TSTP Solution File: NUM545+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM545+1 : 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 : n015.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 10:52:04 EDT 2023
% Result : Theorem 11.62s 3.72s
% Output : CNFRefutation 11.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 44
% Syntax : Number of formulae : 86 ( 28 unt; 31 typ; 3 def)
% Number of atoms : 107 ( 25 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 97 ( 45 ~; 29 |; 10 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 27 >; 20 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 4 con; 0-3 aty)
% Number of variables : 26 (; 24 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > aSubsetOf0 > aElementOf0 > isFinite0 > isCountable0 > aSet0 > aElement0 > sdtpldt0 > sdtmndt0 > #nlpp > szszuzczcdt0 > szmzizndt0 > szmzazxdt0 > slbdtrb0 > sbrdtbr0 > xS > szNzAzT0 > sz00 > slcrc0 > #skF_7 > #skF_11 > #skF_6 > #skF_1 > #skF_4 > #skF_12 > #skF_5 > #skF_10 > #skF_8 > #skF_3 > #skF_2 > #skF_9
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_7',type,
'#skF_7': $i > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $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('#skF_12',type,
'#skF_12': ( $i * $i ) > $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $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(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(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_52,definition,
! [W0] :
( ( W0 = slcrc0 )
<=> ( aSet0(W0)
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
tff(f_97,axiom,
! [W0] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
tff(f_330,axiom,
! [W0] :
( aSet0(W0)
=> ( ( sbrdtbr0(W0) = sz00 )
<=> ( W0 = slcrc0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCardEmpty) ).
tff(f_465,hypothesis,
( ( xS != slcrc0 )
=> aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2035) ).
tff(f_461,hypothesis,
( aSubsetOf0(xS,szNzAzT0)
& isFinite0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1986) ).
tff(f_65,axiom,
! [W0] :
( ( aSet0(W0)
& isCountable0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCountNFin) ).
tff(f_211,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(f_84,definition,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
tff(f_405,definition,
! [W0] :
( ( aSubsetOf0(W0,szNzAzT0)
& isFinite0(W0)
& ( W0 != slcrc0 ) )
=> ! [W1] :
( ( W1 = szmzazxdt0(W0) )
<=> ( aElementOf0(W1,W0)
& ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W2,W1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefMax) ).
tff(f_219,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
tff(f_470,negated_conjecture,
~ ? [W0] :
( aElementOf0(W0,szNzAzT0)
& aSubsetOf0(xS,slbdtrb0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_212,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
tff(f_440,axiom,
slbdtrb0(sz00) = slcrc0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSegZero) ).
tff(c_14,plain,
aSet0(slcrc0),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_34,plain,
! [W0_27] :
( aSubsetOf0(W0_27,W0_27)
| ~ aSet0(W0_27) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_154,plain,
( ( sbrdtbr0(slcrc0) = sz00 )
| ~ aSet0(slcrc0) ),
inference(cnfTransformation,[status(thm)],[f_330]) ).
tff(c_228,plain,
sbrdtbr0(slcrc0) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_154]) ).
tff(c_224,plain,
( aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS))))
| ( xS = slcrc0 ) ),
inference(cnfTransformation,[status(thm)],[f_465]) ).
tff(c_443,plain,
xS = slcrc0,
inference(splitLeft,[status(thm)],[c_224]) ).
tff(c_220,plain,
isFinite0(xS),
inference(cnfTransformation,[status(thm)],[f_461]) ).
tff(c_253,plain,
! [W0_153] :
( ~ isFinite0(W0_153)
| ~ isCountable0(W0_153)
| ~ aSet0(W0_153) ),
inference(cnfTransformation,[status(thm)],[f_65]) ).
tff(c_263,plain,
( ~ isCountable0(xS)
| ~ aSet0(xS) ),
inference(resolution,[status(thm)],[c_220,c_253]) ).
tff(c_264,plain,
~ aSet0(xS),
inference(splitLeft,[status(thm)],[c_263]) ).
tff(c_108,plain,
aSet0(szNzAzT0),
inference(cnfTransformation,[status(thm)],[f_211]) ).
tff(c_222,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnfTransformation,[status(thm)],[f_461]) ).
tff(c_335,plain,
! [W1_167,W0_168] :
( aSet0(W1_167)
| ~ aSubsetOf0(W1_167,W0_168)
| ~ aSet0(W0_168) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_341,plain,
( aSet0(xS)
| ~ aSet0(szNzAzT0) ),
inference(resolution,[status(thm)],[c_222,c_335]) ).
tff(c_345,plain,
aSet0(xS),
inference(demodulation,[status(thm),theory(equality)],[c_108,c_341]) ).
tff(c_347,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_264,c_345]) ).
tff(c_349,plain,
aSet0(xS),
inference(splitRight,[status(thm)],[c_263]) ).
tff(c_378,plain,
! [W0_175] :
( ( slcrc0 = W0_175 )
| ( sbrdtbr0(W0_175) != sz00 )
| ~ aSet0(W0_175) ),
inference(cnfTransformation,[status(thm)],[f_330]) ).
tff(c_392,plain,
( ( xS = slcrc0 )
| ( sbrdtbr0(xS) != sz00 ) ),
inference(resolution,[status(thm)],[c_349,c_378]) ).
tff(c_400,plain,
sbrdtbr0(xS) != sz00,
inference(splitLeft,[status(thm)],[c_392]) ).
tff(c_449,plain,
sbrdtbr0(slcrc0) != sz00,
inference(demodulation,[status(thm),theory(equality)],[c_443,c_400]) ).
tff(c_458,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_228,c_449]) ).
tff(c_460,plain,
xS != slcrc0,
inference(splitRight,[status(thm)],[c_224]) ).
tff(c_178,plain,
! [W0_121] :
( aElementOf0(szmzazxdt0(W0_121),W0_121)
| ( slcrc0 = W0_121 )
| ~ isFinite0(W0_121)
| ~ aSubsetOf0(W0_121,szNzAzT0) ),
inference(cnfTransformation,[status(thm)],[f_405]) ).
tff(c_959,plain,
! [W2_242,W0_243,W1_244] :
( aElementOf0(W2_242,W0_243)
| ~ aElementOf0(W2_242,W1_244)
| ~ aSubsetOf0(W1_244,W0_243)
| ~ aSet0(W0_243) ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_10121,plain,
! [W0_582,W0_583] :
( aElementOf0(szmzazxdt0(W0_582),W0_583)
| ~ aSubsetOf0(W0_582,W0_583)
| ~ aSet0(W0_583)
| ( slcrc0 = W0_582 )
| ~ isFinite0(W0_582)
| ~ aSubsetOf0(W0_582,szNzAzT0) ),
inference(resolution,[status(thm)],[c_178,c_959]) ).
tff(c_114,plain,
! [W0_72] :
( aElementOf0(szszuzczcdt0(W0_72),szNzAzT0)
| ~ aElementOf0(W0_72,szNzAzT0) ),
inference(cnfTransformation,[status(thm)],[f_219]) ).
tff(c_459,plain,
aSubsetOf0(xS,slbdtrb0(szszuzczcdt0(szmzazxdt0(xS)))),
inference(splitRight,[status(thm)],[c_224]) ).
tff(c_226,plain,
! [W0_148] :
( ~ aSubsetOf0(xS,slbdtrb0(W0_148))
| ~ aElementOf0(W0_148,szNzAzT0) ),
inference(cnfTransformation,[status(thm)],[f_470]) ).
tff(c_469,plain,
~ aElementOf0(szszuzczcdt0(szmzazxdt0(xS)),szNzAzT0),
inference(resolution,[status(thm)],[c_459,c_226]) ).
tff(c_473,plain,
~ aElementOf0(szmzazxdt0(xS),szNzAzT0),
inference(resolution,[status(thm)],[c_114,c_469]) ).
tff(c_10169,plain,
( ~ aSet0(szNzAzT0)
| ( xS = slcrc0 )
| ~ isFinite0(xS)
| ~ aSubsetOf0(xS,szNzAzT0) ),
inference(resolution,[status(thm)],[c_10121,c_473]) ).
tff(c_10205,plain,
xS = slcrc0,
inference(demodulation,[status(thm),theory(equality)],[c_222,c_220,c_108,c_10169]) ).
tff(c_10207,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_460,c_10205]) ).
tff(c_10208,plain,
xS = slcrc0,
inference(splitRight,[status(thm)],[c_392]) ).
tff(c_110,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_208,plain,
slbdtrb0(sz00) = slcrc0,
inference(cnfTransformation,[status(thm)],[f_440]) ).
tff(c_240,plain,
( ~ aSubsetOf0(xS,slcrc0)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(superposition,[status(thm),theory(equality)],[c_208,c_226]) ).
tff(c_244,plain,
~ aSubsetOf0(xS,slcrc0),
inference(demodulation,[status(thm),theory(equality)],[c_110,c_240]) ).
tff(c_10212,plain,
~ aSubsetOf0(slcrc0,slcrc0),
inference(demodulation,[status(thm),theory(equality)],[c_10208,c_244]) ).
tff(c_10225,plain,
~ aSet0(slcrc0),
inference(resolution,[status(thm)],[c_34,c_10212]) ).
tff(c_10229,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_14,c_10225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM545+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % 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
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 15:18:29 EDT 2023
% 0.14/0.36 % CPUTime :
% 11.62/3.72 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.62/3.73
% 11.62/3.73 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.91/3.76
% 11.91/3.76 Inference rules
% 11.91/3.76 ----------------------
% 11.91/3.76 #Ref : 1
% 11.91/3.76 #Sup : 1978
% 11.91/3.76 #Fact : 0
% 11.91/3.76 #Define : 0
% 11.91/3.76 #Split : 45
% 11.91/3.76 #Chain : 0
% 11.91/3.76 #Close : 0
% 11.91/3.76
% 11.91/3.76 Ordering : KBO
% 11.91/3.76
% 11.91/3.76 Simplification rules
% 11.91/3.76 ----------------------
% 11.91/3.76 #Subsume : 654
% 11.91/3.76 #Demod : 1795
% 11.91/3.76 #Tautology : 446
% 11.91/3.76 #SimpNegUnit : 210
% 11.91/3.76 #BackRed : 113
% 11.91/3.76
% 11.91/3.76 #Partial instantiations: 0
% 11.91/3.76 #Strategies tried : 1
% 11.91/3.76
% 11.91/3.76 Timing (in seconds)
% 11.91/3.76 ----------------------
% 11.91/3.76 Preprocessing : 0.72
% 11.91/3.76 Parsing : 0.36
% 11.91/3.76 CNF conversion : 0.06
% 11.91/3.76 Main loop : 1.98
% 11.91/3.76 Inferencing : 0.72
% 11.91/3.76 Reduction : 0.57
% 11.91/3.76 Demodulation : 0.38
% 11.91/3.76 BG Simplification : 0.08
% 11.91/3.76 Subsumption : 0.48
% 11.91/3.76 Abstraction : 0.07
% 11.91/3.76 MUC search : 0.00
% 11.91/3.76 Cooper : 0.00
% 11.91/3.76 Total : 2.75
% 11.91/3.76 Index Insertion : 0.00
% 11.91/3.76 Index Deletion : 0.00
% 11.91/3.76 Index Matching : 0.00
% 11.91/3.76 BG Taut test : 0.00
%------------------------------------------------------------------------------