%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT040_1 : TPTP v9.0.0. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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 : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 06:07:58 PM UTC 2025
% Result : Theorem 6.65s 2.63s
% Output : CNFRefutation 6.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 74 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 114 ( 66 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 75 ( 35 ~; 27 |; 5 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 100 ( 7 atm; 14 fun; 49 num; 30 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 10 usr; 13 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 0 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
%$ in > remove > add > #nlpp > count > empty > #skF_1
%Foreground sorts:
tff(collection,type,
collection: $tType ).
%Background operators:
tff('#skE_2',type,
'#skE_2': $int ).
tff('#skE_1',type,
'#skE_1': $int ).
tff('#skF_2',type,
'#skF_2': $int ).
tff('#skF_3',type,
'#skF_3': $int ).
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_151,negated_conjecture,
~ ! [U: collection,Va: $int,Wa: $int] :
( ( $less(Va,3)
& $less(6,Wa)
& in(Va,U)
& in(Wa,U)
& ( count(U) = 2 ) )
=> ~ in(5,U) ),
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_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_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_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_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_113,axiom,
! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002=1.ax',ax2) ).
tff(c_66,plain,
count('#skF_1') = 2,
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_67,plain,
in(5,'#skF_1'),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_134,plain,
! [X14_43a: $int,X15_44: collection] :
( ~ in(X14_43a,X15_44)
| ( count(remove(X14_43a,X15_44)) != count(X15_44) ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_149,plain,
count(remove(5,'#skF_1')) != count('#skF_1'),
inference(resolution,[status(thm)],[c_67,c_134]) ).
tff(c_168,plain,
count(remove(5,'#skF_1')) != 2,
inference(demodulation,[status(thm),theory(equality)],[c_66,c_149]) ).
tff(c_197,plain,
count(remove(5,'#skF_1')) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_168]) ).
tff(c_61,plain,
in('#skF_2','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_140,plain,
count(remove('#skF_2','#skF_1')) != count('#skF_1'),
inference(resolution,[status(thm)],[c_61,c_134]) ).
tff(c_157,plain,
count(remove('#skF_2','#skF_1')) != 2,
inference(demodulation,[status(thm),theory(equality)],[c_66,c_140]) ).
tff(c_306,plain,
count(remove('#skF_2','#skF_1')) = '#skE_3',
inference(define,[status(thm),theory(equality)],[c_157]) ).
tff(c_346,plain,
( ( '#skE_3' = '#skE_1' )
| ( '#skF_2' != 5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_197,c_306]) ).
tff(c_373,plain,
'#skF_2' != 5,
inference(splitLeft,[status(thm)],[c_346]) ).
tff(c_65,plain,
in('#skF_3','#skF_1'),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_146,plain,
count(remove('#skF_3','#skF_1')) != count('#skF_1'),
inference(resolution,[status(thm)],[c_65,c_134]) ).
tff(c_165,plain,
count(remove('#skF_3','#skF_1')) != 2,
inference(demodulation,[status(thm),theory(equality)],[c_66,c_146]) ).
tff(c_261,plain,
count(remove('#skF_3','#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_165]) ).
tff(c_282,plain,
( ( '#skE_2' = '#skE_1' )
| ( '#skF_3' != 5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_261,c_197]) ).
tff(c_293,plain,
'#skF_3' != 5,
inference(splitLeft,[status(thm)],[c_282]) ).
tff(c_521,plain,
! [X16_72a: $int,X17_73: collection] :
( ( add(X16_72a,remove(X16_72a,X17_73)) = X17_73 )
| ~ in(X16_72a,X17_73) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_679,plain,
add('#skF_3',remove('#skF_3','#skF_1')) = '#skF_1',
inference(resolution,[status(thm)],[c_65,c_521]) ).
tff(c_85,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_1313,plain,
! [Z_131a: $int] :
( in(Z_131a,remove('#skF_3','#skF_1'))
| ~ in(Z_131a,'#skF_1')
| ( Z_131a = '#skF_3' ) ),
inference(superposition,[status(thm),theory(equality)],[c_679,c_85]) ).
tff(c_68,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_1666,plain,
! [Z_156a: $int] :
( ( add(Z_156a,remove(Z_156a,remove('#skF_3','#skF_1'))) = remove('#skF_3','#skF_1') )
| ~ in(Z_156a,'#skF_1')
| ( Z_156a = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_1313,c_68]) ).
tff(c_1691,plain,
( ( add(5,remove(5,remove('#skF_3','#skF_1'))) = remove('#skF_3','#skF_1') )
| ( '#skF_3' = 5 ) ),
inference(resolution,[status(thm)],[c_67,c_1666]) ).
tff(c_3304,plain,
add(5,remove(5,remove('#skF_3','#skF_1'))) = remove('#skF_3','#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_293,c_1691]) ).
tff(c_84,plain,
! [X2_8a: $int,X1_7: collection] : in(X2_8a,add(X2_8a,X1_7)),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_3618,plain,
in(5,remove('#skF_3','#skF_1')),
inference(superposition,[status(thm),theory(equality)],[c_3304,c_84]) ).
tff(c_88,plain,
! [U_1a: $int] : ~ in(U_1a,empty),
inference(cnfTransformation,[status(thm)],[f_60]) ).
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_950,plain,
! [X12_104a: $int,X13_105: collection] :
( ( count(remove(X12_104a,X13_105)) = $sum($uminus(1),count(X13_105)) )
| ~ in(X12_104a,X13_105) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).
tff(c_974,plain,
count(remove('#skF_3','#skF_1')) = $sum($uminus(1),count('#skF_1')),
inference(resolution,[status(thm)],[c_65,c_950]) ).
tff(c_1000,plain,
count(remove('#skF_3','#skF_1')) = $sum($uminus(1),2),
inference(demodulation,[status(thm),theory(equality)],[c_66,c_974]) ).
tff(c_1243,plain,
count(remove('#skF_3','#skF_1')) = 1,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1000]) ).
tff(c_220,plain,
count(remove('#skF_3','#skF_1')) = '#skE_2',
inference(define,[status(thm),theory(equality)],[c_165]) ).
tff(c_345,plain,
( ( '#skE_3' = '#skE_2' )
| ( '#skF_3' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_220,c_306]) ).
tff(c_375,plain,
'#skF_3' != '#skF_2',
inference(splitLeft,[status(thm)],[c_345]) ).
tff(c_1720,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_61,c_1666]) ).
tff(c_2408,plain,
add('#skF_2',remove('#skF_2',remove('#skF_3','#skF_1'))) = remove('#skF_3','#skF_1'),
inference(negUnitSimplification,[status(thm)],[c_375,c_1720]) ).
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_903,plain,
! [X8_102a: $int,X9_103: collection] :
( ( count(add(X8_102a,X9_103)) = $sum(1,count(X9_103)) )
| in(X8_102a,X9_103) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).
tff(c_81,plain,
! [X3_9a: $int,X4_10: collection] : ~ in(X3_9a,remove(X3_9a,X4_10)),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_945,plain,
! [X8_102a: $int,X4_10: collection] : ( count(add(X8_102a,remove(X8_102a,X4_10))) = $sum(1,count(remove(X8_102a,X4_10))) ),
inference(resolution,[status(thm)],[c_903,c_81]) ).
tff(c_2424,plain,
( ( $sum(1,count(remove('#skF_2',remove('#skF_3','#skF_1')))) = count(remove('#skF_3','#skF_1')) )
| ( '#skF_2' != '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_2408,c_945]) ).
tff(c_2551,plain,
$sum(1,count(remove('#skF_2',remove('#skF_3','#skF_1')))) = 1,
inference(demodulation,[status(thm),theory(equality)],[c_1243,c_2424]) ).
tff(c_2842,plain,
count(remove('#skF_2',remove('#skF_3','#skF_1'))) = 0,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_2551]) ).
tff(c_77,plain,
! [X7_13: collection] :
( ( empty = X7_13 )
| ( count(X7_13) != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_3104,plain,
remove('#skF_2',remove('#skF_3','#skF_1')) = empty,
inference(superposition,[status(thm),theory(equality)],[c_2842,c_77]) ).
tff(c_82,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_3145,plain,
! [X3_9a: $int] :
( in(X3_9a,empty)
| ~ in(X3_9a,remove('#skF_3','#skF_1'))
| ( X3_9a = '#skF_2' ) ),
inference(superposition,[status(thm),theory(equality)],[c_3104,c_82]) ).
tff(c_3215,plain,
! [X3_9a: $int] :
( ~ in(X3_9a,remove('#skF_3','#skF_1'))
| ( X3_9a = '#skF_2' ) ),
inference(negUnitSimplification,[status(thm)],[c_88,c_3145]) ).
tff(c_3621,plain,
( ( '#skF_2' = 5 )
| ( '#skF_3' != '#skF_3' ) ),
inference(resolution,[status(thm)],[c_3618,c_3215]) ).
tff(c_3656,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_373,c_3621]) ).
tff(c_3659,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3656]) ).
tff(c_3663,plain,
'#skF_3' = '#skF_2',
inference(splitRight,[status(thm)],[c_345]) ).
tff(c_57,plain,
$less(6,'#skF_3'),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_3695,plain,
$less(6,'#skF_2'),
inference(demodulation,[status(thm),theory(equality)],[c_3663,c_57]) ).
tff(c_56,plain,
$less('#skF_2',3),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_3696,plain,
$false,
inference(close,[status(thm),theory('LIA')],[c_3695,c_56]) ).
tff(c_3700,plain,
'#skF_2' = 5,
inference(splitRight,[status(thm)],[c_346]) ).
tff(c_3753,plain,
$less(5,3),
inference(demodulation,[status(thm),theory(equality)],[c_3700,c_56]) ).
tff(c_3757,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3753]) ).
tff(c_3761,plain,
'#skF_3' = 5,
inference(splitRight,[status(thm)],[c_282]) ).
tff(c_3776,plain,
$less(6,5),
inference(demodulation,[status(thm),theory(equality)],[c_3761,c_57]) ).
tff(c_3780,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_3776]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT040_1 : TPTP v9.0.0. Released v5.0.0.
% 0.07/0.13 % 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
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 7 18:16:47 EDT 2025
% 0.14/0.35 % CPUTime :
% 6.65/2.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.65/2.64
% 6.65/2.64 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------