TSTP Solution File: RNG109+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : RNG109+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 : n010.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 10:54:59 EDT 2023
% Result : Theorem 35.61s 21.31s
% Output : CNFRefutation 35.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 64
% Syntax : Number of formulae : 179 ( 63 unt; 47 typ; 4 def)
% Number of atoms : 268 ( 66 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 253 ( 117 ~; 97 |; 21 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 36 ( 36 usr; 6 con; 0-4 aty)
% Number of variables : 86 (; 81 !; 5 ?; 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_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_13 > #skF_11 > #skF_3 > #skF_2 > #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_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_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(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_357,hypothesis,
( ( xa != sz00 )
| ( xb != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2110) ).
tff(f_352,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2091) ).
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_31,axiom,
aElement0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
tff(f_35,axiom,
! [W0] :
( aElement0(W0)
=> aElement0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsU) ).
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_109,axiom,
! [W0] :
( aElement0(W0)
=> ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMnOne) ).
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(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_374,negated_conjecture,
~ ? [W0] :
( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ( W0 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_368,hypothesis,
( aElementOf0(sz00,slsdtgt0(xa))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
tff(f_345,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( ( W1 = slsdtgt0(W0) )
<=> ( aSet0(W1)
& ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( aElement0(W3)
& ( sdtasdt0(W0,W3) = W2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrIdeal) ).
tff(f_172,definition,
! [W0,W1] :
( ( aSet0(W0)
& aSet0(W1) )
=> ! [W2] :
( ( W2 = sdtpldt1(W0,W1) )
<=> ( aSet0(W2)
& ! [W3] :
( aElementOf0(W3,W2)
<=> ? [W4,W5] :
( aElementOf0(W4,W0)
& aElementOf0(W5,W1)
& ( sdtpldt0(W4,W5) = W3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSSum) ).
tff(f_73,axiom,
! [W0] :
( aElement0(W0)
=> ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddInvr) ).
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_30,axiom,
aElement0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
tff(c_212,plain,
( ( xb != sz00 )
| ( xa != sz00 ) ),
inference(cnfTransformation,[status(thm)],[f_357]) ).
tff(c_232,plain,
xa != sz00,
inference(splitLeft,[status(thm)],[c_212]) ).
tff(c_210,plain,
aElement0(xa),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_236,plain,
! [W0_228] :
( ( sdtpldt0(sz00,W0_228) = W0_228 )
| ~ aElement0(W0_228) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_256,plain,
sdtpldt0(sz00,xa) = xa,
inference(resolution,[status(thm)],[c_210,c_236]) ).
tff(c_6,plain,
aElement0(sz10),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_8,plain,
! [W0_2] :
( aElement0(smndt0(W0_2))
| ~ aElement0(W0_2) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_999,plain,
! [W1_270,W0_271] :
( ( sdtasdt0(W1_270,W0_271) = sdtasdt0(W0_271,W1_270) )
| ~ aElement0(W1_270)
| ~ aElement0(W0_271) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_1505,plain,
! [W0_284] :
( ( sdtasdt0(sz10,W0_284) = sdtasdt0(W0_284,sz10) )
| ~ aElement0(W0_284) ),
inference(resolution,[status(thm)],[c_6,c_999]) ).
tff(c_14832,plain,
! [W0_460] :
( ( sdtasdt0(smndt0(W0_460),sz10) = sdtasdt0(sz10,smndt0(W0_460)) )
| ~ aElement0(W0_460) ),
inference(resolution,[status(thm)],[c_8,c_1505]) ).
tff(c_40,plain,
! [W0_23] :
( ( sdtasdt0(smndt0(sz10),W0_23) = smndt0(W0_23) )
| ~ aElement0(W0_23) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_14882,plain,
( ( sdtasdt0(sz10,smndt0(sz10)) = smndt0(sz10) )
| ~ aElement0(sz10)
| ~ aElement0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_14832,c_40]) ).
tff(c_14930,plain,
sdtasdt0(sz10,smndt0(sz10)) = smndt0(sz10),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_14882]) ).
tff(c_158,plain,
! [W0_160,W2_164] :
( doDivides0(W0_160,sdtasdt0(W0_160,W2_164))
| ~ aElement0(W2_164)
| ~ aElement0(sdtasdt0(W0_160,W2_164))
| ~ aElement0(W0_160) ),
inference(cnfTransformation,[status(thm)],[f_295]) ).
tff(c_14967,plain,
( doDivides0(sz10,smndt0(sz10))
| ~ aElement0(smndt0(sz10))
| ~ aElement0(sdtasdt0(sz10,smndt0(sz10)))
| ~ aElement0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_14930,c_158]) ).
tff(c_15012,plain,
( doDivides0(sz10,smndt0(sz10))
| ~ aElement0(smndt0(sz10)) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_14930,c_14967]) ).
tff(c_15202,plain,
~ aElement0(smndt0(sz10)),
inference(splitLeft,[status(thm)],[c_15012]) ).
tff(c_15205,plain,
~ aElement0(sz10),
inference(resolution,[status(thm)],[c_8,c_15202]) ).
tff(c_15209,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_15205]) ).
tff(c_15211,plain,
aElement0(smndt0(sz10)),
inference(splitRight,[status(thm)],[c_15012]) ).
tff(c_1026,plain,
! [W0_271] :
( ( sdtasdt0(xa,W0_271) = sdtasdt0(W0_271,xa) )
| ~ aElement0(W0_271) ),
inference(resolution,[status(thm)],[c_210,c_999]) ).
tff(c_15271,plain,
sdtasdt0(smndt0(sz10),xa) = sdtasdt0(xa,smndt0(sz10)),
inference(resolution,[status(thm)],[c_15211,c_1026]) ).
tff(c_19240,plain,
( ( sdtasdt0(xa,smndt0(sz10)) = smndt0(xa) )
| ~ aElement0(xa) ),
inference(superposition,[status(thm),theory(equality)],[c_15271,c_40]) ).
tff(c_19285,plain,
sdtasdt0(xa,smndt0(sz10)) = smndt0(xa),
inference(demodulation,[status(thm),theory(equality)],[c_210,c_19240]) ).
tff(c_19847,plain,
sdtasdt0(smndt0(sz10),xa) = smndt0(xa),
inference(demodulation,[status(thm),theory(equality)],[c_19285,c_15271]) ).
tff(c_218,plain,
aIdeal0(xI),
inference(cnfTransformation,[status(thm)],[f_361]) ).
tff(c_2107,plain,
! [W2_299,W1_300,W0_301] :
( aElementOf0(sdtasdt0(W2_299,W1_300),W0_301)
| ~ aElement0(W2_299)
| ~ aElementOf0(W1_300,W0_301)
| ~ aIdeal0(W0_301) ),
inference(cnfTransformation,[status(thm)],[f_205]) ).
tff(c_216,plain,
sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) = xI,
inference(cnfTransformation,[status(thm)],[f_361]) ).
tff(c_228,plain,
! [W0_222] :
( ( sz00 = W0_222 )
| ~ aElementOf0(W0_222,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(cnfTransformation,[status(thm)],[f_374]) ).
tff(c_229,plain,
! [W0_222] :
( ( sz00 = W0_222 )
| ~ aElementOf0(W0_222,xI) ),
inference(demodulation,[status(thm),theory(equality)],[c_216,c_228]) ).
tff(c_2118,plain,
! [W2_299,W1_300] :
( ( sdtasdt0(W2_299,W1_300) = sz00 )
| ~ aElement0(W2_299)
| ~ aElementOf0(W1_300,xI)
| ~ aIdeal0(xI) ),
inference(resolution,[status(thm)],[c_2107,c_229]) ).
tff(c_2207,plain,
! [W2_299,W1_300] :
( ( sdtasdt0(W2_299,W1_300) = sz00 )
| ~ aElement0(W2_299)
| ~ aElementOf0(W1_300,xI) ),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_2118]) ).
tff(c_15272,plain,
! [W1_300] :
( ( sdtasdt0(smndt0(sz10),W1_300) = sz00 )
| ~ aElementOf0(W1_300,xI) ),
inference(resolution,[status(thm)],[c_15211,c_2207]) ).
tff(c_20081,plain,
( ( smndt0(xa) = sz00 )
| ~ aElementOf0(xa,xI) ),
inference(superposition,[status(thm),theory(equality)],[c_19847,c_15272]) ).
tff(c_20225,plain,
~ aElementOf0(xa,xI),
inference(splitLeft,[status(thm)],[c_20081]) ).
tff(c_224,plain,
aElementOf0(xa,slsdtgt0(xa)),
inference(cnfTransformation,[status(thm)],[f_368]) ).
tff(c_222,plain,
aElementOf0(sz00,slsdtgt0(xb)),
inference(cnfTransformation,[status(thm)],[f_368]) ).
tff(c_257,plain,
! [W0_229] :
( ( sdtpldt0(W0_229,sz00) = W0_229 )
| ~ aElement0(W0_229) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_277,plain,
sdtpldt0(xa,sz00) = xa,
inference(resolution,[status(thm)],[c_210,c_257]) ).
tff(c_188,plain,
! [W0_181] :
( aSet0(slsdtgt0(W0_181))
| ~ aElement0(W0_181) ),
inference(cnfTransformation,[status(thm)],[f_345]) ).
tff(c_513,plain,
! [W0_249,W1_250] :
( aSet0(sdtpldt1(W0_249,W1_250))
| ~ aSet0(W1_250)
| ~ aSet0(W0_249) ),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_516,plain,
( aSet0(xI)
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa)) ),
inference(superposition,[status(thm),theory(equality)],[c_216,c_513]) ).
tff(c_810,plain,
~ aSet0(slsdtgt0(xa)),
inference(splitLeft,[status(thm)],[c_516]) ).
tff(c_813,plain,
~ aElement0(xa),
inference(resolution,[status(thm)],[c_188,c_810]) ).
tff(c_820,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_210,c_813]) ).
tff(c_822,plain,
aSet0(slsdtgt0(xa)),
inference(splitRight,[status(thm)],[c_516]) ).
tff(c_208,plain,
aElement0(xb),
inference(cnfTransformation,[status(thm)],[f_352]) ).
tff(c_821,plain,
( ~ aSet0(slsdtgt0(xb))
| aSet0(xI) ),
inference(splitRight,[status(thm)],[c_516]) ).
tff(c_848,plain,
~ aSet0(slsdtgt0(xb)),
inference(splitLeft,[status(thm)],[c_821]) ).
tff(c_851,plain,
~ aElement0(xb),
inference(resolution,[status(thm)],[c_188,c_848]) ).
tff(c_858,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_208,c_851]) ).
tff(c_860,plain,
aSet0(slsdtgt0(xb)),
inference(splitRight,[status(thm)],[c_821]) ).
tff(c_7898,plain,
! [W4_390,W5_391,W0_392,W1_393] :
( aElementOf0(sdtpldt0(W4_390,W5_391),sdtpldt1(W0_392,W1_393))
| ~ aElementOf0(W5_391,W1_393)
| ~ aElementOf0(W4_390,W0_392)
| ~ aSet0(W1_393)
| ~ aSet0(W0_392) ),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_7987,plain,
! [W4_390,W5_391] :
( aElementOf0(sdtpldt0(W4_390,W5_391),xI)
| ~ aElementOf0(W5_391,slsdtgt0(xb))
| ~ aElementOf0(W4_390,slsdtgt0(xa))
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(xa)) ),
inference(superposition,[status(thm),theory(equality)],[c_216,c_7898]) ).
tff(c_41292,plain,
! [W4_630,W5_631] :
( aElementOf0(sdtpldt0(W4_630,W5_631),xI)
| ~ aElementOf0(W5_631,slsdtgt0(xb))
| ~ aElementOf0(W4_630,slsdtgt0(xa)) ),
inference(demodulation,[status(thm),theory(equality)],[c_822,c_860,c_7987]) ).
tff(c_41549,plain,
( aElementOf0(xa,xI)
| ~ aElementOf0(sz00,slsdtgt0(xb))
| ~ aElementOf0(xa,slsdtgt0(xa)) ),
inference(superposition,[status(thm),theory(equality)],[c_277,c_41292]) ).
tff(c_41685,plain,
aElementOf0(xa,xI),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_41549]) ).
tff(c_41687,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_20225,c_41685]) ).
tff(c_41688,plain,
smndt0(xa) = sz00,
inference(splitRight,[status(thm)],[c_20081]) ).
tff(c_22,plain,
! [W0_13] :
( ( sdtpldt0(smndt0(W0_13),W0_13) = sz00 )
| ~ aElement0(W0_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_41750,plain,
( ( sdtpldt0(sz00,xa) = sz00 )
| ~ aElement0(xa) ),
inference(superposition,[status(thm),theory(equality)],[c_41688,c_22]) ).
tff(c_41782,plain,
xa = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_210,c_256,c_41750]) ).
tff(c_41784,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_232,c_41782]) ).
tff(c_41785,plain,
xb != sz00,
inference(splitRight,[status(thm)],[c_212]) ).
tff(c_41800,plain,
! [W0_635] :
( ( sdtpldt0(sz00,W0_635) = W0_635 )
| ~ aElement0(W0_635) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_41816,plain,
sdtpldt0(sz00,xb) = xb,
inference(resolution,[status(thm)],[c_208,c_41800]) ).
tff(c_43478,plain,
! [W2_705,W1_706,W0_707] :
( aElementOf0(sdtasdt0(W2_705,W1_706),W0_707)
| ~ aElement0(W2_705)
| ~ aElementOf0(W1_706,W0_707)
| ~ aIdeal0(W0_707) ),
inference(cnfTransformation,[status(thm)],[f_205]) ).
tff(c_43485,plain,
! [W2_705,W1_706] :
( ( sdtasdt0(W2_705,W1_706) = sz00 )
| ~ aElement0(W2_705)
| ~ aElementOf0(W1_706,xI)
| ~ aIdeal0(xI) ),
inference(resolution,[status(thm)],[c_43478,c_229]) ).
tff(c_43720,plain,
! [W2_712,W1_713] :
( ( sdtasdt0(W2_712,W1_713) = sz00 )
| ~ aElement0(W2_712)
| ~ aElementOf0(W1_713,xI) ),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_43485]) ).
tff(c_43762,plain,
! [W0_2,W1_713] :
( ( sdtasdt0(smndt0(W0_2),W1_713) = sz00 )
| ~ aElementOf0(W1_713,xI)
| ~ aElement0(W0_2) ),
inference(resolution,[status(thm)],[c_8,c_43720]) ).
tff(c_42449,plain,
! [W1_677,W0_678] :
( ( sdtasdt0(W1_677,W0_678) = sdtasdt0(W0_678,W1_677) )
| ~ aElement0(W1_677)
| ~ aElement0(W0_678) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_42935,plain,
! [W0_691] :
( ( sdtasdt0(xb,W0_691) = sdtasdt0(W0_691,xb) )
| ~ aElement0(W0_691) ),
inference(resolution,[status(thm)],[c_208,c_42449]) ).
tff(c_49873,plain,
! [W0_813] :
( ( sdtasdt0(smndt0(W0_813),xb) = sdtasdt0(xb,smndt0(W0_813)) )
| ~ aElement0(W0_813) ),
inference(resolution,[status(thm)],[c_8,c_42935]) ).
tff(c_49906,plain,
( ( sdtasdt0(xb,smndt0(sz10)) = smndt0(xb) )
| ~ aElement0(xb)
| ~ aElement0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_49873,c_40]) ).
tff(c_49941,plain,
sdtasdt0(xb,smndt0(sz10)) = smndt0(xb),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_208,c_49906]) ).
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_49984,plain,
( aElement0(smndt0(xb))
| ~ aElement0(smndt0(sz10))
| ~ aElement0(xb) ),
inference(superposition,[status(thm),theory(equality)],[c_49941,c_12]) ).
tff(c_50012,plain,
( aElement0(smndt0(xb))
| ~ aElement0(smndt0(sz10)) ),
inference(demodulation,[status(thm),theory(equality)],[c_208,c_49984]) ).
tff(c_50030,plain,
~ aElement0(smndt0(sz10)),
inference(splitLeft,[status(thm)],[c_50012]) ).
tff(c_50033,plain,
~ aElement0(sz10),
inference(resolution,[status(thm)],[c_8,c_50030]) ).
tff(c_50037,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_50033]) ).
tff(c_50039,plain,
aElement0(smndt0(sz10)),
inference(splitRight,[status(thm)],[c_50012]) ).
tff(c_42470,plain,
! [W0_678] :
( ( sdtasdt0(xb,W0_678) = sdtasdt0(W0_678,xb) )
| ~ aElement0(W0_678) ),
inference(resolution,[status(thm)],[c_208,c_42449]) ).
tff(c_50274,plain,
sdtasdt0(smndt0(sz10),xb) = sdtasdt0(xb,smndt0(sz10)),
inference(resolution,[status(thm)],[c_50039,c_42470]) ).
tff(c_50316,plain,
sdtasdt0(smndt0(sz10),xb) = smndt0(xb),
inference(demodulation,[status(thm),theory(equality)],[c_49941,c_50274]) ).
tff(c_51946,plain,
( ( smndt0(xb) = sz00 )
| ~ aElementOf0(xb,xI)
| ~ aElement0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_43762,c_50316]) ).
tff(c_51981,plain,
( ( smndt0(xb) = sz00 )
| ~ aElementOf0(xb,xI) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_51946]) ).
tff(c_52141,plain,
~ aElementOf0(xb,xI),
inference(splitLeft,[status(thm)],[c_51981]) ).
tff(c_41786,plain,
xa = sz00,
inference(splitRight,[status(thm)],[c_212]) ).
tff(c_226,plain,
aElementOf0(sz00,slsdtgt0(xa)),
inference(cnfTransformation,[status(thm)],[f_368]) ).
tff(c_41789,plain,
aElementOf0(sz00,slsdtgt0(sz00)),
inference(demodulation,[status(thm),theory(equality)],[c_41786,c_226]) ).
tff(c_220,plain,
aElementOf0(xb,slsdtgt0(xb)),
inference(cnfTransformation,[status(thm)],[f_368]) ).
tff(c_4,plain,
aElement0(sz00),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_41936,plain,
sdtpldt1(slsdtgt0(sz00),slsdtgt0(xb)) = xI,
inference(demodulation,[status(thm),theory(equality)],[c_41786,c_216]) ).
tff(c_42137,plain,
! [W0_662,W1_663] :
( aSet0(sdtpldt1(W0_662,W1_663))
| ~ aSet0(W1_663)
| ~ aSet0(W0_662) ),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_42140,plain,
( aSet0(xI)
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(sz00)) ),
inference(superposition,[status(thm),theory(equality)],[c_41936,c_42137]) ).
tff(c_42373,plain,
~ aSet0(slsdtgt0(sz00)),
inference(splitLeft,[status(thm)],[c_42140]) ).
tff(c_42381,plain,
~ aElement0(sz00),
inference(resolution,[status(thm)],[c_188,c_42373]) ).
tff(c_42388,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_42381]) ).
tff(c_42390,plain,
aSet0(slsdtgt0(sz00)),
inference(splitRight,[status(thm)],[c_42140]) ).
tff(c_42389,plain,
( ~ aSet0(slsdtgt0(xb))
| aSet0(xI) ),
inference(splitRight,[status(thm)],[c_42140]) ).
tff(c_42391,plain,
~ aSet0(slsdtgt0(xb)),
inference(splitLeft,[status(thm)],[c_42389]) ).
tff(c_42394,plain,
~ aElement0(xb),
inference(resolution,[status(thm)],[c_188,c_42391]) ).
tff(c_42401,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_208,c_42394]) ).
tff(c_42403,plain,
aSet0(slsdtgt0(xb)),
inference(splitRight,[status(thm)],[c_42389]) ).
tff(c_52369,plain,
! [W4_837,W5_838,W0_839,W1_840] :
( aElementOf0(sdtpldt0(W4_837,W5_838),sdtpldt1(W0_839,W1_840))
| ~ aElementOf0(W5_838,W1_840)
| ~ aElementOf0(W4_837,W0_839)
| ~ aSet0(W1_840)
| ~ aSet0(W0_839) ),
inference(cnfTransformation,[status(thm)],[f_172]) ).
tff(c_52461,plain,
! [W4_837,W5_838] :
( aElementOf0(sdtpldt0(W4_837,W5_838),xI)
| ~ aElementOf0(W5_838,slsdtgt0(xb))
| ~ aElementOf0(W4_837,slsdtgt0(sz00))
| ~ aSet0(slsdtgt0(xb))
| ~ aSet0(slsdtgt0(sz00)) ),
inference(superposition,[status(thm),theory(equality)],[c_41936,c_52369]) ).
tff(c_94423,plain,
! [W4_1127,W5_1128] :
( aElementOf0(sdtpldt0(W4_1127,W5_1128),xI)
| ~ aElementOf0(W5_1128,slsdtgt0(xb))
| ~ aElementOf0(W4_1127,slsdtgt0(sz00)) ),
inference(demodulation,[status(thm),theory(equality)],[c_42390,c_42403,c_52461]) ).
tff(c_94692,plain,
( aElementOf0(xb,xI)
| ~ aElementOf0(xb,slsdtgt0(xb))
| ~ aElementOf0(sz00,slsdtgt0(sz00)) ),
inference(superposition,[status(thm),theory(equality)],[c_41816,c_94423]) ).
tff(c_94817,plain,
aElementOf0(xb,xI),
inference(demodulation,[status(thm),theory(equality)],[c_41789,c_220,c_94692]) ).
tff(c_94819,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_52141,c_94817]) ).
tff(c_94820,plain,
smndt0(xb) = sz00,
inference(splitRight,[status(thm)],[c_51981]) ).
tff(c_94901,plain,
( ( sdtpldt0(sz00,xb) = sz00 )
| ~ aElement0(xb) ),
inference(superposition,[status(thm),theory(equality)],[c_94820,c_22]) ).
tff(c_94937,plain,
xb = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_208,c_41816,c_94901]) ).
tff(c_94939,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_41785,c_94937]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : RNG109+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.14 % 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 : n010.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 17:47:43 EDT 2023
% 0.14/0.35 % CPUTime :
% 35.61/21.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 35.61/21.32
% 35.61/21.32 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 35.61/21.36
% 35.61/21.36 Inference rules
% 35.61/21.36 ----------------------
% 35.61/21.36 #Ref : 0
% 35.61/21.36 #Sup : 20130
% 35.61/21.36 #Fact : 0
% 35.61/21.36 #Define : 0
% 35.61/21.36 #Split : 38
% 35.61/21.36 #Chain : 0
% 35.61/21.36 #Close : 0
% 35.61/21.36
% 35.61/21.36 Ordering : KBO
% 35.61/21.36
% 35.61/21.36 Simplification rules
% 35.61/21.36 ----------------------
% 35.61/21.36 #Subsume : 3317
% 35.61/21.36 #Demod : 26904
% 35.61/21.36 #Tautology : 7169
% 35.61/21.36 #SimpNegUnit : 277
% 35.61/21.36 #BackRed : 69
% 35.61/21.36
% 35.61/21.36 #Partial instantiations: 0
% 35.61/21.36 #Strategies tried : 1
% 35.61/21.36
% 35.61/21.36 Timing (in seconds)
% 35.61/21.36 ----------------------
% 35.61/21.37 Preprocessing : 0.70
% 35.61/21.37 Parsing : 0.35
% 35.61/21.37 CNF conversion : 0.06
% 35.61/21.37 Main loop : 19.52
% 35.61/21.37 Inferencing : 2.91
% 35.61/21.37 Reduction : 11.89
% 35.61/21.37 Demodulation : 10.60
% 35.61/21.37 BG Simplification : 0.18
% 35.61/21.37 Subsumption : 3.93
% 35.61/21.37 Abstraction : 0.26
% 35.61/21.37 MUC search : 0.00
% 35.61/21.37 Cooper : 0.00
% 35.61/21.37 Total : 20.29
% 35.61/21.37 Index Insertion : 0.00
% 35.61/21.37 Index Deletion : 0.00
% 35.61/21.37 Index Matching : 0.00
% 35.61/21.37 BG Taut test : 0.00
%------------------------------------------------------------------------------