%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : RNG112+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 : n005.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 08:31:36 PM UTC 2025
% Result : Theorem 13.51s 4.32s
% Output : CNFRefutation 13.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 38 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 79 ( 32 ~; 35 |; 9 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 39 ( 39 usr; 7 con; 0-4 aty)
% Number of variables : 19 ( 16 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aGcdOfAnd0 > misRelativelyPrime0 > iLess0 > doDivides0 > aElementOf0 > aDivisorOf0 > aSet0 > aNaturalNumber0 > aIdeal0 > aElement0 > sdtpldt1 > sdtpldt0 > sdtasdt0 > sdtasasdt0 > #nlpp > smndt0 > slsdtgt0 > sbrdtbr0 > xc > xb > xa > xI > sz10 > sz00 > #skF_25 > #skF_22 > #skF_6 > #skF_17 > #skF_20 > #skF_4 > #skF_8 > #skF_14 > #skF_15 > #skF_18 > #skF_23 > #skF_5 > #skF_19 > #skF_7 > #skF_9 > #skF_26 > #skF_13 > #skF_11 > #skF_3 > #skF_2 > #skF_24 > #skF_12 > #skF_1 > #skF_16 > #skF_21 > #skF_10
%Foreground sorts:
%Background operators:
%Foreground operators:
tff('#skF_25',type,
'#skF_25': $i > $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i ) > $i ).
tff(sbrdtbr0,type,
sbrdtbr0: $i > $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(aSet0,type,
aSet0: $i > $o ).
tff(xa,type,
xa: $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff(sdtpldt1,type,
sdtpldt1: ( $i * $i ) > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': ( $i * $i ) > $i ).
tff(aElement0,type,
aElement0: $i > $o ).
tff(sz00,type,
sz00: $i ).
tff(misRelativelyPrime0,type,
misRelativelyPrime0: ( $i * $i ) > $o ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff(aIdeal0,type,
aIdeal0: $i > $o ).
tff(xI,type,
xI: $i ).
tff(xc,type,
xc: $i ).
tff('#skF_8',type,
'#skF_8': ( $i * $i * $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i * $i ) > $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff('#skF_18',type,
'#skF_18': ( $i * $i ) > $i ).
tff('#skF_23',type,
'#skF_23': ( $i * $i * $i ) > $i ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff(slsdtgt0,type,
slsdtgt0: $i > $i ).
tff(smndt0,type,
smndt0: $i > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_19',type,
'#skF_19': ( $i * $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i * $i ) > $i ).
tff(doDivides0,type,
doDivides0: ( $i * $i ) > $o ).
tff(aGcdOfAnd0,type,
aGcdOfAnd0: ( $i * $i * $i ) > $o ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xb,type,
xb: $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i * $i ) > $i ).
tff('#skF_26',type,
'#skF_26': $i > $i ).
tff('#skF_13',type,
'#skF_13': $i > $i ).
tff('#skF_11',type,
'#skF_11': $i > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i * $i ) > $i ).
tff(aDivisorOf0,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff('#skF_24',type,
'#skF_24': $i ).
tff(sdtasasdt0,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(iLess0,type,
iLess0: ( $i * $i ) > $o ).
tff('#skF_12',type,
'#skF_12': $i > $i ).
tff(sdteqdtlpzmzozddtrp0,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i ) > $i ).
tff('#skF_21',type,
'#skF_21': ( $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i * $i ) > $i ).
tff(f_373,hypothesis,
? [W0] :
( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ( W0 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2228) ).
tff(f_361,hypothesis,
( aIdeal0(xI)
& ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
tff(f_393,hypothesis,
! [W0] :
( ( aElementOf0(W0,xI)
& ( W0 != sz00 ) )
=> ? [W1] :
( aElementOf0(W1,xI)
& ( W1 != sz00 )
& ! [W2] :
( ( aElementOf0(W2,xI)
& ( W2 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W2),sbrdtbr0(W1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2351) ).
tff(f_408,negated_conjecture,
~ ? [W0] :
( aElementOf0(W0,xI)
& ( W0 != sz00 )
& ! [W1] :
( ( aElementOf0(W1,xI)
& ( W1 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W1),sbrdtbr0(W0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(c_228,plain,
sz00 != '#skF_24',
inference(cnfTransformation,[status(thm)],[f_373]) ).
tff(c_216,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(cnfTransformation,[status(thm)],[f_361]) ).
tff(c_230,plain,
aElementOf0('#skF_24',sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(cnfTransformation,[status(thm)],[f_373]) ).
tff(c_243,plain,
aElementOf0('#skF_24',xI),
inference(demodulation,[status(thm),theory(equality)],[c_216,c_230]) ).
tff(c_801,plain,
! [W0_266] :
( ( '#skF_25'(W0_266) != sz00 )
| ( sz00 = W0_266 )
| ~ aElementOf0(W0_266,xI) ),
inference(cnfTransformation,[status(thm)],[f_393]) ).
tff(c_811,plain,
( ( '#skF_25'('#skF_24') != sz00 )
| ( sz00 = '#skF_24' ) ),
inference(resolution,[status(thm)],[c_243,c_801]) ).
tff(c_818,plain,
'#skF_25'('#skF_24') != sz00,
inference(negUnitSimplification,[status(thm)],[c_228,c_811]) ).
tff(c_236,plain,
! [W0_222] :
( aElementOf0('#skF_25'(W0_222),xI)
| ( sz00 = W0_222 )
| ~ aElementOf0(W0_222,xI) ),
inference(cnfTransformation,[status(thm)],[f_393]) ).
tff(c_242,plain,
! [W0_228] :
( aElementOf0('#skF_26'(W0_228),xI)
| ( sz00 = W0_228 )
| ~ aElementOf0(W0_228,xI) ),
inference(cnfTransformation,[status(thm)],[f_408]) ).
tff(c_238,plain,
! [W0_228] :
( iLess0(sbrdtbr0('#skF_26'(W0_228)),sbrdtbr0(W0_228))
| ( sz00 = W0_228 )
| ~ aElementOf0(W0_228,xI) ),
inference(cnfTransformation,[status(thm)],[f_408]) ).
tff(c_9109,plain,
! [W2_402,W0_403] :
( ~ iLess0(sbrdtbr0(W2_402),sbrdtbr0('#skF_25'(W0_403)))
| ( sz00 = W2_402 )
| ~ aElementOf0(W2_402,xI)
| ( sz00 = W0_403 )
| ~ aElementOf0(W0_403,xI) ),
inference(cnfTransformation,[status(thm)],[f_393]) ).
tff(c_9190,plain,
! [W0_404] :
( ( '#skF_26'('#skF_25'(W0_404)) = sz00 )
| ~ aElementOf0('#skF_26'('#skF_25'(W0_404)),xI)
| ( sz00 = W0_404 )
| ~ aElementOf0(W0_404,xI)
| ( '#skF_25'(W0_404) = sz00 )
| ~ aElementOf0('#skF_25'(W0_404),xI) ),
inference(resolution,[status(thm)],[c_238,c_9109]) ).
tff(c_9307,plain,
! [W0_408] :
( ( '#skF_26'('#skF_25'(W0_408)) = sz00 )
| ( sz00 = W0_408 )
| ~ aElementOf0(W0_408,xI)
| ( '#skF_25'(W0_408) = sz00 )
| ~ aElementOf0('#skF_25'(W0_408),xI) ),
inference(resolution,[status(thm)],[c_242,c_9190]) ).
tff(c_9545,plain,
! [W0_412] :
( ( '#skF_26'('#skF_25'(W0_412)) = sz00 )
| ( '#skF_25'(W0_412) = sz00 )
| ( sz00 = W0_412 )
| ~ aElementOf0(W0_412,xI) ),
inference(resolution,[status(thm)],[c_236,c_9307]) ).
tff(c_1135,plain,
! [W0_281] :
( aElementOf0('#skF_25'(W0_281),xI)
| ( sz00 = W0_281 )
| ~ aElementOf0(W0_281,xI) ),
inference(cnfTransformation,[status(thm)],[f_393]) ).
tff(c_240,plain,
! [W0_228] :
( ( '#skF_26'(W0_228) != sz00 )
| ( sz00 = W0_228 )
| ~ aElementOf0(W0_228,xI) ),
inference(cnfTransformation,[status(thm)],[f_408]) ).
tff(c_1149,plain,
! [W0_281] :
( ( '#skF_26'('#skF_25'(W0_281)) != sz00 )
| ( '#skF_25'(W0_281) = sz00 )
| ( sz00 = W0_281 )
| ~ aElementOf0(W0_281,xI) ),
inference(resolution,[status(thm)],[c_1135,c_240]) ).
tff(c_10450,plain,
! [W0_422] :
( ( '#skF_25'(W0_422) = sz00 )
| ( sz00 = W0_422 )
| ~ aElementOf0(W0_422,xI) ),
inference(superposition,[status(thm),theory(equality)],[c_9545,c_1149]) ).
tff(c_10505,plain,
( ( '#skF_25'('#skF_24') = sz00 )
| ( sz00 = '#skF_24' ) ),
inference(resolution,[status(thm)],[c_243,c_10450]) ).
tff(c_10546,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_228,c_818,c_10505]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG112+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
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 8 18:52:42 EDT 2025
% 0.14/0.34 % CPUTime :
% 13.51/4.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.51/4.33
% 13.51/4.33 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------