TSTP Solution File: BOO018-4 by Toma---0.4
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% File : Toma---0.4
% Problem : BOO018-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n014.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 : Wed Aug 30 18:11:01 EDT 2023
% Result : Unsatisfiable 0.59s 0.85s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO018-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.12 % Command : toma --casc %s
% 0.13/0.34 % Computer : n014.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 : Sun Aug 27 08:23:01 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.59/0.85 % SZS status Unsatisfiable
% 0.59/0.85 % SZS output start Proof
% 0.59/0.85 original problem:
% 0.59/0.85 axioms:
% 0.59/0.85 add(X, Y) = add(Y, X)
% 0.59/0.85 multiply(X, Y) = multiply(Y, X)
% 0.59/0.85 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 0.59/0.85 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 0.59/0.85 add(X, additive_identity()) = X
% 0.59/0.85 multiply(X, multiplicative_identity()) = X
% 0.59/0.85 add(X, inverse(X)) = multiplicative_identity()
% 0.59/0.85 multiply(X, inverse(X)) = additive_identity()
% 0.59/0.85 goal:
% 0.59/0.85 inverse(multiplicative_identity()) != additive_identity()
% 0.59/0.85 To show the unsatisfiability of the original goal,
% 0.59/0.85 it suffices to show that inverse(multiplicative_identity()) = additive_identity() (skolemized goal) is valid under the axioms.
% 0.59/0.85 Here is an equational proof:
% 0.59/0.85 0: add(X0, X1) = add(X1, X0).
% 0.59/0.85 Proof: Axiom.
% 0.59/0.85
% 0.59/0.85 1: multiply(X0, X1) = multiply(X1, X0).
% 0.59/0.85 Proof: Axiom.
% 0.59/0.85
% 0.59/0.85 4: add(X0, additive_identity()) = X0.
% 0.59/0.85 Proof: Axiom.
% 0.59/0.85
% 0.59/0.85 5: multiply(X0, multiplicative_identity()) = X0.
% 0.59/0.85 Proof: Axiom.
% 0.59/0.85
% 0.59/0.85 6: add(X0, inverse(X0)) = multiplicative_identity().
% 0.59/0.85 Proof: Axiom.
% 0.59/0.85
% 0.59/0.85 7: multiply(X0, inverse(X0)) = additive_identity().
% 0.59/0.85 Proof: Axiom.
% 0.59/0.85
% 0.59/0.85 9: add(additive_identity(), X2) = X2.
% 0.59/0.85 Proof: A critical pair between equations 0 and 4.
% 0.59/0.85
% 0.59/0.85 10: multiply(multiplicative_identity(), X2) = X2.
% 0.59/0.85 Proof: A critical pair between equations 1 and 5.
% 0.59/0.85
% 0.59/0.85 30: inverse(multiplicative_identity()) = additive_identity().
% 0.59/0.85 Proof: A critical pair between equations 10 and 7.
% 0.59/0.85
% 0.59/0.85 31: inverse(additive_identity()) = multiplicative_identity().
% 0.59/0.85 Proof: A critical pair between equations 9 and 6.
% 0.59/0.85
% 0.59/0.85 44: inverse(inverse(additive_identity())) = additive_identity().
% 0.59/0.85 Proof: Rewrite equation 30,
% 0.59/0.85 lhs with equations [31]
% 0.59/0.85 rhs with equations [].
% 0.59/0.85
% 0.59/0.85 63: inverse(multiplicative_identity()) = additive_identity().
% 0.59/0.85 Proof: Rewrite lhs with equations [31,44]
% 0.59/0.85 rhs with equations [].
% 0.59/0.85
% 0.59/0.85 % SZS output end Proof
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