TSTP Solution File: RNG010-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG010-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 : 600s
% DateTime : Mon Jul 18 20:35:45 EDT 2022
% Result : Unsatisfiable 0.20s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 18 ( 11 unt; 0 nHn; 12 RR)
% Number of literals : 28 ( 27 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 15 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_multiplicative_zero,axiom,
multiply(additive_identity,X) = additive_identity ).
cnf(right_multiplicative_zero,axiom,
multiply(X,additive_identity) = additive_identity ).
cnf(middle_law,axiom,
multiply(multiply(Y,X),Y) != multiply(Y,multiply(X,Y)) ).
cnf(refute_0_0,plain,
multiply(multiply(additive_identity,X_5),additive_identity) != multiply(additive_identity,multiply(X_5,additive_identity)),
inference(subst,[],[middle_law:[bind(X,$fot(X_5)),bind(Y,$fot(additive_identity))]]) ).
cnf(refute_0_1,plain,
multiply(additive_identity,X_5) = additive_identity,
inference(subst,[],[left_multiplicative_zero:[bind(X,$fot(X_5))]]) ).
cnf(refute_0_2,plain,
( multiply(additive_identity,X_5) != additive_identity
| multiply(additive_identity,additive_identity) != multiply(additive_identity,multiply(X_5,additive_identity))
| multiply(multiply(additive_identity,X_5),additive_identity) = multiply(additive_identity,multiply(X_5,additive_identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(multiply(additive_identity,X_5),additive_identity),multiply(additive_identity,multiply(X_5,additive_identity))) ),[0,0],$fot(additive_identity)]]) ).
cnf(refute_0_3,plain,
( multiply(additive_identity,additive_identity) != multiply(additive_identity,multiply(X_5,additive_identity))
| multiply(multiply(additive_identity,X_5),additive_identity) = multiply(additive_identity,multiply(X_5,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,X_5),additive_identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(additive_identity,additive_identity) != multiply(additive_identity,multiply(X_5,additive_identity)),
inference(resolve,[$cnf( $equal(multiply(multiply(additive_identity,X_5),additive_identity),multiply(additive_identity,multiply(X_5,additive_identity))) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(subst,[],[right_multiplicative_zero:[bind(X,$fot(additive_identity))]]) ).
cnf(refute_0_6,plain,
( multiply(additive_identity,additive_identity) != additive_identity
| additive_identity != multiply(additive_identity,multiply(X_5,additive_identity))
| multiply(additive_identity,additive_identity) = multiply(additive_identity,multiply(X_5,additive_identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(additive_identity,additive_identity),multiply(additive_identity,multiply(X_5,additive_identity))) ),[0],$fot(additive_identity)]]) ).
cnf(refute_0_7,plain,
( additive_identity != multiply(additive_identity,multiply(X_5,additive_identity))
| multiply(additive_identity,additive_identity) = multiply(additive_identity,multiply(X_5,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),additive_identity) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
multiply(additive_identity,multiply(X_5,additive_identity)) = additive_identity,
inference(subst,[],[left_multiplicative_zero:[bind(X,$fot(multiply(X_5,additive_identity)))]]) ).
cnf(refute_0_9,plain,
( multiply(additive_identity,multiply(X_5,additive_identity)) != additive_identity
| additive_identity != additive_identity
| additive_identity = multiply(additive_identity,multiply(X_5,additive_identity)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(additive_identity,multiply(additive_identity,multiply(X_5,additive_identity))) ),[1],$fot(additive_identity)]]) ).
cnf(refute_0_10,plain,
( additive_identity != additive_identity
| additive_identity = multiply(additive_identity,multiply(X_5,additive_identity)) ),
inference(resolve,[$cnf( $equal(multiply(additive_identity,multiply(X_5,additive_identity)),additive_identity) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( additive_identity != additive_identity
| multiply(additive_identity,additive_identity) = multiply(additive_identity,multiply(X_5,additive_identity)) ),
inference(resolve,[$cnf( $equal(additive_identity,multiply(additive_identity,multiply(X_5,additive_identity))) )],[refute_0_10,refute_0_7]) ).
cnf(refute_0_12,plain,
additive_identity != additive_identity,
inference(resolve,[$cnf( $equal(multiply(additive_identity,additive_identity),multiply(additive_identity,multiply(X_5,additive_identity))) )],[refute_0_11,refute_0_4]) ).
cnf(refute_0_13,plain,
additive_identity = additive_identity,
introduced(tautology,[refl,[$fot(additive_identity)]]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( $equal(additive_identity,additive_identity) )],[refute_0_13,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : RNG010-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon May 30 07:08:56 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.37
% 0.20/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.37
%------------------------------------------------------------------------------