%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : NUM524+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/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 : n002.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 07:56:14 PM UTC 2025
% Result : Theorem 201.57s 169.95s
% Output : CNFRefutation 201.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 21 unt; 0 typ; 1 def)
% Number of atoms : 129 ( 44 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 142 ( 59 ~; 61 |; 14 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > iLess0 > doDivides0 > isPrime0 > aNaturalNumber0 > sdtsldt0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xq > xp > xn > xm > sz10 > sz00 > #skF_4 > #skF_3 > #skF_2 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(xq,type,
xq: $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_446,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp)
& ( xn != sz00 )
& ( xm != sz00 )
& ( xp != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2987) ).
tff(f_473,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xn))
& doDivides0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3046) ).
tff(f_474,hypothesis,
xq = sdtsldt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3059) ).
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_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_469,hypothesis,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3014) ).
tff(f_384,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( ( W0 != sz00 )
& doDivides0(W0,W1) )
=> ! [W2] :
( aNaturalNumber0(W2)
=> ( sdtasdt0(W2,sdtsldt0(W1,W0)) = sdtsldt0(sdtasdt0(W2,W1),W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivAsso) ).
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/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
tff(f_476,negated_conjecture,
sdtasdt0(xm,xm) != sdtasdt0(xp,sdtasdt0(xq,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(c_145,plain,
xp != sz00,
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_151,plain,
aNaturalNumber0(xp),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_155,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_446]) ).
tff(c_163,plain,
doDivides0(xp,xn),
inference(cnfTransformation,[status(thm)],[f_473]) ).
tff(c_167,plain,
sdtsldt0(xn,xp) = xq,
inference(cnfTransformation,[status(thm)],[f_474]) ).
tff(c_6605,plain,
! [W1_234,W0_235] :
( aNaturalNumber0(sdtsldt0(W1_234,W0_235))
| ~ doDivides0(W0_235,W1_234)
| ( sz00 = W0_235 )
| ~ aNaturalNumber0(W1_234)
| ~ aNaturalNumber0(W0_235) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_6648,plain,
( aNaturalNumber0(xq)
| ~ doDivides0(xp,xn)
| ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_167,c_6605]) ).
tff(c_6664,plain,
( aNaturalNumber0(xq)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_155,c_163,c_6648]) ).
tff(c_6665,plain,
aNaturalNumber0(xq),
inference(negUnitSimplification,[status(thm)],[c_145,c_6664]) ).
tff(c_153,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_446]) ).
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_159,plain,
sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
inference(cnfTransformation,[status(thm)],[f_469]) ).
tff(c_508,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_159,c_12]) ).
tff(c_512,plain,
( aNaturalNumber0(sdtasdt0(xn,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_508]) ).
tff(c_594,plain,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(splitLeft,[status(thm)],[c_512]) ).
tff(c_597,plain,
~ aNaturalNumber0(xm),
inference(resolution,[status(thm)],[c_12,c_594]) ).
tff(c_601,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_153,c_597]) ).
tff(c_602,plain,
aNaturalNumber0(sdtasdt0(xn,xn)),
inference(splitRight,[status(thm)],[c_512]) ).
tff(c_165,plain,
doDivides0(xp,sdtasdt0(xn,xn)),
inference(cnfTransformation,[status(thm)],[f_473]) ).
tff(c_603,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(splitRight,[status(thm)],[c_512]) ).
tff(c_13280,plain,
! [W0_296,W2_297] :
( ( sdtsldt0(sdtasdt0(W0_296,W2_297),W0_296) = W2_297 )
| ~ aNaturalNumber0(W2_297)
| ~ doDivides0(W0_296,sdtasdt0(W0_296,W2_297))
| ( sz00 = W0_296 )
| ~ aNaturalNumber0(sdtasdt0(W0_296,W2_297))
| ~ aNaturalNumber0(W0_296) ),
inference(cnfTransformation,[status(thm)],[f_323]) ).
tff(c_13382,plain,
( ( sdtsldt0(sdtasdt0(xp,sdtasdt0(xm,xm)),xp) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(sdtasdt0(xm,xm))
| ~ doDivides0(xp,sdtasdt0(xn,xn))
| ( xp = sz00 )
| ~ aNaturalNumber0(sdtasdt0(xp,sdtasdt0(xm,xm)))
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_159,c_13280]) ).
tff(c_13514,plain,
( ( sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm) )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_602,c_159,c_165,c_603,c_159,c_13382]) ).
tff(c_13515,plain,
sdtsldt0(sdtasdt0(xn,xn),xp) = sdtasdt0(xm,xm),
inference(negUnitSimplification,[status(thm)],[c_145,c_13514]) ).
tff(c_121,plain,
! [W2_88,W1_86,W0_85] :
( ( sdtsldt0(sdtasdt0(W2_88,W1_86),W0_85) = sdtasdt0(W2_88,sdtsldt0(W1_86,W0_85)) )
| ~ aNaturalNumber0(W2_88)
| ~ doDivides0(W0_85,W1_86)
| ( sz00 = W0_85 )
| ~ aNaturalNumber0(W1_86)
| ~ aNaturalNumber0(W0_85) ),
inference(cnfTransformation,[status(thm)],[f_384]) ).
tff(c_13872,plain,
( ( sdtasdt0(xn,sdtsldt0(xn,xp)) = sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xp,xn)
| ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_13515,c_121]) ).
tff(c_13885,plain,
( ( sdtasdt0(xn,xq) = sdtasdt0(xm,xm) )
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_155,c_163,c_155,c_167,c_13872]) ).
tff(c_13886,plain,
sdtasdt0(xn,xq) = sdtasdt0(xm,xm),
inference(negUnitSimplification,[status(thm)],[c_145,c_13885]) ).
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_8128,plain,
! [W0_258,W1_259,W2_260] :
( ( sdtasdt0(sdtasdt0(W0_258,W1_259),W2_260) = sdtasdt0(W0_258,sdtasdt0(W1_259,W2_260)) )
| ~ aNaturalNumber0(W2_260)
| ~ aNaturalNumber0(W1_259)
| ~ aNaturalNumber0(W0_258) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_109456,plain,
! [W0_685,W1_686,W2_687] :
( ( sdtasdt0(W0_685,sdtasdt0(sdtsldt0(W1_686,W0_685),W2_687)) = sdtasdt0(W1_686,W2_687) )
| ~ aNaturalNumber0(W2_687)
| ~ aNaturalNumber0(sdtsldt0(W1_686,W0_685))
| ~ aNaturalNumber0(W0_685)
| ~ doDivides0(W0_685,W1_686)
| ( sz00 = W0_685 )
| ~ aNaturalNumber0(W1_686)
| ~ aNaturalNumber0(W0_685) ),
inference(superposition,[status(thm),theory(equality)],[c_109,c_8128]) ).
tff(c_109913,plain,
! [W2_687] :
( ( sdtasdt0(xp,sdtasdt0(xq,W2_687)) = sdtasdt0(xn,W2_687) )
| ~ aNaturalNumber0(W2_687)
| ~ aNaturalNumber0(sdtsldt0(xn,xp))
| ~ aNaturalNumber0(xp)
| ~ doDivides0(xp,xn)
| ( xp = sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_167,c_109456]) ).
tff(c_110137,plain,
! [W2_687] :
( ( sdtasdt0(xp,sdtasdt0(xq,W2_687)) = sdtasdt0(xn,W2_687) )
| ~ aNaturalNumber0(W2_687)
| ( xp = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_151,c_155,c_163,c_151,c_6665,c_167,c_109913]) ).
tff(c_234511,plain,
! [W2_989] :
( ( sdtasdt0(xp,sdtasdt0(xq,W2_989)) = sdtasdt0(xn,W2_989) )
| ~ aNaturalNumber0(W2_989) ),
inference(negUnitSimplification,[status(thm)],[c_145,c_110137]) ).
tff(c_169,plain,
sdtasdt0(xp,sdtasdt0(xq,xq)) != sdtasdt0(xm,xm),
inference(cnfTransformation,[status(thm)],[f_476]) ).
tff(c_234852,plain,
( ( sdtasdt0(xn,xq) != sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(xq) ),
inference(superposition,[status(thm),theory(equality)],[c_234511,c_169]) ).
tff(c_235192,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6665,c_13886,c_234852]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM524+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.13 % 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 : n002.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 : Tue Apr 8 13:16:17 EDT 2025
% 0.13/0.34 % CPUTime :
% 201.57/169.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 201.57/169.96
% 201.57/169.96 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------