%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM475+1 : TPTP v9.0.0. 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 : n027.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 : Wed Apr 9 07:56:03 PM UTC 2025
% Result : Theorem 57.78s 42.51s
% Output : CNFRefutation 57.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 71 ( 33 unt; 0 typ; 2 def)
% Number of atoms : 168 ( 56 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 165 ( 68 ~; 71 |; 14 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xr > 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(xr,type,
xr: $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_364,negated_conjecture,
xn != sdtasdt0(xl,xr),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_352,hypothesis,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324) ).
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_41,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(f_357,hypothesis,
xl != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1347) ).
tff(f_355,hypothesis,
( doDivides0(xl,xm)
& doDivides0(xl,sdtpldt0(xm,xn)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1324_04) ).
tff(f_359,hypothesis,
xq = sdtsldt0(sdtpldt0(xm,xn),xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1379) ).
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_358,hypothesis,
xp = sdtsldt0(xm,xl),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1360) ).
tff(f_360,hypothesis,
sdtlseqdt0(xp,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1395) ).
tff(f_361,hypothesis,
xr = sdtmndt0(xq,xp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1422) ).
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_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_362,hypothesis,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1459) ).
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/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
tff(c_139,plain,
sdtasdt0(xl,xr) != xn,
inference(cnfTransformation,[status(thm)],[f_364]) ).
tff(c_117,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_119,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_717,plain,
! [W1_101,W0_102] :
( ( sdtpldt0(W1_101,W0_102) = sdtpldt0(W0_102,W1_101) )
| ~ aNaturalNumber0(W1_101)
| ~ aNaturalNumber0(W0_102) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_125355,plain,
! [W0_1147] :
( ( sdtpldt0(xm,W0_1147) = sdtpldt0(W0_1147,xm) )
| ~ aNaturalNumber0(W0_1147) ),
inference(resolution,[status(thm)],[c_119,c_717]) ).
tff(c_125419,plain,
sdtpldt0(xn,xm) = sdtpldt0(xm,xn),
inference(resolution,[status(thm)],[c_117,c_125355]) ).
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_141992,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_125419,c_10]) ).
tff(c_142026,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_117,c_119,c_141992]) ).
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_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_29195,plain,
! [W0_585,W1_586] :
( ( sdtasdt0(W0_585,sdtsldt0(W1_586,W0_585)) = W1_586 )
| ~ doDivides0(W0_585,W1_586)
| ( sz00 = W0_585 )
| ~ aNaturalNumber0(W1_586)
| ~ aNaturalNumber0(W0_585) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_29215,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_29195]) ).
tff(c_29222,plain,
( ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_123,c_29215]) ).
tff(c_29223,plain,
( ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(negUnitSimplification,[status(thm)],[c_127,c_29222]) ).
tff(c_145087,plain,
sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
inference(demodulation,[status(thm),theory(equality)],[c_142026,c_29223]) ).
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_29218,plain,
( ( sdtasdt0(xl,xp) = xm )
| ~ doDivides0(xl,xm)
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_129,c_29195]) ).
tff(c_29225,plain,
( ( sdtasdt0(xl,xp) = xm )
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_125,c_29218]) ).
tff(c_29226,plain,
sdtasdt0(xl,xp) = xm,
inference(negUnitSimplification,[status(thm)],[c_127,c_29225]) ).
tff(c_133,plain,
sdtlseqdt0(xp,xq),
inference(cnfTransformation,[status(thm)],[f_360]) ).
tff(c_135,plain,
sdtmndt0(xq,xp) = xr,
inference(cnfTransformation,[status(thm)],[f_361]) ).
tff(c_823,plain,
! [W1_105,W0_106] :
( aNaturalNumber0(sdtmndt0(W1_105,W0_106))
| ~ sdtlseqdt0(W0_106,W1_105)
| ~ aNaturalNumber0(W1_105)
| ~ aNaturalNumber0(W0_106) ),
inference(cnfTransformation,[status(thm)],[f_175]) ).
tff(c_857,plain,
( aNaturalNumber0(xr)
| ~ sdtlseqdt0(xp,xq)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_135,c_823]) ).
tff(c_870,plain,
( aNaturalNumber0(xr)
| ~ aNaturalNumber0(xq)
| ~ aNaturalNumber0(xp) ),
inference(demodulation,[status(thm),theory(equality)],[c_133,c_857]) ).
tff(c_913,plain,
~ aNaturalNumber0(xp),
inference(splitLeft,[status(thm)],[c_870]) ).
tff(c_3861,plain,
! [W1_189,W0_190] :
( aNaturalNumber0(sdtsldt0(W1_189,W0_190))
| ~ doDivides0(W0_190,W1_189)
| ( sz00 = W0_190 )
| ~ aNaturalNumber0(W1_189)
| ~ aNaturalNumber0(W0_190) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_3898,plain,
( aNaturalNumber0(xp)
| ~ doDivides0(xl,xm)
| ( xl = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm),theory(equality)],[c_129,c_3861]) ).
tff(c_3912,plain,
( aNaturalNumber0(xp)
| ( xl = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_119,c_125,c_3898]) ).
tff(c_3914,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_127,c_913,c_3912]) ).
tff(c_3915,plain,
( ~ aNaturalNumber0(xq)
| aNaturalNumber0(xr) ),
inference(splitRight,[status(thm)],[c_870]) ).
tff(c_3959,plain,
~ aNaturalNumber0(xq),
inference(splitLeft,[status(thm)],[c_3915]) ).
tff(c_8385,plain,
! [W1_303,W0_304] :
( aNaturalNumber0(sdtsldt0(W1_303,W0_304))
| ~ doDivides0(W0_304,W1_303)
| ( sz00 = W0_304 )
| ~ aNaturalNumber0(W1_303)
| ~ aNaturalNumber0(W0_304) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_8422,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_8385]) ).
tff(c_8438,plain,
( aNaturalNumber0(xq)
| ( xl = sz00 )
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(demodulation,[status(thm),theory(equality)],[c_121,c_123,c_8422]) ).
tff(c_8439,plain,
~ aNaturalNumber0(sdtpldt0(xm,xn)),
inference(negUnitSimplification,[status(thm)],[c_127,c_3959,c_8438]) ).
tff(c_8840,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[c_10,c_8439]) ).
tff(c_8844,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_119,c_117,c_8840]) ).
tff(c_8845,plain,
aNaturalNumber0(xr),
inference(splitRight,[status(thm)],[c_3915]) ).
tff(c_661,plain,
! [W1_98,W0_99] :
( ( sdtasdt0(W1_98,W0_99) = sdtasdt0(W0_99,W1_98) )
| ~ aNaturalNumber0(W1_98)
| ~ aNaturalNumber0(W0_99) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_143577,plain,
! [W0_1202] :
( ( sdtasdt0(xl,W0_1202) = sdtasdt0(W0_1202,xl) )
| ~ aNaturalNumber0(W0_1202) ),
inference(resolution,[status(thm)],[c_121,c_661]) ).
tff(c_143665,plain,
sdtasdt0(xr,xl) = sdtasdt0(xl,xr),
inference(resolution,[status(thm)],[c_8845,c_143577]) ).
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_144800,plain,
( aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xr) ),
inference(superposition,[status(thm),theory(equality)],[c_143665,c_12]) ).
tff(c_144851,plain,
aNaturalNumber0(sdtasdt0(xl,xr)),
inference(demodulation,[status(thm),theory(equality)],[c_8845,c_121,c_144800]) ).
tff(c_137,plain,
sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
inference(cnfTransformation,[status(thm)],[f_362]) ).
tff(c_28829,plain,
! [W0_576,W2_577,W1_578] :
( ( sdtpldt0(W0_576,W2_577) != sdtpldt0(W0_576,W1_578) )
| ( W2_577 = W1_578 )
| ~ aNaturalNumber0(W2_577)
| ~ aNaturalNumber0(W1_578)
| ~ aNaturalNumber0(W0_576) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_28855,plain,
! [W1_578] :
( ( sdtpldt0(sdtasdt0(xl,xp),xn) != sdtpldt0(sdtasdt0(xl,xp),W1_578) )
| ( sdtasdt0(xl,xr) = W1_578 )
| ~ aNaturalNumber0(sdtasdt0(xl,xr))
| ~ aNaturalNumber0(W1_578)
| ~ aNaturalNumber0(sdtasdt0(xl,xp)) ),
inference(superposition,[status(thm),theory(equality)],[c_137,c_28829]) ).
tff(c_206503,plain,
! [W1_1443] :
( ( sdtpldt0(xm,W1_1443) != sdtasdt0(xl,xq) )
| ( sdtasdt0(xl,xr) = W1_1443 )
| ~ aNaturalNumber0(W1_1443) ),
inference(demodulation,[status(thm),theory(equality)],[c_119,c_29226,c_144851,c_29226,c_145087,c_29226,c_28855]) ).
tff(c_206650,plain,
( ( sdtpldt0(xm,xn) != sdtasdt0(xl,xq) )
| ( sdtasdt0(xl,xr) = xn ) ),
inference(resolution,[status(thm)],[c_117,c_206503]) ).
tff(c_206711,plain,
sdtasdt0(xl,xr) = xn,
inference(demodulation,[status(thm),theory(equality)],[c_145087,c_206650]) ).
tff(c_206713,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_139,c_206711]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.15 % Problem : NUM475+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.16 % 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
% 0.12/0.38 % Computer : n027.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8042.1875MB
% 0.12/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Tue Apr 8 12:48:06 EDT 2025
% 0.12/0.38 % CPUTime :
% 57.78/42.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 57.78/42.52
% 57.78/42.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------