TSTP Solution File: RNG024-6 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : RNG024-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 20:35:47 EDT 2022
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 13 unt; 0 nHn; 11 RR)
% Number of literals : 28 ( 27 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 24 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_additive_inverse,axiom,
add(X,additive_inverse(X)) = additive_identity ).
cnf(right_alternative,axiom,
multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)) ).
cnf(associator,axiom,
associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))) ).
cnf(prove_right_alternative,negated_conjecture,
associator(x,y,y) != additive_identity ).
cnf(refute_0_0,plain,
associator(X_25,X_27,X_27) = add(multiply(multiply(X_25,X_27),X_27),additive_inverse(multiply(X_25,multiply(X_27,X_27)))),
inference(subst,[],[associator:[bind(X,$fot(X_25)),bind(Y,$fot(X_27)),bind(Z,$fot(X_27))]]) ).
cnf(refute_0_1,plain,
multiply(multiply(X_25,X_27),X_27) = multiply(X_25,multiply(X_27,X_27)),
inference(subst,[],[right_alternative:[bind(X,$fot(X_25)),bind(Y,$fot(X_27))]]) ).
cnf(refute_0_2,plain,
( multiply(multiply(X_25,X_27),X_27) != multiply(X_25,multiply(X_27,X_27))
| associator(X_25,X_27,X_27) != add(multiply(multiply(X_25,X_27),X_27),additive_inverse(multiply(X_25,multiply(X_27,X_27))))
| associator(X_25,X_27,X_27) = add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))) ),
introduced(tautology,[equality,[$cnf( $equal(associator(X_25,X_27,X_27),add(multiply(multiply(X_25,X_27),X_27),additive_inverse(multiply(X_25,multiply(X_27,X_27))))) ),[1,0],$fot(multiply(X_25,multiply(X_27,X_27)))]]) ).
cnf(refute_0_3,plain,
( associator(X_25,X_27,X_27) != add(multiply(multiply(X_25,X_27),X_27),additive_inverse(multiply(X_25,multiply(X_27,X_27))))
| associator(X_25,X_27,X_27) = add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))) ),
inference(resolve,[$cnf( $equal(multiply(multiply(X_25,X_27),X_27),multiply(X_25,multiply(X_27,X_27))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
associator(X_25,X_27,X_27) = add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))),
inference(resolve,[$cnf( $equal(associator(X_25,X_27,X_27),add(multiply(multiply(X_25,X_27),X_27),additive_inverse(multiply(X_25,multiply(X_27,X_27))))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))) = additive_identity,
inference(subst,[],[right_additive_inverse:[bind(X,$fot(multiply(X_25,multiply(X_27,X_27))))]]) ).
cnf(refute_0_6,plain,
( add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))) != additive_identity
| associator(X_25,X_27,X_27) != add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27))))
| associator(X_25,X_27,X_27) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(associator(X_25,X_27,X_27),add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27))))) ),[1],$fot(additive_identity)]]) ).
cnf(refute_0_7,plain,
( associator(X_25,X_27,X_27) != add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27))))
| associator(X_25,X_27,X_27) = additive_identity ),
inference(resolve,[$cnf( $equal(add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27)))),additive_identity) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
associator(X_25,X_27,X_27) = additive_identity,
inference(resolve,[$cnf( $equal(associator(X_25,X_27,X_27),add(multiply(X_25,multiply(X_27,X_27)),additive_inverse(multiply(X_25,multiply(X_27,X_27))))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
associator(x,y,y) = additive_identity,
inference(subst,[],[refute_0_8:[bind(X_25,$fot(x)),bind(X_27,$fot(y))]]) ).
cnf(refute_0_10,plain,
( additive_identity != additive_identity
| associator(x,y,y) != additive_identity
| associator(x,y,y) = additive_identity ),
introduced(tautology,[equality,[$cnf( $equal(associator(x,y,y),additive_identity) ),[1],$fot(additive_identity)]]) ).
cnf(refute_0_11,plain,
( additive_identity != additive_identity
| associator(x,y,y) = additive_identity ),
inference(resolve,[$cnf( $equal(associator(x,y,y),additive_identity) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
additive_identity != additive_identity,
inference(resolve,[$cnf( $equal(associator(x,y,y),additive_identity) )],[refute_0_11,prove_right_alternative]) ).
cnf(refute_0_13,plain,
additive_identity = additive_identity,
introduced(tautology,[refl,[$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
% 0.11/0.12 % Problem : RNG024-6 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon May 30 09:19:25 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.38 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.38
%------------------------------------------------------------------------------