TSTP Solution File: NUM469+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM469+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/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 : n010.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 14.98s 5.13s
% Output : CNFRefutation 14.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 29
% Syntax : Number of formulae : 87 ( 34 unt; 15 typ; 2 def)
% Number of atoms : 158 ( 47 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 151 ( 65 ~; 58 |; 15 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 37 (; 36 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xn > xm > xl > sz10 > sz00 > #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(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
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_340,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
tff(f_87,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
tff(f_278,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00 )
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
tff(f_343,hypothesis,
( doDivides0(xl,xm)
& doDivides0(xl,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).
tff(f_67,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
tff(f_349,negated_conjecture,
~ doDivides0(xl,sdtpldt0(xm,xn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
tff(f_307,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
tff(f_93,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
tff(f_323,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2] :
( ( W2 = sdtsldt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
tff(f_41,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(f_53,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
tff(f_347,hypothesis,
( ( xl != sz00 )
=> ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1298) ).
tff(c_119,plain,
aNaturalNumber0(xl),
inference(cnfTransformation,[status(thm)],[f_340]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_241,plain,
! [W0_81] :
( ( sdtasdt0(sz10,W0_81) = W0_81 )
| ~ aNaturalNumber0(W0_81) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_262,plain,
sdtasdt0(sz10,xl) = xl,
inference(resolution,[status(thm)],[c_119,c_241]) ).
tff(c_1092,plain,
! [W1_107,W0_108] :
( sdtlseqdt0(W1_107,sdtasdt0(W1_107,W0_108))
| ( sz00 = W0_108 )
| ~ aNaturalNumber0(W1_107)
| ~ aNaturalNumber0(W0_108) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_1134,plain,
( sdtlseqdt0(sz10,xl)
| ( xl = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_262,c_1092]) ).
tff(c_1199,plain,
( sdtlseqdt0(sz10,xl)
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_119,c_8,c_1134]) ).
tff(c_1576,plain,
xl = sz00,
inference(splitLeft,[status(thm)],[c_1199]) ).
tff(c_121,plain,
doDivides0(xl,xn),
inference(cnfTransformation,[status(thm)],[f_343]) ).
tff(c_1594,plain,
doDivides0(sz00,xn),
inference(demodulation,[status(thm),theory(equality)],[c_1576,c_121]) ).
tff(c_115,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_340]) ).
tff(c_200,plain,
! [W0_80] :
( ( sdtpldt0(sz00,W0_80) = W0_80 )
| ~ aNaturalNumber0(W0_80) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_216,plain,
sdtpldt0(sz00,xn) = xn,
inference(resolution,[status(thm)],[c_115,c_200]) ).
tff(c_117,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_340]) ).
tff(c_261,plain,
sdtasdt0(sz10,xm) = xm,
inference(resolution,[status(thm)],[c_117,c_241]) ).
tff(c_1128,plain,
( sdtlseqdt0(sz10,xm)
| ( xm = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_261,c_1092]) ).
tff(c_1195,plain,
( sdtlseqdt0(sz10,xm)
| ( xm = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_117,c_8,c_1128]) ).
tff(c_1664,plain,
xm = sz00,
inference(splitLeft,[status(thm)],[c_1195]) ).
tff(c_127,plain,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnfTransformation,[status(thm)],[f_349]) ).
tff(c_1592,plain,
~ doDivides0(sz00,sdtpldt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_1576,c_127]) ).
tff(c_1665,plain,
~ doDivides0(sz00,sdtpldt0(sz00,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_1664,c_1592]) ).
tff(c_1682,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_1594,c_216,c_1665]) ).
tff(c_1684,plain,
xm != sz00,
inference(splitRight,[status(thm)],[c_1195]) ).
tff(c_123,plain,
doDivides0(xl,xm),
inference(cnfTransformation,[status(thm)],[f_343]) ).
tff(c_1593,plain,
doDivides0(sz00,xm),
inference(demodulation,[status(thm),theory(equality)],[c_1576,c_123]) ).
tff(c_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_903,plain,
! [W0_102,W1_103] :
( aNaturalNumber0('#skF_2'(W0_102,W1_103))
| ~ doDivides0(W0_102,W1_103)
| ~ aNaturalNumber0(W1_103)
| ~ aNaturalNumber0(W0_102) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_30,plain,
! [W0_18] :
( ( sdtasdt0(sz00,W0_18) = sz00 )
| ~ aNaturalNumber0(W0_18) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_19364,plain,
! [W0_357,W1_358] :
( ( sdtasdt0(sz00,'#skF_2'(W0_357,W1_358)) = sz00 )
| ~ doDivides0(W0_357,W1_358)
| ~ aNaturalNumber0(W1_358)
| ~ aNaturalNumber0(W0_357) ),
inference(resolution,[status(thm)],[c_903,c_30]) ).
tff(c_103,plain,
! [W0_65,W1_66] :
( ( sdtasdt0(W0_65,'#skF_2'(W0_65,W1_66)) = W1_66 )
| ~ doDivides0(W0_65,W1_66)
| ~ aNaturalNumber0(W1_66)
| ~ aNaturalNumber0(W0_65) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_19430,plain,
! [W1_358] :
( ( sz00 = W1_358 )
| ~ doDivides0(sz00,W1_358)
| ~ aNaturalNumber0(W1_358)
| ~ aNaturalNumber0(sz00)
| ~ doDivides0(sz00,W1_358)
| ~ aNaturalNumber0(W1_358)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm),theory(equality)],[c_19364,c_103]) ).
tff(c_19507,plain,
! [W1_359] :
( ( sz00 = W1_359 )
| ~ doDivides0(sz00,W1_359)
| ~ aNaturalNumber0(W1_359) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_19430]) ).
tff(c_19517,plain,
( ( xm = sz00 )
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[c_1593,c_19507]) ).
tff(c_19530,plain,
xm = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_117,c_19517]) ).
tff(c_19532,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1684,c_19530]) ).
tff(c_19534,plain,
xl != sz00,
inference(splitRight,[status(thm)],[c_1199]) ).
tff(c_111,plain,
! [W1_71,W0_70] :
( aNaturalNumber0(sdtsldt0(W1_71,W0_70))
| ~ doDivides0(W0_70,W1_71)
| ( sz00 = W0_70 )
| ~ aNaturalNumber0(W1_71)
| ~ aNaturalNumber0(W0_70) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_10,plain,
! [W0_2,W1_3] :
( aNaturalNumber0(sdtpldt0(W0_2,W1_3))
| ~ aNaturalNumber0(W1_3)
| ~ aNaturalNumber0(W0_2) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_622,plain,
! [W1_93,W0_94] :
( ( sdtpldt0(W1_93,W0_94) = sdtpldt0(W0_94,W1_93) )
| ~ aNaturalNumber0(W1_93)
| ~ aNaturalNumber0(W0_94) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_644,plain,
! [W0_95] :
( ( sdtpldt0(xn,W0_95) = sdtpldt0(W0_95,xn) )
| ~ aNaturalNumber0(W0_95) ),
inference(resolution,[status(thm)],[c_115,c_622]) ).
tff(c_673,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(resolution,[status(thm)],[c_117,c_644]) ).
tff(c_807,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_673,c_10]) ).
tff(c_815,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_115,c_117,c_807]) ).
tff(c_125,plain,
( ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(xm,xn) )
| ( xl = sz00 ) ),
inference(cnfTransformation,[status(thm)],[f_347]) ).
tff(c_23972,plain,
sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(xm,xn),
inference(negUnitSimplification,[status(thm)],[c_19534,c_125]) ).
tff(c_101,plain,
! [W0_65,W2_69] :
( doDivides0(W0_65,sdtasdt0(W0_65,W2_69))
| ~ aNaturalNumber0(W2_69)
| ~ aNaturalNumber0(sdtasdt0(W0_65,W2_69))
| ~ aNaturalNumber0(W0_65) ),
inference(cnfTransformation,[status(thm)],[f_307]) ).
tff(c_23976,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ aNaturalNumber0(sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))))
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_23972,c_101]) ).
tff(c_23988,plain,
( doDivides0(xl,sdtpldt0(xm,xn))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
inference(demodulation,[status(thm),theory(equality)],[c_119,c_815,c_23972,c_23976]) ).
tff(c_23989,plain,
~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))),
inference(negUnitSimplification,[status(thm)],[c_127,c_23988]) ).
tff(c_24003,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(resolution,[status(thm)],[c_10,c_23989]) ).
tff(c_24152,plain,
~ aNaturalNumber0(sdtsldt0(xm,xl)),
inference(splitLeft,[status(thm)],[c_24003]) ).
tff(c_24155,plain,
( ~ doDivides0(xl,xm)
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[c_111,c_24152]) ).
tff(c_24158,plain,
xl = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_119,c_117,c_123,c_24155]) ).
tff(c_24160,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_19534,c_24158]) ).
tff(c_24161,plain,
~ aNaturalNumber0(sdtsldt0(xn,xl)),
inference(splitRight,[status(thm)],[c_24003]) ).
tff(c_24165,plain,
( ~ doDivides0(xl,xn)
| ( xl = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[c_111,c_24161]) ).
tff(c_24168,plain,
xl = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_119,c_115,c_121,c_24165]) ).
tff(c_24170,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_19534,c_24168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM469+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/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
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 3 14:18:28 EDT 2023
% 0.14/0.36 % CPUTime :
% 14.98/5.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.98/5.14
% 14.98/5.14 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.98/5.17
% 14.98/5.17 Inference rules
% 14.98/5.17 ----------------------
% 14.98/5.17 #Ref : 19
% 14.98/5.17 #Sup : 5044
% 14.98/5.17 #Fact : 2
% 14.98/5.17 #Define : 0
% 14.98/5.17 #Split : 22
% 14.98/5.17 #Chain : 0
% 14.98/5.17 #Close : 0
% 14.98/5.17
% 14.98/5.17 Ordering : KBO
% 14.98/5.17
% 14.98/5.17 Simplification rules
% 14.98/5.17 ----------------------
% 14.98/5.17 #Subsume : 444
% 14.98/5.17 #Demod : 7935
% 14.98/5.17 #Tautology : 1885
% 14.98/5.17 #SimpNegUnit : 751
% 14.98/5.17 #BackRed : 304
% 14.98/5.17
% 14.98/5.17 #Partial instantiations: 0
% 14.98/5.17 #Strategies tried : 1
% 14.98/5.17
% 14.98/5.17 Timing (in seconds)
% 14.98/5.17 ----------------------
% 14.98/5.18 Preprocessing : 0.67
% 14.98/5.18 Parsing : 0.34
% 14.98/5.18 CNF conversion : 0.05
% 14.98/5.18 Main loop : 3.37
% 14.98/5.18 Inferencing : 0.86
% 14.98/5.18 Reduction : 1.44
% 14.98/5.18 Demodulation : 1.08
% 14.98/5.18 BG Simplification : 0.10
% 14.98/5.18 Subsumption : 0.74
% 14.98/5.18 Abstraction : 0.10
% 14.98/5.18 MUC search : 0.00
% 14.98/5.18 Cooper : 0.00
% 14.98/5.18 Total : 4.10
% 14.98/5.18 Index Insertion : 0.00
% 14.98/5.18 Index Deletion : 0.00
% 14.98/5.18 Index Matching : 0.00
% 14.98/5.18 BG Taut test : 0.00
%------------------------------------------------------------------------------