multiply(double_divide(X, Y), Y), Z)
% 0.18/0.69 = { by lemma 10 R->L }
% 0.18/0.69 double_divide(double_divide(inverse(W), multiply(double_divide(multiply(double_divide(X, Y), Y), V), V)), double_divide(inverse(Z), multiply(double_divide(inverse(W), U), U)))
% 0.18/0.69 = { by lemma 27 }
% 0.18/0.69 double_divide(double_divide(inverse(W), multiply(double_divide(inverse(X), T), T)), double_divide(inverse(Z), multiply(double_divide(inverse(W), U), U)))
% 0.18/0.69 = { by lemma 10 }
% 0.18/0.69 double_divide(inverse(X), Z)
% 0.18/0.69
% 0.18/0.69 Lemma 32: multiply(double_divide(X, double_divide(Y, X)), Z) = multiply(Y, Z).
% 0.18/0.69 Proof:
% 0.18/0.69 multiply(double_divide(X, double_divide(Y, X)), Z)
% 0.18/0.69 = { by axiom 1 (multiply) }
% 0.18/0.69 inverse(double_divide(Z, double_divide(X, double_divide(Y, X))))
% 0.18/0.69 = { by lemma 24 R->L }
% 0.18/0.69 multiply(double_divide(multiply(double_divide(Y, X), X), multiply(double_divide(inverse(W), V), V)), double_divide(inverse(W), multiply(double_divide(Z, double_divide(X, double_divide(Y, X))), double_divide(X, double_divide(Y, X)))))
% 0.18/0.69 = { by lemma 8 }
% 0.18/0.70 multiply(double_divide(double_divide(Z, multiply(double_divide(multiply(double_divide(Y, X), X), multiply(double_divide(inverse(W), V), V)), W)), U), U)
% 0.18/0.70 = { by lemma 31 }
% 0.18/0.70 multiply(double_divide(double_divide(Z, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(W), V), V)), W)), U), U)
% 0.18/0.70 = { by lemma 9 }
% 0.18/0.70 multiply(Y, Z)
% 0.18/0.70
% 0.18/0.70 Lemma 33: multiply(double_divide(X, Y), Y) = inverse(X).
% 0.18/0.70 Proof:
% 0.18/0.70 multiply(double_divide(X, Y), Y)
% 0.18/0.70 = { by axiom 1 (multiply) }
% 0.18/0.70 inverse(double_divide(Y, double_divide(X, Y)))
% 0.18/0.70 = { by lemma 3 R->L }
% 0.18/0.70 inverse(double_divide(double_divide(Z, multiply(double_divide(Y, double_divide(X, Y)), W)), double_divide(inverse(W), multiply(double_divide(Z, V), V))))
% 0.18/0.70 = { by lemma 32 }
% 0.18/0.70 inverse(double_divide(double_divide(Z, multiply(X, W)), double_divide(inverse(W), multiply(double_divide(Z, V), V))))
% 0.18/0.70 = { by lemma 3 }
% 0.18/0.70 inverse(X)
% 0.18/0.70
% 0.18/0.70 Lemma 34: multiply(multiply(X, Y), inverse(Y)) = inverse(multiply(double_divide(X, Z), Z)).
% 0.18/0.70 Proof:
% 0.18/0.70 multiply(multiply(X, Y), inverse(Y))
% 0.18/0.70 = { by lemma 15 R->L }
% 0.18/0.70 multiply(multiply(multiply(X, multiply(double_divide(W, V), V)), multiply(W, Y)), inverse(Y))
% 0.18/0.70 = { by axiom 1 (multiply) }
% 0.18/0.70 inverse(double_divide(inverse(Y), multiply(multiply(X, multiply(double_divide(W, V), V)), multiply(W, Y))))
% 0.18/0.70 = { by lemma 17 }
% 0.18/0.70 inverse(double_divide(inverse(multiply(double_divide(X, Z), Z)), multiply(multiply(X, multiply(double_divide(W, V), V)), multiply(W, multiply(double_divide(X, Z), Z)))))
% 0.18/0.70 = { by axiom 1 (multiply) R->L }
% 0.18/0.70 multiply(multiply(multiply(X, multiply(double_divide(W, V), V)), multiply(W, multiply(double_divide(X, Z), Z))), inverse(multiply(double_divide(X, Z), Z)))
% 0.18/0.70 = { by lemma 15 }
% 0.18/0.70 multiply(multiply(X, multiply(double_divide(X, Z), Z)), inverse(multiply(double_divide(X, Z), Z)))
% 0.18/0.70 = { by lemma 19 }
% 0.18/0.70 inverse(multiply(double_divide(X, Z), Z))
% 0.18/0.70
% 0.18/0.70 Lemma 35: multiply(multiply(X, inverse(Y)), multiply(Y, Z)) = multiply(X, Z).
% 0.18/0.70 Proof:
% 0.18/0.70 multiply(multiply(X, inverse(Y)), multiply(Y, Z))
% 0.18/0.70 = { by lemma 28 R->L }
% 0.18/0.70 multiply(multiply(X, multiply(double_divide(Y, W), W)), multiply(Y, Z))
% 0.18/0.70 = { by lemma 15 }
% 0.18/0.70 multiply(X, Z)
% 0.18/0.70
% 0.18/0.70 Lemma 36: double_divide(X, double_divide(inverse(Y), multiply(X, multiply(double_divide(Z, W), W)))) = double_divide(Z, Y).
% 0.18/0.70 Proof:
% 0.18/0.70 double_divide(X, double_divide(inverse(Y), multiply(X, multiply(double_divide(Z, W), W))))
% 0.18/0.70 = { by lemma 9 R->L }
% 0.18/0.70 double_divide(X, double_divide(inverse(Y), multiply(double_divide(double_divide(multiply(double_divide(Z, W), W), multiply(double_divide(inverse(X), multiply(double_divide(inverse(V), U), U)), V)), T), T)))
% 0.18/0.70 = { by lemma 11 R->L }
% 0.18/0.70 double_divide(double_divide(double_divide(multiply(double_divide(Z, W), W), multiply(double_divide(inverse(X), multiply(double_divide(inverse(V), U), U)), V)), multiply(double_divide(Z, W), W)), double_divide(inverse(Y), multiply(double_divide(double_divide(multiply(double_divide(Z, W), W), multiply(double_divide(inverse(X), multiply(double_divide(inverse(V), U), U)), V)), T), T)))
% 0.18/0.70 = { by lemma 6 }
% 0.18/0.70 double_divide(double_divide(double_divide(multiply(double_divide(Z, W), W), multiply(double_divide(inverse(X), multiply(double_divide(inverse(V), U), U)), V)), multiply(double_divide(Z, Y), Y)), double_divide(inverse(Y), multiply(double_divide(double_divide(multiply(double_divide(Z, W), W), multiply(double_divide(inverse(X), multiply(double_divide(inverse(V), U), U)), V)), T), T)))
% 0.18/0.70 = { by lemma 3 }
% 0.18/0.70 double_divide(Z, Y)
% 0.18/0.70
% 0.18/0.70 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.18/0.70 Proof:
% 0.18/0.70 multiply(multiply(a3, b3), c3)
% 0.18/0.70 = { by lemma 35 R->L }
% 0.18/0.70 multiply(multiply(multiply(a3, b3), inverse(b3)), multiply(b3, c3))
% 0.18/0.70 = { by lemma 34 }
% 0.18/0.70 multiply(inverse(multiply(double_divide(a3, X), X)), multiply(b3, c3))
% 0.18/0.70 = { by lemma 33 R->L }
% 0.18/0.70 multiply(multiply(double_divide(multiply(double_divide(a3, X), X), inverse(double_divide(a3, X))), inverse(double_divide(a3, X))), multiply(b3, c3))
% 0.18/0.70 = { by lemma 4 R->L }
% 0.18/0.70 multiply(multiply(double_divide(multiply(double_divide(a3, X), X), multiply(double_divide(inverse(Y), multiply(double_divide(Z, W), W)), double_divide(Z, multiply(double_divide(a3, X), Y)))), inverse(double_divide(a3, X))), multiply(b3, c3))
% 0.18/0.70 = { by lemma 32 R->L }
% 0.18/0.70 multiply(multiply(double_divide(multiply(double_divide(a3, X), X), multiply(double_divide(inverse(Y), multiply(double_divide(Z, W), W)), double_divide(Z, multiply(double_divide(double_divide(X, double_divide(a3, X)), double_divide(double_divide(a3, X), double_divide(X, double_divide(a3, X)))), Y)))), inverse(double_divide(a3, X))), multiply(b3, c3))
% 0.18/0.70 = { by lemma 4 }
% 0.18/0.70 multiply(multiply(double_divide(multiply(double_divide(a3, X), X), inverse(double_divide(double_divide(X, double_divide(a3, X)), double_divide(double_divide(a3, X), double_divide(X, double_divide(a3, X)))))), inverse(double_divide(a3, X))), multiply(b3, c3))
% 0.18/0.70 = { by lemma 25 R->L }
% 0.18/0.70 multiply(multiply(double_divide(multiply(double_divide(a3, X), X), inverse(double_divide(double_divide(inverse(V), multiply(double_divide(double_divide(X, double_divide(a3, X)), double_divide(double_divide(a3, X), double_divide(X, double_divide(a3, X)))), double_divide(double_divide(a3, X), double_divide(X, double_divide(a3, X))))), double_divide(multiply(double_divide(X, double_divide(a3, X)), double_divide(a3, X)), multiply(double_divide(inverse(V), U), U))))), inverse(double_divide(a3, X))), multiply(b3, c3))
% 0.18/0.70 = { by lemma 31 }
% 0.18/0.70 multiply(multiply(double_divide(multiply(double_divide(a3, X), X), inverse(double_divide(double_divide(inverse(V), multiply(double_divide(double_divide(X, double_divide(a3, X)), double_divide(double_divide(a3, X), double_divide(X, double_divide(a3, X)))), double_divide(double_divide(a3, X), double_divide(X, double_divide(a3, X))))), double_divide(inverse(X), multiply(double_divide(inverse(V), U), U))))), inverse(double_divide(a3, X))), multiply(b3, c3))
% 0.18/0.70 = { by lemma 10 }
% 0.18/0.70 multiply(multiply(double_divide(multiply(double_divide(a3, X), X), inverse(double_divide(double_divide(X, double_divide(a3, X)), X))), inverse(double_divide(a3, X))), multiply(b3, c3))
% 0.18/0.70 = { by axiom 1 (multiply) R->L }
% 0.18/0.70 multiply(multiply(double_divide(multiply(double_divide(a3, X), X), multiply(X, double_divide(X, double_divide(a3, X)))), inverse(double_divide(a3, X))), multiply(b3, c3))
% 0.18/0.70 = { by axiom 1 (multiply) }
% 0.18/0.70 multiply(multiply(double_divide(inverse(double_divide(X, double_divide(a3, X))), multiply(X, double_divide(X, double_divide(a3, X)))), inverse(double_divide(a3, X))), multiply(b3, c3))
% 0.18/0.70 = { by lemma 21 }
% 0.18/0.70 multiply(multiply(multiply(double_divide(X, double_divide(a3, X)), double_divide(a3, X)), inverse(double_divide(a3, X))), multiply(b3, c3))
% 0.18/0.70 = { by lemma 34 }
% 0.18/0.70 multiply(inverse(multiply(double_divide(double_divide(X, double_divide(a3, X)), T), T)), multiply(b3, c3))
% 0.18/0.70 = { by lemma 33 }
% 0.18/0.70 multiply(inverse(inverse(double_divide(X, double_divide(a3, X)))), multiply(b3, c3))
% 0.18/0.70 = { by lemma 11 R->L }
% 0.18/0.70 multiply(double_divide(double_divide(S, multiply(double_divide(inverse(inverse(inverse(double_divide(X, double_divide(a3, X))))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.70 = { by lemma 33 R->L }
% 0.18/0.70 multiply(double_divide(double_divide(S, multiply(double_divide(inverse(multiply(double_divide(inverse(double_divide(X, double_divide(a3, X))), Z2), Z2)), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.70 = { by lemma 34 R->L }
% 0.18/0.70 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(multiply(inverse(double_divide(X, double_divide(a3, X))), double_divide(X, double_divide(a3, X))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.70 = { by lemma 33 R->L }
% 0.18/0.70 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(multiply(multiply(double_divide(double_divide(X, double_divide(a3, X)), W2), W2), double_divide(X, double_divide(a3, X))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.70 = { by axiom 1 (multiply) }
% 0.18/0.70 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(inverse(double_divide(double_divide(X, double_divide(a3, X)), multiply(double_divide(double_divide(X, double_divide(a3, X)), W2), W2))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.70 = { by lemma 36 R->L }
% 0.18/0.70 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(inverse(double_divide(V2, double_divide(inverse(multiply(double_divide(double_divide(X, double_divide(a3, X)), W2), W2)), multiply(V2, multiply(double_divide(double_divide(X, double_divide(a3, X)), W2), W2))))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.70 = { by lemma 18 R->L }
% 0.18/0.70 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(inverse(double_divide(V2, double_divide(inverse(multiply(double_divide(inverse(inverse(U2)), inverse(U2)), inverse(U2))), multiply(V2, multiply(double_divide(inverse(inverse(U2)), inverse(U2)), inverse(U2)))))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.70 = { by lemma 36 }
% 0.18/0.70 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(inverse(double_divide(inverse(inverse(U2)), multiply(double_divide(inverse(inverse(U2)), inverse(U2)), inverse(U2)))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.70 = { by axiom 1 (multiply) R->L }
% 0.18/0.70 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(multiply(multiply(double_divide(inverse(inverse(U2)), inverse(U2)), inverse(U2)), inverse(inverse(U2))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.70 = { by lemma 19 R->L }
% 0.18/0.70 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(multiply(multiply(double_divide(inverse(inverse(U2)), multiply(multiply(T2, multiply(double_divide(T2, S2), S2)), inverse(U2))), inverse(U2)), inverse(inverse(U2))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.70 = { by lemma 35 R->L }
% 0.18/0.70 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(multiply(multiply(double_divide(inverse(inverse(U2)), multiply(multiply(multiply(T2, multiply(double_divide(T2, S2), S2)), inverse(X3)), multiply(X3, inverse(U2)))), inverse(U2)), inverse(inverse(U2))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.71 = { by lemma 19 }
% 0.18/0.71 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(multiply(multiply(double_divide(inverse(inverse(U2)), multiply(inverse(X3), multiply(X3, inverse(U2)))), inverse(U2)), inverse(inverse(U2))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.71 = { by lemma 26 R->L }
% 0.18/0.71 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(multiply(multiply(double_divide(Y3, double_divide(inverse(inverse(X3)), multiply(Y3, inverse(X3)))), inverse(U2)), inverse(inverse(U2))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.71 = { by lemma 19 R->L }
% 0.18/0.71 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(multiply(multiply(double_divide(Y3, double_divide(inverse(inverse(X3)), multiply(Y3, multiply(multiply(Z3, multiply(double_divide(Z3, W3), W3)), inverse(X3))))), inverse(U2)), inverse(inverse(U2))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.71 = { by lemma 16 }
% 0.18/0.71 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(multiply(multiply(multiply(Z3, multiply(double_divide(Z3, W3), W3)), inverse(U2)), inverse(inverse(U2))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.71 = { by axiom 1 (multiply) }
% 0.18/0.71 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(multiply(multiply(multiply(Z3, inverse(double_divide(W3, double_divide(Z3, W3)))), inverse(U2)), inverse(inverse(U2))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.71 = { by lemma 32 R->L }
% 0.18/0.71 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(multiply(multiply(multiply(double_divide(W3, double_divide(Z3, W3)), inverse(double_divide(W3, double_divide(Z3, W3)))), inverse(U2)), inverse(inverse(U2))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.71 = { by lemma 34 }
% 0.18/0.71 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(inverse(multiply(double_divide(multiply(double_divide(W3, double_divide(Z3, W3)), inverse(double_divide(W3, double_divide(Z3, W3)))), V3), V3)), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.71 = { by lemma 33 }
% 0.18/0.71 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(inverse(inverse(multiply(double_divide(W3, double_divide(Z3, W3)), inverse(double_divide(W3, double_divide(Z3, W3)))))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.71 = { by lemma 30 }
% 0.18/0.71 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(inverse(multiply(U3, inverse(U3))), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.71 = { by lemma 30 }
% 0.18/0.71 multiply(double_divide(double_divide(S, multiply(double_divide(multiply(multiply(T3, inverse(T3)), inverse(double_divide(X, double_divide(a3, X)))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.71 = { by lemma 29 }
% 0.18/0.71 multiply(double_divide(double_divide(S, multiply(double_divide(inverse(double_divide(X, double_divide(a3, X))), multiply(double_divide(inverse(X2), Y2), Y2)), X2)), S), multiply(b3, c3))
% 0.18/0.71 = { by lemma 11 }
% 0.18/0.71 multiply(double_divide(X, double_divide(a3, X)), multiply(b3, c3))
% 0.18/0.71 = { by lemma 32 }
% 0.18/0.71 multiply(a3, multiply(b3, c3))
% 0.18/0.71 % SZS output end Proof
% 0.18/0.71
% 0.18/0.71 RESULT: Unsatisfiable (the axioms are contradictory).
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