TSTP Solution File: NUM574+3 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM574+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 : n005.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 10:52:11 EDT 2023
% Result : Theorem 79.29s 62.15s
% Output : CNFRefutation 79.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 80
% Syntax : Number of formulae : 110 ( 19 unt; 72 typ; 0 def)
% Number of atoms : 103 ( 25 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 96 ( 31 ~; 29 |; 21 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 127 ( 60 >; 67 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 63 ( 63 usr; 12 con; 0-4 aty)
% Number of variables : 23 (; 21 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aFunction0 > aElement0 > slbdtsldtrb0 > sdtpldt0 > sdtmndt0 > sdtlpdtrp0 > sdtlcdtrc0 > sdtlbdtrb0 > sdtexdt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > szDzozmdt0 > szDzizrdt0 > slbdtrb0 > sbrdtbr0 > xk > xj > xi > xc > xT > xS > xN > xK > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_17 > #skF_31 > #skF_33 > #skF_6 > #skF_1 > #skF_18 > #skF_38 > #skF_37 > #skF_4 > #skF_29 > #skF_12 > #skF_30 > #skF_32 > #skF_23 > #skF_35 > #skF_5 > #skF_19 > #skF_10 > #skF_8 > #skF_20 > #skF_28 > #skF_26 > #skF_24 > #skF_34 > #skF_15 > #skF_13 > #skF_14 > #skF_25 > #skF_3 > #skF_2 > #skF_27 > #skF_36 > #skF_21 > #skF_9 > #skF_22 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xk,type,
xk: $i ).
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff(xj,type,
xj: $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(sbrdtbr0,type,
sbrdtbr0: $i > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i * $i ) > $i ).
tff('#skF_31',type,
'#skF_31': ( $i * $i * $i ) > $i ).
tff('#skF_33',type,
'#skF_33': ( $i * $i * $i ) > $i ).
tff(aSet0,type,
aSet0: $i > $o ).
tff(szszuzczcdt0,type,
szszuzczcdt0: $i > $i ).
tff(sdtlbdtrb0,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzozmdt0,type,
szDzozmdt0: $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('#skF_18',type,
'#skF_18': ( $i * $i * $i ) > $i ).
tff(aElement0,type,
aElement0: $i > $o ).
tff(sdtexdt0,type,
sdtexdt0: ( $i * $i ) > $i ).
tff('#skF_38',type,
'#skF_38': $i ).
tff('#skF_37',type,
'#skF_37': $i > $i ).
tff(xi,type,
xi: $i ).
tff(szNzAzT0,type,
szNzAzT0: $i ).
tff(sdtlseqdt0,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xS,type,
xS: $i ).
tff(sz00,type,
sz00: $i ).
tff(sdtlpdtrp0,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff(xc,type,
xc: $i ).
tff('#skF_29',type,
'#skF_29': ( $i * $i * $i ) > $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff('#skF_30',type,
'#skF_30': ( $i * $i * $i ) > $i ).
tff(slbdtsldtrb0,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff('#skF_32',type,
'#skF_32': ( $i * $i * $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i * $i ) > $i ).
tff('#skF_35',type,
'#skF_35': ( $i * $i * $i ) > $i ).
tff(aSubsetOf0,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $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(xN,type,
xN: $i ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff('#skF_20',type,
'#skF_20': ( $i * $i * $i ) > $i ).
tff(szDzizrdt0,type,
szDzizrdt0: $i > $i ).
tff('#skF_28',type,
'#skF_28': ( $i * $i ) > $i ).
tff('#skF_26',type,
'#skF_26': $i > $i ).
tff('#skF_24',type,
'#skF_24': ( $i * $i ) > $i ).
tff('#skF_34',type,
'#skF_34': ( $i * $i * $i ) > $i ).
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(aFunction0,type,
aFunction0: $i > $o ).
tff(isFinite0,type,
isFinite0: $i > $o ).
tff('#skF_25',type,
'#skF_25': ( $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(sdtlcdtrc0,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff('#skF_27',type,
'#skF_27': $i > $i ).
tff(szmzizndt0,type,
szmzizndt0: $i > $i ).
tff('#skF_36',type,
'#skF_36': ( $i * $i * $i * $i ) > $i ).
tff(szmzazxdt0,type,
szmzazxdt0: $i > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i * $i ) > $i ).
tff(xK,type,
xK: $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff(slbdtrb0,type,
slbdtrb0: $i > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i * $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(f_873,hypothesis,
( aFunction0(xN)
& ( szDzozmdt0(xN) = szNzAzT0 )
& ( sdtlpdtrp0(xN,sz00) = xS )
& ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ( ( ( aSet0(sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> aElementOf0(W1,szNzAzT0) ) )
| aSubsetOf0(sdtlpdtrp0(xN,W0),szNzAzT0) )
& isCountable0(sdtlpdtrp0(xN,W0)) )
=> ( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,W0)),sdtlpdtrp0(xN,W0))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,W0))
=> sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,W0)),W1) )
& aSet0(sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& ! [W1] :
( aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
<=> ( aElement0(W1)
& aElementOf0(W1,sdtlpdtrp0(xN,W0))
& ( W1 != szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
=> aElementOf0(W1,sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0)))) )
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),sdtmndt0(sdtlpdtrp0(xN,W0),szmzizndt0(sdtlpdtrp0(xN,W0))))
& isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3623) ).
tff(f_889,hypothesis,
( aElementOf0(xj,szNzAzT0)
& aElementOf0(xi,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786) ).
tff(f_236,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( ( W0 = sz00 )
| ? [W1] :
( aElementOf0(W1,szNzAzT0)
& ( W0 = szszuzczcdt0(W1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
tff(f_928,negated_conjecture,
~ ( sdtlseqdt0(xj,xi)
=> ( ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,sdtlpdtrp0(xN,xj)) )
| aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_919,hypothesis,
( ( sdtlseqdt0(xj,xi)
& ? [W0] :
( aElementOf0(W0,szNzAzT0)
& ( szszuzczcdt0(W0) = xi ) ) )
=> ( sdtlseqdt0(xj,xi)
=> ( ! [W0] :
( aElementOf0(W0,sdtlpdtrp0(xN,xi))
=> aElementOf0(W0,sdtlpdtrp0(xN,xj)) )
& aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3786_02) ).
tff(f_252,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sdtlseqdt0(sz00,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
tff(f_212,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
tff(f_283,axiom,
! [W0,W1] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
tff(c_8322,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(cnfTransformation,[status(thm)],[f_873]) ).
tff(c_8402,plain,
aElementOf0(xi,szNzAzT0),
inference(cnfTransformation,[status(thm)],[f_889]) ).
tff(c_118,plain,
! [W0_75] :
( ( szszuzczcdt0('#skF_7'(W0_75)) = W0_75 )
| ( sz00 = W0_75 )
| ~ aElementOf0(W0_75,szNzAzT0) ),
inference(cnfTransformation,[status(thm)],[f_236]) ).
tff(c_9169,plain,
! [W0_649] :
( aElementOf0('#skF_7'(W0_649),szNzAzT0)
| ( sz00 = W0_649 )
| ~ aElementOf0(W0_649,szNzAzT0) ),
inference(cnfTransformation,[status(thm)],[f_236]) ).
tff(c_8414,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj)),
inference(cnfTransformation,[status(thm)],[f_928]) ).
tff(c_8420,plain,
sdtlseqdt0(xj,xi),
inference(cnfTransformation,[status(thm)],[f_928]) ).
tff(c_8410,plain,
! [W0_588] :
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ( szszuzczcdt0(W0_588) != xi )
| ~ aElementOf0(W0_588,szNzAzT0)
| ~ sdtlseqdt0(xj,xi) ),
inference(cnfTransformation,[status(thm)],[f_919]) ).
tff(c_8424,plain,
! [W0_588] :
( aSubsetOf0(sdtlpdtrp0(xN,xi),sdtlpdtrp0(xN,xj))
| ( szszuzczcdt0(W0_588) != xi )
| ~ aElementOf0(W0_588,szNzAzT0) ),
inference(demodulation,[status(thm),theory(equality)],[c_8420,c_8410]) ).
tff(c_8425,plain,
! [W0_588] :
( ( szszuzczcdt0(W0_588) != xi )
| ~ aElementOf0(W0_588,szNzAzT0) ),
inference(negUnitSimplification,[status(thm)],[c_8414,c_8424]) ).
tff(c_9338,plain,
! [W0_657] :
( ( szszuzczcdt0('#skF_7'(W0_657)) != xi )
| ( sz00 = W0_657 )
| ~ aElementOf0(W0_657,szNzAzT0) ),
inference(resolution,[status(thm)],[c_9169,c_8425]) ).
tff(c_9373,plain,
! [W0_663] :
( ( xi != W0_663 )
| ( sz00 = W0_663 )
| ~ aElementOf0(W0_663,szNzAzT0)
| ( sz00 = W0_663 )
| ~ aElementOf0(W0_663,szNzAzT0) ),
inference(superposition,[status(thm),theory(equality)],[c_118,c_9338]) ).
tff(c_9401,plain,
( ( xi = sz00 )
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolution,[status(thm)],[c_8402,c_9373]) ).
tff(c_9436,plain,
xi = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_8402,c_9401]) ).
tff(c_8418,plain,
aElementOf0('#skF_38',sdtlpdtrp0(xN,xi)),
inference(cnfTransformation,[status(thm)],[f_928]) ).
tff(c_9457,plain,
aElementOf0('#skF_38',sdtlpdtrp0(xN,sz00)),
inference(demodulation,[status(thm),theory(equality)],[c_9436,c_8418]) ).
tff(c_9464,plain,
aElementOf0('#skF_38',xS),
inference(demodulation,[status(thm),theory(equality)],[c_8322,c_9457]) ).
tff(c_8404,plain,
aElementOf0(xj,szNzAzT0),
inference(cnfTransformation,[status(thm)],[f_889]) ).
tff(c_126,plain,
! [W0_80] :
( sdtlseqdt0(sz00,W0_80)
| ~ aElementOf0(W0_80,szNzAzT0) ),
inference(cnfTransformation,[status(thm)],[f_252]) ).
tff(c_110,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_9459,plain,
sdtlseqdt0(xj,sz00),
inference(demodulation,[status(thm),theory(equality)],[c_9436,c_8420]) ).
tff(c_13678,plain,
! [W1_880,W0_881] :
( ( W1_880 = W0_881 )
| ~ sdtlseqdt0(W1_880,W0_881)
| ~ sdtlseqdt0(W0_881,W1_880)
| ~ aElementOf0(W1_880,szNzAzT0)
| ~ aElementOf0(W0_881,szNzAzT0) ),
inference(cnfTransformation,[status(thm)],[f_283]) ).
tff(c_13714,plain,
( ( xj = sz00 )
| ~ sdtlseqdt0(sz00,xj)
| ~ aElementOf0(xj,szNzAzT0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(resolution,[status(thm)],[c_9459,c_13678]) ).
tff(c_13768,plain,
( ( xj = sz00 )
| ~ sdtlseqdt0(sz00,xj) ),
inference(demodulation,[status(thm),theory(equality)],[c_110,c_8404,c_13714]) ).
tff(c_13787,plain,
~ sdtlseqdt0(sz00,xj),
inference(splitLeft,[status(thm)],[c_13768]) ).
tff(c_13790,plain,
~ aElementOf0(xj,szNzAzT0),
inference(resolution,[status(thm)],[c_126,c_13787]) ).
tff(c_13794,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8404,c_13790]) ).
tff(c_13795,plain,
xj = sz00,
inference(splitRight,[status(thm)],[c_13768]) ).
tff(c_8416,plain,
~ aElementOf0('#skF_38',sdtlpdtrp0(xN,xj)),
inference(cnfTransformation,[status(thm)],[f_928]) ).
tff(c_13804,plain,
~ aElementOf0('#skF_38',sdtlpdtrp0(xN,sz00)),
inference(demodulation,[status(thm),theory(equality)],[c_13795,c_8416]) ).
tff(c_13811,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_9464,c_8322,c_13804]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM574+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % 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
% 0.15/0.35 % Computer : n005.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 14:44:57 EDT 2023
% 0.15/0.35 % CPUTime :
% 79.29/62.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 79.29/62.16
% 79.29/62.16 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 79.29/62.19
% 79.29/62.19 Inference rules
% 79.29/62.19 ----------------------
% 79.29/62.19 #Ref : 1
% 79.29/62.19 #Sup : 1024
% 79.29/62.19 #Fact : 0
% 79.29/62.19 #Define : 0
% 79.29/62.19 #Split : 49
% 79.29/62.19 #Chain : 0
% 79.29/62.19 #Close : 0
% 79.29/62.19
% 79.29/62.19 Ordering : KBO
% 79.29/62.19
% 79.29/62.19 Simplification rules
% 79.29/62.19 ----------------------
% 79.29/62.19 #Subsume : 777
% 79.29/62.19 #Demod : 822
% 79.29/62.19 #Tautology : 248
% 79.29/62.19 #SimpNegUnit : 44
% 79.29/62.19 #BackRed : 94
% 79.29/62.19
% 79.29/62.19 #Partial instantiations: 0
% 79.29/62.19 #Strategies tried : 1
% 79.29/62.19
% 79.29/62.19 Timing (in seconds)
% 79.29/62.19 ----------------------
% 79.29/62.19 Preprocessing : 2.02
% 79.29/62.19 Parsing : 0.43
% 79.29/62.19 CNF conversion : 0.16
% 79.29/62.19 Main loop : 59.11
% 79.29/62.19 Inferencing : 0.45
% 79.29/62.19 Reduction : 43.16
% 79.29/62.19 Demodulation : 37.00
% 79.29/62.19 BG Simplification : 0.66
% 79.29/62.19 Subsumption : 12.85
% 79.29/62.19 Abstraction : 0.49
% 79.29/62.19 MUC search : 0.00
% 79.29/62.19 Cooper : 0.00
% 79.29/62.19 Total : 61.19
% 79.29/62.19 Index Insertion : 0.00
% 79.29/62.19 Index Deletion : 0.00
% 79.29/62.19 Index Matching : 0.00
% 79.29/62.19 BG Taut test : 0.00
%------------------------------------------------------------------------------