TSTP Solution File: GRP615-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP615-1 : 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 : n029.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 01:19:08 EDT 2023
% Result : Unsatisfiable 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP615-1 : TPTP v8.1.2. Released v2.6.0.
% 0.10/0.13 % 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 : n029.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 21:32:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Command-line arguments: --no-flatten-goal
% 0.20/0.47
% 0.20/0.47 % SZS status Unsatisfiable
% 0.20/0.47
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.20/0.50 Axiom 2 (single_axiom): double_divide(inverse(double_divide(inverse(double_divide(X, inverse(Y))), Z)), double_divide(X, Z)) = Y.
% 0.20/0.50
% 0.20/0.51 Lemma 3: double_divide(multiply(X, multiply(inverse(Y), Z)), double_divide(Z, X)) = Y.
% 0.20/0.51 Proof:
% 0.20/0.51 double_divide(multiply(X, multiply(inverse(Y), Z)), double_divide(Z, X))
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 double_divide(multiply(X, inverse(double_divide(Z, inverse(Y)))), double_divide(Z, X))
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 double_divide(inverse(double_divide(inverse(double_divide(Z, inverse(Y))), X)), double_divide(Z, X))
% 0.20/0.51 = { by axiom 2 (single_axiom) }
% 0.20/0.51 Y
% 0.20/0.51
% 0.20/0.51 Lemma 4: multiply(double_divide(X, Y), multiply(Y, multiply(inverse(Z), X))) = inverse(Z).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(double_divide(X, Y), multiply(Y, multiply(inverse(Z), X)))
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 inverse(double_divide(multiply(Y, multiply(inverse(Z), X)), double_divide(X, Y)))
% 0.20/0.51 = { by lemma 3 }
% 0.20/0.51 inverse(Z)
% 0.20/0.51
% 0.20/0.51 Lemma 5: multiply(X, multiply(double_divide(Y, Z), multiply(inverse(W), multiply(Z, multiply(inverse(X), Y))))) = inverse(W).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(X, multiply(double_divide(Y, Z), multiply(inverse(W), multiply(Z, multiply(inverse(X), Y)))))
% 0.20/0.51 = { by lemma 3 R->L }
% 0.20/0.51 multiply(double_divide(multiply(Z, multiply(inverse(X), Y)), double_divide(Y, Z)), multiply(double_divide(Y, Z), multiply(inverse(W), multiply(Z, multiply(inverse(X), Y)))))
% 0.20/0.51 = { by lemma 4 }
% 0.20/0.51 inverse(W)
% 0.20/0.51
% 0.20/0.51 Lemma 6: multiply(X, multiply(inverse(Y), inverse(X))) = inverse(Y).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(X, multiply(inverse(Y), inverse(X)))
% 0.20/0.51 = { by lemma 3 R->L }
% 0.20/0.51 multiply(X, multiply(double_divide(multiply(Z, multiply(inverse(inverse(Y)), W)), double_divide(W, Z)), inverse(X)))
% 0.20/0.51 = { by lemma 5 R->L }
% 0.20/0.51 multiply(X, multiply(double_divide(multiply(Z, multiply(inverse(inverse(Y)), W)), double_divide(W, Z)), multiply(inverse(Y), multiply(double_divide(W, Z), multiply(inverse(X), multiply(Z, multiply(inverse(inverse(Y)), W)))))))
% 0.20/0.51 = { by lemma 5 }
% 0.20/0.51 inverse(Y)
% 0.20/0.51
% 0.20/0.51 Lemma 7: double_divide(inverse(X), double_divide(inverse(Y), Y)) = X.
% 0.20/0.51 Proof:
% 0.20/0.51 double_divide(inverse(X), double_divide(inverse(Y), Y))
% 0.20/0.51 = { by lemma 6 R->L }
% 0.20/0.51 double_divide(multiply(Y, multiply(inverse(X), inverse(Y))), double_divide(inverse(Y), Y))
% 0.20/0.51 = { by lemma 3 }
% 0.20/0.51 X
% 0.20/0.51
% 0.20/0.51 Lemma 8: double_divide(multiply(X, Y), double_divide(inverse(Z), Z)) = double_divide(Y, X).
% 0.20/0.51 Proof:
% 0.20/0.51 double_divide(multiply(X, Y), double_divide(inverse(Z), Z))
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 double_divide(inverse(double_divide(Y, X)), double_divide(inverse(Z), Z))
% 0.20/0.51 = { by lemma 7 }
% 0.20/0.51 double_divide(Y, X)
% 0.20/0.51
% 0.20/0.51 Lemma 9: double_divide(multiply(X, inverse(X)), inverse(Y)) = Y.
% 0.20/0.51 Proof:
% 0.20/0.51 double_divide(multiply(X, inverse(X)), inverse(Y))
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 double_divide(inverse(double_divide(inverse(X), X)), inverse(Y))
% 0.20/0.51 = { by lemma 8 R->L }
% 0.20/0.51 double_divide(multiply(inverse(Y), inverse(double_divide(inverse(X), X))), double_divide(inverse(X), X))
% 0.20/0.51 = { by lemma 3 R->L }
% 0.20/0.51 double_divide(multiply(double_divide(multiply(Z, multiply(inverse(inverse(Y)), W)), double_divide(W, Z)), inverse(double_divide(inverse(X), X))), double_divide(inverse(X), X))
% 0.20/0.51 = { by lemma 5 R->L }
% 0.20/0.51 double_divide(multiply(double_divide(multiply(Z, multiply(inverse(inverse(Y)), W)), double_divide(W, Z)), multiply(inverse(Y), multiply(double_divide(W, Z), multiply(inverse(double_divide(inverse(X), X)), multiply(Z, multiply(inverse(inverse(Y)), W)))))), double_divide(inverse(X), X))
% 0.20/0.51 = { by lemma 3 R->L }
% 0.20/0.51 double_divide(multiply(double_divide(multiply(Z, multiply(inverse(inverse(Y)), W)), double_divide(W, Z)), multiply(inverse(Y), multiply(double_divide(W, Z), multiply(inverse(double_divide(inverse(X), X)), multiply(Z, multiply(inverse(inverse(Y)), W)))))), double_divide(multiply(double_divide(W, Z), multiply(inverse(double_divide(inverse(X), X)), multiply(Z, multiply(inverse(inverse(Y)), W)))), double_divide(multiply(Z, multiply(inverse(inverse(Y)), W)), double_divide(W, Z))))
% 0.20/0.51 = { by lemma 3 }
% 0.20/0.51 Y
% 0.20/0.51
% 0.20/0.51 Lemma 10: multiply(inverse(X), multiply(Y, inverse(Y))) = inverse(X).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(inverse(X), multiply(Y, inverse(Y)))
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 multiply(inverse(X), inverse(double_divide(inverse(Y), Y)))
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 inverse(double_divide(inverse(double_divide(inverse(Y), Y)), inverse(X)))
% 0.20/0.51 = { by lemma 4 R->L }
% 0.20/0.51 multiply(double_divide(inverse(Y), Y), multiply(Y, multiply(inverse(double_divide(inverse(double_divide(inverse(Y), Y)), inverse(X))), inverse(Y))))
% 0.20/0.51 = { by lemma 6 }
% 0.20/0.51 multiply(double_divide(inverse(Y), Y), inverse(double_divide(inverse(double_divide(inverse(Y), Y)), inverse(X))))
% 0.20/0.51 = { by axiom 1 (multiply) R->L }
% 0.20/0.51 multiply(double_divide(inverse(Y), Y), multiply(inverse(X), inverse(double_divide(inverse(Y), Y))))
% 0.20/0.51 = { by lemma 6 }
% 0.20/0.51 inverse(X)
% 0.20/0.51
% 0.20/0.51 Lemma 11: double_divide(inverse(X), double_divide(multiply(inverse(X), Y), double_divide(Y, inverse(Z)))) = Z.
% 0.20/0.51 Proof:
% 0.20/0.51 double_divide(inverse(X), double_divide(multiply(inverse(X), Y), double_divide(Y, inverse(Z))))
% 0.20/0.51 = { by lemma 4 R->L }
% 0.20/0.51 double_divide(multiply(double_divide(Y, inverse(Z)), multiply(inverse(Z), multiply(inverse(X), Y))), double_divide(multiply(inverse(X), Y), double_divide(Y, inverse(Z))))
% 0.20/0.51 = { by lemma 3 }
% 0.20/0.51 Z
% 0.20/0.51
% 0.20/0.51 Lemma 12: double_divide(inverse(X), double_divide(inverse(X), Y)) = Y.
% 0.20/0.51 Proof:
% 0.20/0.51 double_divide(inverse(X), double_divide(inverse(X), Y))
% 0.20/0.51 = { by lemma 9 R->L }
% 0.20/0.51 double_divide(inverse(X), double_divide(inverse(X), double_divide(multiply(Z, inverse(Z)), inverse(Y))))
% 0.20/0.51 = { by lemma 10 R->L }
% 0.20/0.51 double_divide(inverse(X), double_divide(multiply(inverse(X), multiply(Z, inverse(Z))), double_divide(multiply(Z, inverse(Z)), inverse(Y))))
% 0.20/0.51 = { by lemma 11 }
% 0.20/0.51 Y
% 0.20/0.51
% 0.20/0.51 Lemma 13: double_divide(inverse(X), double_divide(inverse(inverse(Y)), inverse(X))) = Y.
% 0.20/0.51 Proof:
% 0.20/0.51 double_divide(inverse(X), double_divide(inverse(inverse(Y)), inverse(X)))
% 0.20/0.51 = { by lemma 8 R->L }
% 0.20/0.51 double_divide(inverse(X), double_divide(multiply(inverse(X), inverse(inverse(Y))), double_divide(inverse(inverse(Y)), inverse(Y))))
% 0.20/0.51 = { by lemma 11 }
% 0.20/0.51 Y
% 0.20/0.51
% 0.20/0.51 Lemma 14: inverse(inverse(X)) = X.
% 0.20/0.51 Proof:
% 0.20/0.51 inverse(inverse(X))
% 0.20/0.51 = { by lemma 12 R->L }
% 0.20/0.51 double_divide(inverse(inverse(X)), double_divide(inverse(inverse(X)), inverse(inverse(X))))
% 0.20/0.51 = { by lemma 13 }
% 0.20/0.51 X
% 0.20/0.51
% 0.20/0.51 Lemma 15: double_divide(X, double_divide(X, Y)) = Y.
% 0.20/0.51 Proof:
% 0.20/0.51 double_divide(X, double_divide(X, Y))
% 0.20/0.51 = { by lemma 14 R->L }
% 0.20/0.51 double_divide(X, double_divide(inverse(inverse(X)), Y))
% 0.20/0.51 = { by lemma 14 R->L }
% 0.20/0.51 double_divide(inverse(inverse(X)), double_divide(inverse(inverse(X)), Y))
% 0.20/0.51 = { by lemma 12 }
% 0.20/0.51 Y
% 0.20/0.51
% 0.20/0.51 Lemma 16: double_divide(X, Y) = double_divide(Y, X).
% 0.20/0.51 Proof:
% 0.20/0.51 double_divide(X, Y)
% 0.20/0.51 = { by lemma 15 R->L }
% 0.20/0.51 double_divide(Y, double_divide(Y, double_divide(X, Y)))
% 0.20/0.51 = { by lemma 14 R->L }
% 0.20/0.51 double_divide(Y, double_divide(Y, double_divide(X, inverse(inverse(Y)))))
% 0.20/0.51 = { by lemma 14 R->L }
% 0.20/0.51 double_divide(Y, double_divide(Y, double_divide(inverse(inverse(X)), inverse(inverse(Y)))))
% 0.20/0.51 = { by lemma 14 R->L }
% 0.20/0.51 double_divide(Y, double_divide(inverse(inverse(Y)), double_divide(inverse(inverse(X)), inverse(inverse(Y)))))
% 0.20/0.51 = { by lemma 13 }
% 0.20/0.51 double_divide(Y, X)
% 0.20/0.51
% 0.20/0.51 Lemma 17: multiply(Y, X) = multiply(X, Y).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(Y, X)
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 inverse(double_divide(X, Y))
% 0.20/0.51 = { by lemma 16 R->L }
% 0.20/0.51 inverse(double_divide(Y, X))
% 0.20/0.51 = { by axiom 1 (multiply) R->L }
% 0.20/0.51 multiply(X, Y)
% 0.20/0.51
% 0.20/0.51 Lemma 18: multiply(double_divide(inverse(X), Y), inverse(X)) = inverse(Y).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(double_divide(inverse(X), Y), inverse(X))
% 0.20/0.51 = { by lemma 9 R->L }
% 0.20/0.51 multiply(double_divide(inverse(X), double_divide(multiply(Z, inverse(Z)), inverse(Y))), inverse(X))
% 0.20/0.51 = { by lemma 10 R->L }
% 0.20/0.51 multiply(double_divide(multiply(inverse(X), multiply(Z, inverse(Z))), double_divide(multiply(Z, inverse(Z)), inverse(Y))), inverse(X))
% 0.20/0.51 = { by lemma 4 R->L }
% 0.20/0.51 multiply(double_divide(multiply(inverse(X), multiply(Z, inverse(Z))), double_divide(multiply(Z, inverse(Z)), inverse(Y))), multiply(double_divide(multiply(Z, inverse(Z)), inverse(Y)), multiply(inverse(Y), multiply(inverse(X), multiply(Z, inverse(Z))))))
% 0.20/0.51 = { by lemma 4 }
% 0.20/0.51 inverse(Y)
% 0.20/0.51
% 0.20/0.51 Lemma 19: multiply(X, multiply(Y, inverse(X))) = Y.
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(X, multiply(Y, inverse(X)))
% 0.20/0.51 = { by lemma 14 R->L }
% 0.20/0.51 multiply(X, multiply(inverse(inverse(Y)), inverse(X)))
% 0.20/0.51 = { by lemma 6 }
% 0.20/0.51 inverse(inverse(Y))
% 0.20/0.51 = { by lemma 14 }
% 0.20/0.51 Y
% 0.20/0.51
% 0.20/0.51 Lemma 20: multiply(X, inverse(Y)) = double_divide(Y, inverse(X)).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(X, inverse(Y))
% 0.20/0.51 = { by lemma 18 R->L }
% 0.20/0.51 multiply(X, multiply(double_divide(inverse(X), Y), inverse(X)))
% 0.20/0.51 = { by lemma 19 }
% 0.20/0.51 double_divide(inverse(X), Y)
% 0.20/0.51 = { by lemma 16 }
% 0.20/0.51 double_divide(Y, inverse(X))
% 0.20/0.51
% 0.20/0.51 Lemma 21: double_divide(inverse(X), double_divide(double_divide(Y, Z), multiply(Y, Z))) = X.
% 0.20/0.51 Proof:
% 0.20/0.51 double_divide(inverse(X), double_divide(double_divide(Y, Z), multiply(Y, Z)))
% 0.20/0.51 = { by lemma 16 R->L }
% 0.20/0.51 double_divide(inverse(X), double_divide(double_divide(Z, Y), multiply(Y, Z)))
% 0.20/0.51 = { by lemma 16 R->L }
% 0.20/0.51 double_divide(inverse(X), double_divide(multiply(Y, Z), double_divide(Z, Y)))
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 double_divide(inverse(X), double_divide(inverse(double_divide(Z, Y)), double_divide(Z, Y)))
% 0.20/0.51 = { by lemma 7 }
% 0.20/0.51 X
% 0.20/0.51
% 0.20/0.51 Lemma 22: multiply(X, double_divide(double_divide(Y, Z), multiply(Y, Z))) = X.
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(X, double_divide(double_divide(Y, Z), multiply(Y, Z)))
% 0.20/0.51 = { by lemma 14 R->L }
% 0.20/0.51 multiply(X, inverse(inverse(double_divide(double_divide(Y, Z), multiply(Y, Z)))))
% 0.20/0.51 = { by lemma 20 }
% 0.20/0.51 double_divide(inverse(double_divide(double_divide(Y, Z), multiply(Y, Z))), inverse(X))
% 0.20/0.51 = { by lemma 16 }
% 0.20/0.51 double_divide(inverse(X), inverse(double_divide(double_divide(Y, Z), multiply(Y, Z))))
% 0.20/0.51 = { by lemma 15 R->L }
% 0.20/0.51 double_divide(inverse(X), double_divide(W, double_divide(W, inverse(double_divide(double_divide(Y, Z), multiply(Y, Z))))))
% 0.20/0.51 = { by lemma 20 R->L }
% 0.20/0.51 double_divide(inverse(X), double_divide(W, multiply(double_divide(double_divide(Y, Z), multiply(Y, Z)), inverse(W))))
% 0.20/0.51 = { by lemma 17 R->L }
% 0.20/0.51 double_divide(inverse(X), double_divide(W, multiply(inverse(W), double_divide(double_divide(Y, Z), multiply(Y, Z)))))
% 0.20/0.51 = { by lemma 21 R->L }
% 0.20/0.51 double_divide(inverse(X), double_divide(double_divide(inverse(W), double_divide(double_divide(Y, Z), multiply(Y, Z))), multiply(inverse(W), double_divide(double_divide(Y, Z), multiply(Y, Z)))))
% 0.20/0.51 = { by lemma 21 }
% 0.20/0.51 X
% 0.20/0.51
% 0.20/0.51 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.20/0.51 Proof:
% 0.20/0.51 multiply(multiply(a3, b3), c3)
% 0.20/0.51 = { by lemma 17 R->L }
% 0.20/0.51 multiply(c3, multiply(a3, b3))
% 0.20/0.51 = { by lemma 17 }
% 0.20/0.51 multiply(c3, multiply(b3, a3))
% 0.20/0.51 = { by lemma 17 }
% 0.20/0.51 multiply(multiply(b3, a3), c3)
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 inverse(double_divide(c3, multiply(b3, a3)))
% 0.20/0.51 = { by lemma 16 R->L }
% 0.20/0.51 inverse(double_divide(multiply(b3, a3), c3))
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 inverse(double_divide(inverse(double_divide(a3, b3)), c3))
% 0.20/0.51 = { by lemma 22 R->L }
% 0.20/0.51 inverse(double_divide(inverse(double_divide(a3, b3)), multiply(c3, double_divide(double_divide(X, Y), multiply(X, Y)))))
% 0.20/0.51 = { by axiom 1 (multiply) }
% 0.20/0.51 inverse(double_divide(inverse(double_divide(a3, b3)), inverse(double_divide(double_divide(double_divide(X, Y), multiply(X, Y)), c3))))
% 0.20/0.51 = { by lemma 4 R->L }
% 0.20/0.51 inverse(double_divide(inverse(double_divide(a3, b3)), multiply(double_divide(b3, a3), multiply(a3, multiply(inverse(double_divide(double_divide(double_divide(X, Y), multiply(X, Y)), c3)), b3)))))
% 0.20/0.51 = { by axiom 1 (multiply) R->L }
% 0.20/0.51 inverse(double_divide(inverse(double_divide(a3, b3)), multiply(double_divide(b3, a3), multiply(a3, multiply(multiply(c3, double_divide(double_divide(X, Y), multiply(X, Y))), b3)))))
% 0.20/0.51 = { by lemma 22 }
% 0.20/0.51 inverse(double_divide(inverse(double_divide(a3, b3)), multiply(double_divide(b3, a3), multiply(a3, multiply(c3, b3)))))
% 0.20/0.51 = { by lemma 16 }
% 0.20/0.51 inverse(double_divide(inverse(double_divide(a3, b3)), multiply(double_divide(a3, b3), multiply(a3, multiply(c3, b3)))))
% 0.20/0.51 = { by lemma 17 R->L }
% 0.20/0.51 inverse(double_divide(inverse(double_divide(a3, b3)), multiply(double_divide(a3, b3), multiply(a3, multiply(b3, c3)))))
% 0.20/0.51 = { by lemma 17 }
% 0.20/0.51 inverse(double_divide(inverse(double_divide(a3, b3)), multiply(multiply(a3, multiply(b3, c3)), double_divide(a3, b3))))
% 0.20/0.51 = { by lemma 15 R->L }
% 0.20/0.51 inverse(double_divide(double_divide(Z, double_divide(Z, inverse(double_divide(a3, b3)))), multiply(multiply(a3, multiply(b3, c3)), double_divide(a3, b3))))
% 0.20/0.51 = { by lemma 20 R->L }
% 0.20/0.51 inverse(double_divide(double_divide(Z, multiply(double_divide(a3, b3), inverse(Z))), multiply(multiply(a3, multiply(b3, c3)), double_divide(a3, b3))))
% 0.20/0.51 = { by lemma 19 R->L }
% 0.20/0.52 inverse(double_divide(double_divide(Z, multiply(double_divide(a3, b3), inverse(Z))), multiply(multiply(a3, multiply(b3, c3)), multiply(Z, multiply(double_divide(a3, b3), inverse(Z))))))
% 0.20/0.52 = { by lemma 17 }
% 0.20/0.52 inverse(double_divide(double_divide(Z, multiply(double_divide(a3, b3), inverse(Z))), multiply(multiply(a3, multiply(b3, c3)), multiply(multiply(double_divide(a3, b3), inverse(Z)), Z))))
% 0.20/0.52 = { by axiom 1 (multiply) }
% 0.20/0.52 inverse(double_divide(double_divide(Z, multiply(double_divide(a3, b3), inverse(Z))), inverse(double_divide(multiply(multiply(double_divide(a3, b3), inverse(Z)), Z), multiply(a3, multiply(b3, c3))))))
% 0.20/0.52 = { by lemma 20 R->L }
% 0.20/0.52 inverse(multiply(double_divide(multiply(multiply(double_divide(a3, b3), inverse(Z)), Z), multiply(a3, multiply(b3, c3))), inverse(double_divide(Z, multiply(double_divide(a3, b3), inverse(Z))))))
% 0.20/0.52 = { by axiom 1 (multiply) }
% 0.20/0.52 inverse(multiply(double_divide(inverse(double_divide(Z, multiply(double_divide(a3, b3), inverse(Z)))), multiply(a3, multiply(b3, c3))), inverse(double_divide(Z, multiply(double_divide(a3, b3), inverse(Z))))))
% 0.20/0.52 = { by lemma 18 }
% 0.20/0.52 inverse(inverse(multiply(a3, multiply(b3, c3))))
% 0.20/0.52 = { by axiom 1 (multiply) }
% 0.20/0.52 inverse(inverse(inverse(double_divide(multiply(b3, c3), a3))))
% 0.20/0.52 = { by lemma 14 }
% 0.20/0.52 inverse(double_divide(multiply(b3, c3), a3))
% 0.20/0.52 = { by lemma 16 }
% 0.20/0.52 inverse(double_divide(a3, multiply(b3, c3)))
% 0.20/0.52 = { by lemma 17 R->L }
% 0.20/0.52 inverse(double_divide(a3, multiply(c3, b3)))
% 0.20/0.52 = { by axiom 1 (multiply) R->L }
% 0.20/0.52 multiply(multiply(c3, b3), a3)
% 0.20/0.52 = { by lemma 17 R->L }
% 0.20/0.52 multiply(a3, multiply(c3, b3))
% 0.20/0.52 = { by lemma 17 R->L }
% 0.20/0.52 multiply(a3, multiply(b3, c3))
% 0.20/0.52 % SZS output end Proof
% 0.20/0.52
% 0.20/0.52 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------