TSTP Solution File: NUM478+2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM478+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 : n014.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 10:51:49 EDT 2023
% Result : Theorem 21.10s 9.99s
% Output : CNFRefutation 21.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 23
% Syntax : Number of formulae : 51 ( 18 unt; 16 typ; 0 def)
% Number of atoms : 80 ( 40 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 78 ( 33 ~; 29 |; 9 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 24 (; 23 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xn > xm > xl > sz10 > sz00 > #skF_3 > #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_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_383,hypothesis,
aNaturalNumber0(xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1553) ).
tff(f_373,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524) ).
tff(f_382,hypothesis,
( ( xl != sz00 )
& ? [W0] :
( aNaturalNumber0(W0)
& ( xm = sdtasdt0(xl,W0) ) )
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1524_04) ).
tff(f_81,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
tff(f_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(f_391,negated_conjecture,
~ ( ( aNaturalNumber0(sdtsldt0(xm,xl))
& ( xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ) )
=> ( ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) )
| ( sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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(c_133,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_383]) ).
tff(c_123,plain,
aNaturalNumber0(xl),
inference(cnfTransformation,[status(thm)],[f_373]) ).
tff(c_129,plain,
aNaturalNumber0('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_127,plain,
sdtasdt0(xl,'#skF_3') = xm,
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_58323,plain,
! [W0_739,W1_740,W2_741] :
( ( sdtasdt0(sdtasdt0(W0_739,W1_740),W2_741) = sdtasdt0(W0_739,sdtasdt0(W1_740,W2_741)) )
| ~ aNaturalNumber0(W2_741)
| ~ aNaturalNumber0(W1_740)
| ~ aNaturalNumber0(W0_739) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_58544,plain,
! [W2_741] :
( ( sdtasdt0(xl,sdtasdt0('#skF_3',W2_741)) = sdtasdt0(xm,W2_741) )
| ~ aNaturalNumber0(W2_741)
| ~ aNaturalNumber0('#skF_3')
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_58323]) ).
tff(c_66154,plain,
! [W2_785] :
( ( sdtasdt0(xl,sdtasdt0('#skF_3',W2_785)) = sdtasdt0(xm,W2_785) )
| ~ aNaturalNumber0(W2_785) ),
inference(demodulation,[status(thm),theory(equality)],[c_123,c_129,c_58544]) ).
tff(c_739,plain,
! [W1_99,W0_100] :
( ( sdtasdt0(W1_99,W0_100) = sdtasdt0(W0_100,W1_99) )
| ~ aNaturalNumber0(W1_99)
| ~ aNaturalNumber0(W0_100) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_1700,plain,
! [W0_116] :
( ( sdtasdt0(W0_116,'#skF_3') = sdtasdt0('#skF_3',W0_116) )
| ~ aNaturalNumber0(W0_116) ),
inference(resolution,[status(thm)],[c_129,c_739]) ).
tff(c_1768,plain,
sdtasdt0(xn,'#skF_3') = sdtasdt0('#skF_3',xn),
inference(resolution,[status(thm)],[c_133,c_1700]) ).
tff(c_139,plain,
sdtasdt0(xl,sdtsldt0(xm,xl)) = xm,
inference(cnfTransformation,[status(thm)],[f_391]) ).
tff(c_141,plain,
aNaturalNumber0(sdtsldt0(xm,xl)),
inference(cnfTransformation,[status(thm)],[f_391]) ).
tff(c_131,plain,
xl != sz00,
inference(cnfTransformation,[status(thm)],[f_382]) ).
tff(c_57351,plain,
! [W0_735,W2_736,W1_737] :
( ( sdtasdt0(W0_735,W2_736) != sdtasdt0(W0_735,W1_737) )
| ( W2_736 = W1_737 )
| ~ aNaturalNumber0(W2_736)
| ~ aNaturalNumber0(W1_737)
| ( sz00 = W0_735 )
| ~ aNaturalNumber0(W0_735) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_57571,plain,
! [W2_736] :
( ( sdtasdt0(xl,W2_736) != xm )
| ( W2_736 = '#skF_3' )
| ~ aNaturalNumber0(W2_736)
| ~ aNaturalNumber0('#skF_3')
| ( xl = sz00 )
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_127,c_57351]) ).
tff(c_57886,plain,
! [W2_736] :
( ( sdtasdt0(xl,W2_736) != xm )
| ( W2_736 = '#skF_3' )
| ~ aNaturalNumber0(W2_736)
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_123,c_129,c_57571]) ).
tff(c_58102,plain,
! [W2_738] :
( ( sdtasdt0(xl,W2_738) != xm )
| ( W2_738 = '#skF_3' )
| ~ aNaturalNumber0(W2_738) ),
inference(negUnitSimplification,[status(thm)],[c_131,c_57886]) ).
tff(c_58180,plain,
( ( sdtasdt0(xl,sdtsldt0(xm,xl)) != xm )
| ( sdtsldt0(xm,xl) = '#skF_3' ) ),
inference(resolution,[status(thm)],[c_141,c_58102]) ).
tff(c_58226,plain,
sdtsldt0(xm,xl) = '#skF_3',
inference(demodulation,[status(thm),theory(equality)],[c_139,c_58180]) ).
tff(c_121,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_373]) ).
tff(c_55316,plain,
! [W0_721] :
( ( sdtasdt0(xm,W0_721) = sdtasdt0(W0_721,xm) )
| ~ aNaturalNumber0(W0_721) ),
inference(resolution,[status(thm)],[c_121,c_739]) ).
tff(c_55420,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c_133,c_55316]) ).
tff(c_137,plain,
sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) != sdtasdt0(xn,xm),
inference(cnfTransformation,[status(thm)],[f_391]) ).
tff(c_55559,plain,
sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl))) != sdtasdt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_55420,c_137]) ).
tff(c_58249,plain,
sdtasdt0(xl,sdtasdt0(xn,'#skF_3')) != sdtasdt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_58226,c_55559]) ).
tff(c_58287,plain,
sdtasdt0(xl,sdtasdt0('#skF_3',xn)) != sdtasdt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_1768,c_58249]) ).
tff(c_66187,plain,
~ aNaturalNumber0(xn),
inference(superposition,[status(thm),theory(equality)],[c_66154,c_58287]) ).
tff(c_66255,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_133,c_66187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM478+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % 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
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 3 14:26:03 EDT 2023
% 0.16/0.35 % CPUTime :
% 21.10/9.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.21/10.00
% 21.21/10.00 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.21/10.03
% 21.21/10.03 Inference rules
% 21.21/10.03 ----------------------
% 21.21/10.03 #Ref : 26
% 21.21/10.03 #Sup : 13901
% 21.21/10.03 #Fact : 2
% 21.21/10.03 #Define : 0
% 21.21/10.03 #Split : 31
% 21.21/10.03 #Chain : 0
% 21.21/10.03 #Close : 0
% 21.21/10.03
% 21.21/10.03 Ordering : KBO
% 21.21/10.03
% 21.21/10.03 Simplification rules
% 21.21/10.03 ----------------------
% 21.21/10.03 #Subsume : 861
% 21.21/10.03 #Demod : 21140
% 21.21/10.03 #Tautology : 4404
% 21.21/10.03 #SimpNegUnit : 2562
% 21.21/10.03 #BackRed : 1056
% 21.21/10.03
% 21.21/10.03 #Partial instantiations: 0
% 21.21/10.03 #Strategies tried : 1
% 21.21/10.03
% 21.21/10.03 Timing (in seconds)
% 21.21/10.03 ----------------------
% 21.21/10.03 Preprocessing : 0.68
% 21.21/10.03 Parsing : 0.34
% 21.21/10.03 CNF conversion : 0.05
% 21.21/10.03 Main loop : 8.30
% 21.21/10.03 Inferencing : 1.60
% 21.21/10.03 Reduction : 4.14
% 21.21/10.03 Demodulation : 3.25
% 21.21/10.03 BG Simplification : 0.16
% 21.21/10.03 Subsumption : 1.91
% 21.21/10.03 Abstraction : 0.21
% 21.21/10.03 MUC search : 0.00
% 21.21/10.03 Cooper : 0.00
% 21.21/10.03 Total : 9.02
% 21.21/10.03 Index Insertion : 0.00
% 21.21/10.03 Index Deletion : 0.00
% 21.21/10.03 Index Matching : 0.00
% 21.21/10.03 BG Taut test : 0.00
%------------------------------------------------------------------------------