TSTP Solution File: DAT043_1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : DAT043_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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n003.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 10:37:02 EDT 2023
% Result : Theorem 17.30s 5.30s
% Output : CNFRefutation 17.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 27
% Syntax : Number of formulae : 194 ( 103 unt; 16 typ; 0 def)
% Number of atoms : 276 ( 199 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 205 ( 107 ~; 84 |; 5 &)
% ( 7 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 311 ( 21 atm; 92 fun; 123 num; 75 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 6 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 14 usr; 14 con; 0-2 aty)
% Number of variables : 138 (; 138 !; 0 ?; 138 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > remove > add > #nlpp > count > empty > #skF_1
%Foreground sorts:
tff(collection,type,
collection: $tType ).
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skE_6',type,
'#skE_6': $int ).
tff('#skE_5',type,
'#skE_5': $int ).
tff('#skE_4',type,
'#skE_4': $int ).
tff('#skF_4',type,
'#skF_4': $int ).
tff('#skF_2',type,
'#skF_2': $int ).
tff('#skF_3',type,
'#skF_3': $int ).
tff('#skE_3',type,
'#skE_3': $int ).
%Foreground operators:
tff(empty,type,
empty: collection ).
tff(count,type,
count: collection > $int ).
tff('#skF_1',type,
'#skF_1': collection ).
tff(in,type,
in: ( $int * collection ) > $o ).
tff(remove,type,
remove: ( $int * collection ) > collection ).
tff(add,type,
add: ( $int * collection ) > collection ).
tff(f_150,negated_conjecture,
~ ! [U: collection,Va: $int,Wa: $int,Xa: $int] :
( ( $greater(Va,Wa)
& $greater(Wa,Xa)
& in(Va,U)
& in(Wa,U)
& in(Xa,U) )
=> $greater(count(U),2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f_131,axiom,
! [X14a: $int,X15: collection] :
( ~ in(X14a,X15)
<=> ( count(remove(X14a,X15)) = count(X15) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax6) ).
tff(f_60,axiom,
! [Ua: $int] : ~ in(Ua,empty),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax1) ).
tff(f_126,axiom,
! [X12a: $int,X13: collection] :
( in(X12a,X13)
<=> ( count(remove(X12a,X13)) = $difference(count(X13),1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax5) ).
tff(f_135,axiom,
! [X16a: $int,X17: collection] :
( in(X16a,X17)
=> ( X17 = add(X16a,remove(X16a,X17)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax7) ).
tff(f_71,axiom,
! [Za: $int,X1: collection,X2a: $int] :
( ( in(Za,X1)
| ( Za = X2a ) )
<=> in(Za,add(X2a,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.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/sandbox/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/sandbox/benchmark/Axioms/DAT002=1.ax',ax3) ).
tff(f_122,axiom,
! [X10a: $int,X11: collection] :
( in(X10a,X11)
<=> ( count(add(X10a,X11)) = count(X11) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax4) ).
tff(f_113,axiom,
! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax2) ).
tff(f_109,axiom,
! [X6: collection] : $greatereq(count(X6),0),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax1) ).
tff(c_47,plain,
~ $greater(count('#skF_1'),2),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_73,plain,
~ $less(2,count('#skF_1')),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_47]) ).
tff(c_117,plain,
count('#skF_1') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_73]) ).
tff(c_64,plain,
in('#skF_2','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_148,plain,
! [X14_46a: $int,X15_47: collection] :
( ~ in(X14_46a,X15_47)
| ( count(remove(X14_46a,X15_47)) != count(X15_47) ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_154,plain,
count(remove('#skF_2','#skF_1')) != count('#skF_1'),
inference(resolution,[status(thm)],[c_64,c_148]) ).
tff(c_171,plain,
count(remove('#skF_2','#skF_1')) != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_117,c_154]) ).
tff(c_194,plain,
count(remove('#skF_2','#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_171]) ).
tff(c_72,plain,
in('#skF_4','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_163,plain,
count(remove('#skF_4','#skF_1')) != count('#skF_1'),
inference(resolution,[status(thm)],[c_72,c_148]) ).
tff(c_185,plain,
count(remove('#skF_4','#skF_1')) != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_117,c_163]) ).
tff(c_280,plain,
count(remove('#skF_4','#skF_1')) = '#skE_4',
inference(define,[status(thm),theory(equality)],[c_185]) ).
tff(c_322,plain,
( ( '#skE_4' = '#skE_2' )
| ( '#skF_4' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_194,c_280]) ).
tff(c_349,plain,
'#skF_4' != '#skF_2',
inference(splitLeft,[status(thm)],[c_322]) ).
tff(c_94,plain,
! [U_1a: $int] : ~ in(U_1a,empty),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_68,plain,
in('#skF_3','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_160,plain,
count(remove('#skF_3','#skF_1')) != count('#skF_1'),
inference(resolution,[status(thm)],[c_68,c_148]) ).
tff(c_179,plain,
count(remove('#skF_3','#skF_1')) != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_117,c_160]) ).
tff(c_229,plain,
count(remove('#skF_3','#skF_1')) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_179]) ).
tff(c_320,plain,
( ( '#skE_4' = '#skE_3' )
| ( '#skF_4' != '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_229,c_280]) ).
tff(c_351,plain,
'#skF_4' != '#skF_3',
inference(splitLeft,[status(thm)],[c_320]) ).
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_1297,plain,
! [X12_143a: $int,X13_144: collection] :
( ( count(remove(X12_143a,X13_144)) = $sum($uminus(1),count(X13_144)) )
| ~ in(X12_143a,X13_144) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).
tff(c_1324,plain,
count(remove('#skF_3','#skF_1')) = $sum($uminus(1),count('#skF_1')),
inference(resolution,[status(thm)],[c_68,c_1297]) ).
tff(c_1433,plain,
count(remove('#skF_3','#skF_1')) = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_117,c_1324]) ).
tff(c_233,plain,
count(remove('#skF_3','#skF_1')) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_179]) ).
tff(c_255,plain,
( ( '#skE_3' = '#skE_2' )
| ( '#skF_3' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_233,c_194]) ).
tff(c_267,plain,
'#skF_3' != '#skF_2',
inference(splitLeft,[status(thm)],[c_255]) ).
tff(c_425,plain,
! [X16_73a: $int,X17_74: collection] :
( ( add(X16_73a,remove(X16_73a,X17_74)) = X17_74 )
| ~ in(X16_73a,X17_74) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_672,plain,
add('#skF_3',remove('#skF_3','#skF_1')) = '#skF_1',
inference(resolution,[status(thm)],[c_68,c_425]) ).
tff(c_91,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_1730,plain,
! [Z_169a: $int] :
( in(Z_169a,remove('#skF_3','#skF_1'))
| ~ in(Z_169a,'#skF_1')
| ( Z_169a = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_672,c_91]) ).
tff(c_74,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_2585,plain,
! [Z_214a: $int] :
( ( add(Z_214a,remove(Z_214a,remove('#skF_3','#skF_1'))) = remove('#skF_3','#skF_1') )
| ~ in(Z_214a,'#skF_1')
| ( Z_214a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_1730,c_74]) ).
tff(c_2637,plain,
( ( add('#skF_2',remove('#skF_2',remove('#skF_3','#skF_1'))) = remove('#skF_3','#skF_1') )
| ( '#skF_3' = '#skF_2' ) ),
inference(resolution,[status(thm)],[c_64,c_2585]) ).
tff(c_2889,plain,
add('#skF_2',remove('#skF_2',remove('#skF_3','#skF_1'))) = remove('#skF_3','#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_267,c_2637]) ).
tff(c_2888,plain,
add('#skF_2',remove('#skF_2',remove('#skF_3','#skF_1'))) = remove('#skF_3','#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_267,c_2637]) ).
tff(c_88,plain,
! [X3_9a: $int,X5_11a: $int,X4_10: collection] :
( in(X3_9a,remove(X5_11a,X4_10))
| ~ in(X3_9a,X4_10)
| ( X5_11a = X3_9a ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
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_1046,plain,
! [X8_128a: $int,X9_129: collection] :
( ~ in(X8_128a,X9_129)
| ( count(add(X8_128a,X9_129)) != $sum(1,count(X9_129)) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_28]) ).
tff(c_15908,plain,
! [X3_1648a: $int,X5_1649a: $int,X4_1650: collection] :
( ( count(add(X3_1648a,remove(X5_1649a,X4_1650))) != $sum(1,count(remove(X5_1649a,X4_1650))) )
| ~ in(X3_1648a,X4_1650)
| ( X5_1649a = X3_1648a ) ),
inference(resolution,[status(thm)],[c_88,c_1046]) ).
tff(c_16679,plain,
! [X5_1730a: $int] :
( ( count(add('#skF_4',remove(X5_1730a,'#skF_1'))) != $sum(1,count(remove(X5_1730a,'#skF_1'))) )
| ( X5_1730a = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_72,c_15908]) ).
tff(c_16718,plain,
( ( count(add('#skF_4',add('#skF_2',remove('#skF_2',remove('#skF_3','#skF_1'))))) != $sum(1,count(remove('#skF_3','#skF_1'))) )
| ( '#skF_4' = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_2888,c_16679]) ).
tff(c_16782,plain,
( ( count(add('#skF_4',remove('#skF_3','#skF_1'))) != $sum(1,$sum($uminus(1),'#skE_1')) )
| ( '#skF_4' = '#skF_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1433,c_2889,c_16718]) ).
tff(c_16784,plain,
count(add('#skF_4',remove('#skF_3','#skF_1'))) != $sum(1,$sum($uminus(1),'#skE_1')),
inference(negUnitSimplification,[status(thm)],[c_351,c_16782]) ).
tff(c_16787,plain,
count(add('#skF_4',remove('#skF_3','#skF_1'))) != '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_16784]) ).
tff(c_21943,plain,
count(add('#skF_4',remove('#skF_3','#skF_1'))) = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_16787]) ).
tff(c_534,plain,
! [X3_90a: $int,X5_91a: $int,X4_92: collection] :
( in(X3_90a,remove(X5_91a,X4_92))
| ~ in(X3_90a,X4_92)
| ( X5_91a = X3_90a ) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_80,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_8405,plain,
! [X3_979a: $int,X5_980a: $int,X4_981: collection] :
( ( count(add(X3_979a,remove(X5_980a,X4_981))) = count(remove(X5_980a,X4_981)) )
| ~ in(X3_979a,X4_981)
| ( X5_980a = X3_979a ) ),
inference(resolution,[status(thm)],[c_534,c_80]) ).
tff(c_8528,plain,
! [X5_980a: $int] :
( ( count(add('#skF_4',remove(X5_980a,'#skF_1'))) = count(remove(X5_980a,'#skF_1')) )
| ( X5_980a = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_72,c_8405]) ).
tff(c_21973,plain,
( ( count(remove('#skF_3','#skF_1')) = '#skE_6' )
| ( '#skF_4' = '#skF_3' )
| ( '#skF_4' != '#skF_4' ) ),
inference(superposition,[status(thm),theory(equality)],[c_21943,c_8528]) ).
tff(c_22127,plain,
( ( '#skE_6' = $sum($uminus(1),'#skE_1') )
| ( '#skF_4' = '#skF_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1433,c_21973]) ).
tff(c_22129,plain,
'#skE_6' = $sum($uminus(1),'#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_351,c_22127]) ).
tff(c_21942,plain,
count(add('#skF_4',remove('#skF_3','#skF_1'))) = '#skE_6',
inference(define,[status(thm),theory(equality)],[c_16787]) ).
tff(c_90,plain,
! [X2_8a: $int,X1_7: collection] : in(X2_8a,add(X2_8a,X1_7)),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_1351,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_90,c_1297]) ).
tff(c_4865,plain,
! [X2_504a: $int,X1_505: collection] : ( count(remove(X2_504a,add(X2_504a,X1_505))) = $sum($uminus(1),count(add(X2_504a,X1_505))) ),
inference(resolution,[status(thm)],[c_90,c_1297]) ).
tff(c_84,plain,
count(empty) = 0,
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_76,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_1794,plain,
! [X14_181a: $int,X15_182: collection] :
( ( add(X14_181a,remove(X14_181a,X15_182)) = X15_182 )
| ( count(remove(X14_181a,X15_182)) = count(X15_182) ) ),
inference(resolution,[status(thm)],[c_76,c_425]) ).
tff(c_464,plain,
! [X10_81a: $int,X11_82: collection] :
( ( count(add(X10_81a,X11_82)) = count(X11_82) )
| ~ in(X10_81a,X11_82) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_700,plain,
! [X2_101a: $int,X1_102: collection] : ( count(add(X2_101a,add(X2_101a,X1_102))) = count(add(X2_101a,X1_102)) ),
inference(resolution,[status(thm)],[c_90,c_464]) ).
tff(c_83,plain,
! [X7_13: collection] :
( ( empty = X7_13 )
| ( count(X7_13) != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_1191,plain,
! [X2_136a: $int,X1_137: collection] :
( ( add(X2_136a,add(X2_136a,X1_137)) = empty )
| ( count(add(X2_136a,X1_137)) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_700,c_83]) ).
tff(c_1218,plain,
! [X2_136a: $int,X1_137: collection] :
( in(X2_136a,empty)
| ( count(add(X2_136a,X1_137)) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1191,c_90]) ).
tff(c_1252,plain,
! [X2_136a: $int,X1_137: collection] : ( count(add(X2_136a,X1_137)) != 0 ),
inference(negUnitSimplification,[status(thm)],[c_94,c_1218]) ).
tff(c_1908,plain,
! [X15_183: collection,X14_184a: $int] :
( ( count(X15_183) != 0 )
| ( count(remove(X14_184a,X15_183)) = count(X15_183) ) ),
inference(superposition,[status(thm),theory(equality)],[c_1794,c_1252]) ).
tff(c_1984,plain,
! [X14_184a: $int,X15_183: collection] :
( ( remove(X14_184a,X15_183) = empty )
| ( count(X15_183) != 0 )
| ( count(X15_183) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1908,c_83]) ).
tff(c_323,plain,
! [X14_66a: $int,X15_67: collection] :
( ( count(remove(X14_66a,X15_67)) = count(X15_67) )
| in(X14_66a,X15_67) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_87,plain,
! [X3_9a: $int,X4_10: collection] : ~ in(X3_9a,remove(X3_9a,X4_10)),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_344,plain,
! [X14_66a: $int,X4_10: collection] : ( count(remove(X14_66a,remove(X14_66a,X4_10))) = count(remove(X14_66a,X4_10)) ),
inference(resolution,[status(thm)],[c_323,c_87]) ).
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_894,plain,
! [X8_113a: $int,X9_114: collection] :
( ( count(add(X8_113a,X9_114)) = $sum(1,count(X9_114)) )
| in(X8_113a,X9_114) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_919,plain,
! [X8_113a: $int] : ( count(add(X8_113a,empty)) = $sum(1,count(empty)) ),
inference(resolution,[status(thm)],[c_894,c_94]) ).
tff(c_933,plain,
! [X8_113a: $int] : ( count(add(X8_113a,empty)) = $sum(1,0) ),
inference(demodulation,[status(thm),theory(equality)],[c_84,c_919]) ).
tff(c_935,plain,
! [X8_113a: $int] : ( count(add(X8_113a,empty)) = 1 ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_933]) ).
tff(c_984,plain,
! [X14_118a: $int,X4_119: collection] : ( count(remove(X14_118a,remove(X14_118a,X4_119))) = count(remove(X14_118a,X4_119)) ),
inference(resolution,[status(thm)],[c_323,c_87]) ).
tff(c_1109,plain,
! [X14_132a: $int,X4_133: collection] :
( ( remove(X14_132a,remove(X14_132a,X4_133)) = empty )
| ( count(remove(X14_132a,X4_133)) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_984,c_83]) ).
tff(c_391,plain,
! [X10_70a: $int,X11_71: collection] :
( in(X10_70a,X11_71)
| ( count(add(X10_70a,X11_71)) != count(X11_71) ) ),
inference(cnfTransformation,[status(thm)],[f_122]) ).
tff(c_412,plain,
! [X10_70a: $int,X4_10: collection] : ( count(add(X10_70a,remove(X10_70a,X4_10))) != count(remove(X10_70a,X4_10)) ),
inference(resolution,[status(thm)],[c_391,c_87]) ).
tff(c_1124,plain,
! [X14_132a: $int,X4_133: collection] :
( ( count(remove(X14_132a,remove(X14_132a,X4_133))) != count(add(X14_132a,empty)) )
| ( count(remove(X14_132a,X4_133)) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1109,c_412]) ).
tff(c_1152,plain,
! [X14_132a: $int,X4_133: collection] :
( ( count(remove(X14_132a,X4_133)) != 1 )
| ( count(remove(X14_132a,X4_133)) != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_344,c_935,c_1124]) ).
tff(c_2540,plain,
! [X15_211: collection,X14_212a: $int] :
( ( count(X15_211) != 1 )
| ( count(remove(X14_212a,X15_211)) != 0 )
| ( count(X15_211) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1908,c_1152]) ).
tff(c_2546,plain,
! [X15_183: collection] :
( ( count(X15_183) != 1 )
| ( count(empty) != 0 )
| ( count(X15_183) != 0 )
| ( count(X15_183) != 0 )
| ( count(X15_183) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1984,c_2540]) ).
tff(c_2571,plain,
! [X15_183: collection] :
( ( count(X15_183) != 1 )
| ( count(X15_183) != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_84,c_2546]) ).
tff(c_4895,plain,
! [X2_504a: $int,X1_505: collection] :
( ( $sum($uminus(1),count(add(X2_504a,X1_505))) != 1 )
| ( count(remove(X2_504a,add(X2_504a,X1_505))) != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_4865,c_2571]) ).
tff(c_4976,plain,
! [X2_504a: $int,X1_505: collection] :
( ( $sum($uminus(1),count(add(X2_504a,X1_505))) != 1 )
| ( $sum($uminus(1),count(add(X2_504a,X1_505))) != 0 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1351,c_4895]) ).
tff(c_4978,plain,
! [X2_504a: $int,X1_505: collection] :
( ( count(add(X2_504a,X1_505)) != 2 )
| ( count(add(X2_504a,X1_505)) != 1 ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4976]) ).
tff(c_21978,plain,
( ( '#skE_6' != 2 )
| ( count(add('#skF_4',remove('#skF_3','#skF_1'))) != 1 ) ),
inference(superposition,[status(thm),theory(equality)],[c_21943,c_4978]) ).
tff(c_22135,plain,
( ( '#skE_6' != 2 )
| ( '#skE_6' != 1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_21942,c_21978]) ).
tff(c_22263,plain,
'#skE_6' != 1,
inference(splitLeft,[status(thm)],[c_22135]) ).
tff(c_22267,plain,
$sum($uminus(1),'#skE_1') != 1,
inference(demodulation,[status(thm),theory(equality)],[c_22129,c_22263]) ).
tff(c_22281,plain,
'#skE_1' != 2,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_22267]) ).
tff(c_18,plain,
! [X6_12: collection] : $greatereq(count(X6_12),0),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_85,plain,
! [X6_12: collection] : ~ $less(count(X6_12),0),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_18]) ).
tff(c_4909,plain,
! [X2_504a: $int,X1_505: collection] : ~ $less($sum($uminus(1),count(add(X2_504a,X1_505))),0),
inference(superposition,[status(thm),theory(equality)],[c_4865,c_85]) ).
tff(c_5039,plain,
! [X2_518a: $int,X1_519: collection] : ~ $less(count(add(X2_518a,X1_519)),1),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_4909]) ).
tff(c_5053,plain,
~ $less(count(remove('#skF_3','#skF_1')),1),
inference(superposition,[status(thm),theory(equality)],[c_2888,c_5039]) ).
tff(c_5088,plain,
~ $less($sum($uminus(1),'#skE_1'),1),
inference(demodulation,[status(thm),theory(equality)],[c_1433,c_5053]) ).
tff(c_5090,plain,
~ $less('#skE_1',2),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_5088]) ).
tff(c_114,plain,
count('#skF_1') = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_73]) ).
tff(c_118,plain,
~ $less(2,'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_114,c_73]) ).
tff(c_22285,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_22281,c_5090,c_118]) ).
tff(c_22289,plain,
'#skE_6' = 1,
inference(splitRight,[status(thm)],[c_22135]) ).
tff(c_22047,plain,
( ( count(remove('#skF_3','#skF_1')) = '#skE_6' )
| ( '#skF_4' != '#skF_4' )
| ( '#skF_4' = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_8528,c_21943]) ).
tff(c_22206,plain,
( ( '#skE_6' = $sum($uminus(1),'#skE_1') )
| ( '#skF_4' = '#skF_3' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1433,c_22047]) ).
tff(c_22208,plain,
'#skE_6' = $sum($uminus(1),'#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_351,c_22206]) ).
tff(c_22307,plain,
$sum($uminus(1),'#skE_1') = 1,
inference(demodulation,[status(thm),theory(equality)],[c_22289,c_22208]) ).
tff(c_22309,plain,
'#skE_1' = 2,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_22307]) ).
tff(c_1357,plain,
count(remove('#skF_3','#skF_1')) = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_117,c_1324]) ).
tff(c_22333,plain,
count(remove('#skF_3','#skF_1')) = $sum($uminus(1),2),
inference(demodulation,[status(thm),theory(equality)],[c_22309,c_1357]) ).
tff(c_22922,plain,
count(remove('#skF_3','#skF_1')) = 1,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_22333]) ).
tff(c_2890,plain,
add('#skF_2',remove('#skF_2',remove('#skF_3','#skF_1'))) = remove('#skF_3','#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_267,c_2637]) ).
tff(c_3303,plain,
in('#skF_2',remove('#skF_3','#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_2890,c_90]) ).
tff(c_81,plain,
! [X8_14a: $int,X9_15: collection] :
( ~ in(X8_14a,X9_15)
| ( count(add(X8_14a,X9_15)) != $sum(1,count(X9_15)) ) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_28]) ).
tff(c_3315,plain,
count(add('#skF_2',remove('#skF_3','#skF_1'))) != $sum(1,count(remove('#skF_3','#skF_1'))),
inference(resolution,[status(thm)],[c_3303,c_81]) ).
tff(c_3356,plain,
count(add('#skF_2',remove('#skF_3','#skF_1'))) != $sum(1,$sum($uminus(1),'#skE_1')),
inference(demodulation,[status(thm),theory(equality)],[c_1433,c_3315]) ).
tff(c_3359,plain,
count(add('#skF_2',remove('#skF_3','#skF_1'))) != '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3356]) ).
tff(c_3956,plain,
count(add('#skF_2',remove('#skF_3','#skF_1'))) = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_3359]) ).
tff(c_3955,plain,
count(add('#skF_2',remove('#skF_3','#skF_1'))) != '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3356]) ).
tff(c_3963,plain,
'#skE_5' != '#skE_1',
inference(demodulation,[status(thm),theory(equality)],[c_3956,c_3955]) ).
tff(c_3965,plain,
count(add('#skF_2',remove('#skF_3','#skF_1'))) = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_3359]) ).
tff(c_6655,plain,
! [X8_763a: $int,X9_764: collection] :
( ( count(add(X8_763a,X9_764)) = count(X9_764) )
| ( count(add(X8_763a,X9_764)) = $sum(1,count(X9_764)) ) ),
inference(resolution,[status(thm)],[c_894,c_80]) ).
tff(c_3962,plain,
count(add('#skF_2',remove('#skF_3','#skF_1'))) = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_3359]) ).
tff(c_6674,plain,
( ( $sum(1,count(remove('#skF_3','#skF_1'))) = '#skE_5' )
| ( count(add('#skF_2',remove('#skF_3','#skF_1'))) = count(remove('#skF_3','#skF_1')) ) ),
inference(superposition,[status(thm),theory(equality)],[c_6655,c_3962]) ).
tff(c_6805,plain,
( ( '#skE_5' = $sum(1,$sum($uminus(1),'#skE_1')) )
| ( '#skE_5' = $sum($uminus(1),'#skE_1') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1433,c_3965,c_1433,c_6674]) ).
tff(c_6807,plain,
( ( '#skE_5' = '#skE_1' )
| ( '#skE_5' = $sum($uminus(1),'#skE_1') ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_6805]) ).
tff(c_6944,plain,
'#skE_5' = $sum($uminus(1),'#skE_1'),
inference(negUnitSimplification,[status(thm)],[c_3963,c_6807]) ).
tff(c_2643,plain,
( ( add('#skF_4',remove('#skF_4',remove('#skF_3','#skF_1'))) = remove('#skF_3','#skF_1') )
| ( '#skF_4' = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_72,c_2585]) ).
tff(c_5862,plain,
add('#skF_4',remove('#skF_4',remove('#skF_3','#skF_1'))) = remove('#skF_3','#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_351,c_2643]) ).
tff(c_5861,plain,
add('#skF_4',remove('#skF_4',remove('#skF_3','#skF_1'))) = remove('#skF_3','#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_351,c_2643]) ).
tff(c_16078,plain,
! [X5_1679a: $int] :
( ( count(add('#skF_2',remove(X5_1679a,'#skF_1'))) != $sum(1,count(remove(X5_1679a,'#skF_1'))) )
| ( X5_1679a = '#skF_2' ) ),
inference(resolution,[status(thm)],[c_64,c_15908]) ).
tff(c_16110,plain,
( ( count(add('#skF_2',add('#skF_4',remove('#skF_4',remove('#skF_3','#skF_1'))))) != $sum(1,count(remove('#skF_3','#skF_1'))) )
| ( '#skF_3' = '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_5861,c_16078]) ).
tff(c_16169,plain,
( ( count(add('#skF_2',remove('#skF_3','#skF_1'))) != $sum(1,$sum($uminus(1),'#skE_1')) )
| ( '#skF_3' = '#skF_2' ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1433,c_5862,c_16110]) ).
tff(c_16171,plain,
count(add('#skF_2',remove('#skF_3','#skF_1'))) != $sum(1,$sum($uminus(1),'#skE_1')),
inference(negUnitSimplification,[status(thm)],[c_267,c_16169]) ).
tff(c_16174,plain,
count(add('#skF_2',remove('#skF_3','#skF_1'))) != '#skE_1',
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_16171]) ).
tff(c_21921,plain,
count(add('#skF_2',remove('#skF_3','#skF_1'))) = '#skE_5',
inference(define,[status(thm),theory(equality)],[c_16174]) ).
tff(c_21927,plain,
count(add('#skF_2',remove('#skF_3','#skF_1'))) = $sum($uminus(1),'#skE_1'),
inference(demodulation,[status(thm),theory(equality)],[c_6944,c_21921]) ).
tff(c_27216,plain,
count(add('#skF_2',remove('#skF_3','#skF_1'))) = $sum($uminus(1),2),
inference(demodulation,[status(thm),theory(equality)],[c_22309,c_21927]) ).
tff(c_27220,plain,
count(add('#skF_2',remove('#skF_3','#skF_1'))) = 1,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_27216]) ).
tff(c_82,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_14912,plain,
! [X8_1626a: $int,X9_1627: collection] :
( ( count(remove(X8_1626a,X9_1627)) = $sum($uminus(1),count(X9_1627)) )
| ( count(add(X8_1626a,X9_1627)) = $sum(1,count(X9_1627)) ) ),
inference(resolution,[status(thm)],[c_82,c_1297]) ).
tff(c_15039,plain,
! [X8_1626a: $int,X9_1627: collection] :
( ( remove(X8_1626a,X9_1627) = empty )
| ( $sum($uminus(1),count(X9_1627)) != 0 )
| ( count(add(X8_1626a,X9_1627)) = $sum(1,count(X9_1627)) ) ),
inference(superposition,[status(thm),theory(equality)],[c_14912,c_83]) ).
tff(c_31671,plain,
! [X8_3020a: $int,X9_3021: collection] :
( ( remove(X8_3020a,X9_3021) = empty )
| ( count(X9_3021) != 1 )
| ( count(add(X8_3020a,X9_3021)) = $sum(1,count(X9_3021)) ) ),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_15039]) ).
tff(c_32066,plain,
( ( remove('#skF_3','#skF_1') = add('#skF_2',empty) )
| ( count(remove('#skF_3','#skF_1')) != 1 )
| ( count(add('#skF_2',remove('#skF_3','#skF_1'))) = $sum(1,count(remove('#skF_3','#skF_1'))) ) ),
inference(superposition,[status(thm),theory(equality)],[c_31671,c_2888]) ).
tff(c_32567,plain,
( ( remove('#skF_3','#skF_1') = add('#skF_2',empty) )
| ( $sum(1,1) = 1 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_22922,c_27220,c_22922,c_32066]) ).
tff(c_32658,plain,
remove('#skF_3','#skF_1') = add('#skF_2',empty),
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_32567]) ).
tff(c_5863,plain,
add('#skF_4',remove('#skF_4',remove('#skF_3','#skF_1'))) = remove('#skF_3','#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_351,c_2643]) ).
tff(c_6276,plain,
in('#skF_4',remove('#skF_3','#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_5863,c_90]) ).
tff(c_33711,plain,
in('#skF_4',add('#skF_2',empty)),
inference(demodulation,[status(thm),theory(equality)],[c_32658,c_6276]) ).
tff(c_33756,plain,
( in('#skF_4',empty)
| ( '#skF_4' = '#skF_2' ) ),
inference(resolution,[status(thm)],[c_33711,c_91]) ).
tff(c_33822,plain,
'#skF_4' = '#skF_2',
inference(negUnitSimplification,[status(thm)],[c_94,c_33756]) ).
tff(c_33845,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_349,c_33822]) ).
tff(c_33849,plain,
'#skF_4' = '#skF_3',
inference(splitRight,[status(thm)],[c_320]) ).
tff(c_55,plain,
$greater('#skF_3','#skF_4'),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_60,plain,
$less('#skF_4','#skF_3'),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_55]) ).
tff(c_33912,plain,
$less('#skF_3','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_33849,c_60]) ).
tff(c_33917,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_33912]) ).
tff(c_33921,plain,
'#skF_4' = '#skF_2',
inference(splitRight,[status(thm)],[c_322]) ).
tff(c_33943,plain,
$less('#skF_2','#skF_3'),
inference(demodulation,[status(thm),theory(equality)],[c_33921,c_60]) ).
tff(c_57,plain,
$greater('#skF_2','#skF_3'),
inference(cnfTransformation,[status(thm)],[f_150]) ).
tff(c_59,plain,
$less('#skF_3','#skF_2'),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_57]) ).
tff(c_33944,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_33943,c_59]) ).
tff(c_33948,plain,
'#skF_3' = '#skF_2',
inference(splitRight,[status(thm)],[c_255]) ).
tff(c_33968,plain,
$less('#skF_2','#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_33948,c_59]) ).
tff(c_33974,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_33968]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : DAT043_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 13:16:38 EDT 2023
% 0.14/0.35 % CPUTime :
% 17.30/5.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.30/5.32
% 17.30/5.32 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.74/5.40
% 17.74/5.40 Inference rules
% 17.74/5.40 ----------------------
% 17.74/5.40 #Ref : 0
% 17.74/5.40 #Sup : 5317
% 17.74/5.40 #Fact : 2
% 17.74/5.40 #Define : 8
% 17.74/5.40 #Split : 182
% 17.74/5.40 #Chain : 0
% 17.74/5.40 #Close : 2
% 17.74/5.40
% 17.74/5.40 Ordering : LPO
% 17.74/5.40
% 17.74/5.40 Simplification rules
% 17.74/5.40 ----------------------
% 17.74/5.40 #Subsume : 1029
% 17.74/5.40 #Demod : 5013
% 17.74/5.40 #Tautology : 2193
% 17.74/5.40 #SimpNegUnit : 282
% 17.74/5.40 #BackRed : 57
% 17.74/5.40
% 17.74/5.40 #Partial instantiations: 0
% 17.74/5.40 #Strategies tried : 1
% 17.74/5.40
% 17.74/5.40 Timing (in seconds)
% 17.74/5.40 ----------------------
% 17.74/5.41 Preprocessing : 0.59
% 17.74/5.41 Parsing : 0.31
% 17.74/5.41 CNF conversion : 0.04
% 17.74/5.41 Main loop : 3.55
% 17.74/5.41 Inferencing : 0.79
% 17.74/5.41 Reduction : 1.26
% 17.74/5.41 Demodulation : 0.98
% 17.74/5.41 BG Simplification : 0.28
% 17.74/5.41 Subsumption : 0.78
% 17.74/5.41 Abstraction : 0.16
% 17.74/5.41 MUC search : 0.01
% 17.74/5.41 Cooper : 0.10
% 17.74/5.41 Total : 4.30
% 17.74/5.41 Index Insertion : 0.00
% 17.74/5.41 Index Deletion : 0.00
% 17.74/5.41 Index Matching : 0.00
% 17.74/5.41 BG Taut test : 0.00
%------------------------------------------------------------------------------