TSTP Solution File: NUM556+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM556+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n021.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 10:52:06 EDT 2023
% Result : Theorem 10.65s 3.48s
% Output : CNFRefutation 10.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 59
% Syntax : Number of formulae : 112 ( 32 unt; 46 typ; 0 def)
% Number of atoms : 152 ( 30 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 139 ( 53 ~; 46 |; 25 &)
% ( 3 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 59 ( 34 >; 25 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 38 ( 38 usr; 12 con; 0-3 aty)
% Number of variables : 31 (; 31 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > slbdtsldtrb0 > sdtpldt0 > sdtmndt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > slbdtrb0 > sbrdtbr0 > xy > xx > xk > xT > xS > xQ > xP > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_16 > #skF_20 > #skF_18 > #skF_17 > #skF_6 > #skF_19 > #skF_1 > #skF_4 > #skF_12 > #skF_5 > #skF_10 > #skF_8 > #skF_15 > #skF_13 > #skF_14 > #skF_3 > #skF_2 > #skF_9
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xk,type,
xk: $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': $i > $i ).
tff(sbrdtbr0,type,
sbrdtbr0: $i > $i ).
tff('#skF_20',type,
'#skF_20': $i ).
tff(aSet0,type,
aSet0: $i > $o ).
tff(szszuzczcdt0,type,
szszuzczcdt0: $i > $i ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff('#skF_17',type,
'#skF_17': $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': $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(xP,type,
xP: $i ).
tff(xy,type,
xy: $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(slbdtsldtrb0,type,
slbdtsldtrb0: ( $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('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i ) > $i ).
tff(xT,type,
xT: $i ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i * $i ) > $i ).
tff(slcrc0,type,
slcrc0: $i ).
tff(isFinite0,type,
isFinite0: $i > $o ).
tff(xQ,type,
xQ: $i ).
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(szmzizndt0,type,
szmzizndt0: $i > $i ).
tff(szmzazxdt0,type,
szmzazxdt0: $i > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff(slbdtrb0,type,
slbdtrb0: $i > $i ).
tff(f_696,negated_conjecture,
~ ( ( ! [W0] :
( aElementOf0(W0,xP)
=> aElementOf0(W0,xS) )
| aSubsetOf0(xP,xS) )
& ( sbrdtbr0(xP) = xk ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_673,hypothesis,
( aSet0(sdtmndt0(xQ,xy))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xQ,xy))
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != xy ) ) )
& aSet0(xP)
& ! [W0] :
( aElementOf0(W0,xP)
<=> ( aElement0(W0)
& ( aElementOf0(W0,sdtmndt0(xQ,xy))
| ( W0 = xx ) ) ) )
& ( xP = sdtpldt0(sdtmndt0(xQ,xy),xx) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2357) ).
tff(f_645,hypothesis,
( aElement0(xy)
& aElementOf0(xy,xQ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2304) ).
tff(f_642,hypothesis,
( aSet0(xQ)
& isFinite0(xQ)
& ( sbrdtbr0(xQ) = xk ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2291) ).
tff(f_208,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( aSet0(W1)
& isFinite0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFDiffSet) ).
tff(f_526,hypothesis,
( aSet0(xS)
& aSet0(xT)
& ( xk != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
tff(f_625,hypothesis,
aElementOf0(xx,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2256) ).
tff(f_39,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(f_687,hypothesis,
( ~ aElementOf0(xx,sdtmndt0(xQ,xy))
& aSet0(sdtmndt0(xQ,xy))
& ! [W0] :
( aElementOf0(W0,sdtmndt0(xQ,xy))
<=> ( aElement0(W0)
& aElementOf0(W0,xQ)
& ( W0 != xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2411) ).
tff(f_199,axiom,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( aSet0(W1)
& isFinite0(W1) )
=> isFinite0(sdtpldt0(W1,W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mFConsSet) ).
tff(f_172,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aSet0(W1) )
=> ( ~ aElementOf0(W0,W1)
=> ( sdtmndt0(sdtpldt0(W1,W0),W0) = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDiffCons) ).
tff(f_351,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( ( isFinite0(W0)
& aElementOf0(W1,W0) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0,W1))) = sbrdtbr0(W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardDiff) ).
tff(f_637,hypothesis,
( aSet0(xQ)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xQ,xS)
& ( sbrdtbr0(xQ) = xk )
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
tff(c_378,plain,
( aElementOf0('#skF_20',xP)
| ( sbrdtbr0(xP) != xk ) ),
inference(cnfTransformation,[status(thm)],[f_696]) ).
tff(c_386,plain,
sbrdtbr0(xP) != xk,
inference(splitLeft,[status(thm)],[c_378]) ).
tff(c_342,plain,
aSet0(xP),
inference(cnfTransformation,[status(thm)],[f_673]) ).
tff(c_334,plain,
aElement0(xy),
inference(cnfTransformation,[status(thm)],[f_645]) ).
tff(c_330,plain,
aSet0(xQ),
inference(cnfTransformation,[status(thm)],[f_642]) ).
tff(c_328,plain,
isFinite0(xQ),
inference(cnfTransformation,[status(thm)],[f_642]) ).
tff(c_1712,plain,
! [W1_283,W0_284] :
( isFinite0(sdtmndt0(W1_283,W0_284))
| ~ isFinite0(W1_283)
| ~ aSet0(W1_283)
| ~ aElement0(W0_284) ),
inference(cnfTransformation,[status(thm)],[f_208]) ).
tff(c_352,plain,
( aElementOf0(xx,xP)
| ~ aElement0(xx) ),
inference(cnfTransformation,[status(thm)],[f_673]) ).
tff(c_402,plain,
~ aElement0(xx),
inference(splitLeft,[status(thm)],[c_352]) ).
tff(c_258,plain,
aSet0(xS),
inference(cnfTransformation,[status(thm)],[f_526]) ).
tff(c_314,plain,
aElementOf0(xx,xS),
inference(cnfTransformation,[status(thm)],[f_625]) ).
tff(c_583,plain,
! [W1_211,W0_212] :
( aElement0(W1_211)
| ~ aElementOf0(W1_211,W0_212)
| ~ aSet0(W0_212) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_598,plain,
( aElement0(xx)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_314,c_583]) ).
tff(c_622,plain,
aElement0(xx),
inference(demodulation,[status(thm),theory(equality)],[c_258,c_598]) ).
tff(c_624,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_402,c_622]) ).
tff(c_626,plain,
aElement0(xx),
inference(splitRight,[status(thm)],[c_352]) ).
tff(c_364,plain,
aSet0(sdtmndt0(xQ,xy)),
inference(cnfTransformation,[status(thm)],[f_687]) ).
tff(c_340,plain,
sdtpldt0(sdtmndt0(xQ,xy),xx) = xP,
inference(cnfTransformation,[status(thm)],[f_673]) ).
tff(c_1608,plain,
! [W1_274,W0_275] :
( isFinite0(sdtpldt0(W1_274,W0_275))
| ~ isFinite0(W1_274)
| ~ aSet0(W1_274)
| ~ aElement0(W0_275) ),
inference(cnfTransformation,[status(thm)],[f_199]) ).
tff(c_1614,plain,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ aElement0(xx) ),
inference(superposition,[status(thm),theory(equality)],[c_340,c_1608]) ).
tff(c_1617,plain,
( isFinite0(xP)
| ~ isFinite0(sdtmndt0(xQ,xy)) ),
inference(demodulation,[status(thm),theory(equality)],[c_626,c_364,c_1614]) ).
tff(c_1618,plain,
~ isFinite0(sdtmndt0(xQ,xy)),
inference(splitLeft,[status(thm)],[c_1617]) ).
tff(c_1715,plain,
( ~ isFinite0(xQ)
| ~ aSet0(xQ)
| ~ aElement0(xy) ),
inference(resolution,[status(thm)],[c_1712,c_1618]) ).
tff(c_1722,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_334,c_330,c_328,c_1715]) ).
tff(c_1723,plain,
isFinite0(xP),
inference(splitRight,[status(thm)],[c_1617]) ).
tff(c_625,plain,
aElementOf0(xx,xP),
inference(splitRight,[status(thm)],[c_352]) ).
tff(c_332,plain,
aElementOf0(xy,xQ),
inference(cnfTransformation,[status(thm)],[f_645]) ).
tff(c_326,plain,
sbrdtbr0(xQ) = xk,
inference(cnfTransformation,[status(thm)],[f_642]) ).
tff(c_366,plain,
~ aElementOf0(xx,sdtmndt0(xQ,xy)),
inference(cnfTransformation,[status(thm)],[f_687]) ).
tff(c_6865,plain,
! [W1_480,W0_481] :
( ( sdtmndt0(sdtpldt0(W1_480,W0_481),W0_481) = W1_480 )
| aElementOf0(W0_481,W1_480)
| ~ aSet0(W1_480)
| ~ aElement0(W0_481) ),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_6898,plain,
( ( sdtmndt0(xQ,xy) = sdtmndt0(xP,xx) )
| aElementOf0(xx,sdtmndt0(xQ,xy))
| ~ aSet0(sdtmndt0(xQ,xy))
| ~ aElement0(xx) ),
inference(superposition,[status(thm),theory(equality)],[c_340,c_6865]) ).
tff(c_6904,plain,
( ( sdtmndt0(xQ,xy) = sdtmndt0(xP,xx) )
| aElementOf0(xx,sdtmndt0(xQ,xy)) ),
inference(demodulation,[status(thm),theory(equality)],[c_626,c_364,c_6898]) ).
tff(c_6905,plain,
sdtmndt0(xQ,xy) = sdtmndt0(xP,xx),
inference(negUnitSimplification,[status(thm)],[c_366,c_6904]) ).
tff(c_7218,plain,
! [W0_491,W1_492] :
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0_491,W1_492))) = sbrdtbr0(W0_491) )
| ~ aElementOf0(W1_492,W0_491)
| ~ isFinite0(W0_491)
| ~ aSet0(W0_491) ),
inference(cnfTransformation,[status(thm)],[f_351]) ).
tff(c_7267,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,xx))) = sbrdtbr0(xQ) )
| ~ aElementOf0(xy,xQ)
| ~ isFinite0(xQ)
| ~ aSet0(xQ) ),
inference(superposition,[status(thm),theory(equality)],[c_6905,c_7218]) ).
tff(c_7274,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xP,xx))) = xk,
inference(demodulation,[status(thm),theory(equality)],[c_330,c_328,c_332,c_326,c_7267]) ).
tff(c_160,plain,
! [W0_102,W1_104] :
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(W0_102,W1_104))) = sbrdtbr0(W0_102) )
| ~ aElementOf0(W1_104,W0_102)
| ~ isFinite0(W0_102)
| ~ aSet0(W0_102) ),
inference(cnfTransformation,[status(thm)],[f_351]) ).
tff(c_7278,plain,
( ( sbrdtbr0(xP) = xk )
| ~ aElementOf0(xx,xP)
| ~ isFinite0(xP)
| ~ aSet0(xP) ),
inference(superposition,[status(thm),theory(equality)],[c_7274,c_160]) ).
tff(c_7325,plain,
sbrdtbr0(xP) = xk,
inference(demodulation,[status(thm),theory(equality)],[c_342,c_1723,c_625,c_7278]) ).
tff(c_7327,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_386,c_7325]) ).
tff(c_7329,plain,
sbrdtbr0(xP) = xk,
inference(splitRight,[status(thm)],[c_378]) ).
tff(c_376,plain,
( ~ aElementOf0('#skF_20',xS)
| ( sbrdtbr0(xP) != xk ) ),
inference(cnfTransformation,[status(thm)],[f_696]) ).
tff(c_7339,plain,
~ aElementOf0('#skF_20',xS),
inference(demodulation,[status(thm),theory(equality)],[c_7329,c_376]) ).
tff(c_7328,plain,
aElementOf0('#skF_20',xP),
inference(splitRight,[status(thm)],[c_378]) ).
tff(c_8679,plain,
! [W0_591] :
( ( xx = W0_591 )
| aElementOf0(W0_591,sdtmndt0(xQ,xy))
| ~ aElementOf0(W0_591,xP) ),
inference(cnfTransformation,[status(thm)],[f_673]) ).
tff(c_370,plain,
! [W0_187] :
( aElementOf0(W0_187,xQ)
| ~ aElementOf0(W0_187,sdtmndt0(xQ,xy)) ),
inference(cnfTransformation,[status(thm)],[f_687]) ).
tff(c_8722,plain,
! [W0_594] :
( aElementOf0(W0_594,xQ)
| ( xx = W0_594 )
| ~ aElementOf0(W0_594,xP) ),
inference(resolution,[status(thm)],[c_8679,c_370]) ).
tff(c_7590,plain,
! [W0_524] :
( aElementOf0(W0_524,xS)
| ~ aElementOf0(W0_524,xQ) ),
inference(cnfTransformation,[status(thm)],[f_637]) ).
tff(c_7594,plain,
~ aElementOf0('#skF_20',xQ),
inference(resolution,[status(thm)],[c_7590,c_7339]) ).
tff(c_8731,plain,
( ( xx = '#skF_20' )
| ~ aElementOf0('#skF_20',xP) ),
inference(resolution,[status(thm)],[c_8722,c_7594]) ).
tff(c_8741,plain,
xx = '#skF_20',
inference(demodulation,[status(thm),theory(equality)],[c_7328,c_8731]) ).
tff(c_8752,plain,
aElementOf0('#skF_20',xS),
inference(demodulation,[status(thm),theory(equality)],[c_8741,c_314]) ).
tff(c_8757,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_7339,c_8752]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM556+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 14:39:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 10.65/3.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.65/3.49
% 10.65/3.49 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.65/3.52
% 10.65/3.52 Inference rules
% 10.65/3.52 ----------------------
% 10.65/3.52 #Ref : 2
% 10.65/3.52 #Sup : 1582
% 10.65/3.52 #Fact : 0
% 10.65/3.52 #Define : 0
% 10.65/3.52 #Split : 92
% 10.65/3.52 #Chain : 0
% 10.65/3.52 #Close : 0
% 10.65/3.52
% 10.65/3.52 Ordering : KBO
% 10.65/3.52
% 10.65/3.52 Simplification rules
% 10.65/3.52 ----------------------
% 10.65/3.52 #Subsume : 296
% 10.65/3.52 #Demod : 1552
% 10.65/3.52 #Tautology : 533
% 10.65/3.52 #SimpNegUnit : 131
% 10.65/3.52 #BackRed : 182
% 10.65/3.52
% 10.65/3.52 #Partial instantiations: 0
% 10.65/3.52 #Strategies tried : 1
% 10.65/3.52
% 10.65/3.52 Timing (in seconds)
% 10.65/3.52 ----------------------
% 10.65/3.52 Preprocessing : 0.74
% 10.65/3.52 Parsing : 0.37
% 10.65/3.52 CNF conversion : 0.07
% 10.65/3.52 Main loop : 1.74
% 10.65/3.52 Inferencing : 0.57
% 10.65/3.52 Reduction : 0.61
% 10.65/3.52 Demodulation : 0.40
% 10.65/3.52 BG Simplification : 0.07
% 10.65/3.52 Subsumption : 0.37
% 10.65/3.52 Abstraction : 0.05
% 10.65/3.52 MUC search : 0.00
% 10.65/3.52 Cooper : 0.00
% 10.65/3.52 Total : 2.54
% 10.65/3.52 Index Insertion : 0.00
% 10.65/3.52 Index Deletion : 0.00
% 10.65/3.52 Index Matching : 0.00
% 10.65/3.52 BG Taut test : 0.00
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