%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : DAT037_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 : n012.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 4.55s 2.13s
% Output : CNFRefutation 4.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 52 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 18 ~; 12 |; 1 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 54 ( 0 atm; 8 fun; 31 num; 15 var)
% Number of types : 3 ( 1 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 7 usr; 8 con; 0-2 aty)
% Number of variables : 27 ( 27 !; 0 ?; 27 :)
% 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 ).
%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_145,negated_conjecture,
~ ! [U: collection] :
( ( in(2,U)
& ( count(U) = 1 ) )
=> ~ in(5,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f_60,axiom,
! [Ua: $int] : ~ in(Ua,empty),
file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax1) ).
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_113,axiom,
! [X7: collection] :
( ( X7 = empty )
<=> ( count(X7) = 0 ) ),
file('/export/starexec/sandbox/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/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(c_52,plain,
in(2,'#skF_1'),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_75,plain,
! [U_1a: $int] : ~ in(U_1a,empty),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_53,plain,
count('#skF_1') = 1,
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_54,plain,
in(5,'#skF_1'),
inference(cnfTransformation,[status(thm)],[f_145]) ).
tff(c_115,plain,
! [X14_37a: $int,X15_38: collection] :
( ~ in(X14_37a,X15_38)
| ( count(remove(X14_37a,X15_38)) != count(X15_38) ) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_124,plain,
count(remove(5,'#skF_1')) != count('#skF_1'),
inference(resolution,[status(thm)],[c_54,c_115]) ).
tff(c_134,plain,
count(remove(5,'#skF_1')) != 1,
inference(demodulation,[status(thm),theory(equality)],[c_53,c_124]) ).
tff(c_141,plain,
count(remove(5,'#skF_1')) = '#skE_1',
inference(define,[status(thm),theory(equality)],[c_134]) ).
tff(c_64,plain,
! [X7_13: collection] :
( ( empty = X7_13 )
| ( count(X7_13) != 0 ) ),
inference(cnfTransformation,[status(thm)],[f_113]) ).
tff(c_152,plain,
( ( remove(5,'#skF_1') = empty )
| ( '#skE_1' != 0 ) ),
inference(superposition,[status(thm),theory(equality)],[c_141,c_64]) ).
tff(c_228,plain,
'#skE_1' != 0,
inference(splitLeft,[status(thm)],[c_152]) ).
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_832,plain,
! [X12_79a: $int,X13_80: collection] :
( ( count(remove(X12_79a,X13_80)) = $sum($uminus(1),count(X13_80)) )
| ~ in(X12_79a,X13_80) ),
inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_35]) ).
tff(c_853,plain,
count(remove(5,'#skF_1')) = $sum($uminus(1),count('#skF_1')),
inference(resolution,[status(thm)],[c_54,c_832]) ).
tff(c_870,plain,
'#skE_1' = $sum($uminus(1),1),
inference(demodulation,[status(thm),theory(equality)],[c_141,c_53,c_853]) ).
tff(c_872,plain,
'#skE_1' = 0,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_870]) ).
tff(c_931,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_228,c_872]) ).
tff(c_934,plain,
remove(5,'#skF_1') = empty,
inference(splitRight,[status(thm)],[c_152]) ).
tff(c_987,plain,
! [X16_86a: $int,X17_87: collection] :
( ( add(X16_86a,remove(X16_86a,X17_87)) = X17_87 )
| ~ in(X16_86a,X17_87) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_999,plain,
add(5,remove(5,'#skF_1')) = '#skF_1',
inference(resolution,[status(thm)],[c_54,c_987]) ).
tff(c_1011,plain,
add(5,empty) = '#skF_1',
inference(demodulation,[status(thm),theory(equality)],[c_934,c_999]) ).
tff(c_1109,plain,
! [Z_92a: $int,X1_93: collection,X2_94a: $int] :
( in(Z_92a,X1_93)
| ~ in(Z_92a,add(X2_94a,X1_93))
| ( Z_92a = X2_94a ) ),
inference(cnfTransformation,[status(thm)],[f_71]) ).
tff(c_1115,plain,
! [Z_92a: $int] :
( in(Z_92a,empty)
| ~ in(Z_92a,'#skF_1')
| ( Z_92a = 5 ) ),
inference(superposition,[status(thm),theory(equality)],[c_1011,c_1109]) ).
tff(c_1142,plain,
! [Z_95a: $int] :
( ~ in(Z_95a,'#skF_1')
| ( Z_95a = 5 ) ),
inference(negUnitSimplification,[status(thm)],[c_75,c_1115]) ).
tff(c_1166,plain,
5 = 2,
inference(resolution,[status(thm)],[c_52,c_1142]) ).
tff(c_1169,plain,
$false,
inference(backgroundSimplification,[status(thm),theory('LIA')],[c_1166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : DAT037_1 : TPTP v9.0.0. Released v5.0.0.
% 0.04/0.12 % 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
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Apr 7 18:16:15 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.55/2.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.55/2.13
% 4.55/2.13 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------