TSTP Solution File: NUM459+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM459+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 : n004.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 10:51:44 EDT 2023
% Result : Theorem 9.31s 3.25s
% Output : CNFRefutation 9.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 22
% Syntax : Number of formulae : 62 ( 23 unt; 12 typ; 2 def)
% Number of atoms : 124 ( 43 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 122 ( 48 ~; 45 |; 17 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 37 (; 34 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > aNaturalNumber0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xn > xm > sz10 > sz00 > #skF_2 > #skF_3 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
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_2',type,
'#skF_2': $i ).
tff('#skF_3',type,
'#skF_3': $i ).
tff(xm,type,
xm: $i ).
tff(xn,type,
xn: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_198,negated_conjecture,
~ ( ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xm,W0) = xn ) )
& sdtlseqdt0(xm,xn)
& ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xn,W0) = xm ) )
& sdtlseqdt0(xn,xm) )
=> ( xm = xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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_141,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtpldt0(W0,W1) = sz00 )
=> ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
tff(f_182,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__745) ).
tff(f_61,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
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_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
tff(f_162,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
tff(f_41,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(f_175,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
tff(c_70,plain,
xn != xm,
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_74,plain,
sdtpldt0(xn,'#skF_3') = xm,
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_82,plain,
aNaturalNumber0('#skF_2'),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_76,plain,
aNaturalNumber0('#skF_3'),
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_586,plain,
! [W1_55,W0_56] :
( ( sdtpldt0(W1_55,W0_56) = sdtpldt0(W0_56,W1_55) )
| ~ aNaturalNumber0(W1_55)
| ~ aNaturalNumber0(W0_56) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_906,plain,
! [W0_61] :
( ( sdtpldt0(W0_61,'#skF_3') = sdtpldt0('#skF_3',W0_61) )
| ~ aNaturalNumber0(W0_61) ),
inference(resolution,[status(thm)],[c_76,c_586]) ).
tff(c_954,plain,
sdtpldt0('#skF_2','#skF_3') = sdtpldt0('#skF_3','#skF_2'),
inference(resolution,[status(thm)],[c_82,c_906]) ).
tff(c_46,plain,
! [W1_31,W0_30] :
( ( sz00 = W1_31 )
| ( sdtpldt0(W0_30,W1_31) != sz00 )
| ~ aNaturalNumber0(W1_31)
| ~ aNaturalNumber0(W0_30) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_1116,plain,
( ( sz00 = '#skF_3' )
| ( sdtpldt0('#skF_3','#skF_2') != sz00 )
| ~ aNaturalNumber0('#skF_3')
| ~ aNaturalNumber0('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_954,c_46]) ).
tff(c_1125,plain,
( ( sz00 = '#skF_3' )
| ( sdtpldt0('#skF_3','#skF_2') != sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_76,c_1116]) ).
tff(c_1207,plain,
sdtpldt0('#skF_3','#skF_2') != sz00,
inference(splitLeft,[status(thm)],[c_1125]) ).
tff(c_68,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_80,plain,
sdtpldt0(xm,'#skF_2') = xn,
inference(cnfTransformation,[status(thm)],[f_198]) ).
tff(c_3098,plain,
! [W0_88,W1_89,W2_90] :
( ( sdtpldt0(sdtpldt0(W0_88,W1_89),W2_90) = sdtpldt0(W0_88,sdtpldt0(W1_89,W2_90)) )
| ~ aNaturalNumber0(W2_90)
| ~ aNaturalNumber0(W1_89)
| ~ aNaturalNumber0(W0_88) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_3228,plain,
! [W2_90] :
( ( sdtpldt0(xm,sdtpldt0('#skF_2',W2_90)) = sdtpldt0(xn,W2_90) )
| ~ aNaturalNumber0(W2_90)
| ~ aNaturalNumber0('#skF_2')
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_80,c_3098]) ).
tff(c_7850,plain,
! [W2_117] :
( ( sdtpldt0(xm,sdtpldt0('#skF_2',W2_117)) = sdtpldt0(xn,W2_117) )
| ~ aNaturalNumber0(W2_117) ),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_82,c_3228]) ).
tff(c_7894,plain,
( ( sdtpldt0(xm,sdtpldt0('#skF_3','#skF_2')) = sdtpldt0(xn,'#skF_3') )
| ~ aNaturalNumber0('#skF_3') ),
inference(superposition,[status(thm),theory(equality)],[c_954,c_7850]) ).
tff(c_7928,plain,
sdtpldt0(xm,sdtpldt0('#skF_3','#skF_2')) = xm,
inference(demodulation,[status(thm),theory(equality)],[c_76,c_74,c_7894]) ).
tff(c_302,plain,
! [W0_50] :
( ( sdtpldt0(W0_50,sz00) = W0_50 )
| ~ aNaturalNumber0(W0_50) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_325,plain,
sdtpldt0(xm,sz00) = xm,
inference(resolution,[status(thm)],[c_68,c_302]) ).
tff(c_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_2186,plain,
! [W0_75,W2_76] :
( sdtlseqdt0(W0_75,sdtpldt0(W0_75,W2_76))
| ~ aNaturalNumber0(W2_76)
| ~ aNaturalNumber0(sdtpldt0(W0_75,W2_76))
| ~ aNaturalNumber0(W0_75) ),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_2228,plain,
( sdtlseqdt0(xm,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xm,sz00))
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_325,c_2186]) ).
tff(c_2280,plain,
sdtlseqdt0(xm,xm),
inference(demodulation,[status(thm),theory(equality)],[c_68,c_68,c_325,c_4,c_2228]) ).
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_1119,plain,
( aNaturalNumber0(sdtpldt0('#skF_3','#skF_2'))
| ~ aNaturalNumber0('#skF_3')
| ~ aNaturalNumber0('#skF_2') ),
inference(superposition,[status(thm),theory(equality)],[c_954,c_10]) ).
tff(c_1127,plain,
aNaturalNumber0(sdtpldt0('#skF_3','#skF_2')),
inference(demodulation,[status(thm),theory(equality)],[c_82,c_76,c_1119]) ).
tff(c_7082,plain,
! [W0_112,W2_113] :
( ( sdtmndt0(sdtpldt0(W0_112,W2_113),W0_112) = W2_113 )
| ~ aNaturalNumber0(W2_113)
| ~ sdtlseqdt0(W0_112,sdtpldt0(W0_112,W2_113))
| ~ aNaturalNumber0(sdtpldt0(W0_112,W2_113))
| ~ aNaturalNumber0(W0_112) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_7151,plain,
( ( sdtmndt0(sdtpldt0(xm,sz00),xm) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ sdtlseqdt0(xm,xm)
| ~ aNaturalNumber0(sdtpldt0(xm,sz00))
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_325,c_7082]) ).
tff(c_7210,plain,
sdtmndt0(xm,xm) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_68,c_68,c_325,c_2280,c_4,c_325,c_7151]) ).
tff(c_58,plain,
! [W0_39,W2_42] :
( ( sdtmndt0(sdtpldt0(W0_39,W2_42),W0_39) = W2_42 )
| ~ aNaturalNumber0(W2_42)
| ~ sdtlseqdt0(W0_39,sdtpldt0(W0_39,W2_42))
| ~ aNaturalNumber0(sdtpldt0(W0_39,W2_42))
| ~ aNaturalNumber0(W0_39) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_8151,plain,
( ( sdtmndt0(sdtpldt0(xm,sdtpldt0('#skF_3','#skF_2')),xm) = sdtpldt0('#skF_3','#skF_2') )
| ~ aNaturalNumber0(sdtpldt0('#skF_3','#skF_2'))
| ~ sdtlseqdt0(xm,xm)
| ~ aNaturalNumber0(sdtpldt0(xm,sdtpldt0('#skF_3','#skF_2')))
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_7928,c_58]) ).
tff(c_8176,plain,
sdtpldt0('#skF_3','#skF_2') = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_68,c_68,c_7928,c_2280,c_1127,c_7210,c_7928,c_8151]) ).
tff(c_8178,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1207,c_8176]) ).
tff(c_8179,plain,
sz00 = '#skF_3',
inference(splitRight,[status(thm)],[c_1125]) ).
tff(c_66,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_182]) ).
tff(c_324,plain,
sdtpldt0(xn,sz00) = xn,
inference(resolution,[status(thm)],[c_66,c_302]) ).
tff(c_8256,plain,
sdtpldt0(xn,'#skF_3') = xn,
inference(demodulation,[status(thm),theory(equality)],[c_8179,c_324]) ).
tff(c_8282,plain,
xn = xm,
inference(demodulation,[status(thm),theory(equality)],[c_74,c_8256]) ).
tff(c_8284,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_70,c_8282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM459+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
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 3 14:51:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 9.31/3.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.56/3.26
% 9.56/3.26 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.56/3.29
% 9.56/3.29 Inference rules
% 9.56/3.29 ----------------------
% 9.56/3.29 #Ref : 4
% 9.56/3.29 #Sup : 1922
% 9.56/3.29 #Fact : 0
% 9.56/3.29 #Define : 0
% 9.56/3.29 #Split : 19
% 9.56/3.29 #Chain : 0
% 9.56/3.29 #Close : 0
% 9.56/3.29
% 9.56/3.29 Ordering : KBO
% 9.56/3.29
% 9.56/3.29 Simplification rules
% 9.56/3.29 ----------------------
% 9.56/3.29 #Subsume : 35
% 9.56/3.29 #Demod : 2393
% 9.56/3.29 #Tautology : 567
% 9.56/3.29 #SimpNegUnit : 181
% 9.56/3.29 #BackRed : 39
% 9.56/3.29
% 9.56/3.29 #Partial instantiations: 0
% 9.56/3.29 #Strategies tried : 1
% 9.56/3.29
% 9.56/3.29 Timing (in seconds)
% 9.56/3.29 ----------------------
% 9.56/3.29 Preprocessing : 0.58
% 9.56/3.29 Parsing : 0.30
% 9.56/3.29 CNF conversion : 0.04
% 9.56/3.29 Main loop : 1.64
% 9.56/3.29 Inferencing : 0.42
% 9.56/3.29 Reduction : 0.67
% 9.56/3.29 Demodulation : 0.51
% 9.56/3.29 BG Simplification : 0.06
% 9.56/3.29 Subsumption : 0.37
% 9.56/3.29 Abstraction : 0.06
% 9.56/3.29 MUC search : 0.00
% 9.56/3.29 Cooper : 0.00
% 9.56/3.29 Total : 2.27
% 9.56/3.29 Index Insertion : 0.00
% 9.56/3.29 Index Deletion : 0.00
% 9.56/3.29 Index Matching : 0.00
% 9.56/3.29 BG Taut test : 0.00
%------------------------------------------------------------------------------