%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI615_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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %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 Apr 9 05:40:42 PM UTC 2025
% Result : Theorem 2.90s 1.74s
% Output : CNFRefutation 3.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 10 |; 1 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 75 ( 25 atm; 25 fun; 0 num; 25 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; 0-3 aty)
% Number of functors : 6 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
%$ p > #nlpp
%Foreground sorts:
%Background operators:
tff('#skF_4',type,
'#skF_4': $int ).
tff('#skF_2',type,
'#skF_2': $int ).
tff('#skF_3',type,
'#skF_3': $int ).
tff('#skF_1',type,
'#skF_1': $int ).
%Foreground operators:
tff(p,type,
p: ( $int * $int * $int ) > $o ).
tff(f_41,negated_conjecture,
~ ( ! [Xa: $int,Ya: $int,Za: $int] :
( ( $lesseq($sum(Ya,$uminus(Za)),Xa)
& $lesseq(Xa,$sum(Ya,Za)) )
<=> p(Xa,Ya,Za) )
=> ! [Xa: $int,Ya: $int,Za: $int,Wa: $int] :
( $lesseq(Za,Wa)
=> ( p(Xa,Ya,Za)
=> p(Xa,Ya,Wa) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',interv_with_smaller_radius_contained) ).
tff(c_7,plain,
! [X_1a: $int,Y_2a: $int,Z_3a: $int] :
( p(X_1a,Y_2a,Z_3a)
| ~ $lesseq($sum(Y_2a,$uminus(Z_3a)),X_1a)
| ~ $lesseq(X_1a,$sum(Y_2a,Z_3a)) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_51,plain,
! [X_28a: $int,Y_29a: $int,Z_30a: $int] :
( p(X_28a,Y_29a,Z_30a)
| $less($sum(X_28a,Z_30a),Y_29a)
| $less($sum(Y_29a,Z_30a),X_28a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).
tff(c_24,plain,
~ p('#skF_1','#skF_2','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_61,plain,
( $less($sum('#skF_1','#skF_4'),'#skF_2')
| $less($sum('#skF_2','#skF_4'),'#skF_1') ),
inference(resolution,[status(thm)],[c_51,c_24]) ).
tff(c_63,plain,
( $less($sum('#skF_4','#skF_1'),'#skF_2')
| $less($sum('#skF_4','#skF_2'),'#skF_1') ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_61]) ).
tff(c_70,plain,
$less($sum('#skF_4','#skF_2'),'#skF_1'),
inference(splitLeft,[status(thm)],[c_63]) ).
tff(c_72,plain,
$less($sum('#skF_2','#skF_4'),'#skF_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_70]) ).
tff(c_31,plain,
p('#skF_1','#skF_2','#skF_3'),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_9,plain,
! [X_1a: $int,Y_2a: $int,Z_3a: $int] :
( ~ p(X_1a,Y_2a,Z_3a)
| $lesseq(X_1a,$sum(Y_2a,Z_3a)) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_14,plain,
! [X_1a: $int,Y_2a: $int,Z_3a: $int] :
( ~ p(X_1a,Y_2a,Z_3a)
| ~ $less($sum(Y_2a,Z_3a),X_1a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_9]) ).
tff(c_38,plain,
~ $less($sum('#skF_2','#skF_3'),'#skF_1'),
inference(resolution,[status(thm)],[c_31,c_14]) ).
tff(c_40,plain,
~ $less($sum('#skF_3','#skF_2'),'#skF_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_38]) ).
tff(c_5,plain,
$lesseq('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_16,plain,
~ $less('#skF_4','#skF_3'),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_73,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_72,c_40,c_16]) ).
tff(c_74,plain,
$less($sum('#skF_4','#skF_1'),'#skF_2'),
inference(splitRight,[status(thm)],[c_63]) ).
tff(c_77,plain,
$less($sum('#skF_1','#skF_4'),'#skF_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_74]) ).
tff(c_11,plain,
! [X_1a: $int,Y_2a: $int,Z_3a: $int] :
( ~ p(X_1a,Y_2a,Z_3a)
| $lesseq($sum(Y_2a,$uminus(Z_3a)),X_1a) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_13,plain,
! [X_1a: $int,Y_2a: $int,Z_3a: $int] :
( ~ p(X_1a,Y_2a,Z_3a)
| ~ $less($sum(X_1a,Z_3a),Y_2a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_11]) ).
tff(c_41,plain,
~ $less($sum('#skF_1','#skF_3'),'#skF_2'),
inference(resolution,[status(thm)],[c_31,c_13]) ).
tff(c_43,plain,
~ $less($sum('#skF_3','#skF_1'),'#skF_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_41]) ).
tff(c_80,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_77,c_43,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ARI615_1 : TPTP v9.0.0. Released v5.1.0.
% 0.06/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 7 15:14:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.90/1.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.90/1.75
% 2.90/1.75 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------