TSTP Solution File: RNG119+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : RNG119+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 : n016.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 10:55:01 EDT 2023
% Result : Theorem 7.91s 2.88s
% Output : CNFRefutation 7.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 68
% Syntax : Number of formulae : 109 ( 29 unt; 53 typ; 3 def)
% Number of atoms : 115 ( 20 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 99 ( 40 ~; 28 |; 17 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 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 : 32 (; 31 !; 1 ?; 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_401,hypothesis,
~ doDivides0(xu,xb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2612) ).
tff(f_352,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
tff(f_390,hypothesis,
~ ( aDivisorOf0(xu,xa)
& aDivisorOf0(xu,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2383) ).
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_413,negated_conjecture,
xr != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_410,hypothesis,
( aElement0(xq)
& aElement0(xr)
& ( xb = sdtpldt0(sdtasdt0(xq,xu),xr) )
& ( ( xr = sz00 )
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2666) ).
tff(f_79,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
tff(f_47,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_67,axiom,
! [W0] :
( aElement0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
tff(f_295,definition,
! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( aElement0(W2)
& ( sdtasdt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
tff(c_248,plain,
~ doDivides0(xu,xb),
inference(cnfTransformation,[status(thm)],[f_401]) ).
tff(c_210,plain,
aElement0(xa),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_238,plain,
( ~ aDivisorOf0(xu,xb)
| ~ aDivisorOf0(xu,xa) ),
inference(cnfTransformation,[status(thm)],[f_390]) ).
tff(c_463,plain,
~ aDivisorOf0(xu,xa),
inference(splitLeft,[status(thm)],[c_238]) ).
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_653,plain,
! [W1_238,W0_239] :
( aElement0(W1_238)
| ~ aElementOf0(W1_238,W0_239)
| ~ aSet0(W0_239) ),
inference(cnfTransformation,[status(thm)],[f_137]) ).
tff(c_680,plain,
( aElement0(xu)
| ~ aSet0(xI) ),
inference(resolution,[status(thm)],[c_236,c_653]) ).
tff(c_682,plain,
~ aSet0(xI),
inference(splitLeft,[status(thm)],[c_680]) ).
tff(c_685,plain,
~ aIdeal0(xI),
inference(resolution,[status(thm)],[c_108,c_682]) ).
tff(c_689,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_218,c_685]) ).
tff(c_690,plain,
aElement0(xu),
inference(splitRight,[status(thm)],[c_680]) ).
tff(c_246,plain,
doDivides0(xu,xa),
inference(cnfTransformation,[status(thm)],[f_399]) ).
tff(c_1829,plain,
! [W1_272,W0_273] :
( aDivisorOf0(W1_272,W0_273)
| ~ doDivides0(W1_272,W0_273)
| ~ aElement0(W1_272)
| ~ aElement0(W0_273) ),
inference(cnfTransformation,[status(thm)],[f_304]) ).
tff(c_1835,plain,
( aDivisorOf0(xu,xa)
| ~ aElement0(xu)
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[c_246,c_1829]) ).
tff(c_1839,plain,
aDivisorOf0(xu,xa),
inference(demodulation,[status(thm),theory(equality)],[c_210,c_690,c_1835]) ).
tff(c_1841,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_463,c_1839]) ).
tff(c_1843,plain,
aDivisorOf0(xu,xa),
inference(splitRight,[status(thm)],[c_238]) ).
tff(c_1967,plain,
! [W1_276,W0_277] :
( aElement0(W1_276)
| ~ aDivisorOf0(W1_276,W0_277)
| ~ aElement0(W0_277) ),
inference(cnfTransformation,[status(thm)],[f_304]) ).
tff(c_1970,plain,
( aElement0(xu)
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[c_1843,c_1967]) ).
tff(c_1973,plain,
aElement0(xu),
inference(demodulation,[status(thm),theory(equality)],[c_210,c_1970]) ).
tff(c_208,plain,
aElement0(xb),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_258,plain,
xr = sz00,
inference(cnfTransformation,[status(thm)],[f_413]) ).
tff(c_252,plain,
sdtpldt0(sdtasdt0(xq,xu),xr) = xb,
inference(cnfTransformation,[status(thm)],[f_410]) ).
tff(c_260,plain,
sdtpldt0(sdtasdt0(xq,xu),sz00) = xb,
inference(demodulation,[status(thm),theory(equality)],[c_258,c_252]) ).
tff(c_256,plain,
aElement0(xq),
inference(cnfTransformation,[status(thm)],[f_410]) ).
tff(c_2753,plain,
! [W1_306,W0_307] :
( ( sdtasdt0(W1_306,W0_307) = sdtasdt0(W0_307,W1_306) )
| ~ aElement0(W1_306)
| ~ aElement0(W0_307) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_2824,plain,
! [W0_309] :
( ( sdtasdt0(xq,W0_309) = sdtasdt0(W0_309,xq) )
| ~ aElement0(W0_309) ),
inference(resolution,[status(thm)],[c_256,c_2753]) ).
tff(c_2868,plain,
sdtasdt0(xu,xq) = sdtasdt0(xq,xu),
inference(resolution,[status(thm)],[c_1973,c_2824]) ).
tff(c_12,plain,
! [W0_5,W1_6] :
( aElement0(sdtasdt0(W0_5,W1_6))
| ~ aElement0(W1_6)
| ~ aElement0(W0_5) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_2923,plain,
( aElement0(sdtasdt0(xq,xu))
| ~ aElement0(xq)
| ~ aElement0(xu) ),
inference(superposition,[status(thm),theory(equality)],[c_2868,c_12]) ).
tff(c_2927,plain,
aElement0(sdtasdt0(xq,xu)),
inference(demodulation,[status(thm),theory(equality)],[c_1973,c_256,c_2923]) ).
tff(c_20,plain,
! [W0_12] :
( ( sdtpldt0(W0_12,sz00) = W0_12 )
| ~ aElement0(W0_12) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_2946,plain,
sdtpldt0(sdtasdt0(xq,xu),sz00) = sdtasdt0(xq,xu),
inference(resolution,[status(thm)],[c_2927,c_20]) ).
tff(c_2959,plain,
sdtasdt0(xq,xu) = xb,
inference(demodulation,[status(thm),theory(equality)],[c_260,c_2946]) ).
tff(c_2963,plain,
sdtasdt0(xu,xq) = xb,
inference(demodulation,[status(thm),theory(equality)],[c_2959,c_2868]) ).
tff(c_4488,plain,
! [W0_347,W2_348] :
( doDivides0(W0_347,sdtasdt0(W0_347,W2_348))
| ~ aElement0(W2_348)
| ~ aElement0(sdtasdt0(W0_347,W2_348))
| ~ aElement0(W0_347) ),
inference(cnfTransformation,[status(thm)],[f_295]) ).
tff(c_4521,plain,
( doDivides0(xu,xb)
| ~ aElement0(xq)
| ~ aElement0(sdtasdt0(xu,xq))
| ~ aElement0(xu) ),
inference(superposition,[status(thm),theory(equality)],[c_2963,c_4488]) ).
tff(c_4662,plain,
doDivides0(xu,xb),
inference(demodulation,[status(thm),theory(equality)],[c_1973,c_208,c_2963,c_256,c_4521]) ).
tff(c_4664,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_248,c_4662]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG119+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % 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
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Aug 3 18:24:38 EDT 2023
% 0.14/0.36 % CPUTime :
% 7.91/2.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.91/2.89
% 7.91/2.89 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.91/2.92
% 7.91/2.92 Inference rules
% 7.91/2.92 ----------------------
% 7.91/2.92 #Ref : 0
% 7.91/2.92 #Sup : 1086
% 7.91/2.92 #Fact : 0
% 7.91/2.92 #Define : 0
% 7.91/2.92 #Split : 7
% 7.91/2.92 #Chain : 0
% 7.91/2.92 #Close : 0
% 7.91/2.92
% 7.91/2.92 Ordering : KBO
% 7.91/2.92
% 7.91/2.92 Simplification rules
% 7.91/2.92 ----------------------
% 7.91/2.92 #Subsume : 23
% 7.91/2.92 #Demod : 923
% 7.91/2.92 #Tautology : 571
% 7.91/2.92 #SimpNegUnit : 33
% 7.91/2.92 #BackRed : 3
% 7.91/2.92
% 7.91/2.92 #Partial instantiations: 0
% 7.91/2.92 #Strategies tried : 1
% 7.91/2.92
% 7.91/2.92 Timing (in seconds)
% 7.91/2.92 ----------------------
% 7.91/2.93 Preprocessing : 0.76
% 7.91/2.93 Parsing : 0.37
% 7.91/2.93 CNF conversion : 0.07
% 7.91/2.93 Main loop : 1.09
% 7.91/2.93 Inferencing : 0.36
% 7.91/2.93 Reduction : 0.38
% 7.91/2.93 Demodulation : 0.28
% 7.91/2.93 BG Simplification : 0.06
% 7.91/2.93 Subsumption : 0.20
% 7.91/2.93 Abstraction : 0.04
% 7.91/2.93 MUC search : 0.00
% 7.91/2.93 Cooper : 0.00
% 7.91/2.93 Total : 1.91
% 7.91/2.93 Index Insertion : 0.00
% 7.91/2.93 Index Deletion : 0.00
% 7.91/2.93 Index Matching : 0.00
% 7.91/2.93 BG Taut test : 0.00
%------------------------------------------------------------------------------