TSTP Solution File: DAT050_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : DAT050_1 : 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 10:37:03 EDT 2023
% Result : Theorem 44.29s 25.39s
% Output : CNFRefutation 44.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 27
% Syntax : Number of formulae : 700 ( 391 unt; 17 typ; 0 def)
% Number of atoms : 993 ( 914 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 569 ( 259 ~; 301 |; 1 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 1185 ( 0 atm; 515 fun; 510 num; 160 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 15 usr; 15 con; 0-2 aty)
% Number of variables : 290 (; 290 !; 0 ?; 290 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > remove > add > #nlpp > count > empty > #skF_1
%Foreground sorts:
tff(collection,type,
collection: $tType ).
%Background operators:
tff('#skE_7',type,
'#skE_7': $int ).
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_8',type,
'#skE_8': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skF_2',type,
'#skF_2': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
tff('#skE_9',type,
'#skE_9': $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_140,negated_conjecture,
~ ! [U: collection,Va: $int] : ( count(add(0,remove(Va,add(Va,U)))) = count(add(0,remove(Va,U))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
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(f_78,axiom,
! [X3a: $int,X4: collection,X5a: $int] :
( ( in(X3a,X4)
& ( X3a != X5a ) )
<=> in(X3a,remove(X5a,X4)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax5) ).
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_71,axiom,
! [Za: $int,X1: collection,X2a: $int] :
( ( in(Za,X1)
| ( Za = X2a ) )
<=> in(Za,add(X2a,X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax4) ).
tff(f_131,axiom,
! [X14a: $int,X15: collection] :
( ~ in(X14a,X15)
<=> ( count(remove(X14a,X15)) = count(X15) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax6) ).
tff(f_135,axiom,
! [X16a: $int,X17: collection] :
( in(X16a,X17)
=> ( X17 = add(X16a,remove(X16a,X17)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax7) ).
tff(f_60,axiom,
! [Ua: $int] : ~ in(Ua,empty),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002_0.ax',ax1) ).
tff(f_113,axiom,
! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax2) ).
tff(f_126,axiom,
! [X12a: $int,X13: collection] :
( in(X12a,X13)
<=> ( count(remove(X12a,X13)) = $difference(count(X13),1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/DAT002=1.ax',ax5) ).
tff(c_51,plain,
count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) != count(add(0,remove('#skF_2','#skF_1'))),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_120,plain,
count(add(0,remove('#skF_2','#skF_1'))) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_119,plain,
count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_73,plain,
count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) != count(add(0,remove('#skF_2','#skF_1'))),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_131,plain,
'#skE_2' != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_120,c_119,c_73]) ).
tff(c_130,plain,
count(add(0,remove('#skF_2','#skF_1'))) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_99,plain,
! [X10_43a: $int,X11_44: collection] :
( in(X10_43a,X11_44)
| ( count(add(X10_43a,X11_44)) != count(X11_44) ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_65,plain,
! [X3_9a: $int,X4_10: collection] : ~ in(X3_9a,remove(X3_9a,X4_10)),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_404,plain,
! [X10_78a: $int,X4_79: collection] : ( count(add(X10_78a,remove(X10_78a,X4_79))) != count(remove(X10_78a,X4_79)) ),
inference(resolution,[status(thm)],[c_99,c_65]) ).
tff(c_419,plain,
( ( count(remove(0,'#skF_1')) != '#skE_2' )
| ( '#skF_2' != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_404]) ).
tff(c_424,plain,
count(remove(0,'#skF_1')) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_419]) ).
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_335802,plain,
! [X8_10019a: $int,X9_10020: collection] :
( ( count(add(X8_10019a,X9_10020)) = $sum(1,count(X9_10020)) )
| in(X8_10019a,X9_10020) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_336893,plain,
! [X8_10062a: $int,X4_10063: collection] : ( count(add(X8_10062a,remove(X8_10062a,X4_10063))) = $sum(1,count(remove(X8_10062a,X4_10063))) ),
inference(resolution,[status(thm)],[c_335802,c_65]) ).
tff(c_68,plain,
! [X2_8a: $int,X1_7: collection] : in(X2_8a,add(X2_8a,X1_7)),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_133,plain,
! [X10_52a: $int,X11_53: collection] :
( ( count(add(X10_52a,X11_53)) = count(X11_53) )
| ~ in(X10_52a,X11_53) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_148,plain,
! [X2_8a: $int,X1_7: collection] : ( count(add(X2_8a,add(X2_8a,X1_7))) = count(add(X2_8a,X1_7)) ),
inference(resolution,[status(thm)],[c_68,c_133]) ).
tff(c_421,plain,
count(remove(0,'#skF_1')) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_419]) ).
tff(c_425,plain,
( ( '#skE_3' != '#skE_2' )
| ( '#skF_2' != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_421,c_419]) ).
tff(c_427,plain,
'#skF_2' != 0,
inference(splitLeft,[status(thm)],[c_425]) ).
tff(c_277,plain,
count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_57,plain,
! [X10_16a: $int,X11_17: collection] :
( in(X10_16a,X11_17)
| ( count(add(X10_16a,X11_17)) != count(X11_17) ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_149,plain,
! [X14_54a: $int,X15_55: collection] :
( ~ in(X14_54a,X15_55)
| ( count(remove(X14_54a,X15_55)) != count(X15_55) ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_874,plain,
! [X10_104a: $int,X11_105: collection] :
( ( count(remove(X10_104a,X11_105)) != count(X11_105) )
| ( count(add(X10_104a,X11_105)) != count(X11_105) ) ),
inference(resolution,[status(thm)],[c_57,c_149]) ).
tff(c_888,plain,
( ( count('#skF_1') != '#skE_3' )
| ( count(add(0,'#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_424,c_874]) ).
tff(c_896,plain,
count('#skF_1') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_888]) ).
tff(c_195,plain,
! [X16_58a: $int,X17_59: collection] :
( ( add(X16_58a,remove(X16_58a,X17_59)) = X17_59 )
| ~ in(X16_58a,X17_59) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_806,plain,
! [X10_102a: $int,X11_103: collection] :
( ( add(X10_102a,remove(X10_102a,X11_103)) = X11_103 )
| ( count(add(X10_102a,X11_103)) != count(X11_103) ) ),
inference(resolution,[status(thm)],[c_57,c_195]) ).
tff(c_72,plain,
! [U_1a: $int] : ~ in(U_1a,empty),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_549,plain,
! [X2_86a: $int,X1_87: collection] : ( count(add(X2_86a,add(X2_86a,X1_87))) = count(add(X2_86a,X1_87)) ),
inference(resolution,[status(thm)],[c_68,c_133]) ).
tff(c_61,plain,
! [X7_13: collection] :
( ( empty = X7_13 )
| ( count(X7_13) != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_575,plain,
! [X2_90a: $int,X1_91: collection] :
( ( add(X2_90a,add(X2_90a,X1_91)) = empty )
| ( count(add(X2_90a,X1_91)) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_549,c_61]) ).
tff(c_602,plain,
! [X2_90a: $int,X1_91: collection] :
( in(X2_90a,empty)
| ( count(add(X2_90a,X1_91)) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_575,c_68]) ).
tff(c_627,plain,
! [X2_90a: $int,X1_91: collection] : ( count(add(X2_90a,X1_91)) != 0 ),
inference(negUnitSimplification,[status(thm)],[c_72,c_602]) ).
tff(c_127486,plain,
! [X11_3669: collection,X10_3670a: $int] :
( ( count(X11_3669) != 0 )
| ( count(add(X10_3670a,X11_3669)) != count(X11_3669) ) ),
inference(superposition,[status(thm),theory(equality)],[c_806,c_627]) ).
tff(c_127518,plain,
( ( count(remove('#skF_2','#skF_1')) != 0 )
| ( count(remove('#skF_2','#skF_1')) != '#skE_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_127486]) ).
tff(c_127536,plain,
count(remove('#skF_2','#skF_1')) = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_127518]) ).
tff(c_160,plain,
! [X10_16a: $int,X11_17: collection] :
( ( count(remove(X10_16a,X11_17)) != count(X11_17) )
| ( count(add(X10_16a,X11_17)) != count(X11_17) ) ),
inference(resolution,[status(thm)],[c_57,c_149]) ).
tff(c_127542,plain,
( ( count('#skF_1') != '#skE_6' )
| ( count(add('#skF_2','#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_127536,c_160]) ).
tff(c_127568,plain,
( ( '#skE_6' != '#skE_4' )
| ( count(add('#skF_2','#skF_1')) != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_896,c_127542]) ).
tff(c_127611,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_127568]) ).
tff(c_35,plain,
! [X12_18a: $int,X13_19: collection] :
( ( count(remove(X12_18a,X13_19)) = $difference(count(X13_19),1) )
| ~ in(X12_18a,X13_19) ),
inference(cnfTransformation,[status(thm)],[f_126]) ).
tff(c_649,plain,
! [X12_94a: $int,X13_95: collection] :
( ( count(remove(X12_94a,X13_95)) = $sum($uminus(1),count(X13_95)) )
| ~ in(X12_94a,X13_95) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).
tff(c_132569,plain,
! [X2_3889a: $int,X1_3890: collection] : ( count(remove(X2_3889a,add(X2_3889a,X1_3890))) = $sum($uminus(1),count(add(X2_3889a,X1_3890))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_127588,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_127568]) ).
tff(c_127587,plain,
( ( '#skE_6' != '#skE_4' )
| ( count(add('#skF_2','#skF_1')) != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_896,c_127542]) ).
tff(c_127595,plain,
( ( '#skE_6' != '#skE_4' )
| ( '#skE_7' != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_127588,c_127587]) ).
tff(c_127607,plain,
'#skE_7' != '#skE_4',
inference(splitLeft,[status(thm)],[c_127595]) ).
tff(c_447,plain,
! [X8_81a: $int,X9_82: collection] :
( ( count(add(X8_81a,X9_82)) = $sum(1,count(X9_82)) )
| in(X8_81a,X9_82) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_58,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_130304,plain,
! [X8_3791a: $int,X9_3792: collection] :
( ( count(add(X8_3791a,X9_3792)) = count(X9_3792) )
| ( count(add(X8_3791a,X9_3792)) = $sum(1,count(X9_3792)) ) ),
inference(resolution,[status(thm)],[c_447,c_58]) ).
tff(c_127594,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_127568]) ).
tff(c_130324,plain,
( ( $sum(1,count('#skF_1')) = '#skE_7' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_130304,c_127594]) ).
tff(c_130397,plain,
( ( '#skE_7' = $sum(1,'#skE_4') )
| ( '#skE_7' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_127611,c_896,c_896,c_130324]) ).
tff(c_130399,plain,
'#skE_7' = $sum(1,'#skE_4'),
inference(negUnitSimplification,[status(thm)],[c_127607,c_130397]) ).
tff(c_129999,plain,
! [X2_3779a: $int,X1_3780: collection] : ( count(remove(X2_3779a,add(X2_3779a,X1_3780))) = $sum($uminus(1),count(add(X2_3779a,X1_3780))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_127,plain,
count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_127515,plain,
( ( count(remove('#skF_2',add('#skF_2','#skF_1'))) != 0 )
| ( count(remove('#skF_2',add('#skF_2','#skF_1'))) != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_127486]) ).
tff(c_127604,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_127515]) ).
tff(c_130037,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_8' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_129999,c_127604]) ).
tff(c_130104,plain,
'#skE_8' = $sum($uminus(1),'#skE_7'),
inference(demodulation,[status(thm),theory(equality)],[c_127611,c_130037]) ).
tff(c_127598,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_127515]) ).
tff(c_127597,plain,
( ( count(remove('#skF_2',add('#skF_2','#skF_1'))) != 0 )
| ( count(remove('#skF_2',add('#skF_2','#skF_1'))) != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_127486]) ).
tff(c_127605,plain,
( ( '#skE_8' != 0 )
| ( '#skE_8' != '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_127598,c_127598,c_127597]) ).
tff(c_127609,plain,
'#skE_8' != '#skE_1',
inference(splitLeft,[status(thm)],[c_127605]) ).
tff(c_130147,plain,
$sum($uminus(1),'#skE_7') != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_130104,c_127609]) ).
tff(c_130155,plain,
'#skE_7' != $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_130147]) ).
tff(c_130465,plain,
$sum(1,'#skE_4') != $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_130399,c_130155]) ).
tff(c_130491,plain,
'#skE_4' != '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_130465]) ).
tff(c_679,plain,
! [X2_8a: $int,X1_7: collection] : ( count(remove(X2_8a,add(X2_8a,X1_7))) = $sum($uminus(1),count(add(X2_8a,X1_7))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_130387,plain,
( ( count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) = count(remove('#skF_2',add('#skF_2','#skF_1'))) )
| ( $sum(1,count(remove('#skF_2',add('#skF_2','#skF_1')))) = '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_130304]) ).
tff(c_130457,plain,
( ( $sum($uminus(1),'#skE_7') = '#skE_1' )
| ( $sum(1,$sum($uminus(1),'#skE_7')) = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_127611,c_679,c_277,c_127611,c_679,c_130387]) ).
tff(c_130459,plain,
( ( '#skE_7' = $sum(1,'#skE_1') )
| ( '#skE_7' = '#skE_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_130457]) ).
tff(c_130687,plain,
( ( $sum(1,'#skE_4') = $sum(1,'#skE_1') )
| ( $sum(1,'#skE_4') = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_130399,c_130399,c_130459]) ).
tff(c_130689,plain,
( ( '#skE_4' = '#skE_1' )
| ( '#skE_4' = $sum($uminus(1),'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_130687]) ).
tff(c_130691,plain,
'#skE_4' = $sum($uminus(1),'#skE_1'),
inference(splitLeft,[status(thm)],[c_130689]) ).
tff(c_165,plain,
! [X14_56a: $int,X15_57: collection] :
( ( count(remove(X14_56a,X15_57)) = count(X15_57) )
| in(X14_56a,X15_57) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_128362,plain,
! [X14_3714a: $int,X15_3715: collection] :
( ( count(add(X14_3714a,X15_3715)) = count(X15_3715) )
| ( count(remove(X14_3714a,X15_3715)) = count(X15_3715) ) ),
inference(resolution,[status(thm)],[c_165,c_58]) ).
tff(c_127530,plain,
count(remove('#skF_2','#skF_1')) = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_127518]) ).
tff(c_128385,plain,
( ( count('#skF_1') = '#skE_6' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_128362,c_127530]) ).
tff(c_128445,plain,
( ( '#skE_6' = '#skE_4' )
| ( '#skE_7' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_127611,c_896,c_896,c_128385]) ).
tff(c_128447,plain,
'#skE_6' = '#skE_4',
inference(negUnitSimplification,[status(thm)],[c_127607,c_128445]) ).
tff(c_127524,plain,
count(remove('#skF_2','#skF_1')) = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_127518]) ).
tff(c_127523,plain,
( ( count(remove('#skF_2','#skF_1')) != 0 )
| ( count(remove('#skF_2','#skF_1')) != '#skE_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_127486]) ).
tff(c_127531,plain,
( ( '#skE_6' != 0 )
| ( '#skE_6' != '#skE_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_127524,c_127524,c_127523]) ).
tff(c_127533,plain,
'#skE_6' != '#skE_2',
inference(splitLeft,[status(thm)],[c_127531]) ).
tff(c_128497,plain,
'#skE_4' != '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_128447,c_127533]) ).
tff(c_252,plain,
count(add(0,remove('#skF_2','#skF_1'))) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_51]) ).
tff(c_128500,plain,
count(remove('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_128447,c_127530]) ).
tff(c_130346,plain,
( ( $sum(1,count(remove('#skF_2','#skF_1'))) = '#skE_2' )
| ( count(add(0,remove('#skF_2','#skF_1'))) = count(remove('#skF_2','#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_130304,c_130]) ).
tff(c_130418,plain,
( ( $sum(1,'#skE_4') = '#skE_2' )
| ( '#skE_4' = '#skE_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_252,c_128500,c_128500,c_130346]) ).
tff(c_130419,plain,
$sum(1,'#skE_4') = '#skE_2',
inference(negUnitSimplification,[status(thm)],[c_128497,c_130418]) ).
tff(c_130421,plain,
'#skE_4' = $sum($uminus(1),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_130419]) ).
tff(c_130736,plain,
$sum($uminus(1),'#skE_2') = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_130691,c_130421]) ).
tff(c_130738,plain,
'#skE_2' = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_130736]) ).
tff(c_130753,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_130738,c_131]) ).
tff(c_130754,plain,
'#skE_4' = '#skE_1',
inference(splitRight,[status(thm)],[c_130689]) ).
tff(c_130756,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_130491,c_130754]) ).
tff(c_130893,plain,
'#skE_8' = '#skE_1',
inference(splitRight,[status(thm)],[c_127605]) ).
tff(c_130900,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_130893,c_127604]) ).
tff(c_132607,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_1' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_132569,c_130900]) ).
tff(c_132677,plain,
$sum($uminus(1),'#skE_7') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_127611,c_132607]) ).
tff(c_132679,plain,
'#skE_7' = $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_132677]) ).
tff(c_132731,plain,
count(add('#skF_2','#skF_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_132679,c_127594]) ).
tff(c_131576,plain,
! [X14_3839a: $int,X15_3840: collection] :
( ( count(add(X14_3839a,X15_3840)) = count(X15_3840) )
| ( count(remove(X14_3839a,X15_3840)) = count(X15_3840) ) ),
inference(resolution,[status(thm)],[c_165,c_58]) ).
tff(c_131596,plain,
( ( count('#skF_1') = '#skE_6' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_131576,c_127530]) ).
tff(c_131656,plain,
( ( '#skE_6' = '#skE_4' )
| ( '#skE_7' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_127611,c_896,c_896,c_131596]) ).
tff(c_131658,plain,
'#skE_6' = '#skE_4',
inference(negUnitSimplification,[status(thm)],[c_127607,c_131656]) ).
tff(c_131707,plain,
count(remove('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_131658,c_127530]) ).
tff(c_53,plain,
! [X14_20a: $int,X15_21: collection] :
( ~ in(X14_20a,X15_21)
| ( count(remove(X14_20a,X15_21)) != count(X15_21) ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_133807,plain,
! [X8_3926a: $int,X9_3927: collection] :
( ( count(remove(X8_3926a,X9_3927)) != count(X9_3927) )
| ( count(add(X8_3926a,X9_3927)) = $sum(1,count(X9_3927)) ) ),
inference(resolution,[status(thm)],[c_447,c_53]) ).
tff(c_133822,plain,
( ( count('#skF_1') != '#skE_4' )
| ( count(add('#skF_2','#skF_1')) = $sum(1,count('#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_131707,c_133807]) ).
tff(c_133860,plain,
$sum(1,'#skE_4') = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_132731,c_896,c_896,c_133822]) ).
tff(c_133862,plain,
'#skE_4' = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_133860]) ).
tff(c_133914,plain,
count('#skF_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_133862,c_896]) ).
tff(c_893,plain,
count(add(0,'#skF_1')) = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_888]) ).
tff(c_892,plain,
count('#skF_1') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_888]) ).
tff(c_898,plain,
( ( '#skE_4' != '#skE_3' )
| ( '#skE_5' != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_893,c_892,c_892,c_888]) ).
tff(c_913,plain,
'#skE_5' != '#skE_4',
inference(splitLeft,[status(thm)],[c_898]) ).
tff(c_897,plain,
count(add(0,'#skF_1')) = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_888]) ).
tff(c_123197,plain,
! [X14_3551a: $int,X15_3552: collection] :
( ( count(add(X14_3551a,X15_3552)) = count(X15_3552) )
| ( count(remove(X14_3551a,X15_3552)) = count(X15_3552) ) ),
inference(resolution,[status(thm)],[c_165,c_58]) ).
tff(c_123221,plain,
( ( count('#skF_1') = '#skE_3' )
| ( count(add(0,'#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_123197,c_424]) ).
tff(c_123265,plain,
( ( '#skE_4' = '#skE_3' )
| ( '#skE_5' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_897,c_896,c_123221]) ).
tff(c_123267,plain,
'#skE_4' = '#skE_3',
inference(negUnitSimplification,[status(thm)],[c_913,c_123265]) ).
tff(c_47213,plain,
! [X14_1544a: $int,X15_1545: collection] :
( ( count(add(X14_1544a,X15_1545)) = count(X15_1545) )
| ( count(remove(X14_1544a,X15_1545)) = count(X15_1545) ) ),
inference(resolution,[status(thm)],[c_165,c_58]) ).
tff(c_47249,plain,
( ( count('#skF_1') = '#skE_3' )
| ( count(add(0,'#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_47213,c_424]) ).
tff(c_47306,plain,
( ( '#skE_4' = '#skE_3' )
| ( '#skE_5' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_897,c_896,c_47249]) ).
tff(c_47308,plain,
'#skE_4' = '#skE_3',
inference(negUnitSimplification,[status(thm)],[c_913,c_47306]) ).
tff(c_932,plain,
! [X11_106: collection,X10_107a: $int] :
( ( count(X11_106) != 0 )
| ( count(add(X10_107a,X11_106)) != count(X11_106) ) ),
inference(superposition,[status(thm),theory(equality)],[c_806,c_627]) ).
tff(c_963,plain,
( ( count(remove('#skF_2','#skF_1')) != 0 )
| ( count(remove('#skF_2','#skF_1')) != '#skE_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_932]) ).
tff(c_981,plain,
count(remove('#skF_2','#skF_1')) = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_963]) ).
tff(c_987,plain,
( ( count('#skF_1') != '#skE_6' )
| ( count(add('#skF_2','#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_981,c_160]) ).
tff(c_1013,plain,
( ( '#skE_6' != '#skE_4' )
| ( count(add('#skF_2','#skF_1')) != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_896,c_987]) ).
tff(c_1056,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_1013]) ).
tff(c_5491,plain,
! [X2_327a: $int,X1_328: collection] : ( count(remove(X2_327a,add(X2_327a,X1_328))) = $sum($uminus(1),count(add(X2_327a,X1_328))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_1144,plain,
! [X14_132a: $int,X15_133: collection] :
( ( count(add(X14_132a,X15_133)) = count(X15_133) )
| ( count(remove(X14_132a,X15_133)) = count(X15_133) ) ),
inference(resolution,[status(thm)],[c_165,c_58]) ).
tff(c_1192,plain,
( ( count(add(0,'#skF_1')) = count('#skF_1') )
| ( count('#skF_1') = '#skE_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_424,c_1144]) ).
tff(c_1232,plain,
( ( '#skE_5' = '#skE_4' )
| ( '#skE_4' = '#skE_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_897,c_896,c_1192]) ).
tff(c_1234,plain,
'#skE_4' = '#skE_3',
inference(negUnitSimplification,[status(thm)],[c_913,c_1232]) ).
tff(c_1033,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_1013]) ).
tff(c_1032,plain,
( ( '#skE_6' != '#skE_4' )
| ( count(add('#skF_2','#skF_1')) != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_896,c_987]) ).
tff(c_1040,plain,
( ( '#skE_6' != '#skE_4' )
| ( '#skE_7' != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1033,c_1032]) ).
tff(c_1052,plain,
'#skE_7' != '#skE_4',
inference(splitLeft,[status(thm)],[c_1040]) ).
tff(c_975,plain,
count(remove('#skF_2','#skF_1')) = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_963]) ).
tff(c_1155,plain,
( ( count('#skF_1') = '#skE_6' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_1144,c_975]) ).
tff(c_1205,plain,
( ( '#skE_6' = '#skE_4' )
| ( '#skE_7' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1056,c_896,c_896,c_1155]) ).
tff(c_1207,plain,
'#skE_6' = '#skE_4',
inference(negUnitSimplification,[status(thm)],[c_1052,c_1205]) ).
tff(c_969,plain,
count(remove('#skF_2','#skF_1')) = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_963]) ).
tff(c_968,plain,
( ( count(remove('#skF_2','#skF_1')) != 0 )
| ( count(remove('#skF_2','#skF_1')) != '#skE_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_130,c_932]) ).
tff(c_976,plain,
( ( '#skE_6' != 0 )
| ( '#skE_6' != '#skE_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_969,c_969,c_968]) ).
tff(c_978,plain,
'#skE_6' != '#skE_2',
inference(splitLeft,[status(thm)],[c_976]) ).
tff(c_1340,plain,
'#skE_4' != '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_1207,c_978]) ).
tff(c_1420,plain,
'#skE_3' != '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_1234,c_1340]) ).
tff(c_1339,plain,
count(remove('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_1207,c_975]) ).
tff(c_1365,plain,
count(remove('#skF_2','#skF_1')) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_1234,c_1339]) ).
tff(c_4153,plain,
! [X8_271a: $int,X9_272: collection] :
( ( count(add(X8_271a,X9_272)) = count(X9_272) )
| ( count(add(X8_271a,X9_272)) = $sum(1,count(X9_272)) ) ),
inference(resolution,[status(thm)],[c_447,c_58]) ).
tff(c_4195,plain,
( ( $sum(1,count(remove('#skF_2','#skF_1'))) = '#skE_2' )
| ( count(add(0,remove('#skF_2','#skF_1'))) = count(remove('#skF_2','#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_4153,c_130]) ).
tff(c_4274,plain,
( ( $sum(1,'#skE_3') = '#skE_2' )
| ( '#skE_3' = '#skE_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_252,c_1365,c_1365,c_4195]) ).
tff(c_4275,plain,
$sum(1,'#skE_3') = '#skE_2',
inference(negUnitSimplification,[status(thm)],[c_1420,c_4274]) ).
tff(c_4277,plain,
'#skE_3' = $sum($uminus(1),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4275]) ).
tff(c_1356,plain,
count('#skF_1') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_1234,c_896]) ).
tff(c_1364,plain,
count(remove('#skF_2','#skF_1')) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_1234,c_1339]) ).
tff(c_3485,plain,
! [X8_223a: $int,X9_224: collection] :
( ( count(remove(X8_223a,X9_224)) != count(X9_224) )
| ( count(add(X8_223a,X9_224)) = $sum(1,count(X9_224)) ) ),
inference(resolution,[status(thm)],[c_447,c_53]) ).
tff(c_3506,plain,
( ( count('#skF_1') != '#skE_3' )
| ( count(add('#skF_2','#skF_1')) = $sum(1,count('#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_1364,c_3485]) ).
tff(c_3536,plain,
'#skE_7' = $sum(1,'#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_1056,c_1356,c_1356,c_3506]) ).
tff(c_28,plain,
! [X8_14a: $int,X9_15: collection] :
( ~ in(X8_14a,X9_15)
| ( count(add(X8_14a,X9_15)) != $sum(count(X9_15),1) ) ),
inference(cnfTransformation,[status(thm)],[f_118]) ).
tff(c_378,plain,
! [X8_76a: $int,X9_77: collection] :
( ~ in(X8_76a,X9_77)
| ( count(add(X8_76a,X9_77)) != $sum(1,count(X9_77)) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_28]) ).
tff(c_3791,plain,
! [X10_255a: $int,X11_256: collection] :
( ( count(add(X10_255a,X11_256)) != $sum(1,count(X11_256)) )
| ( count(add(X10_255a,X11_256)) != count(X11_256) ) ),
inference(resolution,[status(thm)],[c_57,c_378]) ).
tff(c_3818,plain,
( ( $sum(1,count(remove('#skF_2',add('#skF_2','#skF_1')))) != '#skE_1' )
| ( count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) != count(remove('#skF_2',add('#skF_2','#skF_1'))) ) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_3791]) ).
tff(c_3850,plain,
( ( $sum(1,$sum($uminus(1),count(add('#skF_2','#skF_1')))) != '#skE_1' )
| ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) != '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_277,c_679,c_679,c_3818]) ).
tff(c_3853,plain,
( ( count(add('#skF_2','#skF_1')) != '#skE_1' )
| ( count(add('#skF_2','#skF_1')) != $sum(1,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3850]) ).
tff(c_3909,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_3853]) ).
tff(c_4073,plain,
count(add('#skF_2','#skF_1')) = $sum(1,'#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_3536,c_3909]) ).
tff(c_4192,plain,
( ( $sum(1,count(remove('#skF_2',add('#skF_2','#skF_1')))) = '#skE_1' )
| ( count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) = count(remove('#skF_2',add('#skF_2','#skF_1'))) ) ),
inference(superposition,[status(thm),theory(equality)],[c_4153,c_127]) ).
tff(c_4270,plain,
( ( $sum(1,$sum($uminus(1),$sum(1,'#skE_3'))) = '#skE_1' )
| ( $sum($uminus(1),$sum(1,'#skE_3')) = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_277,c_4073,c_679,c_4073,c_679,c_4192]) ).
tff(c_4272,plain,
( ( '#skE_3' = $sum($uminus(1),'#skE_1') )
| ( '#skE_3' = '#skE_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4270]) ).
tff(c_4390,plain,
( ( $sum($uminus(1),'#skE_2') = $sum($uminus(1),'#skE_1') )
| ( $sum($uminus(1),'#skE_2') = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4277,c_4277,c_4272]) ).
tff(c_4392,plain,
( ( '#skE_2' = '#skE_1' )
| ( '#skE_2' = $sum(1,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4390]) ).
tff(c_4394,plain,
'#skE_2' = $sum(1,'#skE_1'),
inference(splitLeft,[status(thm)],[c_4392]) ).
tff(c_3314,plain,
! [X2_215a: $int,X1_216: collection] : ( count(remove(X2_215a,add(X2_215a,X1_216))) = $sum($uminus(1),count(add(X2_215a,X1_216))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_960,plain,
( ( count(remove('#skF_2',add('#skF_2','#skF_1'))) != 0 )
| ( count(remove('#skF_2',add('#skF_2','#skF_1'))) != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_932]) ).
tff(c_1049,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_960]) ).
tff(c_3352,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_8' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_3314,c_1049]) ).
tff(c_3427,plain,
'#skE_8' = $sum($uminus(1),'#skE_7'),
inference(demodulation,[status(thm),theory(equality)],[c_1056,c_3352]) ).
tff(c_1043,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_960]) ).
tff(c_1042,plain,
( ( count(remove('#skF_2',add('#skF_2','#skF_1'))) != 0 )
| ( count(remove('#skF_2',add('#skF_2','#skF_1'))) != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_932]) ).
tff(c_1050,plain,
( ( '#skE_8' != 0 )
| ( '#skE_8' != '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1043,c_1043,c_1042]) ).
tff(c_1054,plain,
'#skE_8' != '#skE_1',
inference(splitLeft,[status(thm)],[c_1050]) ).
tff(c_3471,plain,
$sum($uminus(1),'#skE_7') != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_3427,c_1054]) ).
tff(c_3479,plain,
'#skE_7' != $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3471]) ).
tff(c_3562,plain,
$sum(1,'#skE_3') != $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_3536,c_3479]) ).
tff(c_3582,plain,
'#skE_3' != '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3562]) ).
tff(c_4333,plain,
$sum($uminus(1),'#skE_2') != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_4277,c_3582]) ).
tff(c_4375,plain,
'#skE_2' != $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4333]) ).
tff(c_4559,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4394,c_4375]) ).
tff(c_4560,plain,
'#skE_2' = '#skE_1',
inference(splitRight,[status(thm)],[c_4392]) ).
tff(c_4562,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_131,c_4560]) ).
tff(c_4567,plain,
'#skE_8' = '#skE_1',
inference(splitRight,[status(thm)],[c_1050]) ).
tff(c_4621,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_4567,c_1049]) ).
tff(c_5510,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_1' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_5491,c_4621]) ).
tff(c_5557,plain,
$sum($uminus(1),'#skE_7') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_1056,c_5510]) ).
tff(c_5559,plain,
'#skE_7' = $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5557]) ).
tff(c_1039,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_1013]) ).
tff(c_5608,plain,
count(add('#skF_2','#skF_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_5559,c_1039]) ).
tff(c_5138,plain,
! [X14_317a: $int,X15_318: collection] :
( ( count(add(X14_317a,X15_318)) = count(X15_318) )
| ( count(remove(X14_317a,X15_318)) = count(X15_318) ) ),
inference(resolution,[status(thm)],[c_165,c_58]) ).
tff(c_5168,plain,
( ( count('#skF_1') = '#skE_3' )
| ( count(add(0,'#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_5138,c_424]) ).
tff(c_5221,plain,
( ( '#skE_4' = '#skE_3' )
| ( '#skE_5' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_897,c_896,c_5168]) ).
tff(c_5223,plain,
'#skE_4' = '#skE_3',
inference(negUnitSimplification,[status(thm)],[c_913,c_5221]) ).
tff(c_5283,plain,
count('#skF_1') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_5223,c_896]) ).
tff(c_5158,plain,
( ( count('#skF_1') = '#skE_6' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_5138,c_975]) ).
tff(c_5214,plain,
( ( '#skE_6' = '#skE_4' )
| ( '#skE_7' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1056,c_896,c_896,c_5158]) ).
tff(c_5216,plain,
'#skE_6' = '#skE_4',
inference(negUnitSimplification,[status(thm)],[c_1052,c_5214]) ).
tff(c_5266,plain,
count(remove('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_5216,c_975]) ).
tff(c_5291,plain,
count(remove('#skF_2','#skF_1')) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_5223,c_5266]) ).
tff(c_7572,plain,
! [X8_408a: $int,X9_409: collection] :
( ( count(remove(X8_408a,X9_409)) != count(X9_409) )
| ( count(add(X8_408a,X9_409)) = $sum(1,count(X9_409)) ) ),
inference(resolution,[status(thm)],[c_447,c_53]) ).
tff(c_7590,plain,
( ( count('#skF_1') != '#skE_3' )
| ( count(add('#skF_2','#skF_1')) = $sum(1,count('#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_5291,c_7572]) ).
tff(c_7626,plain,
$sum(1,'#skE_3') = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_5608,c_5283,c_5283,c_7590]) ).
tff(c_7628,plain,
'#skE_3' = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_7626]) ).
tff(c_7681,plain,
count(remove(0,'#skF_1')) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_7628,c_424]) ).
tff(c_7674,plain,
count('#skF_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_7628,c_5283]) ).
tff(c_64,plain,
! [X3_9a: $int,X4_10: collection,X5_11a: $int] :
( in(X3_9a,X4_10)
| ~ in(X3_9a,remove(X5_11a,X4_10)) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_6385,plain,
! [X10_359a: $int,X4_360: collection,X5_361a: $int] :
( in(X10_359a,X4_360)
| ( count(add(X10_359a,remove(X5_361a,X4_360))) != count(remove(X5_361a,X4_360)) ) ),
inference(resolution,[status(thm)],[c_99,c_64]) ).
tff(c_52,plain,
! [X16_22a: $int,X17_23: collection] :
( ( add(X16_22a,remove(X16_22a,X17_23)) = X17_23 )
| ~ in(X16_22a,X17_23) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_39344,plain,
! [X10_973a: $int,X4_974: collection,X5_975a: $int] :
( ( add(X10_973a,remove(X10_973a,X4_974)) = X4_974 )
| ( count(add(X10_973a,remove(X5_975a,X4_974))) != count(remove(X5_975a,X4_974)) ) ),
inference(resolution,[status(thm)],[c_6385,c_52]) ).
tff(c_39423,plain,
( ( add(0,remove(0,add('#skF_2','#skF_1'))) = add('#skF_2','#skF_1') )
| ( count(remove('#skF_2',add('#skF_2','#skF_1'))) != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_39344]) ).
tff(c_39478,plain,
( ( add(0,remove(0,add('#skF_2','#skF_1'))) = add('#skF_2','#skF_1') )
| ( $sum($uminus(1),$sum(1,'#skE_1')) != '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_5608,c_679,c_39423]) ).
tff(c_39791,plain,
add(0,remove(0,add('#skF_2','#skF_1'))) = add('#skF_2','#skF_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_39478]) ).
tff(c_40751,plain,
in(0,add('#skF_2','#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_39791,c_68]) ).
tff(c_69,plain,
! [Z_6a: $int,X1_7: collection,X2_8a: $int] :
( in(Z_6a,X1_7)
| ~ in(Z_6a,add(X2_8a,X1_7))
| ( Z_6a = X2_8a ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_40913,plain,
( in(0,'#skF_1')
| ( '#skF_2' = 0 ) ),
inference(resolution,[status(thm)],[c_40751,c_69]) ).
tff(c_40937,plain,
in(0,'#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_427,c_40913]) ).
tff(c_56,plain,
! [X12_18a: $int,X13_19: collection] :
( ( count(remove(X12_18a,X13_19)) = $sum($uminus(1),count(X13_19)) )
| ~ in(X12_18a,X13_19) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).
tff(c_40993,plain,
count(remove(0,'#skF_1')) = $sum($uminus(1),count('#skF_1')),
inference(resolution,[status(thm)],[c_40937,c_56]) ).
tff(c_41047,plain,
$sum($uminus(1),'#skE_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_7681,c_7674,c_40993]) ).
tff(c_41050,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_41047]) ).
tff(c_41054,plain,
'#skE_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_1040]) ).
tff(c_41100,plain,
count(add('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_41054,c_1039]) ).
tff(c_47418,plain,
count(add('#skF_2','#skF_1')) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_47308,c_41100]) ).
tff(c_48743,plain,
! [X2_1604a: $int,X1_1605: collection] : ( count(remove(X2_1604a,add(X2_1604a,X1_1605))) = $sum($uminus(1),count(add(X2_1604a,X1_1605))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_41854,plain,
! [X14_1322a: $int,X15_1323: collection] :
( ( count(add(X14_1322a,X15_1323)) = count(X15_1323) )
| ( count(remove(X14_1322a,X15_1323)) = count(X15_1323) ) ),
inference(resolution,[status(thm)],[c_165,c_58]) ).
tff(c_41887,plain,
( ( count('#skF_1') = '#skE_3' )
| ( count(add(0,'#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_41854,c_424]) ).
tff(c_41944,plain,
( ( '#skE_4' = '#skE_3' )
| ( '#skE_5' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_897,c_896,c_41887]) ).
tff(c_41946,plain,
'#skE_4' = '#skE_3',
inference(negUnitSimplification,[status(thm)],[c_913,c_41944]) ).
tff(c_42075,plain,
count(add('#skF_2','#skF_1')) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_41946,c_41100]) ).
tff(c_43416,plain,
! [X2_1385a: $int,X1_1386: collection] : ( count(remove(X2_1385a,add(X2_1385a,X1_1386))) = $sum($uminus(1),count(add(X2_1385a,X1_1386))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_43451,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_8' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_43416,c_1049]) ).
tff(c_43518,plain,
'#skE_8' = $sum($uminus(1),'#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_42075,c_43451]) ).
tff(c_41103,plain,
'#skE_8' != '#skE_1',
inference(splitLeft,[status(thm)],[c_1050]) ).
tff(c_43561,plain,
$sum($uminus(1),'#skE_3') != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_43518,c_41103]) ).
tff(c_43569,plain,
'#skE_3' != $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_43561]) ).
tff(c_44829,plain,
! [X8_1422a: $int,X9_1423: collection] :
( ( count(add(X8_1422a,X9_1423)) = count(X9_1423) )
| ( count(add(X8_1422a,X9_1423)) = $sum(1,count(X9_1423)) ) ),
inference(resolution,[status(thm)],[c_447,c_58]) ).
tff(c_44884,plain,
( ( $sum(1,count(remove('#skF_2',add('#skF_2','#skF_1')))) = '#skE_1' )
| ( count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) = count(remove('#skF_2',add('#skF_2','#skF_1'))) ) ),
inference(superposition,[status(thm),theory(equality)],[c_44829,c_127]) ).
tff(c_44970,plain,
( ( $sum(1,$sum($uminus(1),'#skE_3')) = '#skE_1' )
| ( $sum($uminus(1),'#skE_3') = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_277,c_42075,c_679,c_42075,c_679,c_44884]) ).
tff(c_44972,plain,
( ( '#skE_3' = '#skE_1' )
| ( '#skE_3' = $sum(1,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_44970]) ).
tff(c_45047,plain,
'#skE_3' = '#skE_1',
inference(negUnitSimplification,[status(thm)],[c_43569,c_44972]) ).
tff(c_42053,plain,
count(add('#skF_2','#skF_1')) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_41946,c_41100]) ).
tff(c_46199,plain,
count(add('#skF_2','#skF_1')) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_45047,c_42053]) ).
tff(c_42057,plain,
count('#skF_1') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_41946,c_896]) ).
tff(c_45089,plain,
count('#skF_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_45047,c_42057]) ).
tff(c_675,plain,
! [X10_16a: $int,X11_17: collection] :
( ( count(remove(X10_16a,X11_17)) = $sum($uminus(1),count(X11_17)) )
| ( count(add(X10_16a,X11_17)) != count(X11_17) ) ),
inference(resolution,[status(thm)],[c_57,c_649]) ).
tff(c_980,plain,
count(remove('#skF_2','#skF_1')) = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_963]) ).
tff(c_44887,plain,
( ( $sum(1,count(remove('#skF_2','#skF_1'))) = '#skE_2' )
| ( count(add(0,remove('#skF_2','#skF_1'))) = count(remove('#skF_2','#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_44829,c_130]) ).
tff(c_44974,plain,
( ( $sum(1,'#skE_6') = '#skE_2' )
| ( '#skE_6' = '#skE_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_252,c_980,c_980,c_44887]) ).
tff(c_44975,plain,
$sum(1,'#skE_6') = '#skE_2',
inference(negUnitSimplification,[status(thm)],[c_978,c_44974]) ).
tff(c_44977,plain,
'#skE_6' = $sum($uminus(1),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_44975]) ).
tff(c_45497,plain,
count(remove('#skF_2','#skF_1')) = $sum($uminus(1),'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_44977,c_975]) ).
tff(c_45551,plain,
( ( $sum($uminus(1),count('#skF_1')) = $sum($uminus(1),'#skE_2') )
| ( count(add('#skF_2','#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_675,c_45497]) ).
tff(c_45657,plain,
( ( $sum($uminus(1),'#skE_2') = $sum($uminus(1),'#skE_1') )
| ( count(add('#skF_2','#skF_1')) != '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_45089,c_45089,c_45551]) ).
tff(c_45660,plain,
( ( '#skE_2' = '#skE_1' )
| ( count(add('#skF_2','#skF_1')) != '#skE_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_45657]) ).
tff(c_46407,plain,
'#skE_2' = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_46199,c_45660]) ).
tff(c_46408,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_131,c_46407]) ).
tff(c_46412,plain,
'#skE_8' = '#skE_1',
inference(splitRight,[status(thm)],[c_1050]) ).
tff(c_46420,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_46412,c_1049]) ).
tff(c_48781,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_1' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_48743,c_46420]) ).
tff(c_48847,plain,
$sum($uminus(1),'#skE_3') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_47418,c_48781]) ).
tff(c_48849,plain,
'#skE_3' = $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_48847]) ).
tff(c_48913,plain,
count(remove(0,'#skF_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_48849,c_424]) ).
tff(c_47364,plain,
count('#skF_1') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_47308,c_896]) ).
tff(c_48909,plain,
count('#skF_1') = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_48849,c_47364]) ).
tff(c_47361,plain,
'#skE_7' = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_47308,c_41054]) ).
tff(c_48910,plain,
'#skE_7' = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_48849,c_47361]) ).
tff(c_49385,plain,
! [X8_1625a: $int,X9_1626: collection] :
( ( count(add(X8_1625a,X9_1626)) = count(X9_1626) )
| ( count(add(X8_1625a,X9_1626)) = $sum(1,count(X9_1626)) ) ),
inference(resolution,[status(thm)],[c_447,c_58]) ).
tff(c_49420,plain,
( ( $sum(1,count(remove('#skF_2',add('#skF_2','#skF_1')))) = '#skE_1' )
| ( count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) = count(remove('#skF_2',add('#skF_2','#skF_1'))) ) ),
inference(superposition,[status(thm),theory(equality)],[c_49385,c_127]) ).
tff(c_49492,plain,
( ( $sum(1,$sum($uminus(1),count(add('#skF_2','#skF_1')))) = '#skE_1' )
| ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_277,c_679,c_679,c_49420]) ).
tff(c_49495,plain,
( ( count(add('#skF_2','#skF_1')) = '#skE_1' )
| ( count(add('#skF_2','#skF_1')) = $sum(1,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_49492]) ).
tff(c_50104,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_49495]) ).
tff(c_50275,plain,
count(add('#skF_2','#skF_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_48910,c_50104]) ).
tff(c_47567,plain,
! [X10_1556a: $int,X4_1557: collection,X5_1558a: $int] :
( in(X10_1556a,X4_1557)
| ( count(add(X10_1556a,remove(X5_1558a,X4_1557))) != count(remove(X5_1558a,X4_1557)) ) ),
inference(resolution,[status(thm)],[c_99,c_64]) ).
tff(c_74195,plain,
! [X10_2128a: $int,X4_2129: collection,X5_2130a: $int] :
( ( add(X10_2128a,remove(X10_2128a,X4_2129)) = X4_2129 )
| ( count(add(X10_2128a,remove(X5_2130a,X4_2129))) != count(remove(X5_2130a,X4_2129)) ) ),
inference(resolution,[status(thm)],[c_47567,c_52]) ).
tff(c_74274,plain,
( ( add(0,remove(0,add('#skF_2','#skF_1'))) = add('#skF_2','#skF_1') )
| ( count(remove('#skF_2',add('#skF_2','#skF_1'))) != '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_74195]) ).
tff(c_74332,plain,
( ( add(0,remove(0,add('#skF_2','#skF_1'))) = add('#skF_2','#skF_1') )
| ( $sum($uminus(1),$sum(1,'#skE_1')) != '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_50275,c_679,c_74274]) ).
tff(c_74343,plain,
add(0,remove(0,add('#skF_2','#skF_1'))) = add('#skF_2','#skF_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_74332]) ).
tff(c_75753,plain,
in(0,add('#skF_2','#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_74343,c_68]) ).
tff(c_75917,plain,
( in(0,'#skF_1')
| ( '#skF_2' = 0 ) ),
inference(resolution,[status(thm)],[c_75753,c_69]) ).
tff(c_75944,plain,
in(0,'#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_427,c_75917]) ).
tff(c_76000,plain,
count(remove(0,'#skF_1')) = $sum($uminus(1),count('#skF_1')),
inference(resolution,[status(thm)],[c_75944,c_56]) ).
tff(c_76056,plain,
$sum($uminus(1),$sum(1,'#skE_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_48913,c_48909,c_76000]) ).
tff(c_76059,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_76056]) ).
tff(c_76063,plain,
'#skE_6' = '#skE_2',
inference(splitRight,[status(thm)],[c_976]) ).
tff(c_76064,plain,
count(remove('#skF_2','#skF_1')) = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_963]) ).
tff(c_76070,plain,
( ( count('#skF_1') != '#skE_6' )
| ( count(add('#skF_2','#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_76064,c_160]) ).
tff(c_76096,plain,
( ( '#skE_6' != '#skE_4' )
| ( count(add('#skF_2','#skF_1')) != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_896,c_76070]) ).
tff(c_120813,plain,
( ( '#skE_4' != '#skE_2' )
| ( count(add('#skF_2','#skF_1')) != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_76063,c_76096]) ).
tff(c_120876,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_120813]) ).
tff(c_122145,plain,
! [X2_3508a: $int,X1_3509: collection] : ( count(remove(X2_3508a,add(X2_3508a,X1_3509))) = $sum($uminus(1),count(add(X2_3508a,X1_3509))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_98812,plain,
! [X14_2958a: $int,X15_2959: collection] :
( ( count(add(X14_2958a,X15_2959)) = count(X15_2959) )
| ( count(remove(X14_2958a,X15_2959)) = count(X15_2959) ) ),
inference(resolution,[status(thm)],[c_165,c_58]) ).
tff(c_98848,plain,
( ( count('#skF_1') = '#skE_3' )
| ( count(add(0,'#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_98812,c_424]) ).
tff(c_98905,plain,
( ( '#skE_4' = '#skE_3' )
| ( '#skE_5' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_897,c_896,c_98848]) ).
tff(c_98907,plain,
'#skE_4' = '#skE_3',
inference(negUnitSimplification,[status(thm)],[c_913,c_98905]) ).
tff(c_76173,plain,
( ( '#skE_4' != '#skE_2' )
| ( count(add('#skF_2','#skF_1')) != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_76063,c_76096]) ).
tff(c_76175,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_76173]) ).
tff(c_76174,plain,
( ( '#skE_4' != '#skE_2' )
| ( count(add('#skF_2','#skF_1')) != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_76063,c_76096]) ).
tff(c_76182,plain,
( ( '#skE_4' != '#skE_2' )
| ( '#skE_7' != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_76175,c_76174]) ).
tff(c_76184,plain,
'#skE_7' != '#skE_4',
inference(splitLeft,[status(thm)],[c_76182]) ).
tff(c_76186,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_76173]) ).
tff(c_76758,plain,
! [X14_2459a: $int,X15_2460: collection] :
( ( count(add(X14_2459a,X15_2460)) = count(X15_2460) )
| ( count(remove(X14_2459a,X15_2460)) = count(X15_2460) ) ),
inference(resolution,[status(thm)],[c_165,c_58]) ).
tff(c_76114,plain,
count(remove('#skF_2','#skF_1')) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_76063,c_975]) ).
tff(c_76775,plain,
( ( count('#skF_1') = '#skE_2' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_76758,c_76114]) ).
tff(c_76831,plain,
( ( '#skE_4' = '#skE_2' )
| ( '#skE_7' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_76186,c_896,c_896,c_76775]) ).
tff(c_76833,plain,
'#skE_4' = '#skE_2',
inference(negUnitSimplification,[status(thm)],[c_76184,c_76831]) ).
tff(c_76785,plain,
( ( count('#skF_1') = '#skE_3' )
| ( count(add(0,'#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_76758,c_424]) ).
tff(c_76838,plain,
( ( '#skE_4' = '#skE_3' )
| ( '#skE_5' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_897,c_896,c_76785]) ).
tff(c_76840,plain,
'#skE_4' = '#skE_3',
inference(negUnitSimplification,[status(thm)],[c_913,c_76838]) ).
tff(c_76901,plain,
'#skE_3' = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_76833,c_76840]) ).
tff(c_76880,plain,
'#skE_7' != '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_76840,c_76184]) ).
tff(c_76915,plain,
'#skE_7' != '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_76901,c_76880]) ).
tff(c_76882,plain,
count('#skF_1') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_76840,c_896]) ).
tff(c_76916,plain,
count('#skF_1') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_76901,c_76882]) ).
tff(c_78352,plain,
! [X8_2521a: $int,X9_2522: collection] :
( ( count(add(X8_2521a,X9_2522)) = count(X9_2522) )
| ( count(add(X8_2521a,X9_2522)) = $sum(1,count(X9_2522)) ) ),
inference(resolution,[status(thm)],[c_447,c_58]) ).
tff(c_76181,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_76173]) ).
tff(c_78383,plain,
( ( $sum(1,count('#skF_1')) = '#skE_7' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_78352,c_76181]) ).
tff(c_78462,plain,
( ( '#skE_7' = $sum(1,'#skE_2') )
| ( '#skE_7' = '#skE_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_76186,c_76916,c_76916,c_78383]) ).
tff(c_78464,plain,
'#skE_7' = $sum(1,'#skE_2'),
inference(negUnitSimplification,[status(thm)],[c_76915,c_78462]) ).
tff(c_78438,plain,
( ( count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) = count(remove('#skF_2',add('#skF_2','#skF_1'))) )
| ( $sum(1,count(remove('#skF_2',add('#skF_2','#skF_1')))) = '#skE_1' ) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_78352]) ).
tff(c_78516,plain,
( ( $sum($uminus(1),'#skE_7') = '#skE_1' )
| ( $sum(1,$sum($uminus(1),'#skE_7')) = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_76186,c_679,c_277,c_76186,c_679,c_78438]) ).
tff(c_78518,plain,
( ( '#skE_7' = $sum(1,'#skE_1') )
| ( '#skE_7' = '#skE_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_78516]) ).
tff(c_78568,plain,
( ( $sum(1,'#skE_2') = $sum(1,'#skE_1') )
| ( $sum(1,'#skE_2') = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_78464,c_78464,c_78518]) ).
tff(c_78570,plain,
( ( '#skE_2' = '#skE_1' )
| ( '#skE_2' = $sum($uminus(1),'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_78568]) ).
tff(c_78572,plain,
'#skE_2' = $sum($uminus(1),'#skE_1'),
inference(splitLeft,[status(thm)],[c_78570]) ).
tff(c_78618,plain,
count('#skF_1') = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_78572,c_76916]) ).
tff(c_76918,plain,
count(remove(0,'#skF_1')) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_76901,c_424]) ).
tff(c_78617,plain,
count(remove(0,'#skF_1')) = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_78572,c_76918]) ).
tff(c_489,plain,
! [X8_81a: $int,X4_10: collection] : ( count(add(X8_81a,remove(X8_81a,X4_10))) = $sum(1,count(remove(X8_81a,X4_10))) ),
inference(resolution,[status(thm)],[c_447,c_65]) ).
tff(c_79585,plain,
count(remove('#skF_2','#skF_1')) = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_78572,c_76114]) ).
tff(c_78627,plain,
count(add(0,remove('#skF_2','#skF_1'))) = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_78572,c_130]) ).
tff(c_77262,plain,
! [X10_2478a: $int,X4_2479: collection,X5_2480a: $int] :
( in(X10_2478a,X4_2479)
| ( count(add(X10_2478a,remove(X5_2480a,X4_2479))) != count(remove(X5_2480a,X4_2479)) ) ),
inference(resolution,[status(thm)],[c_99,c_64]) ).
tff(c_97521,plain,
! [X10_2922a: $int,X4_2923: collection,X5_2924a: $int] :
( ( add(X10_2922a,remove(X10_2922a,X4_2923)) = X4_2923 )
| ( count(add(X10_2922a,remove(X5_2924a,X4_2923))) != count(remove(X5_2924a,X4_2923)) ) ),
inference(resolution,[status(thm)],[c_77262,c_52]) ).
tff(c_97569,plain,
( ( add(0,remove(0,'#skF_1')) = '#skF_1' )
| ( count(remove('#skF_2','#skF_1')) != $sum($uminus(1),'#skE_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_78627,c_97521]) ).
tff(c_97624,plain,
add(0,remove(0,'#skF_1')) = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_79585,c_97569]) ).
tff(c_485,plain,
! [X8_81a: $int,X9_82: collection] :
( ( count(add(X8_81a,X9_82)) = count(X9_82) )
| ( count(add(X8_81a,X9_82)) = $sum(1,count(X9_82)) ) ),
inference(resolution,[status(thm)],[c_447,c_58]) ).
tff(c_97787,plain,
( ( count(add(0,remove(0,'#skF_1'))) = count(remove(0,'#skF_1')) )
| ( $sum(1,count(remove(0,'#skF_1'))) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_97624,c_485]) ).
tff(c_97996,plain,
( ( $sum(1,$sum($uminus(1),'#skE_1')) = $sum($uminus(1),'#skE_1') )
| ( $sum(1,$sum($uminus(1),'#skE_1')) = $sum($uminus(1),'#skE_1') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_78618,c_78617,c_78617,c_489,c_78617,c_97787]) ).
tff(c_97999,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_97996]) ).
tff(c_98000,plain,
'#skE_2' = '#skE_1',
inference(splitRight,[status(thm)],[c_78570]) ).
tff(c_98002,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_131,c_98000]) ).
tff(c_98007,plain,
'#skE_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_76182]) ).
tff(c_98061,plain,
count(add('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_98007,c_76181]) ).
tff(c_99017,plain,
count(add('#skF_2','#skF_1')) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_98907,c_98061]) ).
tff(c_99215,plain,
! [X2_2972a: $int,X1_2973: collection] : ( count(remove(X2_2972a,add(X2_2972a,X1_2973))) = $sum($uminus(1),count(add(X2_2972a,X1_2973))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_76164,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_960]) ).
tff(c_99243,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_8' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_99215,c_76164]) ).
tff(c_99304,plain,
'#skE_8' = $sum($uminus(1),'#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_99017,c_99243]) ).
tff(c_76158,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_960]) ).
tff(c_76165,plain,
( ( '#skE_8' != 0 )
| ( '#skE_8' != '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_76158,c_76158,c_1042]) ).
tff(c_76167,plain,
'#skE_8' != '#skE_1',
inference(splitLeft,[status(thm)],[c_76165]) ).
tff(c_99347,plain,
$sum($uminus(1),'#skE_3') != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_99304,c_76167]) ).
tff(c_99355,plain,
'#skE_3' != $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_99347]) ).
tff(c_100629,plain,
! [X8_3017a: $int,X9_3018: collection] :
( ( count(add(X8_3017a,X9_3018)) = count(X9_3018) )
| ( count(add(X8_3017a,X9_3018)) = $sum(1,count(X9_3018)) ) ),
inference(resolution,[status(thm)],[c_447,c_58]) ).
tff(c_100673,plain,
( ( $sum(1,count(remove('#skF_2',add('#skF_2','#skF_1')))) = '#skE_1' )
| ( count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) = count(remove('#skF_2',add('#skF_2','#skF_1'))) ) ),
inference(superposition,[status(thm),theory(equality)],[c_100629,c_127]) ).
tff(c_100751,plain,
( ( $sum(1,$sum($uminus(1),'#skE_3')) = '#skE_1' )
| ( $sum($uminus(1),'#skE_3') = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_277,c_99017,c_679,c_99017,c_679,c_100673]) ).
tff(c_100753,plain,
( ( '#skE_3' = '#skE_1' )
| ( '#skE_3' = $sum(1,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_100751]) ).
tff(c_100801,plain,
'#skE_3' = '#skE_1',
inference(negUnitSimplification,[status(thm)],[c_99355,c_100753]) ).
tff(c_98959,plain,
count(add('#skF_2','#skF_1')) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_98907,c_98061]) ).
tff(c_101142,plain,
count(add('#skF_2','#skF_1')) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_100801,c_98959]) ).
tff(c_98963,plain,
count('#skF_1') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_98907,c_896]) ).
tff(c_100845,plain,
count('#skF_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_100801,c_98963]) ).
tff(c_103134,plain,
! [X10_3083a: $int,X11_3084: collection] :
( ( count(remove(X10_3083a,X11_3084)) = $sum($uminus(1),count(X11_3084)) )
| ( count(add(X10_3083a,X11_3084)) != count(X11_3084) ) ),
inference(resolution,[status(thm)],[c_57,c_649]) ).
tff(c_103191,plain,
( ( $sum($uminus(1),count('#skF_1')) = '#skE_2' )
| ( count(add('#skF_2','#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_103134,c_76114]) ).
tff(c_103282,plain,
'#skE_2' = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_101142,c_100845,c_100845,c_103191]) ).
tff(c_104390,plain,
count(remove('#skF_2','#skF_1')) = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_103282,c_76114]) ).
tff(c_100478,plain,
! [X8_3015a: $int,X9_3016: collection] :
( ( count(remove(X8_3015a,X9_3016)) != count(X9_3016) )
| ( count(add(X8_3015a,X9_3016)) = $sum(1,count(X9_3016)) ) ),
inference(resolution,[status(thm)],[c_447,c_53]) ).
tff(c_100514,plain,
( ( count('#skF_1') != '#skE_3' )
| ( count(add(0,'#skF_1')) = $sum(1,count('#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_424,c_100478]) ).
tff(c_100546,plain,
'#skE_5' = $sum(1,'#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_98963,c_897,c_98963,c_100514]) ).
tff(c_100564,plain,
count(add(0,'#skF_1')) = $sum(1,'#skE_3'),
inference(demodulation,[status(thm),theory(equality)],[c_100546,c_897]) ).
tff(c_100835,plain,
count(add(0,'#skF_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_100801,c_100564]) ).
tff(c_103354,plain,
count(add(0,remove('#skF_2','#skF_1'))) = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_103282,c_130]) ).
tff(c_99987,plain,
! [X10_3003a: $int,X4_3004: collection,X5_3005a: $int] :
( in(X10_3003a,X4_3004)
| ( count(add(X10_3003a,remove(X5_3005a,X4_3004))) != count(remove(X5_3005a,X4_3004)) ) ),
inference(resolution,[status(thm)],[c_99,c_64]) ).
tff(c_120677,plain,
! [X10_3449a: $int,X4_3450: collection,X5_3451a: $int] :
( ( count(add(X10_3449a,X4_3450)) = count(X4_3450) )
| ( count(add(X10_3449a,remove(X5_3451a,X4_3450))) != count(remove(X5_3451a,X4_3450)) ) ),
inference(resolution,[status(thm)],[c_99987,c_58]) ).
tff(c_120725,plain,
( ( count(add(0,'#skF_1')) = count('#skF_1') )
| ( count(remove('#skF_2','#skF_1')) != $sum($uminus(1),'#skE_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_103354,c_120677]) ).
tff(c_120799,plain,
$sum(1,'#skE_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_104390,c_100835,c_100845,c_120725]) ).
tff(c_120802,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_120799]) ).
tff(c_120806,plain,
'#skE_8' = '#skE_1',
inference(splitRight,[status(thm)],[c_76165]) ).
tff(c_120827,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_120806,c_76164]) ).
tff(c_122173,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_1' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_122145,c_120827]) ).
tff(c_122235,plain,
$sum($uminus(1),'#skE_7') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_120876,c_122173]) ).
tff(c_122237,plain,
'#skE_7' = $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_122235]) ).
tff(c_120821,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_120813]) ).
tff(c_122289,plain,
count(add('#skF_2','#skF_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_122237,c_120821]) ).
tff(c_120815,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_120813]) ).
tff(c_120814,plain,
( ( '#skE_4' != '#skE_2' )
| ( count(add('#skF_2','#skF_1')) != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_76063,c_76096]) ).
tff(c_120822,plain,
( ( '#skE_4' != '#skE_2' )
| ( '#skE_7' != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_120815,c_120814]) ).
tff(c_120873,plain,
'#skE_7' != '#skE_4',
inference(splitLeft,[status(thm)],[c_120822]) ).
tff(c_120922,plain,
! [X14_3467a: $int,X15_3468: collection] :
( ( count(add(X14_3467a,X15_3468)) = count(X15_3468) )
| ( count(remove(X14_3467a,X15_3468)) = count(X15_3468) ) ),
inference(resolution,[status(thm)],[c_165,c_58]) ).
tff(c_120933,plain,
( ( count('#skF_1') = '#skE_2' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_120922,c_76114]) ).
tff(c_120983,plain,
( ( '#skE_4' = '#skE_2' )
| ( '#skE_7' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_120876,c_896,c_896,c_120933]) ).
tff(c_120985,plain,
'#skE_4' = '#skE_2',
inference(negUnitSimplification,[status(thm)],[c_120873,c_120983]) ).
tff(c_120946,plain,
( ( count('#skF_1') = '#skE_3' )
| ( count(add(0,'#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_120922,c_424]) ).
tff(c_120991,plain,
( ( '#skE_4' = '#skE_3' )
| ( '#skE_5' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_897,c_896,c_120946]) ).
tff(c_120993,plain,
'#skE_4' = '#skE_3',
inference(negUnitSimplification,[status(thm)],[c_913,c_120991]) ).
tff(c_121035,plain,
'#skE_3' = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_120985,c_120993]) ).
tff(c_121031,plain,
count('#skF_1') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_120993,c_896]) ).
tff(c_121161,plain,
count('#skF_1') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_121035,c_121031]) ).
tff(c_123061,plain,
! [X8_3543a: $int,X9_3544: collection] :
( ( count(remove(X8_3543a,X9_3544)) != count(X9_3544) )
| ( count(add(X8_3543a,X9_3544)) = $sum(1,count(X9_3544)) ) ),
inference(resolution,[status(thm)],[c_447,c_53]) ).
tff(c_123088,plain,
( ( count('#skF_1') != '#skE_2' )
| ( count(add('#skF_2','#skF_1')) = $sum(1,count('#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_76114,c_123061]) ).
tff(c_123119,plain,
$sum(1,'#skE_2') = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_122289,c_121161,c_121161,c_123088]) ).
tff(c_123121,plain,
'#skE_2' = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_123119]) ).
tff(c_123130,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_131,c_123121]) ).
tff(c_123134,plain,
'#skE_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_120822]) ).
tff(c_123152,plain,
count(add('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_123134,c_120821]) ).
tff(c_123332,plain,
count(add('#skF_2','#skF_1')) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_123267,c_123152]) ).
tff(c_124019,plain,
! [X2_3574a: $int,X1_3575: collection] : ( count(remove(X2_3574a,add(X2_3574a,X1_3575))) = $sum($uminus(1),count(add(X2_3574a,X1_3575))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_124038,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_1' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_124019,c_120827]) ).
tff(c_124089,plain,
$sum($uminus(1),'#skE_3') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_123332,c_124038]) ).
tff(c_124091,plain,
'#skE_3' = $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_124089]) ).
tff(c_123313,plain,
count(add('#skF_2','#skF_1')) = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_123267,c_123152]) ).
tff(c_124384,plain,
count(add('#skF_2','#skF_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_124091,c_123313]) ).
tff(c_123318,plain,
count('#skF_1') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_123267,c_896]) ).
tff(c_124149,plain,
count('#skF_1') = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_124091,c_123318]) ).
tff(c_127254,plain,
! [X10_3667a: $int,X11_3668: collection] :
( ( count(remove(X10_3667a,X11_3668)) = $sum($uminus(1),count(X11_3668)) )
| ( count(add(X10_3667a,X11_3668)) != count(X11_3668) ) ),
inference(resolution,[status(thm)],[c_57,c_649]) ).
tff(c_127306,plain,
( ( $sum($uminus(1),count('#skF_1')) = '#skE_2' )
| ( count(add('#skF_2','#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_127254,c_76114]) ).
tff(c_127397,plain,
'#skE_2' = $sum($uminus(1),$sum(1,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_124384,c_124149,c_124149,c_127306]) ).
tff(c_127399,plain,
'#skE_2' = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_127397]) ).
tff(c_127445,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_131,c_127399]) ).
tff(c_127448,plain,
'#skE_4' != '#skE_3',
inference(splitRight,[status(thm)],[c_898]) ).
tff(c_133913,plain,
'#skE_3' != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_133862,c_127448]) ).
tff(c_54,plain,
! [X14_20a: $int,X15_21: collection] :
( ( count(remove(X14_20a,X15_21)) = count(X15_21) )
| in(X14_20a,X15_21) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_139182,plain,
! [X14_4024a: $int,X15_4025: collection] :
( ( count(remove(X14_4024a,X15_4025)) = $sum($uminus(1),count(X15_4025)) )
| ( count(remove(X14_4024a,X15_4025)) = count(X15_4025) ) ),
inference(resolution,[status(thm)],[c_54,c_649]) ).
tff(c_139260,plain,
( ( $sum($uminus(1),count('#skF_1')) = '#skE_3' )
| ( count(remove(0,'#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_139182,c_424]) ).
tff(c_139366,plain,
( ( '#skE_3' = $sum($uminus(1),'#skE_1') )
| ( '#skE_3' = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_133914,c_424,c_133914,c_139260]) ).
tff(c_139368,plain,
'#skE_3' = $sum($uminus(1),'#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_133913,c_139366]) ).
tff(c_139422,plain,
count(remove(0,'#skF_1')) = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_139368,c_424]) ).
tff(c_133916,plain,
count(remove('#skF_2','#skF_1')) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_133862,c_131707]) ).
tff(c_325,plain,
! [X3_71a: $int,X5_72a: $int,X4_73: collection] :
( in(X3_71a,remove(X5_72a,X4_73))
| ~ in(X3_71a,X4_73)
| ( X5_72a = X3_71a ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_137002,plain,
! [X3_3987a: $int,X5_3988a: $int,X4_3989: collection] :
( ( count(add(X3_3987a,remove(X5_3988a,X4_3989))) = count(remove(X5_3988a,X4_3989)) )
| ~ in(X3_3987a,X4_3989)
| ( X5_3988a = X3_3987a ) ),
inference(resolution,[status(thm)],[c_325,c_58]) ).
tff(c_183881,plain,
! [X14_5939a: $int,X5_5940a: $int,X15_5941: collection] :
( ( count(add(X14_5939a,remove(X5_5940a,X15_5941))) = count(remove(X5_5940a,X15_5941)) )
| ( X5_5940a = X14_5939a )
| ( count(remove(X14_5939a,X15_5941)) = count(X15_5941) ) ),
inference(resolution,[status(thm)],[c_54,c_137002]) ).
tff(c_134323,plain,
! [X8_3935a: $int,X9_3936: collection] :
( ( count(add(X8_3935a,X9_3936)) = count(X9_3936) )
| ( count(add(X8_3935a,X9_3936)) = $sum(1,count(X9_3936)) ) ),
inference(resolution,[status(thm)],[c_447,c_58]) ).
tff(c_134375,plain,
( ( $sum(1,count(remove('#skF_2','#skF_1'))) = '#skE_2' )
| ( count(add(0,remove('#skF_2','#skF_1'))) = count(remove('#skF_2','#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_134323,c_130]) ).
tff(c_134459,plain,
( ( '#skE_2' = $sum(1,'#skE_1') )
| ( '#skE_2' = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_252,c_133916,c_133916,c_134375]) ).
tff(c_134461,plain,
'#skE_2' = $sum(1,'#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_131,c_134459]) ).
tff(c_134523,plain,
count(add(0,remove('#skF_2','#skF_1'))) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_134461,c_130]) ).
tff(c_183986,plain,
( ( count(remove('#skF_2','#skF_1')) = $sum(1,'#skE_1') )
| ( '#skF_2' = 0 )
| ( count(remove(0,'#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_183881,c_134523]) ).
tff(c_184595,plain,
( ( $sum(1,'#skE_1') = '#skE_1' )
| ( '#skF_2' = 0 )
| ( $sum($uminus(1),'#skE_1') = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_133914,c_139422,c_133916,c_183986]) ).
tff(c_184596,plain,
( ( $sum(1,'#skE_1') = '#skE_1' )
| ( $sum($uminus(1),'#skE_1') = '#skE_1' ) ),
inference(negUnitSimplification,[status(thm)],[c_427,c_184595]) ).
tff(c_184599,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_184596]) ).
tff(c_184603,plain,
'#skE_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_127595]) ).
tff(c_189753,plain,
count(add('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_184603,c_127594]) ).
tff(c_190540,plain,
! [X2_6139a: $int,X1_6140: collection] : ( count(remove(X2_6139a,add(X2_6139a,X1_6140))) = $sum($uminus(1),count(add(X2_6139a,X1_6140))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_184660,plain,
count(add('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_184603,c_127594]) ).
tff(c_186761,plain,
! [X2_6034a: $int,X1_6035: collection] : ( count(remove(X2_6034a,add(X2_6034a,X1_6035))) = $sum($uminus(1),count(add(X2_6034a,X1_6035))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_186802,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_8' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_186761,c_127604]) ).
tff(c_186877,plain,
'#skE_8' = $sum($uminus(1),'#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_184660,c_186802]) ).
tff(c_184605,plain,
'#skE_8' != '#skE_1',
inference(splitLeft,[status(thm)],[c_127605]) ).
tff(c_186916,plain,
$sum($uminus(1),'#skE_4') != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_186877,c_184605]) ).
tff(c_186926,plain,
'#skE_4' != $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_186916]) ).
tff(c_188542,plain,
! [X8_6078a: $int,X9_6079: collection] :
( ( count(add(X8_6078a,X9_6079)) = count(X9_6079) )
| ( count(add(X8_6078a,X9_6079)) = $sum(1,count(X9_6079)) ) ),
inference(resolution,[status(thm)],[c_447,c_58]) ).
tff(c_188603,plain,
( ( $sum(1,count(remove('#skF_2',add('#skF_2','#skF_1')))) = '#skE_1' )
| ( count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) = count(remove('#skF_2',add('#skF_2','#skF_1'))) ) ),
inference(superposition,[status(thm),theory(equality)],[c_188542,c_127]) ).
tff(c_188693,plain,
( ( $sum(1,$sum($uminus(1),'#skE_4')) = '#skE_1' )
| ( $sum($uminus(1),'#skE_4') = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_277,c_184660,c_679,c_184660,c_679,c_188603]) ).
tff(c_188695,plain,
( ( '#skE_4' = '#skE_1' )
| ( '#skE_4' = $sum(1,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_188693]) ).
tff(c_188769,plain,
'#skE_4' = '#skE_1',
inference(negUnitSimplification,[status(thm)],[c_186926,c_188695]) ).
tff(c_184659,plain,
count(add('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_184603,c_127594]) ).
tff(c_188975,plain,
count(add('#skF_2','#skF_1')) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_188769,c_184659]) ).
tff(c_188814,plain,
count('#skF_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_188769,c_896]) ).
tff(c_189498,plain,
! [X10_6106a: $int,X11_6107: collection] :
( ( count(remove(X10_6106a,X11_6107)) = $sum($uminus(1),count(X11_6107)) )
| ( count(add(X10_6106a,X11_6107)) != count(X11_6107) ) ),
inference(resolution,[status(thm)],[c_57,c_649]) ).
tff(c_127535,plain,
count(remove('#skF_2','#skF_1')) = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_127518]) ).
tff(c_188606,plain,
( ( $sum(1,count(remove('#skF_2','#skF_1'))) = '#skE_2' )
| ( count(add(0,remove('#skF_2','#skF_1'))) = count(remove('#skF_2','#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_188542,c_130]) ).
tff(c_188697,plain,
( ( $sum(1,'#skE_6') = '#skE_2' )
| ( '#skE_6' = '#skE_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_252,c_127535,c_127535,c_188606]) ).
tff(c_188698,plain,
$sum(1,'#skE_6') = '#skE_2',
inference(negUnitSimplification,[status(thm)],[c_127533,c_188697]) ).
tff(c_188700,plain,
'#skE_6' = $sum($uminus(1),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_188698]) ).
tff(c_188766,plain,
count(remove('#skF_2','#skF_1')) = $sum($uminus(1),'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_188700,c_127530]) ).
tff(c_189509,plain,
( ( $sum($uminus(1),count('#skF_1')) = $sum($uminus(1),'#skE_2') )
| ( count(add('#skF_2','#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_189498,c_188766]) ).
tff(c_189625,plain,
$sum($uminus(1),'#skE_2') = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_188975,c_188814,c_188814,c_189509]) ).
tff(c_189627,plain,
'#skE_2' = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_189625]) ).
tff(c_189692,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_131,c_189627]) ).
tff(c_189696,plain,
'#skE_8' = '#skE_1',
inference(splitRight,[status(thm)],[c_127605]) ).
tff(c_189703,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_189696,c_127604]) ).
tff(c_190559,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_1' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_190540,c_189703]) ).
tff(c_190610,plain,
$sum($uminus(1),'#skE_4') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_189753,c_190559]) ).
tff(c_190612,plain,
'#skE_4' = $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_190610]) ).
tff(c_190673,plain,
count('#skF_1') = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_190612,c_896]) ).
tff(c_127449,plain,
'#skE_5' = '#skE_4',
inference(splitRight,[status(thm)],[c_898]) ).
tff(c_127468,plain,
count(add(0,'#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_127449,c_897]) ).
tff(c_190670,plain,
count(add(0,'#skF_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_190612,c_127468]) ).
tff(c_192381,plain,
! [X8_6194a: $int,X9_6195: collection] :
( ( count(add(X8_6194a,X9_6195)) = count(X9_6195) )
| ( count(add(X8_6194a,X9_6195)) = $sum(1,count(X9_6195)) ) ),
inference(resolution,[status(thm)],[c_447,c_58]) ).
tff(c_192428,plain,
( ( $sum(1,count(remove('#skF_2','#skF_1'))) = '#skE_2' )
| ( count(add(0,remove('#skF_2','#skF_1'))) = count(remove('#skF_2','#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_192381,c_130]) ).
tff(c_192510,plain,
( ( $sum(1,'#skE_6') = '#skE_2' )
| ( '#skE_6' = '#skE_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_252,c_127535,c_127535,c_192428]) ).
tff(c_192511,plain,
$sum(1,'#skE_6') = '#skE_2',
inference(negUnitSimplification,[status(thm)],[c_127533,c_192510]) ).
tff(c_192513,plain,
'#skE_6' = $sum($uminus(1),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_192511]) ).
tff(c_184602,plain,
'#skE_6' != '#skE_4',
inference(splitRight,[status(thm)],[c_127595]) ).
tff(c_190669,plain,
'#skE_6' != $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_190612,c_184602]) ).
tff(c_192560,plain,
$sum($uminus(1),'#skE_2') != $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_192513,c_190669]) ).
tff(c_192577,plain,
'#skE_2' != $sum(2,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_192560]) ).
tff(c_192583,plain,
count(remove('#skF_2','#skF_1')) = $sum($uminus(1),'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_192513,c_127530]) ).
tff(c_193190,plain,
! [X14_6209a: $int,X15_6210: collection] :
( ( count(remove(X14_6209a,X15_6210)) = $sum($uminus(1),count(X15_6210)) )
| ( count(remove(X14_6209a,X15_6210)) = count(X15_6210) ) ),
inference(resolution,[status(thm)],[c_54,c_649]) ).
tff(c_192580,plain,
count(remove('#skF_2','#skF_1')) = $sum($uminus(1),'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_192513,c_127530]) ).
tff(c_193203,plain,
( ( $sum($uminus(1),count('#skF_1')) = $sum($uminus(1),'#skE_2') )
| ( count(remove('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_193190,c_192580]) ).
tff(c_193306,plain,
( ( $sum($uminus(1),'#skE_2') = $sum($uminus(1),$sum(1,'#skE_1')) )
| ( $sum($uminus(1),'#skE_2') = $sum(1,'#skE_1') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_192583,c_190673,c_190673,c_193203]) ).
tff(c_193308,plain,
( ( '#skE_2' = $sum(1,'#skE_1') )
| ( '#skE_2' = $sum(2,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_193306]) ).
tff(c_193560,plain,
'#skE_2' = $sum(1,'#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_192577,c_193308]) ).
tff(c_193563,plain,
count(remove('#skF_2','#skF_1')) = $sum($uminus(1),$sum(1,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_193560,c_192580]) ).
tff(c_193595,plain,
count(remove('#skF_2','#skF_1')) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_193563]) ).
tff(c_194078,plain,
! [X3_6230a: $int,X5_6231a: $int,X4_6232: collection] :
( ( count(add(X3_6230a,remove(X5_6231a,X4_6232))) = count(remove(X5_6231a,X4_6232)) )
| ~ in(X3_6230a,X4_6232)
| ( X5_6231a = X3_6230a ) ),
inference(resolution,[status(thm)],[c_325,c_58]) ).
tff(c_232882,plain,
! [X10_7938a: $int,X5_7939a: $int,X11_7940: collection] :
( ( count(add(X10_7938a,remove(X5_7939a,X11_7940))) = count(remove(X5_7939a,X11_7940)) )
| ( X5_7939a = X10_7938a )
| ( count(add(X10_7938a,X11_7940)) != count(X11_7940) ) ),
inference(resolution,[status(thm)],[c_57,c_194078]) ).
tff(c_193593,plain,
count(add(0,remove('#skF_2','#skF_1'))) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_193560,c_130]) ).
tff(c_232957,plain,
( ( count(remove('#skF_2','#skF_1')) = $sum(1,'#skE_1') )
| ( '#skF_2' = 0 )
| ( count(add(0,'#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_232882,c_193593]) ).
tff(c_233161,plain,
( ( $sum(1,'#skE_1') = '#skE_1' )
| ( '#skF_2' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_190673,c_190670,c_193595,c_232957]) ).
tff(c_233162,plain,
$sum(1,'#skE_1') = '#skE_1',
inference(negUnitSimplification,[status(thm)],[c_427,c_233161]) ).
tff(c_233165,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_233162]) ).
tff(c_233169,plain,
'#skE_6' = '#skE_2',
inference(splitRight,[status(thm)],[c_127531]) ).
tff(c_233178,plain,
count(remove('#skF_2','#skF_1')) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_233169,c_127530]) ).
tff(c_233184,plain,
( ( count('#skF_1') != '#skE_2' )
| ( count(add('#skF_2','#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_233178,c_160]) ).
tff(c_233210,plain,
( ( '#skE_4' != '#skE_2' )
| ( count(add('#skF_2','#skF_1')) != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_896,c_233184]) ).
tff(c_233242,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_233210]) ).
tff(c_233231,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_233210]) ).
tff(c_233230,plain,
( ( '#skE_4' != '#skE_2' )
| ( count(add('#skF_2','#skF_1')) != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_896,c_896,c_233184]) ).
tff(c_233238,plain,
( ( '#skE_4' != '#skE_2' )
| ( '#skE_7' != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_233231,c_233230]) ).
tff(c_233240,plain,
'#skE_7' != '#skE_4',
inference(splitLeft,[status(thm)],[c_233238]) ).
tff(c_233916,plain,
! [X14_7972a: $int,X15_7973: collection] :
( ( count(add(X14_7972a,X15_7973)) = count(X15_7973) )
| ( count(remove(X14_7972a,X15_7973)) = count(X15_7973) ) ),
inference(resolution,[status(thm)],[c_165,c_58]) ).
tff(c_233176,plain,
count(remove('#skF_2','#skF_1')) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_233169,c_127530]) ).
tff(c_233936,plain,
( ( count('#skF_1') = '#skE_2' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_233916,c_233176]) ).
tff(c_233996,plain,
( ( '#skE_4' = '#skE_2' )
| ( '#skE_7' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_233242,c_896,c_896,c_233936]) ).
tff(c_233998,plain,
'#skE_4' = '#skE_2',
inference(negUnitSimplification,[status(thm)],[c_233240,c_233996]) ).
tff(c_234052,plain,
count('#skF_1') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_233998,c_896]) ).
tff(c_236080,plain,
! [X8_8057a: $int,X9_8058: collection] :
( ( count(remove(X8_8057a,X9_8058)) != count(X9_8058) )
| ( count(add(X8_8057a,X9_8058)) = $sum(1,count(X9_8058)) ) ),
inference(resolution,[status(thm)],[c_447,c_53]) ).
tff(c_236110,plain,
( ( count('#skF_1') != '#skE_2' )
| ( count(add('#skF_2','#skF_1')) = $sum(1,count('#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_233176,c_236080]) ).
tff(c_236145,plain,
'#skE_7' = $sum(1,'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_233242,c_234052,c_234052,c_236110]) ).
tff(c_233237,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_233210]) ).
tff(c_236189,plain,
count(add('#skF_2','#skF_1')) = $sum(1,'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_236145,c_233237]) ).
tff(c_236778,plain,
! [X8_8080a: $int,X9_8081: collection] :
( ( count(add(X8_8080a,X9_8081)) = count(X9_8081) )
| ( count(add(X8_8080a,X9_8081)) = $sum(1,count(X9_8081)) ) ),
inference(resolution,[status(thm)],[c_447,c_58]) ).
tff(c_236827,plain,
( ( $sum(1,count(remove('#skF_2',add('#skF_2','#skF_1')))) = '#skE_1' )
| ( count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) = count(remove('#skF_2',add('#skF_2','#skF_1'))) ) ),
inference(superposition,[status(thm),theory(equality)],[c_236778,c_127]) ).
tff(c_236909,plain,
( ( $sum(1,$sum($uminus(1),$sum(1,'#skE_2'))) = '#skE_1' )
| ( $sum($uminus(1),$sum(1,'#skE_2')) = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_277,c_236189,c_679,c_236189,c_679,c_236827]) ).
tff(c_236911,plain,
( ( '#skE_2' = $sum($uminus(1),'#skE_1') )
| ( '#skE_2' = '#skE_1' ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_236909]) ).
tff(c_236962,plain,
'#skE_2' = $sum($uminus(1),'#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_131,c_236911]) ).
tff(c_237024,plain,
'#skE_6' = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_236962,c_233169]) ).
tff(c_237030,plain,
count(add(0,remove('#skF_2','#skF_1'))) = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_236962,c_130]) ).
tff(c_859,plain,
! [X11_103: collection,X10_102a: $int] :
( ( count(X11_103) != 0 )
| ( count(add(X10_102a,X11_103)) != count(X11_103) ) ),
inference(superposition,[status(thm),theory(equality)],[c_806,c_627]) ).
tff(c_237136,plain,
( ( count(remove('#skF_2','#skF_1')) != 0 )
| ( count(remove('#skF_2','#skF_1')) != $sum($uminus(1),'#skE_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_237030,c_859]) ).
tff(c_237220,plain,
count(remove('#skF_2','#skF_1')) = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_237136]) ).
tff(c_237237,plain,
count(remove('#skF_2','#skF_1')) = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_237024,c_237220]) ).
tff(c_237027,plain,
count(add(0,remove('#skF_2','#skF_1'))) = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_236962,c_130]) ).
tff(c_235720,plain,
! [X10_8046a: $int,X4_8047: collection,X5_8048a: $int] :
( in(X10_8046a,X4_8047)
| ( count(add(X10_8046a,remove(X5_8048a,X4_8047))) != count(remove(X5_8048a,X4_8047)) ) ),
inference(resolution,[status(thm)],[c_99,c_64]) ).
tff(c_258484,plain,
! [X10_8638a: $int,X4_8639: collection,X5_8640a: $int] :
( ( add(X10_8638a,remove(X10_8638a,X4_8639)) = X4_8639 )
| ( count(add(X10_8638a,remove(X5_8640a,X4_8639))) != count(remove(X5_8640a,X4_8639)) ) ),
inference(resolution,[status(thm)],[c_235720,c_52]) ).
tff(c_258533,plain,
( ( add(0,remove(0,'#skF_1')) = '#skF_1' )
| ( count(remove('#skF_2','#skF_1')) != $sum($uminus(1),'#skE_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_237027,c_258484]) ).
tff(c_258596,plain,
add(0,remove(0,'#skF_1')) = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_237237,c_258533]) ).
tff(c_67,plain,
! [Z_6a: $int,X1_7: collection,X2_8a: $int] :
( ~ in(Z_6a,X1_7)
| in(Z_6a,add(X2_8a,X1_7)) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_234696,plain,
! [Z_8008a: $int,X2_8009a: $int,X1_8010: collection] :
( ( count(add(Z_8008a,add(X2_8009a,X1_8010))) = count(add(X2_8009a,X1_8010)) )
| ~ in(Z_8008a,X1_8010) ),
inference(resolution,[status(thm)],[c_67,c_133]) ).
tff(c_234736,plain,
! [X2_8a: $int,X2_8009a: $int,X1_7: collection] : ( count(add(X2_8a,add(X2_8009a,add(X2_8a,X1_7)))) = count(add(X2_8009a,add(X2_8a,X1_7))) ),
inference(resolution,[status(thm)],[c_68,c_234696]) ).
tff(c_258703,plain,
! [X2_8009a: $int] : ( count(add(X2_8009a,add(0,remove(0,'#skF_1')))) = count(add(0,add(X2_8009a,'#skF_1'))) ),
inference(superposition,[status(thm),theory(equality)],[c_258596,c_234736]) ).
tff(c_258963,plain,
! [X2_8009a: $int] : ( count(add(0,add(X2_8009a,'#skF_1'))) = count(add(X2_8009a,'#skF_1')) ),
inference(demodulation,[status(thm),theory(equality)],[c_258596,c_258703]) ).
tff(c_236187,plain,
count(add('#skF_2','#skF_1')) = $sum(1,'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_236145,c_233237]) ).
tff(c_236970,plain,
count(add('#skF_2','#skF_1')) = $sum(1,$sum($uminus(1),'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_236962,c_236187]) ).
tff(c_237588,plain,
count(add('#skF_2','#skF_1')) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_236970]) ).
tff(c_239565,plain,
! [X3_8172a: $int,X5_8173a: $int,X4_8174: collection] :
( ( count(add(X3_8172a,remove(X5_8173a,X4_8174))) = count(remove(X5_8173a,X4_8174)) )
| ~ in(X3_8172a,X4_8174)
| ( X5_8173a = X3_8172a ) ),
inference(resolution,[status(thm)],[c_325,c_58]) ).
tff(c_271678,plain,
! [X10_8810a: $int,X5_8811a: $int,X11_8812: collection] :
( ( count(add(X10_8810a,remove(X5_8811a,X11_8812))) = count(remove(X5_8811a,X11_8812)) )
| ( X5_8811a = X10_8810a )
| ( count(add(X10_8810a,X11_8812)) != count(X11_8812) ) ),
inference(resolution,[status(thm)],[c_57,c_239565]) ).
tff(c_271807,plain,
( ( count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_1' )
| ( '#skF_2' = 0 )
| ( count(add(0,add('#skF_2','#skF_1'))) != count(add('#skF_2','#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_271678,c_127]) ).
tff(c_272003,plain,
( ( $sum($uminus(1),'#skE_1') = '#skE_1' )
| ( '#skF_2' = 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_258963,c_237588,c_679,c_271807]) ).
tff(c_272004,plain,
$sum($uminus(1),'#skE_1') = '#skE_1',
inference(negUnitSimplification,[status(thm)],[c_427,c_272003]) ).
tff(c_272007,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_272004]) ).
tff(c_272011,plain,
'#skE_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_233238]) ).
tff(c_272017,plain,
count(add('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_272011,c_233237]) ).
tff(c_274192,plain,
! [X2_8896a: $int,X1_8897: collection] : ( count(remove(X2_8896a,add(X2_8896a,X1_8897))) = $sum($uminus(1),count(add(X2_8896a,X1_8897))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_233224,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_127515]) ).
tff(c_274227,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_8' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_274192,c_233224]) ).
tff(c_274294,plain,
'#skE_8' = $sum($uminus(1),'#skE_4'),
inference(demodulation,[status(thm),theory(equality)],[c_272017,c_274227]) ).
tff(c_233218,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_8',
inference(define,[status(thm),theory(equality)],[c_127515]) ).
tff(c_233225,plain,
( ( '#skE_8' != 0 )
| ( '#skE_8' != '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_233218,c_233218,c_127597]) ).
tff(c_233227,plain,
'#skE_8' != '#skE_1',
inference(splitLeft,[status(thm)],[c_233225]) ).
tff(c_274337,plain,
$sum($uminus(1),'#skE_4') != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_274294,c_233227]) ).
tff(c_274345,plain,
'#skE_4' != $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_274337]) ).
tff(c_275719,plain,
! [X8_8936a: $int,X9_8937: collection] :
( ( count(add(X8_8936a,X9_8937)) = count(X9_8937) )
| ( count(add(X8_8936a,X9_8937)) = $sum(1,count(X9_8937)) ) ),
inference(resolution,[status(thm)],[c_447,c_58]) ).
tff(c_275780,plain,
( ( $sum(1,count(remove('#skF_2',add('#skF_2','#skF_1')))) = '#skE_1' )
| ( count(add(0,remove('#skF_2',add('#skF_2','#skF_1')))) = count(remove('#skF_2',add('#skF_2','#skF_1'))) ) ),
inference(superposition,[status(thm),theory(equality)],[c_275719,c_127]) ).
tff(c_275870,plain,
( ( $sum(1,$sum($uminus(1),'#skE_4')) = '#skE_1' )
| ( $sum($uminus(1),'#skE_4') = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_277,c_272017,c_679,c_272017,c_679,c_275780]) ).
tff(c_275872,plain,
( ( '#skE_4' = '#skE_1' )
| ( '#skE_4' = $sum(1,'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_275870]) ).
tff(c_275923,plain,
'#skE_4' = '#skE_1',
inference(negUnitSimplification,[status(thm)],[c_274345,c_275872]) ).
tff(c_275966,plain,
count('#skF_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_275923,c_896]) ).
tff(c_275963,plain,
count(add(0,'#skF_1')) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_275923,c_127468]) ).
tff(c_272016,plain,
count(add('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_272011,c_233237]) ).
tff(c_276122,plain,
count(add('#skF_2','#skF_1')) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_275923,c_272016]) ).
tff(c_278026,plain,
! [X3_9018a: $int,X5_9019a: $int,X4_9020: collection] :
( ( count(add(X3_9018a,remove(X5_9019a,X4_9020))) = count(remove(X5_9019a,X4_9020)) )
| ~ in(X3_9018a,X4_9020)
| ( X5_9019a = X3_9018a ) ),
inference(resolution,[status(thm)],[c_325,c_58]) ).
tff(c_325805,plain,
! [X14_9721a: $int,X5_9722a: $int,X15_9723: collection] :
( ( count(add(X14_9721a,remove(X5_9722a,X15_9723))) = count(remove(X5_9722a,X15_9723)) )
| ( X5_9722a = X14_9721a )
| ( count(remove(X14_9721a,X15_9723)) = count(X15_9723) ) ),
inference(resolution,[status(thm)],[c_54,c_278026]) ).
tff(c_325956,plain,
( ( count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_1' )
| ( '#skF_2' = 0 )
| ( count(remove(0,add('#skF_2','#skF_1'))) = count(add('#skF_2','#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_325805,c_127]) ).
tff(c_326554,plain,
( ( $sum($uminus(1),'#skE_1') = '#skE_1' )
| ( '#skF_2' = 0 )
| ( count(remove(0,add('#skF_2','#skF_1'))) = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_276122,c_276122,c_679,c_325956]) ).
tff(c_326556,plain,
( ( $sum($uminus(1),'#skE_1') = '#skE_1' )
| ( count(remove(0,add('#skF_2','#skF_1'))) = '#skE_1' ) ),
inference(negUnitSimplification,[status(thm)],[c_427,c_326554]) ).
tff(c_326847,plain,
count(remove(0,add('#skF_2','#skF_1'))) = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_326556]) ).
tff(c_60,plain,
! [X8_14a: $int,X9_15: collection] :
( ( count(add(X8_14a,X9_15)) = $sum(1,count(X9_15)) )
| in(X8_14a,X9_15) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_272703,plain,
! [Z_8835a: $int,X2_8836a: $int,X1_8837: collection] :
( ( count(remove(Z_8835a,add(X2_8836a,X1_8837))) != count(add(X2_8836a,X1_8837)) )
| ~ in(Z_8835a,X1_8837) ),
inference(resolution,[status(thm)],[c_67,c_149]) ).
tff(c_272728,plain,
! [X8_14a: $int,X2_8836a: $int,X9_15: collection] :
( ( count(remove(X8_14a,add(X2_8836a,X9_15))) != count(add(X2_8836a,X9_15)) )
| ( count(add(X8_14a,X9_15)) = $sum(1,count(X9_15)) ) ),
inference(resolution,[status(thm)],[c_60,c_272703]) ).
tff(c_326859,plain,
( ( count(add('#skF_2','#skF_1')) != '#skE_1' )
| ( count(add(0,'#skF_1')) = $sum(1,count('#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_326847,c_272728]) ).
tff(c_327125,plain,
$sum(1,'#skE_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_275966,c_275963,c_276122,c_326859]) ).
tff(c_327128,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_327125]) ).
tff(c_327132,plain,
'#skE_8' = '#skE_1',
inference(splitRight,[status(thm)],[c_233225]) ).
tff(c_327141,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_327132,c_233224]) ).
tff(c_327147,plain,
( ( count(add('#skF_2','#skF_1')) != '#skE_1' )
| ( count(add('#skF_2',add('#skF_2','#skF_1'))) != count(add('#skF_2','#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_327141,c_160]) ).
tff(c_327172,plain,
count(add('#skF_2','#skF_1')) != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_148,c_327147]) ).
tff(c_327196,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_327172]) ).
tff(c_329190,plain,
! [X2_9829a: $int,X1_9830: collection] : ( count(remove(X2_9829a,add(X2_9829a,X1_9830))) = $sum($uminus(1),count(add(X2_9829a,X1_9830))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_327139,plain,
count(remove('#skF_2',add('#skF_2','#skF_1'))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_327132,c_233224]) ).
tff(c_329231,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_1' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_329190,c_327139]) ).
tff(c_329305,plain,
$sum($uminus(1),'#skE_7') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_327196,c_329231]) ).
tff(c_329307,plain,
'#skE_7' = $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_329305]) ).
tff(c_327239,plain,
( ( '#skE_4' != '#skE_2' )
| ( '#skE_7' != '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_327196,c_233210]) ).
tff(c_327241,plain,
'#skE_7' != '#skE_4',
inference(splitLeft,[status(thm)],[c_327239]) ).
tff(c_327242,plain,
! [X14_9762a: $int,X15_9763: collection] :
( ( count(add(X14_9762a,X15_9763)) = count(X15_9763) )
| ( count(remove(X14_9762a,X15_9763)) = count(X15_9763) ) ),
inference(resolution,[status(thm)],[c_165,c_58]) ).
tff(c_327253,plain,
( ( count('#skF_1') = '#skE_2' )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_327242,c_233176]) ).
tff(c_327303,plain,
( ( '#skE_4' = '#skE_2' )
| ( '#skE_7' = '#skE_4' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_327196,c_896,c_896,c_327253]) ).
tff(c_327305,plain,
'#skE_4' = '#skE_2',
inference(negUnitSimplification,[status(thm)],[c_327241,c_327303]) ).
tff(c_327351,plain,
'#skE_7' != '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_327305,c_327241]) ).
tff(c_329354,plain,
'#skE_2' != $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_329307,c_327351]) ).
tff(c_327192,plain,
count(add('#skF_2','#skF_1')) = '#skE_7',
inference(define,[status(thm),theory(equality)],[c_327172]) ).
tff(c_329360,plain,
count(add('#skF_2','#skF_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_329307,c_327192]) ).
tff(c_327355,plain,
count('#skF_1') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_327305,c_896]) ).
tff(c_330039,plain,
! [X8_9858a: $int,X9_9859: collection] :
( ( count(add(X8_9858a,X9_9859)) = count(X9_9859) )
| ( count(add(X8_9858a,X9_9859)) = $sum(1,count(X9_9859)) ) ),
inference(resolution,[status(thm)],[c_447,c_58]) ).
tff(c_329357,plain,
count(add('#skF_2','#skF_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_329307,c_327192]) ).
tff(c_330061,plain,
( ( $sum(1,count('#skF_1')) = $sum(1,'#skE_1') )
| ( count(add('#skF_2','#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_330039,c_329357]) ).
tff(c_330147,plain,
( ( $sum(1,'#skE_2') = $sum(1,'#skE_1') )
| ( '#skE_2' = $sum(1,'#skE_1') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_329360,c_327355,c_327355,c_330061]) ).
tff(c_330148,plain,
$sum(1,'#skE_2') = $sum(1,'#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_329354,c_330147]) ).
tff(c_330150,plain,
'#skE_2' = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_330148]) ).
tff(c_330218,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_131,c_330150]) ).
tff(c_330222,plain,
'#skE_7' = '#skE_4',
inference(splitRight,[status(thm)],[c_327239]) ).
tff(c_330239,plain,
count(add('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_330222,c_327192]) ).
tff(c_332267,plain,
! [X2_9936a: $int,X1_9937: collection] : ( count(remove(X2_9936a,add(X2_9936a,X1_9937))) = $sum($uminus(1),count(add(X2_9936a,X1_9937))) ),
inference(resolution,[status(thm)],[c_68,c_649]) ).
tff(c_332302,plain,
( ( $sum($uminus(1),count(add('#skF_2','#skF_1'))) = '#skE_1' )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_332267,c_327139]) ).
tff(c_332368,plain,
$sum($uminus(1),'#skE_4') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_330239,c_332302]) ).
tff(c_332370,plain,
'#skE_4' = $sum(1,'#skE_1'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_332368]) ).
tff(c_330236,plain,
count(add('#skF_2','#skF_1')) = '#skE_4',
inference(demodulation,[status(thm),theory(equality)],[c_330222,c_327192]) ).
tff(c_332929,plain,
count(add('#skF_2','#skF_1')) = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_332370,c_330236]) ).
tff(c_332434,plain,
count('#skF_1') = $sum(1,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_332370,c_896]) ).
tff(c_335546,plain,
! [X10_10017a: $int,X11_10018: collection] :
( ( count(remove(X10_10017a,X11_10018)) = $sum($uminus(1),count(X11_10018)) )
| ( count(add(X10_10017a,X11_10018)) != count(X11_10018) ) ),
inference(resolution,[status(thm)],[c_57,c_649]) ).
tff(c_335606,plain,
( ( $sum($uminus(1),count('#skF_1')) = '#skE_2' )
| ( count(add('#skF_2','#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_335546,c_233176]) ).
tff(c_335705,plain,
'#skE_2' = $sum($uminus(1),$sum(1,'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_332929,c_332434,c_332434,c_335606]) ).
tff(c_335707,plain,
'#skE_2' = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_335705]) ).
tff(c_335759,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_131,c_335707]) ).
tff(c_335763,plain,
'#skF_2' = 0,
inference(splitRight,[status(thm)],[c_425]) ).
tff(c_335769,plain,
count(add(0,remove(0,'#skF_1'))) = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_335763,c_130]) ).
tff(c_336904,plain,
$sum(1,count(remove(0,'#skF_1'))) = '#skE_2',
inference(superposition,[status(thm),theory(equality)],[c_336893,c_335769]) ).
tff(c_336934,plain,
$sum(1,'#skE_3') = '#skE_2',
inference(demodulation,[status(thm),theory(equality)],[c_424,c_336904]) ).
tff(c_336936,plain,
'#skE_3' = $sum($uminus(1),'#skE_2'),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_336934]) ).
tff(c_215,plain,
! [X2_8a: $int,X1_7: collection] : ( add(X2_8a,remove(X2_8a,add(X2_8a,X1_7))) = add(X2_8a,X1_7) ),
inference(resolution,[status(thm)],[c_68,c_195]) ).
tff(c_335768,plain,
count(add(0,remove(0,add(0,'#skF_1')))) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_335763,c_335763,c_127]) ).
tff(c_336036,plain,
count(add(0,'#skF_1')) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_215,c_335768]) ).
tff(c_336152,plain,
! [X14_10034a: $int,X15_10035: collection] :
( ( count(add(X14_10034a,X15_10035)) = count(X15_10035) )
| ( count(remove(X14_10034a,X15_10035)) = count(X15_10035) ) ),
inference(resolution,[status(thm)],[c_165,c_58]) ).
tff(c_336165,plain,
( ( count('#skF_1') = '#skE_3' )
| ( count(add(0,'#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_336152,c_424]) ).
tff(c_336200,plain,
( ( count('#skF_1') = '#skE_3' )
| ( count('#skF_1') = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_336036,c_336165]) ).
tff(c_336220,plain,
count('#skF_1') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_336200]) ).
tff(c_336224,plain,
( ( '#skE_4' = '#skE_3' )
| ( '#skE_4' = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_336220,c_336220,c_336200]) ).
tff(c_336242,plain,
'#skE_4' = '#skE_1',
inference(splitLeft,[status(thm)],[c_336224]) ).
tff(c_336223,plain,
count('#skF_1') = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_336200]) ).
tff(c_336249,plain,
count('#skF_1') = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_336242,c_336223]) ).
tff(c_336434,plain,
! [X14_10044a: $int,X15_10045: collection] :
( ( add(X14_10044a,remove(X14_10044a,X15_10045)) = X15_10045 )
| ( count(remove(X14_10044a,X15_10045)) = count(X15_10045) ) ),
inference(resolution,[status(thm)],[c_54,c_195]) ).
tff(c_336458,plain,
( ( count('#skF_1') = '#skE_2' )
| ( count(remove(0,'#skF_1')) = count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_336434,c_335769]) ).
tff(c_336494,plain,
( ( '#skE_2' = '#skE_1' )
| ( count(remove(0,'#skF_1')) = '#skE_1' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_336249,c_336249,c_336458]) ).
tff(c_336496,plain,
count(remove(0,'#skF_1')) = '#skE_1',
inference(negUnitSimplification,[status(thm)],[c_131,c_336494]) ).
tff(c_336623,plain,
! [X10_10048a: $int,X11_10049: collection] :
( ( count(remove(X10_10048a,X11_10049)) != count(X11_10049) )
| ( count(add(X10_10048a,X11_10049)) != count(X11_10049) ) ),
inference(resolution,[status(thm)],[c_57,c_149]) ).
tff(c_336629,plain,
( ( count('#skF_1') != '#skE_1' )
| ( count(add(0,'#skF_1')) != count('#skF_1') ) ),
inference(superposition,[status(thm),theory(equality)],[c_336496,c_336623]) ).
tff(c_336649,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_336249,c_336036,c_336249,c_336629]) ).
tff(c_336652,plain,
'#skE_4' = '#skE_3',
inference(splitRight,[status(thm)],[c_336224]) ).
tff(c_336660,plain,
count('#skF_1') = '#skE_3',
inference(demodulation,[status(thm),theory(equality)],[c_336652,c_336223]) ).
tff(c_336974,plain,
count('#skF_1') = $sum($uminus(1),'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_336936,c_336660]) ).
tff(c_336979,plain,
count(remove(0,'#skF_1')) = $sum($uminus(1),'#skE_2'),
inference(demodulation,[status(thm),theory(equality)],[c_336936,c_424]) ).
tff(c_339083,plain,
! [X8_10136a: $int,X9_10137: collection] :
( ( count(remove(X8_10136a,X9_10137)) != count(X9_10137) )
| ( count(add(X8_10136a,X9_10137)) = $sum(1,count(X9_10137)) ) ),
inference(resolution,[status(thm)],[c_335802,c_53]) ).
tff(c_339101,plain,
( ( count('#skF_1') != $sum($uminus(1),'#skE_2') )
| ( count(add(0,'#skF_1')) = $sum(1,count('#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_336979,c_339083]) ).
tff(c_339126,plain,
$sum(1,$sum($uminus(1),'#skE_2')) = '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_336974,c_336036,c_336974,c_339101]) ).
tff(c_339128,plain,
'#skE_2' = '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_339126]) ).
tff(c_339139,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_131,c_339128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : DAT050_1 : TPTP v8.1.2. Released v5.0.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n026.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 : Thu Aug 3 13:29:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 44.29/25.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 44.77/25.54
% 44.77/25.54 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 44.86/25.61
% 44.86/25.61 Inference rules
% 44.86/25.61 ----------------------
% 44.86/25.61 #Ref : 0
% 44.86/25.61 #Sup : 67120
% 44.86/25.61 #Fact : 28
% 44.86/25.61 #Define : 48
% 44.86/25.61 #Split : 1752
% 44.86/25.61 #Chain : 0
% 44.86/25.61 #Close : 0
% 44.86/25.61
% 44.86/25.61 Ordering : LPO
% 44.86/25.61
% 44.86/25.61 Simplification rules
% 44.86/25.61 ----------------------
% 44.86/25.61 #Subsume : 19125
% 44.86/25.61 #Demod : 42345
% 44.86/25.61 #Tautology : 18611
% 44.86/25.61 #SimpNegUnit : 1916
% 44.86/25.61 #BackRed : 458
% 44.86/25.62
% 44.86/25.62 #Partial instantiations: 0
% 44.86/25.62 #Strategies tried : 1
% 44.86/25.62
% 44.86/25.62 Timing (in seconds)
% 44.86/25.62 ----------------------
% 44.86/25.62 Preprocessing : 0.62
% 44.86/25.62 Parsing : 0.33
% 44.86/25.62 CNF conversion : 0.03
% 44.86/25.62 Main loop : 23.65
% 44.86/25.62 Inferencing : 4.37
% 44.86/25.62 Reduction : 8.18
% 44.86/25.62 Demodulation : 6.35
% 44.86/25.62 BG Simplification : 1.26
% 44.86/25.62 Subsumption : 7.85
% 44.86/25.62 Abstraction : 0.98
% 44.86/25.62 MUC search : 0.00
% 44.86/25.62 Cooper : 0.15
% 44.86/25.62 Total : 24.51
% 44.86/25.62 Index Insertion : 0.00
% 44.86/25.62 Index Deletion : 0.00
% 44.86/25.62 Index Matching : 0.00
% 44.86/25.62 BG Taut test : 0.00
%------------------------------------------------------------------------------