TSTP Solution File: GRP495-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP495-1 : 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 : n021.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 01:18:39 EDT 2023
% Result : Unsatisfiable 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP495-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % 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 : n021.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 : Tue Aug 29 02:41:44 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.40 Command-line arguments: --no-flatten-goal
% 0.19/0.40
% 0.19/0.40 % SZS status Unsatisfiable
% 0.19/0.40
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.19/0.43 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.19/0.43 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.19/0.43 Axiom 4 (single_axiom): double_divide(double_divide(identity, X), double_divide(double_divide(double_divide(Y, Z), double_divide(identity, identity)), double_divide(X, Z))) = Y.
% 0.19/0.43
% 0.19/0.43 Lemma 5: double_divide(double_divide(identity, X), double_divide(double_divide(double_divide(Y, Z), inverse(identity)), double_divide(X, Z))) = Y.
% 0.19/0.43 Proof:
% 0.19/0.43 double_divide(double_divide(identity, X), double_divide(double_divide(double_divide(Y, Z), inverse(identity)), double_divide(X, Z)))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 double_divide(double_divide(identity, X), double_divide(double_divide(double_divide(Y, Z), double_divide(identity, identity)), double_divide(X, Z)))
% 0.19/0.43 = { by axiom 4 (single_axiom) }
% 0.19/0.43 Y
% 0.19/0.43
% 0.19/0.43 Lemma 6: double_divide(double_divide(identity, X), double_divide(identity, double_divide(X, inverse(Y)))) = Y.
% 0.19/0.43 Proof:
% 0.19/0.43 double_divide(double_divide(identity, X), double_divide(identity, double_divide(X, inverse(Y))))
% 0.19/0.43 = { by axiom 2 (identity) }
% 0.19/0.43 double_divide(double_divide(identity, X), double_divide(double_divide(identity, inverse(identity)), double_divide(X, inverse(Y))))
% 0.19/0.43 = { by axiom 2 (identity) }
% 0.19/0.43 double_divide(double_divide(identity, X), double_divide(double_divide(double_divide(Y, inverse(Y)), inverse(identity)), double_divide(X, inverse(Y))))
% 0.19/0.43 = { by lemma 5 }
% 0.19/0.43 Y
% 0.19/0.43
% 0.19/0.43 Lemma 7: double_divide(double_divide(identity, X), inverse(identity)) = X.
% 0.19/0.43 Proof:
% 0.19/0.43 double_divide(double_divide(identity, X), inverse(identity))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 double_divide(double_divide(identity, X), double_divide(identity, identity))
% 0.19/0.43 = { by axiom 2 (identity) }
% 0.19/0.43 double_divide(double_divide(identity, X), double_divide(identity, double_divide(X, inverse(X))))
% 0.19/0.43 = { by lemma 6 }
% 0.19/0.43 X
% 0.19/0.43
% 0.19/0.43 Lemma 8: inverse(identity) = identity.
% 0.19/0.43 Proof:
% 0.19/0.43 inverse(identity)
% 0.19/0.43 = { by lemma 7 R->L }
% 0.19/0.43 double_divide(double_divide(identity, inverse(identity)), inverse(identity))
% 0.19/0.43 = { by axiom 2 (identity) R->L }
% 0.19/0.43 double_divide(identity, inverse(identity))
% 0.19/0.43 = { by axiom 2 (identity) R->L }
% 0.19/0.43 identity
% 0.19/0.43
% 0.19/0.43 Lemma 9: inverse(double_divide(X, Y)) = multiply(Y, X).
% 0.19/0.43 Proof:
% 0.19/0.43 inverse(double_divide(X, Y))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 double_divide(double_divide(X, Y), identity)
% 0.19/0.43 = { by axiom 3 (multiply) R->L }
% 0.19/0.43 multiply(Y, X)
% 0.19/0.43
% 0.19/0.43 Lemma 10: multiply(X, identity) = X.
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(X, identity)
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 inverse(double_divide(identity, X))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 double_divide(double_divide(identity, X), identity)
% 0.19/0.43 = { by lemma 8 R->L }
% 0.19/0.43 double_divide(double_divide(identity, X), inverse(identity))
% 0.19/0.43 = { by lemma 7 }
% 0.19/0.43 X
% 0.19/0.43
% 0.19/0.43 Lemma 11: double_divide(identity, inverse(X)) = X.
% 0.19/0.43 Proof:
% 0.19/0.43 double_divide(identity, inverse(X))
% 0.19/0.43 = { by lemma 7 R->L }
% 0.19/0.43 double_divide(double_divide(identity, double_divide(identity, inverse(X))), inverse(identity))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 double_divide(double_divide(identity, double_divide(identity, inverse(X))), double_divide(identity, identity))
% 0.19/0.43 = { by axiom 2 (identity) }
% 0.19/0.43 double_divide(double_divide(identity, double_divide(identity, inverse(X))), double_divide(identity, double_divide(double_divide(identity, inverse(X)), inverse(double_divide(identity, inverse(X))))))
% 0.19/0.43 = { by lemma 9 }
% 0.19/0.43 double_divide(double_divide(identity, double_divide(identity, inverse(X))), double_divide(identity, double_divide(double_divide(identity, inverse(X)), multiply(inverse(X), identity))))
% 0.19/0.43 = { by lemma 10 }
% 0.19/0.43 double_divide(double_divide(identity, double_divide(identity, inverse(X))), double_divide(identity, double_divide(double_divide(identity, inverse(X)), inverse(X))))
% 0.19/0.43 = { by lemma 6 }
% 0.19/0.43 X
% 0.19/0.43
% 0.19/0.43 Lemma 12: double_divide(identity, X) = inverse(X).
% 0.19/0.43 Proof:
% 0.19/0.43 double_divide(identity, X)
% 0.19/0.43 = { by lemma 10 R->L }
% 0.19/0.43 multiply(double_divide(identity, X), identity)
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 inverse(double_divide(identity, double_divide(identity, X)))
% 0.19/0.43 = { by lemma 8 R->L }
% 0.19/0.43 inverse(double_divide(inverse(identity), double_divide(identity, X)))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 inverse(double_divide(double_divide(identity, identity), double_divide(identity, X)))
% 0.19/0.43 = { by lemma 11 R->L }
% 0.19/0.43 inverse(double_divide(double_divide(identity, identity), double_divide(identity, double_divide(identity, inverse(X)))))
% 0.19/0.43 = { by lemma 6 }
% 0.19/0.43 inverse(X)
% 0.19/0.43
% 0.19/0.43 Lemma 13: inverse(inverse(X)) = X.
% 0.19/0.43 Proof:
% 0.19/0.43 inverse(inverse(X))
% 0.19/0.43 = { by lemma 12 R->L }
% 0.19/0.43 inverse(double_divide(identity, X))
% 0.19/0.43 = { by lemma 9 }
% 0.19/0.43 multiply(X, identity)
% 0.19/0.43 = { by lemma 10 }
% 0.19/0.43 X
% 0.19/0.43
% 0.19/0.43 Lemma 14: double_divide(inverse(X), double_divide(Y, double_divide(X, Y))) = identity.
% 0.19/0.43 Proof:
% 0.19/0.43 double_divide(inverse(X), double_divide(Y, double_divide(X, Y)))
% 0.19/0.43 = { by lemma 12 R->L }
% 0.19/0.43 double_divide(double_divide(identity, X), double_divide(Y, double_divide(X, Y)))
% 0.19/0.43 = { by lemma 7 R->L }
% 0.19/0.43 double_divide(double_divide(identity, X), double_divide(double_divide(double_divide(identity, Y), inverse(identity)), double_divide(X, Y)))
% 0.19/0.43 = { by lemma 5 }
% 0.19/0.43 identity
% 0.19/0.43
% 0.19/0.43 Lemma 15: double_divide(X, double_divide(multiply(inverse(Y), X), Y)) = identity.
% 0.19/0.43 Proof:
% 0.19/0.43 double_divide(X, double_divide(multiply(inverse(Y), X), Y))
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 double_divide(X, double_divide(inverse(double_divide(X, inverse(Y))), Y))
% 0.19/0.43 = { by lemma 12 R->L }
% 0.19/0.43 double_divide(X, double_divide(double_divide(identity, double_divide(X, inverse(Y))), Y))
% 0.19/0.43 = { by lemma 10 R->L }
% 0.19/0.43 double_divide(multiply(X, identity), double_divide(double_divide(identity, double_divide(X, inverse(Y))), Y))
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 double_divide(inverse(double_divide(identity, X)), double_divide(double_divide(identity, double_divide(X, inverse(Y))), Y))
% 0.19/0.43 = { by lemma 6 R->L }
% 0.19/0.43 double_divide(inverse(double_divide(identity, X)), double_divide(double_divide(identity, double_divide(X, inverse(Y))), double_divide(double_divide(identity, X), double_divide(identity, double_divide(X, inverse(Y))))))
% 0.19/0.43 = { by lemma 14 }
% 0.19/0.44 identity
% 0.19/0.44
% 0.19/0.44 Lemma 16: double_divide(X, multiply(double_divide(X, Y), Y)) = identity.
% 0.19/0.44 Proof:
% 0.19/0.44 double_divide(X, multiply(double_divide(X, Y), Y))
% 0.19/0.44 = { by lemma 9 R->L }
% 0.19/0.44 double_divide(X, inverse(double_divide(Y, double_divide(X, Y))))
% 0.19/0.44 = { by axiom 1 (inverse) }
% 0.19/0.44 double_divide(X, double_divide(double_divide(Y, double_divide(X, Y)), identity))
% 0.19/0.44 = { by lemma 13 R->L }
% 0.19/0.44 double_divide(inverse(inverse(X)), double_divide(double_divide(Y, double_divide(X, Y)), identity))
% 0.19/0.44 = { by lemma 14 R->L }
% 0.19/0.44 double_divide(inverse(inverse(X)), double_divide(double_divide(Y, double_divide(X, Y)), double_divide(inverse(X), double_divide(Y, double_divide(X, Y)))))
% 0.19/0.44 = { by lemma 14 }
% 0.19/0.44 identity
% 0.19/0.44
% 0.19/0.44 Lemma 17: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(inverse(X), multiply(X, Y))
% 0.19/0.44 = { by lemma 9 R->L }
% 0.19/0.44 multiply(inverse(X), inverse(double_divide(Y, X)))
% 0.19/0.44 = { by axiom 1 (inverse) }
% 0.19/0.44 multiply(inverse(X), double_divide(double_divide(Y, X), identity))
% 0.19/0.44 = { by lemma 12 R->L }
% 0.19/0.44 multiply(double_divide(identity, X), double_divide(double_divide(Y, X), identity))
% 0.19/0.44 = { by lemma 8 R->L }
% 0.19/0.44 multiply(double_divide(inverse(identity), X), double_divide(double_divide(Y, X), identity))
% 0.19/0.44 = { by lemma 8 R->L }
% 0.19/0.44 multiply(double_divide(inverse(identity), X), double_divide(double_divide(Y, X), inverse(identity)))
% 0.19/0.44 = { by axiom 2 (identity) }
% 0.19/0.44 multiply(double_divide(inverse(double_divide(Z, inverse(Z))), X), double_divide(double_divide(Y, X), inverse(identity)))
% 0.19/0.44 = { by lemma 9 }
% 0.19/0.44 multiply(double_divide(multiply(inverse(Z), Z), X), double_divide(double_divide(Y, X), inverse(identity)))
% 0.19/0.44 = { by lemma 12 R->L }
% 0.19/0.44 multiply(double_divide(multiply(double_divide(identity, Z), Z), X), double_divide(double_divide(Y, X), inverse(identity)))
% 0.19/0.44 = { by lemma 9 R->L }
% 0.19/0.44 inverse(double_divide(double_divide(double_divide(Y, X), inverse(identity)), double_divide(multiply(double_divide(identity, Z), Z), X)))
% 0.19/0.44 = { by lemma 12 R->L }
% 0.19/0.44 double_divide(identity, double_divide(double_divide(double_divide(Y, X), inverse(identity)), double_divide(multiply(double_divide(identity, Z), Z), X)))
% 0.19/0.44 = { by lemma 16 R->L }
% 0.19/0.44 double_divide(double_divide(identity, multiply(double_divide(identity, Z), Z)), double_divide(double_divide(double_divide(Y, X), inverse(identity)), double_divide(multiply(double_divide(identity, Z), Z), X)))
% 0.19/0.44 = { by lemma 5 }
% 0.19/0.44 Y
% 0.19/0.44
% 0.19/0.44 Lemma 18: double_divide(X, double_divide(Y, X)) = Y.
% 0.19/0.44 Proof:
% 0.19/0.44 double_divide(X, double_divide(Y, X))
% 0.19/0.44 = { by lemma 11 R->L }
% 0.19/0.44 double_divide(identity, inverse(double_divide(X, double_divide(Y, X))))
% 0.19/0.44 = { by lemma 9 }
% 0.19/0.44 double_divide(identity, multiply(double_divide(Y, X), X))
% 0.19/0.44 = { by lemma 12 }
% 0.19/0.44 inverse(multiply(double_divide(Y, X), X))
% 0.19/0.44 = { by lemma 10 R->L }
% 0.19/0.44 multiply(inverse(multiply(double_divide(Y, X), X)), identity)
% 0.19/0.44 = { by lemma 8 R->L }
% 0.19/0.44 multiply(inverse(multiply(double_divide(Y, X), X)), inverse(identity))
% 0.19/0.44 = { by lemma 16 R->L }
% 0.19/0.44 multiply(inverse(multiply(double_divide(Y, X), X)), inverse(double_divide(Y, multiply(double_divide(Y, X), X))))
% 0.19/0.44 = { by lemma 9 }
% 0.19/0.44 multiply(inverse(multiply(double_divide(Y, X), X)), multiply(multiply(double_divide(Y, X), X), Y))
% 0.19/0.44 = { by lemma 17 }
% 0.19/0.44 Y
% 0.19/0.44
% 0.19/0.44 Lemma 19: double_divide(double_divide(X, Y), X) = Y.
% 0.19/0.44 Proof:
% 0.19/0.44 double_divide(double_divide(X, Y), X)
% 0.19/0.44 = { by lemma 18 R->L }
% 0.19/0.44 double_divide(double_divide(X, Y), double_divide(Y, double_divide(X, Y)))
% 0.19/0.44 = { by lemma 18 }
% 0.19/0.44 Y
% 0.19/0.44
% 0.19/0.44 Lemma 20: multiply(X, double_divide(X, Y)) = inverse(Y).
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(X, double_divide(X, Y))
% 0.19/0.44 = { by lemma 9 R->L }
% 0.19/0.44 inverse(double_divide(double_divide(X, Y), X))
% 0.19/0.44 = { by lemma 19 }
% 0.19/0.44 inverse(Y)
% 0.19/0.44
% 0.19/0.44 Lemma 21: double_divide(inverse(X), Y) = multiply(X, inverse(Y)).
% 0.19/0.44 Proof:
% 0.19/0.44 double_divide(inverse(X), Y)
% 0.19/0.44 = { by lemma 5 R->L }
% 0.19/0.44 double_divide(double_divide(identity, Z), double_divide(double_divide(double_divide(double_divide(inverse(X), Y), double_divide(multiply(inverse(X), double_divide(inverse(X), Y)), X)), inverse(identity)), double_divide(Z, double_divide(multiply(inverse(X), double_divide(inverse(X), Y)), X))))
% 0.19/0.44 = { by lemma 15 }
% 0.19/0.44 double_divide(double_divide(identity, Z), double_divide(double_divide(identity, inverse(identity)), double_divide(Z, double_divide(multiply(inverse(X), double_divide(inverse(X), Y)), X))))
% 0.19/0.44 = { by lemma 12 }
% 0.19/0.44 double_divide(inverse(Z), double_divide(double_divide(identity, inverse(identity)), double_divide(Z, double_divide(multiply(inverse(X), double_divide(inverse(X), Y)), X))))
% 0.19/0.44 = { by lemma 11 }
% 0.19/0.44 double_divide(inverse(Z), double_divide(identity, double_divide(Z, double_divide(multiply(inverse(X), double_divide(inverse(X), Y)), X))))
% 0.19/0.44 = { by lemma 6 R->L }
% 0.19/0.44 double_divide(double_divide(double_divide(identity, double_divide(Z, double_divide(multiply(inverse(X), double_divide(inverse(X), Y)), X))), double_divide(identity, double_divide(double_divide(Z, double_divide(multiply(inverse(X), double_divide(inverse(X), Y)), X)), inverse(inverse(Z))))), double_divide(identity, double_divide(Z, double_divide(multiply(inverse(X), double_divide(inverse(X), Y)), X))))
% 0.19/0.44 = { by lemma 19 }
% 0.19/0.44 double_divide(identity, double_divide(double_divide(Z, double_divide(multiply(inverse(X), double_divide(inverse(X), Y)), X)), inverse(inverse(Z))))
% 0.19/0.44 = { by lemma 12 }
% 0.19/0.44 inverse(double_divide(double_divide(Z, double_divide(multiply(inverse(X), double_divide(inverse(X), Y)), X)), inverse(inverse(Z))))
% 0.19/0.44 = { by lemma 9 }
% 0.19/0.44 multiply(inverse(inverse(Z)), double_divide(Z, double_divide(multiply(inverse(X), double_divide(inverse(X), Y)), X)))
% 0.19/0.44 = { by lemma 13 }
% 0.19/0.44 multiply(Z, double_divide(Z, double_divide(multiply(inverse(X), double_divide(inverse(X), Y)), X)))
% 0.19/0.44 = { by lemma 20 }
% 0.19/0.44 inverse(double_divide(multiply(inverse(X), double_divide(inverse(X), Y)), X))
% 0.19/0.44 = { by lemma 9 }
% 0.19/0.44 multiply(X, multiply(inverse(X), double_divide(inverse(X), Y)))
% 0.19/0.44 = { by lemma 20 }
% 0.19/0.44 multiply(X, inverse(Y))
% 0.19/0.44
% 0.19/0.44 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.19/0.44 Proof:
% 0.19/0.44 multiply(multiply(a3, b3), c3)
% 0.19/0.44 = { by lemma 9 R->L }
% 0.19/0.44 multiply(inverse(double_divide(b3, a3)), c3)
% 0.19/0.45 = { by lemma 5 R->L }
% 0.19/0.45 double_divide(double_divide(identity, a3), double_divide(double_divide(double_divide(multiply(inverse(double_divide(b3, a3)), c3), double_divide(b3, a3)), inverse(identity)), double_divide(a3, double_divide(b3, a3))))
% 0.19/0.45 = { by lemma 17 R->L }
% 0.19/0.45 double_divide(double_divide(identity, a3), double_divide(double_divide(multiply(inverse(c3), multiply(c3, double_divide(multiply(inverse(double_divide(b3, a3)), c3), double_divide(b3, a3)))), inverse(identity)), double_divide(a3, double_divide(b3, a3))))
% 0.19/0.45 = { by lemma 13 R->L }
% 0.19/0.45 double_divide(double_divide(identity, a3), double_divide(double_divide(multiply(inverse(c3), multiply(c3, inverse(inverse(double_divide(multiply(inverse(double_divide(b3, a3)), c3), double_divide(b3, a3)))))), inverse(identity)), double_divide(a3, double_divide(b3, a3))))
% 0.19/0.45 = { by axiom 1 (inverse) }
% 0.19/0.45 double_divide(double_divide(identity, a3), double_divide(double_divide(multiply(inverse(c3), multiply(c3, inverse(double_divide(double_divide(multiply(inverse(double_divide(b3, a3)), c3), double_divide(b3, a3)), identity)))), inverse(identity)), double_divide(a3, double_divide(b3, a3))))
% 0.19/0.45 = { by lemma 21 R->L }
% 0.19/0.45 double_divide(double_divide(identity, a3), double_divide(double_divide(multiply(inverse(c3), double_divide(inverse(c3), double_divide(double_divide(multiply(inverse(double_divide(b3, a3)), c3), double_divide(b3, a3)), identity))), inverse(identity)), double_divide(a3, double_divide(b3, a3))))
% 0.19/0.45 = { by lemma 15 R->L }
% 0.19/0.45 double_divide(double_divide(identity, a3), double_divide(double_divide(multiply(inverse(c3), double_divide(inverse(c3), double_divide(double_divide(multiply(inverse(double_divide(b3, a3)), c3), double_divide(b3, a3)), double_divide(c3, double_divide(multiply(inverse(double_divide(b3, a3)), c3), double_divide(b3, a3)))))), inverse(identity)), double_divide(a3, double_divide(b3, a3))))
% 0.19/0.45 = { by lemma 14 }
% 0.19/0.45 double_divide(double_divide(identity, a3), double_divide(double_divide(multiply(inverse(c3), identity), inverse(identity)), double_divide(a3, double_divide(b3, a3))))
% 0.19/0.45 = { by lemma 10 }
% 0.19/0.45 double_divide(double_divide(identity, a3), double_divide(double_divide(inverse(c3), inverse(identity)), double_divide(a3, double_divide(b3, a3))))
% 0.19/0.45 = { by lemma 12 }
% 0.19/0.45 double_divide(inverse(a3), double_divide(double_divide(inverse(c3), inverse(identity)), double_divide(a3, double_divide(b3, a3))))
% 0.19/0.45 = { by lemma 21 }
% 0.19/0.45 multiply(a3, inverse(double_divide(double_divide(inverse(c3), inverse(identity)), double_divide(a3, double_divide(b3, a3)))))
% 0.19/0.45 = { by lemma 9 }
% 0.19/0.45 multiply(a3, multiply(double_divide(a3, double_divide(b3, a3)), double_divide(inverse(c3), inverse(identity))))
% 0.19/0.45 = { by lemma 21 }
% 0.19/0.45 multiply(a3, multiply(double_divide(a3, double_divide(b3, a3)), multiply(c3, inverse(inverse(identity)))))
% 0.19/0.45 = { by lemma 13 }
% 0.19/0.45 multiply(a3, multiply(double_divide(a3, double_divide(b3, a3)), multiply(c3, identity)))
% 0.19/0.45 = { by lemma 10 }
% 0.19/0.45 multiply(a3, multiply(double_divide(a3, double_divide(b3, a3)), c3))
% 0.19/0.45 = { by lemma 18 }
% 0.19/0.45 multiply(a3, multiply(b3, c3))
% 0.19/0.45 % SZS output end Proof
% 0.19/0.45
% 0.19/0.45 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------