TSTP Solution File: NUM473+1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM473+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 : n025.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 10:51:48 EDT 2023
% Result : Theorem 105.44s 88.05s
% Output : CNFRefutation 105.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 38
% Syntax : Number of formulae : 139 ( 56 unt; 17 typ; 2 def)
% Number of atoms : 310 ( 101 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 315 ( 127 ~; 140 |; 28 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Maximal term depth : 3 ( 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 : 62 (; 62 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xq > xp > xn > xm > xl > sz10 > sz00 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xq,type,
xq: $i ).
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(xp,type,
xp: $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_362,negated_conjecture,
~ sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_357,hypothesis,
xl != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1347) ).
tff(f_352,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
tff(f_355,hypothesis,
( doDivides0(xl,xm)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324_04) ).
tff(f_358,hypothesis,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).
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_359,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).
tff(f_212,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
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_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_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
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(f_296,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
tff(f_360,hypothesis,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1409) ).
tff(f_258,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
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_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_189,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
tff(c_135,plain,
~ sdtlseqdt0(xp,xq),
inference(cnfTransformation,[status(thm)],[f_362]) ).
tff(c_127,plain,
xl != sz00,
inference(cnfTransformation,[status(thm)],[f_357]) ).
tff(c_121,plain,
aNaturalNumber0(xl),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_119,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_125,plain,
doDivides0(xl,xm),
inference(cnfTransformation,[status(thm)],[f_355]) ).
tff(c_129,plain,
sdtsldt0(xm,xl) = xp,
inference(cnfTransformation,[status(thm)],[f_358]) ).
tff(c_37322,plain,
! [W1_473,W0_474] :
( aNaturalNumber0(sdtsldt0(W1_473,W0_474))
| ~ doDivides0(W0_474,W1_473)
| ( sz00 = W0_474 )
| ~ aNaturalNumber0(W1_473)
| ~ aNaturalNumber0(W0_474) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_37362,plain,
( aNaturalNumber0(xp)
| ~ doDivides0(xl,xm)
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_129,c_37322]) ).
tff(c_37379,plain,
( aNaturalNumber0(xp)
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_125,c_37362]) ).
tff(c_37380,plain,
aNaturalNumber0(xp),
inference(negUnitSimplification,[status(thm)],[c_127,c_37379]) ).
tff(c_117,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_352]) ).
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_123,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnfTransformation,[status(thm)],[f_355]) ).
tff(c_131,plain,
sdtsldt0(sdtpldt0(xm,xn),xl) = xq,
inference(cnfTransformation,[status(thm)],[f_359]) ).
tff(c_37359,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_131,c_37322]) ).
tff(c_37376,plain,
( aNaturalNumber0(xq)
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_123,c_37359]) ).
tff(c_37377,plain,
( aNaturalNumber0(xq)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(negUnitSimplification,[status(thm)],[c_127,c_37376]) ).
tff(c_42022,plain,
~ aNaturalNumber0(sdtpldt0(xm,xn)),
inference(splitLeft,[status(thm)],[c_37377]) ).
tff(c_42025,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[c_10,c_42022]) ).
tff(c_42029,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_119,c_117,c_42025]) ).
tff(c_42030,plain,
aNaturalNumber0(xq),
inference(splitRight,[status(thm)],[c_37377]) ).
tff(c_70,plain,
! [W1_50,W0_49] :
( sdtlseqdt0(W1_50,W0_49)
| sdtlseqdt0(W0_49,W1_50)
| ~ aNaturalNumber0(W1_50)
| ~ aNaturalNumber0(W0_49) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_72,plain,
! [W1_50] :
( sdtlseqdt0(W1_50,W1_50)
| ~ aNaturalNumber0(W1_50) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_330,plain,
! [W0_86] :
( ( sdtpldt0(W0_86,sz00) = W0_86 )
| ~ aNaturalNumber0(W0_86) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_350,plain,
sdtpldt0(xm,sz00) = xm,
inference(resolution,[status(thm)],[c_119,c_330]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_199,plain,
! [W0_83] :
( ( sdtasdt0(sz10,W0_83) = W0_83 )
| ~ aNaturalNumber0(W0_83) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_218,plain,
sdtasdt0(sz10,xn) = xn,
inference(resolution,[status(thm)],[c_117,c_199]) ).
tff(c_1371,plain,
! [W1_110,W0_111] :
( sdtlseqdt0(W1_110,sdtasdt0(W1_110,W0_111))
| ( sz00 = W0_111 )
| ~ aNaturalNumber0(W1_110)
| ~ aNaturalNumber0(W0_111) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_1437,plain,
( sdtlseqdt0(sz10,xn)
| ( xn = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_218,c_1371]) ).
tff(c_1518,plain,
( sdtlseqdt0(sz10,xn)
| ( xn = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_117,c_8,c_1437]) ).
tff(c_3426,plain,
xn = sz00,
inference(splitLeft,[status(thm)],[c_1518]) ).
tff(c_3444,plain,
sdtsldt0(sdtpldt0(xm,sz00),xl) = xq,
inference(demodulation,[status(thm),theory(equality)],[c_3426,c_131]) ).
tff(c_3466,plain,
xq = xp,
inference(demodulation,[status(thm),theory(equality)],[c_129,c_350,c_3444]) ).
tff(c_3595,plain,
~ sdtlseqdt0(xp,xp),
inference(demodulation,[status(thm),theory(equality)],[c_3466,c_135]) ).
tff(c_3605,plain,
~ aNaturalNumber0(xp),
inference(resolution,[status(thm)],[c_72,c_3595]) ).
tff(c_4102,plain,
! [W1_178,W0_179] :
( aNaturalNumber0(sdtsldt0(W1_178,W0_179))
| ~ doDivides0(W0_179,W1_178)
| ( sz00 = W0_179 )
| ~ aNaturalNumber0(W1_178)
| ~ aNaturalNumber0(W0_179) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_4136,plain,
( aNaturalNumber0(xp)
| ~ doDivides0(xl,xm)
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_129,c_4102]) ).
tff(c_4149,plain,
( aNaturalNumber0(xp)
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_125,c_4136]) ).
tff(c_4151,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_127,c_3605,c_4149]) ).
tff(c_4153,plain,
xn != sz00,
inference(splitRight,[status(thm)],[c_1518]) ).
tff(c_6,plain,
sz10 != sz00,
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_299,plain,
! [W0_85] :
( ( sdtasdt0(W0_85,sz10) = W0_85 )
| ~ aNaturalNumber0(W0_85) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_319,plain,
sdtasdt0(xm,sz10) = xm,
inference(resolution,[status(thm)],[c_119,c_299]) ).
tff(c_1416,plain,
( sdtlseqdt0(xm,xm)
| ( sz10 = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_319,c_1371]) ).
tff(c_1499,plain,
( sdtlseqdt0(xm,xm)
| ( sz10 = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_119,c_1416]) ).
tff(c_1500,plain,
sdtlseqdt0(xm,xm),
inference(negUnitSimplification,[status(thm)],[c_6,c_1499]) ).
tff(c_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_42124,plain,
! [W0_528,W2_529] :
( ( sdtmndt0(sdtpldt0(W0_528,W2_529),W0_528) = W2_529 )
| ~ aNaturalNumber0(W2_529)
| ~ sdtlseqdt0(W0_528,sdtpldt0(W0_528,W2_529))
| ~ aNaturalNumber0(sdtpldt0(W0_528,W2_529))
| ~ aNaturalNumber0(W0_528) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_42175,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_350,c_42124]) ).
tff(c_42218,plain,
sdtmndt0(xm,xm) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_119,c_119,c_350,c_1500,c_4,c_350,c_42175]) ).
tff(c_37650,plain,
! [W0_481,W1_482] :
( ( sdtasdt0(W0_481,sdtsldt0(W1_482,W0_481)) = W1_482 )
| ~ doDivides0(W0_481,W1_482)
| ( sz00 = W0_481 )
| ~ aNaturalNumber0(W1_482)
| ~ aNaturalNumber0(W0_481) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_37673,plain,
( ( sdtasdt0(xl,xp) = xm )
| ~ doDivides0(xl,xm)
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_129,c_37650]) ).
tff(c_37680,plain,
( ( sdtasdt0(xl,xp) = xm )
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_125,c_37673]) ).
tff(c_37681,plain,
sdtasdt0(xl,xp) = xm,
inference(negUnitSimplification,[status(thm)],[c_127,c_37680]) ).
tff(c_3348,plain,
! [W0_158,W1_159] :
( iLess0(W0_158,W1_159)
| ~ sdtlseqdt0(W0_158,W1_159)
| ( W1_159 = W0_158 )
| ~ aNaturalNumber0(W1_159)
| ~ aNaturalNumber0(W0_158) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_58796,plain,
! [W1_576,W0_577] :
( iLess0(W1_576,W0_577)
| ( W1_576 = W0_577 )
| sdtlseqdt0(W0_577,W1_576)
| ~ aNaturalNumber0(W1_576)
| ~ aNaturalNumber0(W0_577) ),
inference(resolution,[status(thm)],[c_70,c_3348]) ).
tff(c_58853,plain,
( iLess0(xq,xp)
| ( xq = xp )
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_58796,c_135]) ).
tff(c_58915,plain,
( iLess0(xq,xp)
| ( xq = xp ) ),
inference(demodulation,[status(thm),theory(equality)],[c_37380,c_42030,c_58853]) ).
tff(c_58916,plain,
xq = xp,
inference(splitLeft,[status(thm)],[c_58915]) ).
tff(c_42031,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(splitRight,[status(thm)],[c_37377]) ).
tff(c_37670,plain,
( ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_131,c_37650]) ).
tff(c_37677,plain,
( ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_123,c_37670]) ).
tff(c_37678,plain,
( ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(negUnitSimplification,[status(thm)],[c_127,c_37677]) ).
tff(c_56608,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(demodulation,[status(thm),theory(equality)],[c_42031,c_37678]) ).
tff(c_133,plain,
sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(cnfTransformation,[status(thm)],[f_360]) ).
tff(c_42199,plain,
( ( sdtmndt0(sdtpldt0(xm,xn),xm) = xn )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[c_133,c_42124]) ).
tff(c_42235,plain,
sdtmndt0(sdtpldt0(xm,xn),xm) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_119,c_42031,c_117,c_42199]) ).
tff(c_56615,plain,
sdtmndt0(sdtasdt0(xl,xq),xm) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_56608,c_42235]) ).
tff(c_58928,plain,
sdtmndt0(sdtasdt0(xl,xp),xm) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_58916,c_56615]) ).
tff(c_58989,plain,
xn = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_42218,c_37681,c_58928]) ).
tff(c_58991,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4153,c_58989]) ).
tff(c_58993,plain,
xq != xp,
inference(splitRight,[status(thm)],[c_58915]) ).
tff(c_109,plain,
! [W0_70,W1_71] :
( ( sdtasdt0(W0_70,sdtsldt0(W1_71,W0_70)) = W1_71 )
| ~ doDivides0(W0_70,W1_71)
| ( sz00 = W0_70 )
| ~ aNaturalNumber0(W1_71)
| ~ aNaturalNumber0(W0_70) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_42402,plain,
! [W0_530,W1_531,W2_532] :
( sdtlseqdt0(sdtasdt0(W0_530,W1_531),sdtasdt0(W0_530,W2_532))
| ~ sdtlseqdt0(W1_531,W2_532)
| ( W2_532 = W1_531 )
| ( sz00 = W0_530 )
| ~ aNaturalNumber0(W2_532)
| ~ aNaturalNumber0(W1_531)
| ~ aNaturalNumber0(W0_530) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_193751,plain,
! [W0_1085,W1_1086,W1_1087] :
( sdtlseqdt0(sdtasdt0(W0_1085,W1_1086),W1_1087)
| ~ sdtlseqdt0(W1_1086,sdtsldt0(W1_1087,W0_1085))
| ( sdtsldt0(W1_1087,W0_1085) = W1_1086 )
| ( sz00 = W0_1085 )
| ~ aNaturalNumber0(sdtsldt0(W1_1087,W0_1085))
| ~ aNaturalNumber0(W1_1086)
| ~ aNaturalNumber0(W0_1085)
| ~ doDivides0(W0_1085,W1_1087)
| ( sz00 = W0_1085 )
| ~ aNaturalNumber0(W1_1087)
| ~ aNaturalNumber0(W0_1085) ),
inference(superposition,[status(thm),theory(equality)],[c_109,c_42402]) ).
tff(c_692,plain,
! [W1_96,W0_97] :
( ( sdtasdt0(W1_96,W0_97) = sdtasdt0(W0_97,W1_96) )
| ~ aNaturalNumber0(W1_96)
| ~ aNaturalNumber0(W0_97) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_44128,plain,
! [W0_538] :
( ( sdtasdt0(xl,W0_538) = sdtasdt0(W0_538,xl) )
| ~ aNaturalNumber0(W0_538) ),
inference(resolution,[status(thm)],[c_121,c_692]) ).
tff(c_44190,plain,
sdtasdt0(xq,xl) = sdtasdt0(xl,xq),
inference(resolution,[status(thm)],[c_42030,c_44128]) ).
tff(c_12,plain,
! [W0_4,W1_5] :
( aNaturalNumber0(sdtasdt0(W0_4,W1_5))
| ~ aNaturalNumber0(W1_5)
| ~ aNaturalNumber0(W0_4) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_53997,plain,
( aNaturalNumber0(sdtasdt0(xl,xq))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xq) ),
inference(superposition,[status(thm),theory(equality)],[c_44190,c_12]) ).
tff(c_54046,plain,
aNaturalNumber0(sdtasdt0(xl,xq)),
inference(demodulation,[status(thm),theory(equality)],[c_42030,c_121,c_53997]) ).
tff(c_3387,plain,
( iLess0(xm,sdtpldt0(xm,xn))
| ( sdtpldt0(xm,xn) = xm )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[c_133,c_3348]) ).
tff(c_3424,plain,
( iLess0(xm,sdtpldt0(xm,xn))
| ( sdtpldt0(xm,xn) = xm )
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(demodulation,[status(thm),theory(equality)],[c_119,c_3387]) ).
tff(c_66211,plain,
( iLess0(xm,sdtasdt0(xl,xq))
| ( sdtasdt0(xl,xq) = xm ) ),
inference(demodulation,[status(thm),theory(equality)],[c_54046,c_56608,c_56608,c_56608,c_3424]) ).
tff(c_66212,plain,
sdtasdt0(xl,xq) = xm,
inference(splitLeft,[status(thm)],[c_66211]) ).
tff(c_66223,plain,
sdtmndt0(xm,xm) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_66212,c_56615]) ).
tff(c_66243,plain,
xn = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_42218,c_66223]) ).
tff(c_66245,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_4153,c_66243]) ).
tff(c_66247,plain,
sdtasdt0(xl,xq) != xm,
inference(splitRight,[status(thm)],[c_66211]) ).
tff(c_1588,plain,
! [W1_114,W0_115] :
( ( W1_114 = W0_115 )
| ~ sdtlseqdt0(W1_114,W0_115)
| ~ sdtlseqdt0(W0_115,W1_114)
| ~ aNaturalNumber0(W1_114)
| ~ aNaturalNumber0(W0_115) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_1612,plain,
( ( sdtpldt0(xm,xn) = xm )
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(resolution,[status(thm)],[c_133,c_1588]) ).
tff(c_1646,plain,
( ( sdtpldt0(xm,xn) = xm )
| ~ sdtlseqdt0(sdtpldt0(xm,xn),xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(demodulation,[status(thm),theory(equality)],[c_119,c_1612]) ).
tff(c_67509,plain,
( ( sdtasdt0(xl,xq) = xm )
| ~ sdtlseqdt0(sdtasdt0(xl,xq),xm) ),
inference(demodulation,[status(thm),theory(equality)],[c_54046,c_56608,c_56608,c_56608,c_1646]) ).
tff(c_67510,plain,
~ sdtlseqdt0(sdtasdt0(xl,xq),xm),
inference(negUnitSimplification,[status(thm)],[c_66247,c_67509]) ).
tff(c_193860,plain,
( ~ sdtlseqdt0(xq,sdtsldt0(xm,xl))
| ( sdtsldt0(xm,xl) = xq )
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ aNaturalNumber0(xq)
| ~ doDivides0(xl,xm)
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(resolution,[status(thm)],[c_193751,c_67510]) ).
tff(c_194531,plain,
( ~ sdtlseqdt0(xq,xp)
| ( xq = xp )
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_125,c_42030,c_37380,c_129,c_129,c_129,c_193860]) ).
tff(c_194532,plain,
~ sdtlseqdt0(xq,xp),
inference(negUnitSimplification,[status(thm)],[c_127,c_58993,c_194531]) ).
tff(c_194979,plain,
( sdtlseqdt0(xp,xq)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_70,c_194532]) ).
tff(c_194992,plain,
sdtlseqdt0(xp,xq),
inference(demodulation,[status(thm),theory(equality)],[c_37380,c_42030,c_194979]) ).
tff(c_194994,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_135,c_194992]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM473+1 : 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
% 0.14/0.35 % Computer : n025.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 14:36:34 EDT 2023
% 0.14/0.35 % CPUTime :
% 105.44/88.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 105.55/88.06
% 105.55/88.06 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 105.73/88.11
% 105.73/88.11 Inference rules
% 105.73/88.11 ----------------------
% 105.73/88.11 #Ref : 20
% 105.73/88.11 #Sup : 41706
% 105.73/88.11 #Fact : 16
% 105.73/88.11 #Define : 0
% 105.73/88.11 #Split : 39
% 105.73/88.11 #Chain : 0
% 105.73/88.11 #Close : 0
% 105.73/88.11
% 105.73/88.11 Ordering : KBO
% 105.73/88.11
% 105.73/88.11 Simplification rules
% 105.73/88.11 ----------------------
% 105.73/88.11 #Subsume : 4323
% 105.73/88.11 #Demod : 89053
% 105.73/88.11 #Tautology : 10538
% 105.73/88.11 #SimpNegUnit : 7054
% 105.73/88.11 #BackRed : 951
% 105.73/88.11
% 105.73/88.11 #Partial instantiations: 0
% 105.73/88.11 #Strategies tried : 1
% 105.73/88.11
% 105.73/88.11 Timing (in seconds)
% 105.73/88.11 ----------------------
% 105.73/88.11 Preprocessing : 0.68
% 105.73/88.11 Parsing : 0.35
% 105.73/88.11 CNF conversion : 0.05
% 105.73/88.11 Main loop : 86.22
% 105.73/88.11 Inferencing : 6.56
% 105.73/88.11 Reduction : 59.05
% 105.73/88.11 Demodulation : 50.54
% 105.73/88.11 BG Simplification : 0.48
% 105.73/88.11 Subsumption : 17.61
% 105.73/88.11 Abstraction : 0.75
% 105.73/88.11 MUC search : 0.00
% 105.73/88.11 Cooper : 0.00
% 105.73/88.12 Total : 86.98
% 105.73/88.12 Index Insertion : 0.00
% 105.73/88.12 Index Deletion : 0.00
% 105.73/88.12 Index Matching : 0.00
% 105.73/88.12 BG Taut test : 0.00
%------------------------------------------------------------------------------