TSTP Solution File: NUM507+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM507+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n021.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 10:51:55 EDT 2023
% Result : Theorem 25.60s 12.51s
% Output : CNFRefutation 25.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 43
% Syntax : Number of formulae : 171 ( 67 unt; 20 typ; 2 def)
% Number of atoms : 361 ( 92 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 371 ( 161 ~; 148 |; 37 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 13 >; 9 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 82 (; 82 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > xp > xn > xm > xk > sz10 > sz00 > #skF_4 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xk,type,
xk: $i ).
tff(xr,type,
xr: $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff('#skF_4',type,
'#skF_4': $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(isPrime0,type,
isPrime0: $i > $o ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
tff('#skF_3',type,
'#skF_3': $i > $i ).
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_423,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
tff(f_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
tff(f_403,definition,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ( W0 != sz00 )
& ( W0 != sz10 )
& ! [W1] :
( ( aNaturalNumber0(W1)
& doDivides0(W1,W0) )
=> ( ( W1 = sz10 )
| ( W1 = W0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
tff(f_87,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
tff(f_442,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
tff(f_477,hypothesis,
( ( xk != xp )
& sdtlseqdt0(xk,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2377) ).
tff(f_189,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
tff(f_456,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
tff(f_470,hypothesis,
( aNaturalNumber0(xr)
& doDivides0(xr,xk)
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
tff(f_53,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
tff(f_296,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> iLess0(W0,W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
tff(f_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
tff(f_41,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
tff(f_234,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != W1 )
& sdtlseqdt0(W0,W1) )
=> ! [W2] :
( aNaturalNumber0(W2)
=> ( ( sdtpldt0(W2,W0) != sdtpldt0(W2,W1) )
& sdtlseqdt0(sdtpldt0(W2,W0),sdtpldt0(W2,W1))
& ( sdtpldt0(W0,W2) != sdtpldt0(W1,W2) )
& sdtlseqdt0(sdtpldt0(W0,W2),sdtpldt0(W1,W2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
tff(f_212,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
tff(f_482,negated_conjecture,
~ ( ( sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) )
& sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_473,hypothesis,
( sdtlseqdt0(xr,xk)
& doDivides0(xr,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).
tff(f_201,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
tff(f_115,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
tff(c_147,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_145,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_423]) ).
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_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_135,plain,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(cnfTransformation,[status(thm)],[f_403]) ).
tff(c_195,plain,
~ isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_135]) ).
tff(c_143,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_423]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_35586,plain,
! [W0_459] :
( ( sdtasdt0(sz10,W0_459) = W0_459 )
| ~ aNaturalNumber0(W0_459) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_35607,plain,
sdtasdt0(sz10,xp) = xp,
inference(resolution,[status(thm)],[c_143,c_35586]) ).
tff(c_38376,plain,
! [W1_496,W0_497] :
( sdtlseqdt0(W1_496,sdtasdt0(W1_496,W0_497))
| ( sz00 = W0_497 )
| ~ aNaturalNumber0(W1_496)
| ~ aNaturalNumber0(W0_497) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_38466,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_35607,c_38376]) ).
tff(c_38600,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_38466]) ).
tff(c_38785,plain,
xp = sz00,
inference(splitLeft,[status(thm)],[c_38600]) ).
tff(c_153,plain,
isPrime0(xp),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_38837,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_38785,c_153]) ).
tff(c_38875,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_195,c_38837]) ).
tff(c_38877,plain,
xp != sz00,
inference(splitRight,[status(thm)],[c_38600]) ).
tff(c_189,plain,
xp != xk,
inference(cnfTransformation,[status(thm)],[f_477]) ).
tff(c_187,plain,
sdtlseqdt0(xk,xp),
inference(cnfTransformation,[status(thm)],[f_477]) ).
tff(c_38663,plain,
! [W1_498,W0_499] :
( ( W1_498 = W0_499 )
| ~ sdtlseqdt0(W1_498,W0_499)
| ~ sdtlseqdt0(W0_499,W1_498)
| ~ aNaturalNumber0(W1_498)
| ~ aNaturalNumber0(W0_499) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_38695,plain,
( ( xp = xk )
| ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_187,c_38663]) ).
tff(c_38748,plain,
( ( xp = xk )
| ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_38695]) ).
tff(c_38749,plain,
( ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk) ),
inference(negUnitSimplification,[status(thm)],[c_189,c_38748]) ).
tff(c_38783,plain,
~ aNaturalNumber0(xk),
inference(splitLeft,[status(thm)],[c_38749]) ).
tff(c_151,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnfTransformation,[status(thm)],[f_442]) ).
tff(c_167,plain,
sdtsldt0(sdtasdt0(xn,xm),xp) = xk,
inference(cnfTransformation,[status(thm)],[f_456]) ).
tff(c_43935,plain,
! [W1_557,W0_558] :
( aNaturalNumber0(sdtsldt0(W1_557,W0_558))
| ~ doDivides0(W0_558,W1_557)
| ( sz00 = W0_558 )
| ~ aNaturalNumber0(W1_557)
| ~ aNaturalNumber0(W0_558) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_43981,plain,
( aNaturalNumber0(xk)
| ~ doDivides0(xp,sdtasdt0(xn,xm))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_167,c_43935]) ).
tff(c_43998,plain,
( aNaturalNumber0(xk)
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_151,c_43981]) ).
tff(c_43999,plain,
~ aNaturalNumber0(sdtasdt0(xn,xm)),
inference(negUnitSimplification,[status(thm)],[c_38877,c_38783,c_43998]) ).
tff(c_44412,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_12,c_43999]) ).
tff(c_44416,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_44412]) ).
tff(c_44417,plain,
~ sdtlseqdt0(xp,xk),
inference(splitRight,[status(thm)],[c_38749]) ).
tff(c_181,plain,
aNaturalNumber0(xr),
inference(cnfTransformation,[status(thm)],[f_470]) ).
tff(c_36137,plain,
! [W1_470,W0_471] :
( ( sdtpldt0(W1_470,W0_471) = sdtpldt0(W0_471,W1_470) )
| ~ aNaturalNumber0(W1_470)
| ~ aNaturalNumber0(W0_471) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_36223,plain,
! [W0_473] :
( ( sdtpldt0(xm,W0_473) = sdtpldt0(W0_473,xm) )
| ~ aNaturalNumber0(W0_473) ),
inference(resolution,[status(thm)],[c_145,c_36137]) ).
tff(c_36269,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(resolution,[status(thm)],[c_147,c_36223]) ).
tff(c_409,plain,
! [W0_104] :
( ( sdtasdt0(sz10,W0_104) = W0_104 )
| ~ aNaturalNumber0(W0_104) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_428,plain,
sdtasdt0(sz10,xp) = xp,
inference(resolution,[status(thm)],[c_143,c_409]) ).
tff(c_1571,plain,
! [W1_127,W0_128] :
( sdtlseqdt0(W1_127,sdtasdt0(W1_127,W0_128))
| ( sz00 = W0_128 )
| ~ aNaturalNumber0(W1_127)
| ~ aNaturalNumber0(W0_128) ),
inference(cnfTransformation,[status(thm)],[f_278]) ).
tff(c_1610,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_428,c_1571]) ).
tff(c_1693,plain,
( sdtlseqdt0(sz10,xp)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_8,c_1610]) ).
tff(c_6589,plain,
xp = sz00,
inference(splitLeft,[status(thm)],[c_1693]) ).
tff(c_6628,plain,
isPrime0(sz00),
inference(demodulation,[status(thm),theory(equality)],[c_6589,c_153]) ).
tff(c_6653,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_195,c_6628]) ).
tff(c_6655,plain,
xp != sz00,
inference(splitRight,[status(thm)],[c_1693]) ).
tff(c_12056,plain,
! [W0_274,W1_275] :
( iLess0(W0_274,W1_275)
| ~ sdtlseqdt0(W0_274,W1_275)
| ( W1_275 = W0_274 )
| ~ aNaturalNumber0(W1_275)
| ~ aNaturalNumber0(W0_274) ),
inference(cnfTransformation,[status(thm)],[f_296]) ).
tff(c_12119,plain,
( iLess0(xk,xp)
| ( xp = xk )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_187,c_12056]) ).
tff(c_12188,plain,
( iLess0(xk,xp)
| ( xp = xk )
| ~ aNaturalNumber0(xk) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_12119]) ).
tff(c_12189,plain,
( iLess0(xk,xp)
| ~ aNaturalNumber0(xk) ),
inference(negUnitSimplification,[status(thm)],[c_189,c_12188]) ).
tff(c_12197,plain,
~ aNaturalNumber0(xk),
inference(splitLeft,[status(thm)],[c_12189]) ).
tff(c_865,plain,
! [W1_119,W0_120] :
( ( sdtasdt0(W1_119,W0_120) = sdtasdt0(W0_120,W1_119) )
| ~ aNaturalNumber0(W1_119)
| ~ aNaturalNumber0(W0_120) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_13469,plain,
! [W0_289] :
( ( sdtasdt0(xn,W0_289) = sdtasdt0(W0_289,xn) )
| ~ aNaturalNumber0(W0_289) ),
inference(resolution,[status(thm)],[c_147,c_865]) ).
tff(c_13566,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c_145,c_13469]) ).
tff(c_13585,plain,
( aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_13566,c_12]) ).
tff(c_13595,plain,
aNaturalNumber0(sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_13585]) ).
tff(c_13576,plain,
doDivides0(xp,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_13566,c_151]) ).
tff(c_13574,plain,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(demodulation,[status(thm),theory(equality)],[c_13566,c_167]) ).
tff(c_14276,plain,
! [W1_297,W0_298] :
( aNaturalNumber0(sdtsldt0(W1_297,W0_298))
| ~ doDivides0(W0_298,W1_297)
| ( sz00 = W0_298 )
| ~ aNaturalNumber0(W1_297)
| ~ aNaturalNumber0(W0_298) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_14313,plain,
( aNaturalNumber0(xk)
| ~ doDivides0(xp,sdtasdt0(xm,xn))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_13574,c_14276]) ).
tff(c_14327,plain,
( aNaturalNumber0(xk)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_13595,c_13576,c_14313]) ).
tff(c_14329,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6655,c_12197,c_14327]) ).
tff(c_14331,plain,
aNaturalNumber0(xk),
inference(splitRight,[status(thm)],[c_12189]) ).
tff(c_989,plain,
! [W1_122,W0_123] :
( ( sdtpldt0(W1_122,W0_123) = sdtpldt0(W0_123,W1_122) )
| ~ aNaturalNumber0(W1_122)
| ~ aNaturalNumber0(W0_123) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_11576,plain,
! [W0_271] :
( ( sdtpldt0(xm,W0_271) = sdtpldt0(W0_271,xm) )
| ~ aNaturalNumber0(W0_271) ),
inference(resolution,[status(thm)],[c_145,c_989]) ).
tff(c_11667,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(resolution,[status(thm)],[c_147,c_11576]) ).
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_31098,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_11667,c_10]) ).
tff(c_31114,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_31098]) ).
tff(c_35270,plain,
! [W2_451,W0_452,W1_453] :
( sdtlseqdt0(sdtpldt0(W2_451,W0_452),sdtpldt0(W2_451,W1_453))
| ~ aNaturalNumber0(W2_451)
| ~ sdtlseqdt0(W0_452,W1_453)
| ( W1_453 = W0_452 )
| ~ aNaturalNumber0(W1_453)
| ~ aNaturalNumber0(W0_452) ),
inference(cnfTransformation,[status(thm)],[f_234]) ).
tff(c_14468,plain,
! [W1_299,W0_300] :
( ( W1_299 = W0_300 )
| ~ sdtlseqdt0(W1_299,W0_300)
| ~ sdtlseqdt0(W0_300,W1_299)
| ~ aNaturalNumber0(W1_299)
| ~ aNaturalNumber0(W0_300) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_14514,plain,
( ( xp = xk )
| ~ sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_187,c_14468]) ).
tff(c_14589,plain,
( ( xp = xk )
| ~ sdtlseqdt0(xp,xk) ),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_14331,c_14514]) ).
tff(c_14590,plain,
~ sdtlseqdt0(xp,xk),
inference(negUnitSimplification,[status(thm)],[c_189,c_14589]) ).
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_17287,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_11667,c_10]) ).
tff(c_17307,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_17287]) ).
tff(c_21205,plain,
! [W2_356,W0_357,W1_358] :
( sdtlseqdt0(sdtpldt0(W2_356,W0_357),sdtpldt0(W2_356,W1_358))
| ~ aNaturalNumber0(W2_356)
| ~ sdtlseqdt0(W0_357,W1_358)
| ( W1_358 = W0_357 )
| ~ aNaturalNumber0(W1_358)
| ~ aNaturalNumber0(W0_357) ),
inference(cnfTransformation,[status(thm)],[f_234]) ).
tff(c_191,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(cnfTransformation,[status(thm)],[f_482]) ).
tff(c_196,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(splitLeft,[status(thm)],[c_191]) ).
tff(c_17268,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xn),xr),sdtpldt0(sdtpldt0(xm,xn),xp)),
inference(demodulation,[status(thm),theory(equality)],[c_11667,c_11667,c_196]) ).
tff(c_21208,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xr,xp)
| ( xr = xp )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xr) ),
inference(resolution,[status(thm)],[c_21205,c_17268]) ).
tff(c_21368,plain,
( ~ sdtlseqdt0(xr,xp)
| ( xr = xp ) ),
inference(demodulation,[status(thm),theory(equality)],[c_181,c_143,c_17307,c_21208]) ).
tff(c_21526,plain,
~ sdtlseqdt0(xr,xp),
inference(splitLeft,[status(thm)],[c_21368]) ).
tff(c_21535,plain,
( sdtlseqdt0(xp,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_70,c_21526]) ).
tff(c_21548,plain,
sdtlseqdt0(xp,xr),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_181,c_21535]) ).
tff(c_185,plain,
sdtlseqdt0(xr,xk),
inference(cnfTransformation,[status(thm)],[f_473]) ).
tff(c_17062,plain,
! [W0_329,W2_330,W1_331] :
( sdtlseqdt0(W0_329,W2_330)
| ~ sdtlseqdt0(W1_331,W2_330)
| ~ sdtlseqdt0(W0_329,W1_331)
| ~ aNaturalNumber0(W2_330)
| ~ aNaturalNumber0(W1_331)
| ~ aNaturalNumber0(W0_329) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_17138,plain,
! [W0_329] :
( sdtlseqdt0(W0_329,xk)
| ~ sdtlseqdt0(W0_329,xr)
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(W0_329) ),
inference(resolution,[status(thm)],[c_185,c_17062]) ).
tff(c_29057,plain,
! [W0_387] :
( sdtlseqdt0(W0_387,xk)
| ~ sdtlseqdt0(W0_387,xr)
| ~ aNaturalNumber0(W0_387) ),
inference(demodulation,[status(thm),theory(equality)],[c_181,c_14331,c_17138]) ).
tff(c_29063,plain,
( sdtlseqdt0(xp,xk)
| ~ aNaturalNumber0(xp) ),
inference(resolution,[status(thm)],[c_21548,c_29057]) ).
tff(c_29098,plain,
sdtlseqdt0(xp,xk),
inference(demodulation,[status(thm),theory(equality)],[c_143,c_29063]) ).
tff(c_29100,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_14590,c_29098]) ).
tff(c_29101,plain,
xr = xp,
inference(splitRight,[status(thm)],[c_21368]) ).
tff(c_14516,plain,
( ( xr = xk )
| ~ sdtlseqdt0(xk,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_185,c_14468]) ).
tff(c_14593,plain,
( ( xr = xk )
| ~ sdtlseqdt0(xk,xr) ),
inference(demodulation,[status(thm),theory(equality)],[c_14331,c_181,c_14516]) ).
tff(c_14698,plain,
~ sdtlseqdt0(xk,xr),
inference(splitLeft,[status(thm)],[c_14593]) ).
tff(c_29158,plain,
~ sdtlseqdt0(xk,xp),
inference(demodulation,[status(thm),theory(equality)],[c_29101,c_14698]) ).
tff(c_29227,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_187,c_29158]) ).
tff(c_29228,plain,
xr = xk,
inference(splitRight,[status(thm)],[c_14593]) ).
tff(c_29271,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xk),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(demodulation,[status(thm),theory(equality)],[c_29228,c_196]) ).
tff(c_31075,plain,
~ sdtlseqdt0(sdtpldt0(sdtpldt0(xm,xn),xk),sdtpldt0(sdtpldt0(xm,xn),xp)),
inference(demodulation,[status(thm),theory(equality)],[c_11667,c_11667,c_29271]) ).
tff(c_35275,plain,
( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ sdtlseqdt0(xk,xp)
| ( xp = xk )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xk) ),
inference(resolution,[status(thm)],[c_35270,c_31075]) ).
tff(c_35410,plain,
xp = xk,
inference(demodulation,[status(thm),theory(equality)],[c_14331,c_143,c_187,c_31114,c_35275]) ).
tff(c_35412,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_189,c_35410]) ).
tff(c_35413,plain,
sdtpldt0(sdtpldt0(xn,xm),xr) = sdtpldt0(sdtpldt0(xn,xm),xp),
inference(splitRight,[status(thm)],[c_191]) ).
tff(c_36442,plain,
sdtpldt0(sdtpldt0(xm,xn),xr) = sdtpldt0(sdtpldt0(xm,xn),xp),
inference(demodulation,[status(thm),theory(equality)],[c_36269,c_36269,c_35413]) ).
tff(c_35686,plain,
! [W0_461,W1_462] :
( aNaturalNumber0(sdtpldt0(W0_461,W1_462))
| ~ aNaturalNumber0(W1_462)
| ~ aNaturalNumber0(W0_461) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_35731,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(superposition,[status(thm),theory(equality)],[c_35413,c_35686]) ).
tff(c_35755,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_181,c_35731]) ).
tff(c_35940,plain,
~ aNaturalNumber0(sdtpldt0(xn,xm)),
inference(splitLeft,[status(thm)],[c_35755]) ).
tff(c_35943,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(resolution,[status(thm)],[c_10,c_35940]) ).
tff(c_35947,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_147,c_145,c_35943]) ).
tff(c_35949,plain,
aNaturalNumber0(sdtpldt0(xn,xm)),
inference(splitRight,[status(thm)],[c_35755]) ).
tff(c_36161,plain,
! [W0_471] :
( ( sdtpldt0(sdtpldt0(xn,xm),W0_471) = sdtpldt0(W0_471,sdtpldt0(xn,xm)) )
| ~ aNaturalNumber0(W0_471) ),
inference(resolution,[status(thm)],[c_35949,c_36137]) ).
tff(c_36936,plain,
! [W0_482] :
( ( sdtpldt0(sdtpldt0(xm,xn),W0_482) = sdtpldt0(W0_482,sdtpldt0(xm,xn)) )
| ~ aNaturalNumber0(W0_482) ),
inference(demodulation,[status(thm),theory(equality)],[c_36269,c_36269,c_36161]) ).
tff(c_36980,plain,
( ( sdtpldt0(sdtpldt0(xm,xn),xp) = sdtpldt0(xr,sdtpldt0(xm,xn)) )
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_36442,c_36936]) ).
tff(c_37010,plain,
sdtpldt0(sdtpldt0(xm,xn),xp) = sdtpldt0(xr,sdtpldt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_181,c_36980]) ).
tff(c_36440,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_36269,c_35949]) ).
tff(c_37219,plain,
sdtpldt0(sdtpldt0(xm,xn),xr) = sdtpldt0(xr,sdtpldt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_37010,c_36442]) ).
tff(c_68060,plain,
! [W0_716,W2_717,W1_718] :
( ( sdtpldt0(W0_716,W2_717) != sdtpldt0(W0_716,W1_718) )
| ( W2_717 = W1_718 )
| ~ aNaturalNumber0(W2_717)
| ~ aNaturalNumber0(W1_718)
| ~ aNaturalNumber0(W0_716) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_68116,plain,
! [W2_717] :
( ( sdtpldt0(sdtpldt0(xm,xn),W2_717) != sdtpldt0(xr,sdtpldt0(xm,xn)) )
| ( xr = W2_717 )
| ~ aNaturalNumber0(W2_717)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(superposition,[status(thm),theory(equality)],[c_37219,c_68060]) ).
tff(c_68357,plain,
! [W2_719] :
( ( sdtpldt0(sdtpldt0(xm,xn),W2_719) != sdtpldt0(xr,sdtpldt0(xm,xn)) )
| ( xr = W2_719 )
| ~ aNaturalNumber0(W2_719) ),
inference(demodulation,[status(thm),theory(equality)],[c_36440,c_181,c_68116]) ).
tff(c_68374,plain,
( ( xr = xp )
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_37010,c_68357]) ).
tff(c_68391,plain,
xr = xp,
inference(demodulation,[status(thm),theory(equality)],[c_143,c_68374]) ).
tff(c_68455,plain,
sdtlseqdt0(xp,xk),
inference(demodulation,[status(thm),theory(equality)],[c_68391,c_185]) ).
tff(c_68484,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_44417,c_68455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM507+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/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 14:40:21 EDT 2023
% 0.13/0.35 % CPUTime :
% 25.60/12.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.60/12.53
% 25.60/12.53 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.60/12.57
% 25.60/12.57 Inference rules
% 25.60/12.57 ----------------------
% 25.60/12.57 #Ref : 18
% 25.60/12.57 #Sup : 13533
% 25.60/12.57 #Fact : 4
% 25.60/12.57 #Define : 0
% 25.60/12.57 #Split : 104
% 25.60/12.57 #Chain : 0
% 25.60/12.57 #Close : 0
% 25.60/12.57
% 25.60/12.57 Ordering : KBO
% 25.60/12.57
% 25.60/12.57 Simplification rules
% 25.60/12.57 ----------------------
% 25.60/12.57 #Subsume : 714
% 25.60/12.57 #Demod : 27626
% 25.60/12.57 #Tautology : 5650
% 25.60/12.57 #SimpNegUnit : 2500
% 25.60/12.57 #BackRed : 3249
% 25.60/12.57
% 25.60/12.57 #Partial instantiations: 0
% 25.60/12.57 #Strategies tried : 1
% 25.60/12.57
% 25.60/12.57 Timing (in seconds)
% 25.60/12.57 ----------------------
% 25.60/12.58 Preprocessing : 0.71
% 25.60/12.58 Parsing : 0.36
% 25.60/12.58 CNF conversion : 0.06
% 25.60/12.58 Main loop : 10.65
% 25.60/12.58 Inferencing : 1.95
% 25.60/12.58 Reduction : 5.90
% 25.60/12.58 Demodulation : 4.89
% 25.60/12.58 BG Simplification : 0.16
% 25.60/12.58 Subsumption : 2.08
% 25.60/12.58 Abstraction : 0.20
% 25.60/12.58 MUC search : 0.00
% 25.60/12.58 Cooper : 0.00
% 25.60/12.58 Total : 11.44
% 25.60/12.58 Index Insertion : 0.00
% 25.60/12.58 Index Deletion : 0.00
% 25.60/12.58 Index Matching : 0.00
% 25.60/12.58 BG Taut test : 0.00
%------------------------------------------------------------------------------