%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM538+2 : 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 : n004.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 6.39s 2.54s
% Output : CNFRefutation 6.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 12 unt; 0 typ; 1 def)
% Number of atoms : 92 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 96 ( 38 ~; 37 |; 7 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 29 ( 29 !; 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_360,negated_conjecture,
~ ( ( aSet0(sdtmndt0(xS,xx))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) ) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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_84,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
tff(f_93,axiom,
! [W0] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> isFinite0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubFSet) ).
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(c_172,plain,
~ aElementOf0(xx,sdtmndt0(xS,xx)),
inference(cnfTransformation,[status(thm)],[f_360]) ).
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_256,plain,
! [W1_117,W0_118] :
( aElement0(W1_117)
| ~ aElementOf0(W1_117,W0_118)
| ~ aSet0(W0_118) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_262,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_162,c_256]) ).
tff(c_271,plain,
aElement0(xx),
inference(demodulation,[status(thm),theory(equality)],[c_160,c_262]) ).
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_170,plain,
aSet0(sdtmndt0(xS,xx)),
inference(cnfTransformation,[status(thm)],[f_360]) ).
tff(c_164,plain,
isFinite0(xS),
inference(cnfTransformation,[status(thm)],[f_346]) ).
tff(c_776,plain,
! [W0_182,W1_183] :
( aElementOf0('#skF_2'(W0_182,W1_183),W1_183)
| aSubsetOf0(W1_183,W0_182)
| ~ aSet0(W1_183)
| ~ aSet0(W0_182) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_174,plain,
! [W0_102] :
( aElementOf0(W0_102,xS)
| ~ aElementOf0(W0_102,sdtmndt0(xS,xx)) ),
inference(cnfTransformation,[status(thm)],[f_360]) ).
tff(c_798,plain,
! [W0_182] :
( aElementOf0('#skF_2'(W0_182,sdtmndt0(xS,xx)),xS)
| aSubsetOf0(sdtmndt0(xS,xx),W0_182)
| ~ aSet0(sdtmndt0(xS,xx))
| ~ aSet0(W0_182) ),
inference(resolution,[status(thm)],[c_776,c_174]) ).
tff(c_1395,plain,
! [W0_220] :
( aElementOf0('#skF_2'(W0_220,sdtmndt0(xS,xx)),xS)
| aSubsetOf0(sdtmndt0(xS,xx),W0_220)
| ~ aSet0(W0_220) ),
inference(demodulation,[status(thm),theory(equality)],[c_170,c_798]) ).
tff(c_28,plain,
! [W0_14,W1_20] :
( ~ aElementOf0('#skF_2'(W0_14,W1_20),W0_14)
| aSubsetOf0(W1_20,W0_14)
| ~ aSet0(W1_20)
| ~ aSet0(W0_14) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_1399,plain,
( ~ aSet0(sdtmndt0(xS,xx))
| aSubsetOf0(sdtmndt0(xS,xx),xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_1395,c_28]) ).
tff(c_1407,plain,
aSubsetOf0(sdtmndt0(xS,xx),xS),
inference(demodulation,[status(thm),theory(equality)],[c_160,c_170,c_1399]) ).
tff(c_32,plain,
! [W1_26,W0_24] :
( isFinite0(W1_26)
| ~ aSubsetOf0(W1_26,W0_24)
| ~ isFinite0(W0_24)
| ~ aSet0(W0_24) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_1420,plain,
( isFinite0(sdtmndt0(xS,xx))
| ~ isFinite0(xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_1407,c_32]) ).
tff(c_1435,plain,
isFinite0(sdtmndt0(xS,xx)),
inference(demodulation,[status(thm),theory(equality)],[c_160,c_164,c_1420]) ).
tff(c_2371,plain,
! [W0_269,W1_270] :
( ( szszuzczcdt0(sbrdtbr0(W0_269)) = sbrdtbr0(sdtpldt0(W0_269,W1_270)) )
| aElementOf0(W1_270,W0_269)
| ~ aElement0(W1_270)
| ~ isFinite0(W0_269)
| ~ aSet0(W0_269) ),
inference(cnfTransformation,[status(thm)],[f_342]) ).
tff(c_166,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(cnfTransformation,[status(thm)],[f_360]) ).
tff(c_2453,plain,
! [W1_270] :
( ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1_270)) != sbrdtbr0(xS) )
| aElementOf0(W1_270,sdtmndt0(xS,xx))
| ~ aElement0(W1_270)
| ~ isFinite0(sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx)) ),
inference(superposition,[status(thm),theory(equality)],[c_2371,c_166]) ).
tff(c_2536,plain,
! [W1_273] :
( ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1_273)) != sbrdtbr0(xS) )
| aElementOf0(W1_273,sdtmndt0(xS,xx))
| ~ aElement0(W1_273) ),
inference(demodulation,[status(thm),theory(equality)],[c_170,c_1435,c_2453]) ).
tff(c_2544,plain,
( aElementOf0(xx,sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ~ aElementOf0(xx,xS)
| ~ aSet0(xS) ),
inference(superposition,[status(thm),theory(equality)],[c_94,c_2536]) ).
tff(c_2549,plain,
aElementOf0(xx,sdtmndt0(xS,xx)),
inference(demodulation,[status(thm),theory(equality)],[c_160,c_162,c_271,c_2544]) ).
tff(c_2551,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_172,c_2549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : NUM538+2 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.15 % 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
% 0.15/0.36 % Computer : n004.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 8 13:24:37 EDT 2025
% 0.15/0.37 % CPUTime :
% 6.39/2.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.39/2.54
% 6.39/2.54 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------