%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT035_1 : TPTP v9.0.0. Released v5.0.0.
% 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 : n008.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 06:07:57 PM UTC 2025
% Result : Theorem 5.72s 2.36s
% Output : CNFRefutation 5.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 4 ~; 6 |; 0 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number arithmetic : 50 ( 13 atm; 16 fun; 13 num; 8 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > remove > add > #nlpp > count > empty > #skF_1
%Foreground sorts:
tff(collection,type,
collection: $tType ).
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skF_2',type,
'#skF_2': $int ).
tff('#skF_3',type,
'#skF_3': $int ).
%Foreground operators:
tff(empty,type,
empty: collection ).
tff(count,type,
count: collection > $int ).
tff('#skF_1',type,
'#skF_1': collection ).
tff(in,type,
in: ( $int * collection ) > $o ).
tff(remove,type,
remove: ( $int * collection ) > collection ).
tff(add,type,
add: ( $int * collection ) > collection ).
tff(f_142,negated_conjecture,
~ ! [U: collection,Va: $int,Wa: $int] :
( $greater(Wa,0)
=> $greatereq($sum(count(U),Wa),count(add(Va,U))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f_118,axiom,
! [X8a: $int,X9: collection] :
( ~ in(X8a,X9)
<=> ( count(add(X8a,X9)) = $sum(count(X9),1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax3) ).
tff(f_122,axiom,
! [X10a: $int,X11: collection] :
( in(X10a,X11)
<=> ( count(add(X10a,X11)) = count(X11) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax4) ).
tff(c_47,plain,
~ $greatereq($sum(count('#skF_1'),'#skF_3'),count(add('#skF_2','#skF_1'))),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_55,plain,
$less($sum('#skF_3',count('#skF_1')),count(add('#skF_2','#skF_1'))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_47]) ).
tff(c_130,plain,
count(add('#skF_2','#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_55]) ).
tff(c_108,plain,
count('#skF_1') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_55]) ).
tff(c_25,plain,
! [X8_14a: $int,X9_15: collection] :
( ( count(add(X8_14a,X9_15)) = $sum(count(X9_15),1) )
| in(X8_14a,X9_15) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_463,plain,
! [X8_76a: $int,X9_77: collection] :
( ( count(add(X8_76a,X9_77)) = $sum(1,count(X9_77)) )
| in(X8_76a,X9_77) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_62,plain,
! [X10_16a: $int,X11_17: collection] :
( ( count(add(X10_16a,X11_17)) = count(X11_17) )
| ~ in(X10_16a,X11_17) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_2770,plain,
! [X8_181a: $int,X9_182: collection] :
( ( count(add(X8_181a,X9_182)) = count(X9_182) )
| ( count(add(X8_181a,X9_182)) = $sum(1,count(X9_182)) ) ),
inference(resolution,[status(thm)],[c_463,c_62]) ).
tff(c_111,plain,
count(add('#skF_2','#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_55]) ).
tff(c_2810,plain,
( ( $sum(1,count('#skF_1')) = '#skE_2' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_2770,c_111]) ).
tff(c_2869,plain,
( ( '#skE_2' = $sum(1,'#skE_1') )
| ( '#skE_2' = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_130,c_108,c_108,c_2810]) ).
tff(c_2901,plain,
'#skE_2' = '#skE_1',
inference(splitLeft,[status(thm)],[c_2869]) ).
tff(c_104,plain,
count(add('#skF_2','#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_55]) ).
tff(c_103,plain,
count('#skF_1') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_55]) ).
tff(c_77,plain,
$less($sum('#skF_3',count('#skF_1')),count(add('#skF_2','#skF_1'))),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_47]) ).
tff(c_106,plain,
$less($sum('#skF_3','#skE_1'),'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_104,c_103,c_77]) ).
tff(c_113,plain,
$less($sum('#skE_1','#skF_3'),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_106]) ).
tff(c_2909,plain,
$less($sum('#skE_1','#skF_3'),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_2901,c_113]) ).
tff(c_2916,plain,
$less('#skF_3',0),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2909]) ).
tff(c_49,plain,
$greater('#skF_3',0),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_51,plain,
$less(0,'#skF_3'),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_49]) ).
tff(c_2917,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2916,c_51]) ).
tff(c_2920,plain,
'#skE_2' = $sum(1,'#skE_1'),
inference(splitRight,[status(thm)],[c_2869]) ).
tff(c_2935,plain,
$less($sum('#skE_1','#skF_3'),$sum(1,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_2920,c_113]) ).
tff(c_2941,plain,
$less('#skF_3',1),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2935]) ).
tff(c_2942,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_2941,c_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : DAT035_1 : TPTP v9.0.0. Released v5.0.0.
% 0.06/0.11 % 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
% 0.11/0.32 % Computer : n008.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 7 18:16:03 EDT 2025
% 0.11/0.32 % CPUTime :
% 5.72/2.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.72/2.37
% 5.72/2.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------