%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI598_1 : TPTP v9.0.0. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n005.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 Apr 9 05:40:39 PM UTC 2025
% Result : Theorem 2.69s 1.62s
% Output : CNFRefutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 9 ( 7 ~; 0 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 37 ( 0 atm; 15 fun; 17 num; 5 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 5 ( 4 !; 1 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
%$ p > #nlpp
%Foreground sorts:
%Background operators:
tff(a,type,
a: $int ).
%Foreground operators:
tff(p,type,
p: $int > $o ).
tff(f_34,negated_conjecture,
~ ( ( p(a)
& p($sum($product(3,a),1)) )
=> ? [Xa: $int] : p($product(2,Xa)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_or_3aplus1_even) ).
tff(c_4,plain,
p($sum($product(3,a),1)),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_35,plain,
p($sum(1,$product(3,a))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_4]) ).
tff(c_19,plain,
! [X_1a: $int] : ~ p($product(2,X_1a)),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_40,plain,
! [X_1a: $int] : ( $product(2,X_1a) != $sum(1,$product(3,a)) ),
inference(resolution,[status(thm)],[c_35,c_19]) ).
tff(c_42,plain,
~ $divides(2,$sum(1,$product(3,a))),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_40]) ).
tff(c_11,plain,
p(a),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_27,plain,
! [X_10a: $int] : ~ p($product(2,X_10a)),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_32,plain,
! [X_10a: $int] : ( a != $product(2,X_10a) ),
inference(resolution,[status(thm)],[c_11,c_27]) ).
tff(c_34,plain,
~ $divides(2,a),
inference(quantifierElimination,[status(thm),theory('LIA')],[c_32]) ).
tff(c_43,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_42,c_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ARI598_1 : TPTP v9.0.0. Released v5.1.0.
% 0.10/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n005.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 : Mon Apr 7 15:14:12 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.69/1.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.69/1.62
% 2.69/1.62 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------