TSTP Solution File: RNG123+1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : RNG123+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 : n026.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 10:55:02 EDT 2023
% Result : Theorem 29.30s 16.24s
% Output : CNFRefutation 29.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 59
% Syntax : Number of formulae : 69 ( 11 unt; 53 typ; 1 def)
% Number of atoms : 31 ( 3 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 25 ( 10 ~; 8 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 88 ( 41 >; 47 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 12 con; 0-4 aty)
% Number of variables : 8 (; 8 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aGcdOfAnd0 > misRelativelyPrime0 > iLess0 > doDivides0 > aElementOf0 > aDivisorOf0 > aSet0 > aNaturalNumber0 > aIdeal0 > aElement0 > sdtpldt1 > sdtpldt0 > sdtasdt0 > sdtasasdt0 > #nlpp > smndt0 > slsdtgt0 > sbrdtbr0 > xu > xr > xq > 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(xq,type,
xq: $i ).
tff('#skF_22',type,
'#skF_22': ( $i * $i ) > $i ).
tff(xr,type,
xr: $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_417,negated_conjecture,
~ aElementOf0(xr,xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_361,hypothesis,
( aIdeal0(xI)
& ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2174) ).
tff(f_414,hypothesis,
aElementOf0(xb,xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2699) ).
tff(f_413,hypothesis,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2690) ).
tff(f_415,hypothesis,
xr = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2718) ).
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(c_266,plain,
~ aElementOf0(xr,xI),
inference(cnfTransformation,[status(thm)],[f_417]) ).
tff(c_218,plain,
aIdeal0(xI),
inference(cnfTransformation,[status(thm)],[f_361]) ).
tff(c_262,plain,
aElementOf0(xb,xI),
inference(cnfTransformation,[status(thm)],[f_414]) ).
tff(c_260,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_264,plain,
sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = xr,
inference(cnfTransformation,[status(thm)],[f_415]) ).
tff(c_4647,plain,
! [W1_347,W2_348,W0_349] :
( aElementOf0(sdtpldt0(W1_347,W2_348),W0_349)
| ~ aElementOf0(W2_348,W0_349)
| ~ aElementOf0(W1_347,W0_349)
| ~ aIdeal0(W0_349) ),
inference(cnfTransformation,[status(thm)],[f_205]) ).
tff(c_45901,plain,
! [W0_586] :
( aElementOf0(xr,W0_586)
| ~ aElementOf0(xb,W0_586)
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),W0_586)
| ~ aIdeal0(W0_586) ),
inference(superposition,[status(thm),theory(equality)],[c_264,c_4647]) ).
tff(c_45916,plain,
( aElementOf0(xr,xI)
| ~ aElementOf0(xb,xI)
| ~ aIdeal0(xI) ),
inference(resolution,[status(thm)],[c_260,c_45901]) ).
tff(c_45926,plain,
aElementOf0(xr,xI),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_262,c_45916]) ).
tff(c_45928,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_266,c_45926]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG123+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
% 0.14/0.34 % Computer : n026.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 : Thu Aug 3 18:17:02 EDT 2023
% 0.14/0.34 % CPUTime :
% 29.30/16.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.30/16.25
% 29.30/16.25 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 29.30/16.28
% 29.30/16.28 Inference rules
% 29.30/16.28 ----------------------
% 29.30/16.28 #Ref : 0
% 29.30/16.28 #Sup : 10353
% 29.30/16.28 #Fact : 0
% 29.30/16.28 #Define : 0
% 29.30/16.28 #Split : 19
% 29.30/16.28 #Chain : 0
% 29.30/16.28 #Close : 0
% 29.30/16.28
% 29.30/16.28 Ordering : KBO
% 29.30/16.28
% 29.30/16.28 Simplification rules
% 29.30/16.28 ----------------------
% 29.30/16.28 #Subsume : 229
% 29.30/16.28 #Demod : 15297
% 29.30/16.28 #Tautology : 3845
% 29.30/16.28 #SimpNegUnit : 104
% 29.30/16.28 #BackRed : 1
% 29.30/16.28
% 29.30/16.28 #Partial instantiations: 0
% 29.30/16.28 #Strategies tried : 1
% 29.30/16.28
% 29.30/16.28 Timing (in seconds)
% 29.30/16.28 ----------------------
% 29.30/16.28 Preprocessing : 0.74
% 29.30/16.28 Parsing : 0.36
% 29.30/16.28 CNF conversion : 0.07
% 29.30/16.28 Main loop : 14.32
% 29.30/16.28 Inferencing : 2.19
% 29.30/16.28 Reduction : 8.74
% 29.30/16.28 Demodulation : 7.79
% 29.30/16.28 BG Simplification : 0.14
% 29.30/16.28 Subsumption : 2.60
% 29.30/16.28 Abstraction : 0.17
% 29.30/16.28 MUC search : 0.00
% 29.30/16.28 Cooper : 0.00
% 29.30/16.28 Total : 15.11
% 29.30/16.28 Index Insertion : 0.00
% 29.30/16.28 Index Deletion : 0.00
% 29.30/16.28 Index Matching : 0.00
% 29.30/16.28 BG Taut test : 0.00
%------------------------------------------------------------------------------