%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI607_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 : n029.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 05:40:40 PM UTC 2025
% Result : Theorem 2.82s 1.64s
% Output : CNFRefutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 31 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 10 ~; 6 |; 0 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 72 ( 22 atm; 12 fun; 30 num; 8 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 5 usr; 8 con; 0-2 aty)
% Number of variables : 8 ( 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp > f
%Foreground sorts:
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
%Foreground operators:
tff(f,type,
f: $int > $int ).
tff(f_34,negated_conjecture,
~ ( ! [Xa: $int,Ya: $int] :
( $lesseq(Xa,Ya)
=> $lesseq(f(Xa),f(Ya)) )
=> $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_mon_implies_f2plusf5_gt_f7plusf3) ).
tff(c_2,plain,
~ $lesseq($sum(f(2),f(5)),$sum(f(7),f(3))),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_3,plain,
$less($sum(f(7),f(3)),$sum(f(5),f(2))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).
tff(c_8,plain,
$less($sum(f(7),f(3)),$sum(f(2),f(5))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3]) ).
tff(c_17,plain,
f(3) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_8]) ).
tff(c_18,plain,
f(2) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_8]) ).
tff(c_4,plain,
! [X_1a: $int,Y_2a: $int] :
( $lesseq(f(X_1a),f(Y_2a))
| ~ $lesseq(X_1a,Y_2a) ),
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_6,plain,
! [Y_2a: $int,X_1a: $int] :
( ~ $less(f(Y_2a),f(X_1a))
| $less(Y_2a,X_1a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_4]) ).
tff(c_104,plain,
! [Y_21a: $int] :
( ~ $less(f(Y_21a),'#skE_3')
| $less(Y_21a,2) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_6]) ).
tff(c_123,plain,
( ~ $less('#skE_2','#skE_3')
| $less(3,2) ),
inference(superposition,[status(thm),theory(equality)],[c_17,c_104]) ).
tff(c_125,plain,
~ $less('#skE_2','#skE_3'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_123]) ).
tff(c_19,plain,
f(5) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_8]) ).
tff(c_16,plain,
f(7) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_8]) ).
tff(c_131,plain,
! [X_24a: $int] :
( ~ $less('#skE_1',f(X_24a))
| $less(7,X_24a) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_6]) ).
tff(c_147,plain,
( ~ $less('#skE_1','#skE_4')
| $less(7,5) ),
inference(superposition,[status(thm),theory(equality)],[c_19,c_131]) ).
tff(c_149,plain,
~ $less('#skE_1','#skE_4'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_147]) ).
tff(c_13,plain,
f(5) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_8]) ).
tff(c_12,plain,
f(2) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_8]) ).
tff(c_11,plain,
f(3) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_8]) ).
tff(c_10,plain,
f(7) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_8]) ).
tff(c_15,plain,
$less($sum('#skE_1','#skE_2'),$sum('#skE_3','#skE_4')),
inference(demodulation,[status(thm),theory(equality)],[c_13,c_12,c_11,c_10,c_8]) ).
tff(c_21,plain,
$less($sum('#skE_2','#skE_1'),$sum('#skE_3','#skE_4')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_15]) ).
tff(c_156,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_125,c_149,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ARI607_1 : TPTP v9.0.0. Released v5.1.0.
% 0.06/0.12 % 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
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 15:14:19 EDT 2025
% 0.12/0.34 % CPUTime :
% 2.82/1.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.82/1.64
% 2.82/1.64 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------