TSTP Solution File: NUM468+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM468+2 : 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/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 : n003.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 10:51:47 EDT 2023
% Result : Theorem 20.80s 7.96s
% Output : CNFRefutation 20.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 52 ( 17 unt; 17 typ; 0 def)
% Number of atoms : 92 ( 50 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 94 ( 37 ~; 36 |; 13 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 10 >; 9 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 22 (; 20 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xn > xm > xl > sz10 > sz00 > #skF_3 > #skF_4 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xl,type,
xl: $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff(sdtmndt0,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(sdtlseqdt0,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sz00,type,
sz00: $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
tff('#skF_4',type,
'#skF_4': $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff(xm,type,
xm: $i ).
tff(sdtsldt0,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(xn,type,
xn: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_366,negated_conjecture,
~ ( ( xl != sz00 )
=> ( ( aNaturalNumber0(sdtsldt0(xm,xl))
& ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ) )
=> ( ( aNaturalNumber0(sdtsldt0(xn,xl))
& ( xn = sdtasdt0(xl,sdtsldt0(xn,xl)) ) )
=> ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_340,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).
tff(f_353,hypothesis,
( ? [W0] :
( aNaturalNumber0(W0)
& ( xm = sdtasdt0(xl,W0) ) )
& doDivides0(xl,xm)
& ? [W0] :
( aNaturalNumber0(W0)
& ( xn = sdtasdt0(xl,W0) ) )
& doDivides0(xl,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).
tff(f_131,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1,W2] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
tff(f_103,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
tff(c_139,plain,
sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
inference(cnfTransformation,[status(thm)],[f_366]) ).
tff(c_141,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(cnfTransformation,[status(thm)],[f_366]) ).
tff(c_143,plain,
xl != sz00,
inference(cnfTransformation,[status(thm)],[f_366]) ).
tff(c_119,plain,
aNaturalNumber0(xl),
inference(cnfTransformation,[status(thm)],[f_340]) ).
tff(c_131,plain,
aNaturalNumber0('#skF_4'),
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_129,plain,
sdtasdt0(xl,'#skF_4') = xm,
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_17366,plain,
! [W0_374,W2_375,W1_376] :
( ( sdtasdt0(W0_374,W2_375) != sdtasdt0(W0_374,W1_376) )
| ( W2_375 = W1_376 )
| ~ aNaturalNumber0(W2_375)
| ~ aNaturalNumber0(W1_376)
| ( sz00 = W0_374 )
| ~ aNaturalNumber0(W0_374) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_17638,plain,
! [W2_375] :
( ( sdtasdt0(xl,W2_375) != xm )
| ( W2_375 = '#skF_4' )
| ~ aNaturalNumber0(W2_375)
| ~ aNaturalNumber0('#skF_4')
| ( xl = sz00 )
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_129,c_17366]) ).
tff(c_18007,plain,
! [W2_375] :
( ( sdtasdt0(xl,W2_375) != xm )
| ( W2_375 = '#skF_4' )
| ~ aNaturalNumber0(W2_375)
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_119,c_131,c_17638]) ).
tff(c_18799,plain,
! [W2_381] :
( ( sdtasdt0(xl,W2_381) != xm )
| ( W2_381 = '#skF_4' )
| ~ aNaturalNumber0(W2_381) ),
inference(negUnitSimplification,[status(thm)],[c_143,c_18007]) ).
tff(c_18853,plain,
( ( sdtasdt0(xl,sdtsldt0(xm,xl)) != xm )
| ( sdtsldt0(xm,xl) = '#skF_4' ) ),
inference(resolution,[status(thm)],[c_141,c_18799]) ).
tff(c_18894,plain,
sdtsldt0(xm,xl) = '#skF_4',
inference(demodulation,[status(thm),theory(equality)],[c_139,c_18853]) ).
tff(c_135,plain,
sdtasdt0(xl,sdtsldt0(xn,xl)) = xn,
inference(cnfTransformation,[status(thm)],[f_366]) ).
tff(c_137,plain,
aNaturalNumber0(sdtsldt0(xn,xl)),
inference(cnfTransformation,[status(thm)],[f_366]) ).
tff(c_125,plain,
aNaturalNumber0('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_123,plain,
sdtasdt0(xl,'#skF_3') = xn,
inference(cnfTransformation,[status(thm)],[f_353]) ).
tff(c_17632,plain,
! [W1_376] :
( ( sdtasdt0(xl,W1_376) != xn )
| ( W1_376 = '#skF_3' )
| ~ aNaturalNumber0('#skF_3')
| ~ aNaturalNumber0(W1_376)
| ( xl = sz00 )
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_123,c_17366]) ).
tff(c_17998,plain,
! [W1_376] :
( ( sdtasdt0(xl,W1_376) != xn )
| ( W1_376 = '#skF_3' )
| ~ aNaturalNumber0(W1_376)
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_119,c_125,c_17632]) ).
tff(c_18050,plain,
! [W1_377] :
( ( sdtasdt0(xl,W1_377) != xn )
| ( W1_377 = '#skF_3' )
| ~ aNaturalNumber0(W1_377) ),
inference(negUnitSimplification,[status(thm)],[c_143,c_17998]) ).
tff(c_18113,plain,
( ( sdtasdt0(xl,sdtsldt0(xn,xl)) != xn )
| ( sdtsldt0(xn,xl) = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_137,c_18050]) ).
tff(c_18158,plain,
sdtsldt0(xn,xl) = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_135,c_18113]) ).
tff(c_133,plain,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) != sdtpldt0(xm,xn),
inference(cnfTransformation,[status(thm)],[f_366]) ).
tff(c_18193,plain,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),'#skF_3')) != sdtpldt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_18158,c_133]) ).
tff(c_28077,plain,
sdtasdt0(xl,sdtpldt0('#skF_4','#skF_3')) != sdtpldt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_18894,c_18193]) ).
tff(c_20375,plain,
! [W0_393,W1_394,W2_395] :
( ( sdtpldt0(sdtasdt0(W0_393,W1_394),sdtasdt0(W0_393,W2_395)) = sdtasdt0(W0_393,sdtpldt0(W1_394,W2_395)) )
| ~ aNaturalNumber0(W2_395)
| ~ aNaturalNumber0(W1_394)
| ~ aNaturalNumber0(W0_393) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_20737,plain,
! [W2_395] :
( ( sdtpldt0(xm,sdtasdt0(xl,W2_395)) = sdtasdt0(xl,sdtpldt0('#skF_4',W2_395)) )
| ~ aNaturalNumber0(W2_395)
| ~ aNaturalNumber0('#skF_4')
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_129,c_20375]) ).
tff(c_34722,plain,
! [W2_446] :
( ( sdtpldt0(xm,sdtasdt0(xl,W2_446)) = sdtasdt0(xl,sdtpldt0('#skF_4',W2_446)) )
| ~ aNaturalNumber0(W2_446) ),
inference(demodulation,[status(thm),theory(equality)],[c_119,c_131,c_20737]) ).
tff(c_34793,plain,
( ( sdtasdt0(xl,sdtpldt0('#skF_4','#skF_3')) = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_123,c_34722]) ).
tff(c_34842,plain,
sdtasdt0(xl,sdtpldt0('#skF_4','#skF_3')) = sdtpldt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_125,c_34793]) ).
tff(c_34844,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_28077,c_34842]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : NUM468+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14 % 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
% 0.14/0.35 % Computer : n003.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
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 14:52:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 20.80/7.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.80/7.96
% 20.80/7.96 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.80/7.99
% 20.80/7.99 Inference rules
% 20.80/7.99 ----------------------
% 20.80/7.99 #Ref : 12
% 20.80/7.99 #Sup : 7248
% 20.80/7.99 #Fact : 2
% 20.80/7.99 #Define : 0
% 20.80/7.99 #Split : 56
% 20.80/7.99 #Chain : 0
% 20.80/7.99 #Close : 0
% 20.80/7.99
% 20.80/7.99 Ordering : KBO
% 20.80/7.99
% 20.80/7.99 Simplification rules
% 20.80/7.99 ----------------------
% 20.80/7.99 #Subsume : 236
% 20.80/7.99 #Demod : 12506
% 20.80/7.99 #Tautology : 3077
% 20.80/7.99 #SimpNegUnit : 1103
% 20.80/7.99 #BackRed : 1114
% 20.80/7.99
% 20.80/7.99 #Partial instantiations: 0
% 20.80/7.99 #Strategies tried : 1
% 20.80/7.99
% 20.80/7.99 Timing (in seconds)
% 20.80/7.99 ----------------------
% 20.80/8.00 Preprocessing : 0.69
% 20.80/8.00 Parsing : 0.34
% 20.80/8.00 CNF conversion : 0.05
% 20.80/8.00 Main loop : 6.18
% 20.80/8.00 Inferencing : 1.21
% 20.80/8.00 Reduction : 3.20
% 20.80/8.00 Demodulation : 2.60
% 20.80/8.00 BG Simplification : 0.12
% 20.80/8.00 Subsumption : 1.23
% 20.80/8.00 Abstraction : 0.15
% 20.80/8.00 MUC search : 0.00
% 20.80/8.00 Cooper : 0.00
% 20.80/8.00 Total : 6.92
% 20.97/8.00 Index Insertion : 0.00
% 20.97/8.00 Index Deletion : 0.00
% 20.97/8.00 Index Matching : 0.00
% 20.97/8.00 BG Taut test : 0.00
%------------------------------------------------------------------------------