%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM538+1 : TPTP v9.0.0. Released v4.0.0.
% 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 : n020.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 07:56:18 PM UTC 2025
% Result : Theorem 6.43s 2.46s
% Output : CNFRefutation 6.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 13 unt; 0 typ; 1 def)
% Number of atoms : 84 ( 11 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 92 ( 41 ~; 32 |; 7 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 27 ( 27 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > sdtpldt0 > sdtmndt0 > #nlpp > szszuzczcdt0 > sbrdtbr0 > xx > xS > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_6 > #skF_1 > #skF_4 > #skF_5 > #skF_3 > #skF_2
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(sbrdtbr0,type,
sbrdtbr0: $i > $i ).
tff(aSet0,type,
aSet0: $i > $o ).
tff(szszuzczcdt0,type,
szszuzczcdt0: $i > $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(sdtmndt0,type,
sdtmndt0: ( $i * $i ) > $i ).
tff('#skF_1',type,
'#skF_1': $i > $i ).
tff(aElement0,type,
aElement0: $i > $o ).
tff(szNzAzT0,type,
szNzAzT0: $i ).
tff(sdtlseqdt0,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xS,type,
xS: $i ).
tff(sz00,type,
sz00: $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xx,type,
xx: $i ).
tff(aSubsetOf0,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff(isCountable0,type,
isCountable0: $i > $o ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slcrc0,type,
slcrc0: $i ).
tff(isFinite0,type,
isFinite0: $i > $o ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff(f_343,hypothesis,
aSet0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1522) ).
tff(f_346,hypothesis,
( isFinite0(xS)
& aElementOf0(xx,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1522_02) ).
tff(f_39,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
tff(f_163,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
tff(f_208,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( aSet0(W1)
& isFinite0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFDiffSet) ).
tff(f_156,definition,
! [W0,W1] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
tff(f_342,axiom,
! [W0] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardCons) ).
tff(f_348,negated_conjecture,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(c_160,plain,
aSet0(xS),
inference(cnfTransformation,[status(thm)],[f_343]) ).
tff(c_162,plain,
aElementOf0(xx,xS),
inference(cnfTransformation,[status(thm)],[f_346]) ).
tff(c_208,plain,
! [W1_110,W0_111] :
( aElement0(W1_110)
| ~ aElementOf0(W1_110,W0_111)
| ~ aSet0(W0_111) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_214,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_162,c_208]) ).
tff(c_220,plain,
aElement0(xx),
inference(demodulation,[status(thm),theory(equality)],[c_160,c_214]) ).
tff(c_94,plain,
! [W0_55,W1_57] :
( ( sdtpldt0(sdtmndt0(W0_55,W1_57),W1_57) = W0_55 )
| ~ aElementOf0(W1_57,W0_55)
| ~ aSet0(W0_55) ),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_164,plain,
isFinite0(xS),
inference(cnfTransformation,[status(thm)],[f_346]) ).
tff(c_104,plain,
! [W1_71,W0_69] :
( isFinite0(sdtmndt0(W1_71,W0_69))
| ~ isFinite0(W1_71)
| ~ aSet0(W1_71)
| ~ aElement0(W0_69) ),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_70,plain,
! [W0_44,W1_45] :
( aSet0(sdtmndt0(W0_44,W1_45))
| ~ aElement0(W1_45)
| ~ aSet0(W0_44) ),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_1291,plain,
! [W0_227,W1_228] :
( ( szszuzczcdt0(sbrdtbr0(W0_227)) = sbrdtbr0(sdtpldt0(W0_227,W1_228)) )
| aElementOf0(W1_228,W0_227)
| ~ aElement0(W1_228)
| ~ isFinite0(W0_227)
| ~ aSet0(W0_227) ),
inference(cnfTransformation,[status(thm)],[f_342]) ).
tff(c_166,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(cnfTransformation,[status(thm)],[f_348]) ).
tff(c_1376,plain,
! [W1_228] :
( ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1_228)) != sbrdtbr0(xS) )
| aElementOf0(W1_228,sdtmndt0(xS,xx))
| ~ aElement0(W1_228)
| ~ isFinite0(sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(superposition,[status(thm),theory(equality)],[c_1291,c_166]) ).
tff(c_1583,plain,
~ aSet0(sdtmndt0(xS,xx)),
inference(splitLeft,[status(thm)],[c_1376]) ).
tff(c_1586,plain,
( ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_70,c_1583]) ).
tff(c_1590,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_160,c_220,c_1586]) ).
tff(c_1591,plain,
! [W1_228] :
( ~ isFinite0(sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1_228)) != sbrdtbr0(xS) )
| aElementOf0(W1_228,sdtmndt0(xS,xx))
| ~ aElement0(W1_228) ),
inference(splitRight,[status(thm)],[c_1376]) ).
tff(c_1664,plain,
~ isFinite0(sdtmndt0(xS,xx)),
inference(splitLeft,[status(thm)],[c_1591]) ).
tff(c_1667,plain,
( ~ isFinite0(xS)
| ~ aSet0(xS)
| ~ aElement0(xx) ),
inference(resolution,[status(thm)],[c_104,c_1664]) ).
tff(c_1671,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_220,c_160,c_164,c_1667]) ).
tff(c_1794,plain,
! [W1_250] :
( ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1_250)) != sbrdtbr0(xS) )
| aElementOf0(W1_250,sdtmndt0(xS,xx))
| ~ aElement0(W1_250) ),
inference(splitRight,[status(thm)],[c_1591]) ).
tff(c_1802,plain,
( aElementOf0(xx,sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ~ aElementOf0(xx,xS)
| ~ aSet0(xS) ),
inference(superposition,[status(thm),theory(equality)],[c_94,c_1794]) ).
tff(c_1807,plain,
aElementOf0(xx,sdtmndt0(xS,xx)),
inference(demodulation,[status(thm),theory(equality)],[c_160,c_162,c_220,c_1802]) ).
tff(c_72,plain,
! [W3_54,W0_44] :
( ~ aElementOf0(W3_54,sdtmndt0(W0_44,W3_54))
| ~ aElement0(W3_54)
| ~ aSet0(W0_44) ),
inference(cnfTransformation,[status(thm)],[f_156]) ).
tff(c_1818,plain,
( ~ aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_1807,c_72]) ).
tff(c_1832,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_160,c_220,c_1818]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : NUM538+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.16 % 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
% 0.14/0.39 % Computer : n020.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8042.1875MB
% 0.14/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Tue Apr 8 13:23:34 EDT 2025
% 0.14/0.39 % CPUTime :
% 6.43/2.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.43/2.46
% 6.43/2.46 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------