TSTP Solution File: BOO011-2 by Toma---0.4
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% File : Toma---0.4
% Problem : BOO011-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n011.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 18:10:57 EDT 2023
% Result : Unsatisfiable 0.20s 0.67s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO011-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n011.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 08:35:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.67 % SZS status Unsatisfiable
% 0.20/0.67 % SZS output start Proof
% 0.20/0.67 original problem:
% 0.20/0.67 axioms:
% 0.20/0.67 add(X, Y) = add(Y, X)
% 0.20/0.67 multiply(X, Y) = multiply(Y, X)
% 0.20/0.67 add(multiply(X, Y), Z) = multiply(add(X, Z), add(Y, Z))
% 0.20/0.67 add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z))
% 0.20/0.67 multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z))
% 0.20/0.67 multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z))
% 0.20/0.67 add(X, inverse(X)) = multiplicative_identity()
% 0.20/0.67 add(inverse(X), X) = multiplicative_identity()
% 0.20/0.67 multiply(X, inverse(X)) = additive_identity()
% 0.20/0.67 multiply(inverse(X), X) = additive_identity()
% 0.20/0.67 multiply(X, multiplicative_identity()) = X
% 0.20/0.67 multiply(multiplicative_identity(), X) = X
% 0.20/0.67 add(X, additive_identity()) = X
% 0.20/0.67 add(additive_identity(), X) = X
% 0.20/0.67 goal:
% 0.20/0.67 inverse(additive_identity()) != multiplicative_identity()
% 0.20/0.67 To show the unsatisfiability of the original goal,
% 0.20/0.67 it suffices to show that inverse(additive_identity()) = multiplicative_identity() (skolemized goal) is valid under the axioms.
% 0.20/0.67 Here is an equational proof:
% 0.20/0.67 6: add(X0, inverse(X0)) = multiplicative_identity().
% 0.20/0.67 Proof: Axiom.
% 0.20/0.67
% 0.20/0.67 13: add(additive_identity(), X0) = X0.
% 0.20/0.67 Proof: Axiom.
% 0.20/0.67
% 0.20/0.67 16: multiplicative_identity() = inverse(additive_identity()).
% 0.20/0.67 Proof: A critical pair between equations 6 and 13.
% 0.20/0.67
% 0.20/0.67 37: inverse(additive_identity()) = multiplicative_identity().
% 0.20/0.67 Proof: Rewrite lhs with equations []
% 0.20/0.67 rhs with equations [16].
% 0.20/0.67
% 0.20/0.67 % SZS output end Proof
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