%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : RNG125+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 : n029.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 08:31:39 PM UTC 2025
% Result : Theorem 7.89s 2.70s
% Output : CNFRefutation 7.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 20 unt; 0 typ; 2 def)
% Number of atoms : 73 ( 3 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 67 ( 31 ~; 18 |; 9 &)
% ( 2 <=>; 7 =>; 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 : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 10 con; 0-4 aty)
% Number of variables : 18 ( 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aGcdOfAnd0 > misRelativelyPrime0 > iLess0 > doDivides0 > aElementOf0 > aDivisorOf0 > aSet0 > aNaturalNumber0 > aIdeal0 > aElement0 > sdtpldt1 > sdtpldt0 > sdtasdt0 > sdtasasdt0 > #nlpp > smndt0 > slsdtgt0 > sbrdtbr0 > xu > xc > xb > xa > xI > sz10 > sz00 > #skF_22 > #skF_6 > #skF_17 > #skF_25 > #skF_20 > #skF_4 > #skF_8 > #skF_14 > #skF_15 > #skF_26 > #skF_18 > #skF_23 > #skF_5 > #skF_19 > #skF_7 > #skF_9 > #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_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_25',type,
'#skF_25': $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(xu,type,
xu: $i ).
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('#skF_26',type,
'#skF_26': $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_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_390,hypothesis,
~ ( aDivisorOf0(xu,xa)
& aDivisorOf0(xu,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2383) ).
tff(f_352,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
tff(f_361,hypothesis,
( aIdeal0(xI)
& ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
tff(f_205,definition,
! [W0] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1] :
( aElementOf0(W1,W0)
=> ( ! [W2] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
tff(f_386,hypothesis,
( aElementOf0(xu,xI)
& ( xu != sz00 )
& ! [W0] :
( ( aElementOf0(W0,xI)
& ( W0 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
tff(f_137,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(f_399,hypothesis,
~ ~ doDivides0(xu,xa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2479) ).
tff(f_304,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( aElement0(W1)
& doDivides0(W1,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDvs) ).
tff(f_402,hypothesis,
~ ~ doDivides0(xu,xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).
tff(c_238,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(cnfTransformation,[status(thm)],[f_390]) ).
tff(c_347,plain,
~ aDivisorOf0(xu,xa),
inference(splitLeft,[status(thm)],[c_238]) ).
tff(c_210,plain,
aElement0(xa),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_218,plain,
aIdeal0(xI),
inference(cnfTransformation,[status(thm)],[f_361]) ).
tff(c_108,plain,
! [W0_117] :
( aSet0(W0_117)
| ~ aIdeal0(W0_117) ),
inference(cnfTransformation,[status(thm)],[f_205]) ).
tff(c_236,plain,
aElementOf0(xu,xI),
inference(cnfTransformation,[status(thm)],[f_386]) ).
tff(c_584,plain,
! [W1_237,W0_238] :
( aElement0(W1_237)
| ~ aElementOf0(W1_237,W0_238)
| ~ aSet0(W0_238) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_611,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[c_236,c_584]) ).
tff(c_613,plain,
~ aSet0(xI),
inference(splitLeft,[status(thm)],[c_611]) ).
tff(c_616,plain,
~ aIdeal0(xI),
inference(resolution,[status(thm)],[c_108,c_613]) ).
tff(c_620,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_218,c_616]) ).
tff(c_621,plain,
aElement0(xu),
inference(splitRight,[status(thm)],[c_611]) ).
tff(c_246,plain,
doDivides0(xu,xa),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_1780,plain,
! [W1_276,W0_277] :
( aDivisorOf0(W1_276,W0_277)
| ~ doDivides0(W1_276,W0_277)
| ~ aElement0(W1_276)
| ~ aElement0(W0_277) ),
inference(cnfTransformation,[status(thm)],[f_304]) ).
tff(c_1786,plain,
( aDivisorOf0(xu,xa)
| ~ aElement0(xu)
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[c_246,c_1780]) ).
tff(c_1793,plain,
aDivisorOf0(xu,xa),
inference(demodulation,[status(thm),theory(equality)],[c_210,c_621,c_1786]) ).
tff(c_1795,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_347,c_1793]) ).
tff(c_1796,plain,
~ aDivisorOf0(xu,xb),
inference(splitRight,[status(thm)],[c_238]) ).
tff(c_208,plain,
aElement0(xb),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_1797,plain,
aDivisorOf0(xu,xa),
inference(splitRight,[status(thm)],[c_238]) ).
tff(c_2009,plain,
! [W1_283,W0_284] :
( aElement0(W1_283)
| ~ aDivisorOf0(W1_283,W0_284)
| ~ aElement0(W0_284) ),
inference(cnfTransformation,[status(thm)],[f_304]) ).
tff(c_2012,plain,
( aElement0(xu)
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[c_1797,c_2009]) ).
tff(c_2015,plain,
aElement0(xu),
inference(demodulation,[status(thm),theory(equality)],[c_210,c_2012]) ).
tff(c_248,plain,
doDivides0(xu,xb),
inference(cnfTransformation,[status(thm)],[f_402]) ).
tff(c_3198,plain,
! [W1_325,W0_326] :
( aDivisorOf0(W1_325,W0_326)
| ~ doDivides0(W1_325,W0_326)
| ~ aElement0(W1_325)
| ~ aElement0(W0_326) ),
inference(cnfTransformation,[status(thm)],[f_304]) ).
tff(c_3207,plain,
( aDivisorOf0(xu,xb)
| ~ aElement0(xu)
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[c_248,c_3198]) ).
tff(c_3214,plain,
aDivisorOf0(xu,xb),
inference(demodulation,[status(thm),theory(equality)],[c_208,c_2015,c_3207]) ).
tff(c_3216,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1796,c_3214]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG125+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 : n029.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 18:55:49 EDT 2025
% 0.14/0.34 % CPUTime :
% 7.89/2.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.89/2.71
% 7.89/2.71 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------