TSTP Solution File: PUZ133_2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : PUZ133_2 : TPTP v8.1.2. 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 : 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 : 300s
% DateTime : Tue Aug 22 10:54:16 EDT 2023
% Result : Theorem 3.97s 2.19s
% Output : CNFRefutation 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 121 ( 53 unt; 10 typ; 0 def)
% Number of atoms : 295 ( 94 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 261 ( 77 ~; 166 |; 12 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number arithmetic : 874 ( 175 atm; 495 fun; 154 num; 50 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 50 (; 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp > q > perm > p > queens_q > queens_p
%Foreground sorts:
%Background operators:
tff(n,type,
n: $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skF_2',type,
'#skF_2': $int ).
tff('#skF_1',type,
'#skF_1': $int ).
%Foreground operators:
tff(q,type,
q: $int > $int ).
tff(perm,type,
perm: $int > $int ).
tff(queens_q,type,
queens_q: $o ).
tff(queens_p,type,
queens_p: $o ).
tff(p,type,
p: $int > $int ).
tff(f_89,negated_conjecture,
~ ( ( queens_p
& ! [Ia: $int] : ( q(Ia) = p(perm(Ia)) ) )
=> queens_q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',queens_sym) ).
tff(f_81,axiom,
( ! [Ia: $int,Ja: $int] :
( ( $lesseq(1,Ia)
& $lesseq(Ia,n)
& $lesseq($sum(1,Ia),Ja)
& $lesseq(Ja,n)
& ( $lesseq($sum(1,Ia),Ja)
<=> $lesseq($sum(1,perm(Ja)),perm(Ia)) ) )
=> ( ( q(Ia) != q(Ja) )
& ( $sum(q(Ia),Ia) != $sum(q(Ja),Ja) )
& ( $difference(q(Ia),Ia) != $difference(q(Ja),Ja) ) ) )
=> queens_q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',queens_q) ).
tff(f_57,axiom,
! [Ia: $int] : ( perm(Ia) = $difference($sum(1,n),Ia) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permutation) ).
tff(f_54,axiom,
( queens_p
=> ! [Ia: $int,Ja: $int] :
( ( $lesseq(1,Ia)
& $lesseq(Ia,n)
& $lesseq($sum(1,Ia),Ja)
& $lesseq(Ja,n) )
=> ( ( p(Ia) != p(Ja) )
& ( $sum(p(Ia),Ia) != $sum(p(Ja),Ja) )
& ( $difference(p(Ia),Ia) != $difference(p(Ja),Ja) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',queens_p) ).
tff(c_26,plain,
~ queens_q,
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_19,plain,
( queens_q
| $lesseq($sum(1,'#skF_1'),'#skF_2') ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_50,plain,
( queens_q
| ~ $less('#skF_2',$sum(1,'#skF_1')) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_19]) ).
tff(c_84,plain,
~ $less('#skF_2',$sum(1,'#skF_1')),
inference(negUnitSimplification,[status(thm)],[c_26,c_50]) ).
tff(c_17,plain,
( queens_q
| $lesseq('#skF_2',n) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_51,plain,
( queens_q
| ~ $less(n,'#skF_2') ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_17]) ).
tff(c_86,plain,
~ $less(n,'#skF_2'),
inference(negUnitSimplification,[status(thm)],[c_26,c_51]) ).
tff(c_8,plain,
! [I_3a: $int] : ( perm(I_3a) = $difference($sum(1,n),I_3a) ),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_9,plain,
! [I_3a: $int] : ( perm(I_3a) = $sum(1,$sum(n,$uminus(I_3a))) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_8]) ).
tff(c_65,plain,
! [I_3a: $int] : ( perm(I_3a) = $sum(1,$sum($uminus(I_3a),n)) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_9]) ).
tff(c_47,plain,
! [I_4a: $int] : ( q(I_4a) = p(perm(I_4a)) ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_11,plain,
( ( $difference(q('#skF_2'),'#skF_2') = $difference(q('#skF_1'),'#skF_1') )
| ( $sum(q('#skF_2'),'#skF_2') = $sum(q('#skF_1'),'#skF_1') )
| ( q('#skF_2') = q('#skF_1') )
| queens_q ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_63,plain,
( ( q('#skF_2') = $sum($uminus('#skF_1'),$sum('#skF_2',q('#skF_1'))) )
| ( q('#skF_2') = $sum('#skF_1',$sum($uminus('#skF_2'),q('#skF_1'))) )
| ( q('#skF_2') = q('#skF_1') )
| queens_q ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_11]) ).
tff(c_97,plain,
( ( p(perm('#skF_2')) = $sum($uminus('#skF_1'),$sum('#skF_2',p(perm('#skF_1')))) )
| ( p(perm('#skF_2')) = $sum('#skF_1',$sum($uminus('#skF_2'),p(perm('#skF_1')))) )
| ( p(perm('#skF_2')) = p(perm('#skF_1')) )
| queens_q ),
inference(demodulation,[status(thm),theory(equality)],[c_47,c_47,c_47,c_47,c_47,c_47,c_63]) ).
tff(c_99,plain,
( ( p(perm('#skF_2')) = $sum($uminus('#skF_1'),$sum('#skF_2',p(perm('#skF_1')))) )
| ( p(perm('#skF_2')) = $sum('#skF_1',$sum($uminus('#skF_2'),p(perm('#skF_1')))) )
| ( p(perm('#skF_2')) = p(perm('#skF_1')) ) ),
inference(negUnitSimplification,[status(thm)],[c_26,c_97]) ).
tff(c_102,plain,
( ( p(perm('#skF_2')) = $sum('#skF_2',$sum($uminus('#skF_1'),p(perm('#skF_1')))) )
| ( p(perm('#skF_2')) = $sum($uminus('#skF_2'),$sum('#skF_1',p(perm('#skF_1')))) )
| ( p(perm('#skF_2')) = p(perm('#skF_1')) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_99]) ).
tff(c_125,plain,
( ( p($sum(1,$sum($uminus('#skF_2'),n))) = $sum('#skF_2',$sum($uminus('#skF_1'),p($sum(1,$sum($uminus('#skF_1'),n))))) )
| ( p($sum(1,$sum($uminus('#skF_2'),n))) = $sum($uminus('#skF_2'),$sum('#skF_1',p($sum(1,$sum($uminus('#skF_1'),n))))) )
| ( p($sum(1,$sum($uminus('#skF_2'),n))) = p($sum(1,$sum($uminus('#skF_1'),n))) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_65,c_65,c_65,c_65,c_65,c_65,c_102]) ).
tff(c_128,plain,
( ( p($sum(1,$sum($uminus('#skF_2'),n))) = $sum($uminus('#skF_1'),$sum('#skF_2',p($sum(1,$sum($uminus('#skF_1'),n))))) )
| ( p($sum(1,$sum($uminus('#skF_2'),n))) = $sum('#skF_1',$sum($uminus('#skF_2'),p($sum(1,$sum($uminus('#skF_1'),n))))) )
| ( p($sum(1,$sum($uminus('#skF_2'),n))) = p($sum(1,$sum($uminus('#skF_1'),n))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_125]) ).
tff(c_193,plain,
p($sum(1,$sum($uminus('#skF_2'),n))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_128]) ).
tff(c_23,plain,
( queens_q
| $lesseq(1,'#skF_1') ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_48,plain,
( queens_q
| ~ $less('#skF_1',1) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_23]) ).
tff(c_80,plain,
~ $less('#skF_1',1),
inference(negUnitSimplification,[status(thm)],[c_26,c_48]) ).
tff(c_186,plain,
p($sum(1,$sum($uminus('#skF_1'),n))) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_128]) ).
tff(c_185,plain,
p($sum(1,$sum($uminus('#skF_2'),n))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_128]) ).
tff(c_132,plain,
( ( p($sum(1,$sum($uminus('#skF_2'),n))) = $sum($uminus('#skF_1'),$sum('#skF_2',p($sum(1,$sum($uminus('#skF_1'),n))))) )
| ( p($sum(1,$sum($uminus('#skF_2'),n))) = $sum('#skF_1',$sum($uminus('#skF_2'),p($sum(1,$sum($uminus('#skF_1'),n))))) )
| ( p($sum(1,$sum($uminus('#skF_2'),n))) = p($sum(1,$sum($uminus('#skF_1'),n))) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_125]) ).
tff(c_188,plain,
( ( $sum($uminus('#skF_1'),$sum('#skF_2','#skE_2')) = '#skE_1' )
| ( $sum('#skF_1',$sum($uminus('#skF_2'),'#skE_2')) = '#skE_1' )
| ( '#skE_2' = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_186,c_185,c_186,c_185,c_186,c_185,c_132]) ).
tff(c_198,plain,
( ( '#skF_2' = $sum('#skF_1',$sum($uminus('#skE_2'),'#skE_1')) )
| ( '#skF_2' = $sum('#skF_1',$sum('#skE_2',$uminus('#skE_1'))) )
| ( '#skE_2' = '#skE_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_188]) ).
tff(c_268,plain,
'#skE_2' = '#skE_1',
inference(splitLeft,[status(thm)],[c_198]) ).
tff(c_228,plain,
p($sum(1,$sum($uminus('#skF_1'),n))) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_128]) ).
tff(c_30,plain,
queens_p,
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_5,plain,
! [J_2a: $int,I_1a: $int] :
( ( p(J_2a) != p(I_1a) )
| ~ queens_p
| ~ $lesseq(1,I_1a)
| ~ $lesseq(I_1a,n)
| ~ $lesseq($sum(1,I_1a),J_2a)
| ~ $lesseq(J_2a,n) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_66,plain,
! [J_2a: $int,I_1a: $int] :
( ( p(J_2a) != p(I_1a) )
| ~ queens_p
| $less(I_1a,1)
| $less(n,I_1a)
| $less(J_2a,$sum(1,I_1a))
| $less(n,J_2a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).
tff(c_135,plain,
! [J_2a: $int,I_1a: $int] :
( ( p(J_2a) != p(I_1a) )
| $less(I_1a,1)
| $less(n,I_1a)
| $less(J_2a,$sum(1,I_1a))
| $less(n,J_2a) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_66]) ).
tff(c_253,plain,
! [I_1a: $int] :
( ( p(I_1a) != '#skE_2' )
| $less(I_1a,1)
| $less(n,I_1a)
| $less($sum(1,$sum($uminus('#skF_1'),n)),$sum(1,I_1a))
| $less(n,$sum(1,$sum($uminus('#skF_1'),n))) ),
inference(superposition,[status(thm),theory(equality)],[c_228,c_135]) ).
tff(c_255,plain,
! [I_1a: $int] :
( ( p(I_1a) != '#skE_2' )
| $less(I_1a,1)
| $less(n,I_1a)
| $less(n,$sum(I_1a,'#skF_1'))
| $less('#skF_1',1) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_253]) ).
tff(c_316,plain,
! [I_1a: $int] :
( ( p(I_1a) != '#skE_1' )
| $less(I_1a,1)
| $less(n,I_1a)
| $less(n,$sum(I_1a,'#skF_1'))
| $less('#skF_1',1) ),
inference(demodulation,[status(thm),theory(equality)],[c_268,c_255]) ).
tff(c_319,plain,
! [I_107a: $int] :
( ( p(I_107a) != '#skE_1' )
| $less(I_107a,1)
| $less(n,I_107a)
| $less(n,$sum(I_107a,'#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_80,c_316]) ).
tff(c_329,plain,
( $less($sum(1,$sum($uminus('#skF_2'),n)),1)
| $less(n,$sum(1,$sum($uminus('#skF_2'),n)))
| $less(n,$sum($sum(1,$sum($uminus('#skF_2'),n)),'#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_193,c_319]) ).
tff(c_331,plain,
( $less(n,'#skF_2')
| $less('#skF_2',1)
| $less('#skF_2',$sum(1,'#skF_1')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_329]) ).
tff(c_333,plain,
$less('#skF_2',1),
inference(negUnitSimplification,[status(thm)],[c_84,c_86,c_331]) ).
tff(c_334,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_333,c_84,c_80]) ).
tff(c_335,plain,
( ( '#skF_2' = $sum('#skF_1',$sum('#skE_2',$uminus('#skE_1'))) )
| ( '#skF_2' = $sum('#skF_1',$sum($uminus('#skE_2'),'#skE_1')) ) ),
inference(splitRight,[status(thm)],[c_198]) ).
tff(c_338,plain,
( ( '#skF_2' = $sum('#skE_2',$sum($uminus('#skE_1'),'#skF_1')) )
| ( '#skF_2' = $sum($uminus('#skE_2'),$sum('#skE_1','#skF_1')) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_335]) ).
tff(c_340,plain,
'#skF_2' = $sum($uminus('#skE_2'),$sum('#skE_1','#skF_1')),
inference(splitLeft,[status(thm)],[c_338]) ).
tff(c_342,plain,
'#skF_2' = $sum('#skE_1',$sum('#skF_1',$uminus('#skE_2'))),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_340]) ).
tff(c_352,plain,
~ $less($sum('#skE_1',$sum('#skF_1',$uminus('#skE_2'))),$sum(1,'#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_342,c_84]) ).
tff(c_362,plain,
~ $less('#skE_1',$sum(1,'#skE_2')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_352]) ).
tff(c_201,plain,
p($sum(1,$sum($uminus('#skF_2'),n))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_128]) ).
tff(c_217,plain,
! [I_1a: $int] :
( ( p(I_1a) != '#skE_1' )
| $less(I_1a,1)
| $less(n,I_1a)
| $less($sum(1,$sum($uminus('#skF_2'),n)),$sum(1,I_1a))
| $less(n,$sum(1,$sum($uminus('#skF_2'),n))) ),
inference(superposition,[status(thm),theory(equality)],[c_201,c_135]) ).
tff(c_219,plain,
! [I_1a: $int] :
( ( p(I_1a) != '#skE_1' )
| $less(I_1a,1)
| $less(n,I_1a)
| $less(n,$sum(I_1a,'#skF_2'))
| $less('#skF_2',1) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_217]) ).
tff(c_421,plain,
! [I_1a: $int] :
( ( p(I_1a) != '#skE_1' )
| $less(I_1a,1)
| $less(n,I_1a)
| $less(n,$sum(I_1a,$sum('#skE_1',$sum('#skF_1',$uminus('#skE_2')))))
| $less($sum('#skE_1',$sum('#skF_1',$uminus('#skE_2'))),1) ),
inference(demodulation,[status(thm),theory(equality)],[c_342,c_342,c_219]) ).
tff(c_423,plain,
! [I_1a: $int] :
( ( p(I_1a) != '#skE_1' )
| $less(I_1a,1)
| $less(n,I_1a)
| $less($sum('#skE_2',n),$sum(I_1a,$sum('#skF_1','#skE_1')))
| $less($sum('#skF_1','#skE_1'),$sum(1,'#skE_2')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_421]) ).
tff(c_424,plain,
$less($sum('#skF_1','#skE_1'),$sum(1,'#skE_2')),
inference(splitLeft,[status(thm)],[c_423]) ).
tff(c_426,plain,
$less($sum('#skE_1','#skF_1'),$sum(1,'#skE_2')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_424]) ).
tff(c_427,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_426,c_362,c_80]) ).
tff(c_429,plain,
~ $less($sum('#skF_1','#skE_1'),$sum(1,'#skE_2')),
inference(splitRight,[status(thm)],[c_423]) ).
tff(c_433,plain,
~ $less($sum('#skE_1','#skF_1'),$sum(1,'#skE_2')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_429]) ).
tff(c_348,plain,
p($sum(1,$sum($uminus($sum('#skE_1',$sum('#skF_1',$uminus('#skE_2')))),n))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_342,c_193]) ).
tff(c_358,plain,
p($sum(1,$sum($uminus('#skE_1'),$sum('#skE_2',$sum($uminus('#skF_1'),n))))) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_348]) ).
tff(c_361,plain,
p($sum(1,$sum($uminus('#skE_1'),$sum($uminus('#skF_1'),$sum(n,'#skE_2'))))) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_358]) ).
tff(c_196,plain,
p($sum(1,$sum($uminus('#skF_1'),n))) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_128]) ).
tff(c_3,plain,
! [J_2a: $int,I_1a: $int] :
( ( $sum(p(J_2a),J_2a) != $sum(p(I_1a),I_1a) )
| ~ queens_p
| ~ $lesseq(1,I_1a)
| ~ $lesseq(I_1a,n)
| ~ $lesseq($sum(1,I_1a),J_2a)
| ~ $lesseq(J_2a,n) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_70,plain,
! [J_2a: $int,I_1a: $int] :
( ( p(J_2a) != $sum(I_1a,$sum($uminus(J_2a),p(I_1a))) )
| ~ queens_p
| $less(I_1a,1)
| $less(n,I_1a)
| $less(J_2a,$sum(1,I_1a))
| $less(n,J_2a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_3]) ).
tff(c_140,plain,
! [J_2a: $int,I_1a: $int] :
( ( p(J_2a) != $sum(I_1a,$sum($uminus(J_2a),p(I_1a))) )
| $less(I_1a,1)
| $less(n,I_1a)
| $less(J_2a,$sum(1,I_1a))
| $less(n,J_2a) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_70]) ).
tff(c_537,plain,
! [J_122a: $int,I_124a: $int] :
( ( p(J_122a) != $sum($uminus(J_122a),$sum(I_124a,p(I_124a))) )
| $less(I_124a,1)
| $less(n,I_124a)
| $less(J_122a,$sum(1,I_124a))
| $less(n,J_122a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_140]) ).
tff(c_556,plain,
! [I_124a: $int] :
( ( $sum($uminus($sum(1,$sum($uminus('#skF_1'),n))),$sum(I_124a,p(I_124a))) != '#skE_2' )
| $less(I_124a,1)
| $less(n,I_124a)
| $less($sum(1,$sum($uminus('#skF_1'),n)),$sum(1,I_124a))
| $less(n,$sum(1,$sum($uminus('#skF_1'),n))) ),
inference(superposition,[status(thm),theory(equality)],[c_196,c_537]) ).
tff(c_558,plain,
! [I_124a: $int] :
( ( p(I_124a) != $sum(1,$sum(n,$sum($uminus('#skF_1'),$sum($uminus(I_124a),'#skE_2')))) )
| $less(I_124a,1)
| $less(n,I_124a)
| $less(n,$sum(I_124a,'#skF_1'))
| $less('#skF_1',1) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_556]) ).
tff(c_579,plain,
! [I_124a: $int] :
( ( p(I_124a) != $sum(1,$sum(n,$sum($uminus('#skF_1'),$sum($uminus(I_124a),'#skE_2')))) )
| $less(I_124a,1)
| $less(n,I_124a)
| $less(n,$sum(I_124a,'#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_80,c_558]) ).
tff(c_582,plain,
! [I_126a: $int] :
( ( p(I_126a) != $sum(1,$sum(n,$sum($uminus(I_126a),$sum('#skE_2',$uminus('#skF_1'))))) )
| $less(I_126a,1)
| $less(n,I_126a)
| $less(n,$sum(I_126a,'#skF_1')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_579]) ).
tff(c_589,plain,
( ( $sum(1,$sum(n,$sum($uminus($sum(1,$sum($uminus('#skE_1'),$sum($uminus('#skF_1'),$sum(n,'#skE_2'))))),$sum('#skE_2',$uminus('#skF_1'))))) != '#skE_1' )
| $less($sum(1,$sum($uminus('#skE_1'),$sum($uminus('#skF_1'),$sum(n,'#skE_2')))),1)
| $less(n,$sum(1,$sum($uminus('#skE_1'),$sum($uminus('#skF_1'),$sum(n,'#skE_2')))))
| $less(n,$sum($sum(1,$sum($uminus('#skE_1'),$sum($uminus('#skF_1'),$sum(n,'#skE_2')))),'#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_361,c_582]) ).
tff(c_590,plain,
( $less($sum(n,'#skE_2'),$sum('#skE_1','#skF_1'))
| $less($sum('#skF_1','#skE_1'),$sum(1,'#skE_2'))
| $less('#skE_1',$sum(1,'#skE_2')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_589]) ).
tff(c_592,plain,
( $less($sum('#skE_2',n),$sum('#skE_1','#skF_1'))
| $less($sum('#skE_1','#skF_1'),$sum(1,'#skE_2'))
| $less('#skE_1',$sum(1,'#skE_2')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_590]) ).
tff(c_615,plain,
$less($sum('#skE_2',n),$sum('#skE_1','#skF_1')),
inference(negUnitSimplification,[status(thm)],[c_362,c_433,c_592]) ).
tff(c_617,plain,
$less($sum(n,'#skE_2'),$sum('#skE_1','#skF_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_615]) ).
tff(c_355,plain,
~ $less(n,$sum('#skE_1',$sum('#skF_1',$uminus('#skE_2')))),
inference(demodulation,[status(thm),theory(equality)],[c_342,c_86]) ).
tff(c_357,plain,
~ $less($sum('#skE_2',n),$sum('#skE_1','#skF_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_355]) ).
tff(c_364,plain,
~ $less($sum(n,'#skE_2'),$sum('#skE_1','#skF_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_357]) ).
tff(c_620,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_617,c_364]) ).
tff(c_621,plain,
'#skF_2' = $sum('#skE_2',$sum($uminus('#skE_1'),'#skF_1')),
inference(splitRight,[status(thm)],[c_338]) ).
tff(c_624,plain,
'#skF_2' = $sum($uminus('#skE_1'),$sum('#skF_1','#skE_2')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_621]) ).
tff(c_636,plain,
~ $less($sum($uminus('#skE_1'),$sum('#skF_1','#skE_2')),$sum(1,'#skF_1')),
inference(demodulation,[status(thm),theory(equality)],[c_624,c_84]) ).
tff(c_646,plain,
~ $less('#skE_2',$sum(1,'#skE_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_636]) ).
tff(c_720,plain,
! [I_1a: $int] :
( ( p(I_1a) != '#skE_1' )
| $less(I_1a,1)
| $less(n,I_1a)
| $less(n,$sum(I_1a,$sum($uminus('#skE_1'),$sum('#skF_1','#skE_2'))))
| $less($sum($uminus('#skE_1'),$sum('#skF_1','#skE_2')),1) ),
inference(demodulation,[status(thm),theory(equality)],[c_624,c_624,c_219]) ).
tff(c_722,plain,
! [I_1a: $int] :
( ( p(I_1a) != '#skE_1' )
| $less(I_1a,1)
| $less(n,I_1a)
| $less($sum('#skE_1',n),$sum(I_1a,$sum('#skF_1','#skE_2')))
| $less($sum('#skF_1','#skE_2'),$sum(1,'#skE_1')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_720]) ).
tff(c_723,plain,
$less($sum('#skF_1','#skE_2'),$sum(1,'#skE_1')),
inference(splitLeft,[status(thm)],[c_722]) ).
tff(c_725,plain,
$less($sum('#skE_2','#skF_1'),$sum(1,'#skE_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_723]) ).
tff(c_726,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_725,c_646,c_80]) ).
tff(c_728,plain,
~ $less($sum('#skF_1','#skE_2'),$sum(1,'#skE_1')),
inference(splitRight,[status(thm)],[c_722]) ).
tff(c_732,plain,
~ $less($sum('#skE_2','#skF_1'),$sum(1,'#skE_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_728]) ).
tff(c_639,plain,
~ $less(n,$sum($uminus('#skE_1'),$sum('#skF_1','#skE_2'))),
inference(demodulation,[status(thm),theory(equality)],[c_624,c_86]) ).
tff(c_641,plain,
~ $less($sum('#skE_1',n),$sum('#skE_2','#skF_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_639]) ).
tff(c_648,plain,
~ $less($sum(n,'#skE_1'),$sum('#skE_2','#skF_1')),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_641]) ).
tff(c_632,plain,
p($sum(1,$sum($uminus($sum($uminus('#skE_1'),$sum('#skF_1','#skE_2'))),n))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_624,c_193]) ).
tff(c_642,plain,
p($sum(1,$sum('#skE_1',$sum($uminus('#skE_2'),$sum($uminus('#skF_1'),n))))) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_632]) ).
tff(c_645,plain,
p($sum(1,$sum('#skE_1',$sum($uminus('#skF_1'),$sum(n,$uminus('#skE_2')))))) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_642]) ).
tff(c_1,plain,
! [J_2a: $int,I_1a: $int] :
( ( $difference(p(J_2a),J_2a) != $difference(p(I_1a),I_1a) )
| ~ queens_p
| ~ $lesseq(1,I_1a)
| ~ $lesseq(I_1a,n)
| ~ $lesseq($sum(1,I_1a),J_2a)
| ~ $lesseq(J_2a,n) ),
inference(cnfTransformation,[status(thm)],[f_54]) ).
tff(c_74,plain,
! [J_2a: $int,I_1a: $int] :
( ( p(J_2a) != $sum($uminus(I_1a),$sum(J_2a,p(I_1a))) )
| ~ queens_p
| $less(I_1a,1)
| $less(n,I_1a)
| $less(J_2a,$sum(1,I_1a))
| $less(n,J_2a) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_1]) ).
tff(c_149,plain,
! [J_2a: $int,I_1a: $int] :
( ( p(J_2a) != $sum($uminus(I_1a),$sum(J_2a,p(I_1a))) )
| $less(I_1a,1)
| $less(n,I_1a)
| $less(J_2a,$sum(1,I_1a))
| $less(n,J_2a) ),
inference(demodulation,[status(thm),theory(equality)],[c_30,c_74]) ).
tff(c_695,plain,
! [J_132a: $int,I_134a: $int] :
( ( p(J_132a) != $sum(J_132a,$sum($uminus(I_134a),p(I_134a))) )
| $less(I_134a,1)
| $less(n,I_134a)
| $less(J_132a,$sum(1,I_134a))
| $less(n,J_132a) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_149]) ).
tff(c_714,plain,
! [I_134a: $int] :
( ( $sum($sum(1,$sum($uminus('#skF_1'),n)),$sum($uminus(I_134a),p(I_134a))) != '#skE_2' )
| $less(I_134a,1)
| $less(n,I_134a)
| $less($sum(1,$sum($uminus('#skF_1'),n)),$sum(1,I_134a))
| $less(n,$sum(1,$sum($uminus('#skF_1'),n))) ),
inference(superposition,[status(thm),theory(equality)],[c_196,c_695]) ).
tff(c_716,plain,
! [I_134a: $int] :
( ( p(I_134a) != $sum($uminus(1),$sum($uminus(n),$sum('#skF_1',$sum(I_134a,'#skE_2')))) )
| $less(I_134a,1)
| $less(n,I_134a)
| $less(n,$sum(I_134a,'#skF_1'))
| $less('#skF_1',1) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_714]) ).
tff(c_861,plain,
! [I_134a: $int] :
( ( p(I_134a) != $sum($uminus(1),$sum($uminus(n),$sum('#skF_1',$sum(I_134a,'#skE_2')))) )
| $less(I_134a,1)
| $less(n,I_134a)
| $less(n,$sum(I_134a,'#skF_1')) ),
inference(negUnitSimplification,[status(thm)],[c_80,c_716]) ).
tff(c_864,plain,
! [I_144a: $int] :
( ( p(I_144a) != $sum($uminus(1),$sum($uminus(n),$sum(I_144a,$sum('#skE_2','#skF_1')))) )
| $less(I_144a,1)
| $less(n,I_144a)
| $less(n,$sum(I_144a,'#skF_1')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_861]) ).
tff(c_871,plain,
( ( $sum($uminus(1),$sum($uminus(n),$sum($sum(1,$sum('#skE_1',$sum($uminus('#skF_1'),$sum(n,$uminus('#skE_2'))))),$sum('#skE_2','#skF_1')))) != '#skE_1' )
| $less($sum(1,$sum('#skE_1',$sum($uminus('#skF_1'),$sum(n,$uminus('#skE_2'))))),1)
| $less(n,$sum(1,$sum('#skE_1',$sum($uminus('#skF_1'),$sum(n,$uminus('#skE_2'))))))
| $less(n,$sum($sum(1,$sum('#skE_1',$sum($uminus('#skF_1'),$sum(n,$uminus('#skE_2'))))),'#skF_1')) ),
inference(superposition,[status(thm),theory(equality)],[c_645,c_864]) ).
tff(c_872,plain,
( $less($sum('#skE_1',n),$sum('#skE_2','#skF_1'))
| $less($sum('#skF_1','#skE_2'),$sum(1,'#skE_1'))
| $less('#skE_2',$sum(1,'#skE_1')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_871]) ).
tff(c_874,plain,
( $less($sum(n,'#skE_1'),$sum('#skE_2','#skF_1'))
| $less($sum('#skE_2','#skF_1'),$sum(1,'#skE_1'))
| $less('#skE_2',$sum(1,'#skE_1')) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_872]) ).
tff(c_878,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_646,c_732,c_648,c_874]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ133_2 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % 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
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 17:54:32 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.97/2.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.97/2.20
% 3.97/2.20 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.52/2.25
% 4.52/2.25 Inference rules
% 4.52/2.25 ----------------------
% 4.52/2.25 #Ref : 1
% 4.52/2.25 #Sup : 82
% 4.52/2.25 #Fact : 0
% 4.52/2.25 #Define : 2
% 4.52/2.25 #Split : 8
% 4.52/2.25 #Chain : 0
% 4.52/2.25 #Close : 3
% 4.52/2.25
% 4.52/2.25 Ordering : LPO
% 4.52/2.25
% 4.52/2.25 Simplification rules
% 4.52/2.25 ----------------------
% 4.52/2.25 #Subsume : 25
% 4.52/2.25 #Demod : 50
% 4.52/2.25 #Tautology : 35
% 4.52/2.25 #SimpNegUnit : 32
% 4.52/2.25 #BackRed : 10
% 4.52/2.25
% 4.52/2.25 #Partial instantiations: 0
% 4.52/2.25 #Strategies tried : 1
% 4.52/2.25
% 4.52/2.25 Timing (in seconds)
% 4.52/2.25 ----------------------
% 4.52/2.25 Preprocessing : 0.60
% 4.52/2.25 Parsing : 0.30
% 4.52/2.25 CNF conversion : 0.03
% 4.52/2.25 Main loop : 0.52
% 4.52/2.25 Inferencing : 0.08
% 4.52/2.25 Reduction : 0.16
% 4.52/2.25 Demodulation : 0.12
% 4.52/2.25 BG Simplification : 0.08
% 4.52/2.25 Subsumption : 0.09
% 4.52/2.25 Abstraction : 0.02
% 4.52/2.25 MUC search : 0.02
% 4.52/2.25 Cooper : 0.06
% 4.52/2.25 Total : 1.18
% 4.52/2.25 Index Insertion : 0.00
% 4.52/2.25 Index Deletion : 0.00
% 4.52/2.25 Index Matching : 0.00
% 4.52/2.25 BG Taut test : 0.00
%------------------------------------------------------------------------------