TSTP Solution File: NUM454+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM454+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 : n008.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 10:51:43 EDT 2023
% Result : Theorem 25.73s 11.37s
% Output : CNFRefutation 25.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 64
% Syntax : Number of formulae : 198 ( 61 unt; 45 typ; 1 def)
% Number of atoms : 336 ( 160 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 332 ( 149 ~; 146 |; 21 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 70 ( 38 >; 32 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 7 con; 0-3 aty)
% Number of variables : 91 (; 90 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdteqdtlpzmzozddtrp0 > aSubsetOf0 > aElementOf0 > aDivisorOf0 > isPrime0 > isOpen0 > isFinite0 > isClosed0 > aSet0 > aInteger0 > szAzrzSzezqlpdtcmdtrp0 > sdtslmnbsdt0 > sdtpldt0 > sdtbsmnsldt0 > sdtasdt0 > #nlpp > stldt0 > smndt0 > sbsmnsldt0 > xp > xS > sz10 > sz00 > cS2076 > cS2043 > cS1395 > #skF_11 > #skF_2 > #skF_18 > #skF_6 > #skF_19 > #skF_17 > #skF_12 > #skF_8 > #skF_4 > #skF_3 > #skF_13 > #skF_14 > #skF_5 > #skF_10 > #skF_7 > #skF_15 > #skF_1 > #skF_9 > #skF_20 > #skF_16
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(aInteger0,type,
aInteger0: $i > $o ).
tff(sbsmnsldt0,type,
sbsmnsldt0: $i > $i ).
tff('#skF_11',type,
'#skF_11': ( $i * $i ) > $i ).
tff(cS2043,type,
cS2043: $i ).
tff(stldt0,type,
stldt0: $i > $i ).
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': $i > $i ).
tff(aSet0,type,
aSet0: $i > $o ).
tff('#skF_18',type,
'#skF_18': $i > $i ).
tff(isClosed0,type,
isClosed0: $i > $o ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i ) > $i ).
tff(szAzrzSzezqlpdtcmdtrp0,type,
szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff(cS1395,type,
cS1395: $i ).
tff('#skF_19',type,
'#skF_19': $i > $i ).
tff('#skF_17',type,
'#skF_17': ( $i * $i ) > $i ).
tff(cS2076,type,
cS2076: $i ).
tff(xS,type,
xS: $i ).
tff('#skF_12',type,
'#skF_12': ( $i * $i * $i ) > $i ).
tff(sz00,type,
sz00: $i ).
tff('#skF_8',type,
'#skF_8': $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff('#skF_13',type,
'#skF_13': ( $i * $i ) > $i ).
tff('#skF_14',type,
'#skF_14': ( $i * $i ) > $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtslmnbsdt0,type,
sdtslmnbsdt0: ( $i * $i ) > $i ).
tff(isPrime0,type,
isPrime0: $i > $o ).
tff(smndt0,type,
smndt0: $i > $i ).
tff(aSubsetOf0,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(isOpen0,type,
isOpen0: $i > $o ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i ) > $i ).
tff('#skF_10',type,
'#skF_10': ( $i * $i ) > $i ).
tff('#skF_7',type,
'#skF_7': ( $i * $i * $i ) > $i ).
tff(aElementOf0,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtbsmnsldt0,type,
sdtbsmnsldt0: ( $i * $i ) > $i ).
tff('#skF_15',type,
'#skF_15': ( $i * $i * $i ) > $i ).
tff(isFinite0,type,
isFinite0: $i > $o ).
tff(aDivisorOf0,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(xp,type,
xp: $i ).
tff(sdteqdtlpzmzozddtrp0,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff('#skF_9',type,
'#skF_9': ( $i * $i ) > $i ).
tff('#skF_20',type,
'#skF_20': $i > $i ).
tff('#skF_16',type,
'#skF_16': ( $i * $i * $i ) > $i ).
tff(f_439,hypothesis,
( aInteger0(xp)
& ( xp != sz00 )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2171) ).
tff(f_31,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
tff(f_453,negated_conjecture,
~ ( ( sdtpldt0(sz10,xp) != smndt0(sz10) )
| ( sdtpldt0(sz10,smndt0(xp)) != smndt0(sz10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(f_41,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
tff(f_115,axiom,
! [W0] :
( aInteger0(W0)
=> ( ( sdtasdt0(smndt0(sz10),W0) = smndt0(W0) )
& ( smndt0(W0) = sdtasdt0(W0,smndt0(sz10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).
tff(f_87,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
tff(f_125,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> ( ( sdtasdt0(W0,W1) = sz00 )
=> ( ( W0 = sz00 )
| ( W1 = sz00 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).
tff(f_47,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
tff(f_67,axiom,
! [W0] :
( aInteger0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
tff(f_61,axiom,
! [W0,W1] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
tff(f_73,axiom,
! [W0] :
( aInteger0(W0)
=> ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
tff(f_55,axiom,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( sdtpldt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtpldt0(W0,W1),W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
tff(f_35,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
tff(f_30,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
tff(f_109,axiom,
! [W0] :
( aInteger0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
tff(f_140,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
tff(f_93,axiom,
! [W0] :
( aInteger0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).
tff(f_103,axiom,
! [W0,W1,W2] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W0,W1),W2) = sdtpldt0(sdtasdt0(W0,W2),sdtasdt0(W1,W2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistrib) ).
tff(f_447,hypothesis,
( ( sdtpldt0(sz10,xp) != sz10 )
& ( sdtpldt0(sz10,smndt0(xp)) != sz10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2258) ).
tff(c_284,plain,
xp != sz00,
inference(cnfTransformation,[status(thm)],[f_439]) ).
tff(c_6,plain,
aInteger0(sz10),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_286,plain,
aInteger0(xp),
inference(cnfTransformation,[status(thm)],[f_439]) ).
tff(c_298,plain,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(cnfTransformation,[status(thm)],[f_453]) ).
tff(c_542,plain,
! [W0_198,W1_199] :
( aInteger0(sdtpldt0(W0_198,W1_199))
| ~ aInteger0(W1_199)
| ~ aInteger0(W0_198) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_587,plain,
( aInteger0(smndt0(sz10))
| ~ aInteger0(xp)
| ~ aInteger0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_298,c_542]) ).
tff(c_609,plain,
aInteger0(smndt0(sz10)),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_286,c_587]) ).
tff(c_44,plain,
! [W0_24] :
( ( sdtasdt0(smndt0(sz10),W0_24) = smndt0(W0_24) )
| ~ aInteger0(W0_24) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_1168,plain,
! [W1_220,W0_221] :
( ( sdtasdt0(W1_220,W0_221) = sdtasdt0(W0_221,W1_220) )
| ~ aInteger0(W1_220)
| ~ aInteger0(W0_221) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_1568,plain,
! [W0_229] :
( ( sdtasdt0(xp,W0_229) = sdtasdt0(W0_229,xp) )
| ~ aInteger0(W0_229) ),
inference(resolution,[status(thm)],[c_286,c_1168]) ).
tff(c_1607,plain,
sdtasdt0(smndt0(sz10),xp) = sdtasdt0(xp,smndt0(sz10)),
inference(resolution,[status(thm)],[c_609,c_1568]) ).
tff(c_1635,plain,
( ( sdtasdt0(xp,smndt0(sz10)) = smndt0(xp) )
| ~ aInteger0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_44,c_1607]) ).
tff(c_1651,plain,
sdtasdt0(xp,smndt0(sz10)) = smndt0(xp),
inference(demodulation,[status(thm),theory(equality)],[c_286,c_1635]) ).
tff(c_1780,plain,
sdtasdt0(smndt0(sz10),xp) = smndt0(xp),
inference(demodulation,[status(thm),theory(equality)],[c_1651,c_1607]) ).
tff(c_6520,plain,
! [W1_297,W0_298] :
( ( sz00 = W1_297 )
| ( sz00 = W0_298 )
| ( sdtasdt0(W0_298,W1_297) != sz00 )
| ~ aInteger0(W1_297)
| ~ aInteger0(W0_298) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_6590,plain,
( ( xp = sz00 )
| ( smndt0(sz10) = sz00 )
| ( smndt0(xp) != sz00 )
| ~ aInteger0(xp)
| ~ aInteger0(smndt0(sz10)) ),
inference(superposition,[status(thm),theory(equality)],[c_1780,c_6520]) ).
tff(c_6752,plain,
( ( xp = sz00 )
| ( smndt0(sz10) = sz00 )
| ( smndt0(xp) != sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_609,c_286,c_6590]) ).
tff(c_6753,plain,
( ( smndt0(sz10) = sz00 )
| ( smndt0(xp) != sz00 ) ),
inference(negUnitSimplification,[status(thm)],[c_284,c_6752]) ).
tff(c_6835,plain,
smndt0(xp) != sz00,
inference(splitLeft,[status(thm)],[c_6753]) ).
tff(c_42,plain,
! [W0_24] :
( ( sdtasdt0(W0_24,smndt0(sz10)) = smndt0(W0_24) )
| ~ aInteger0(W0_24) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_12,plain,
! [W0_5,W1_6] :
( aInteger0(sdtasdt0(W0_5,W1_6))
| ~ aInteger0(W1_6)
| ~ aInteger0(W0_5) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_1625,plain,
( aInteger0(sdtasdt0(xp,smndt0(sz10)))
| ~ aInteger0(xp)
| ~ aInteger0(smndt0(sz10)) ),
inference(superposition,[status(thm),theory(equality)],[c_1607,c_12]) ).
tff(c_1643,plain,
aInteger0(sdtasdt0(xp,smndt0(sz10))),
inference(demodulation,[status(thm),theory(equality)],[c_609,c_286,c_1625]) ).
tff(c_1683,plain,
( aInteger0(smndt0(xp))
| ~ aInteger0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_42,c_1643]) ).
tff(c_1695,plain,
aInteger0(smndt0(xp)),
inference(demodulation,[status(thm),theory(equality)],[c_286,c_1683]) ).
tff(c_18,plain,
! [W0_12] :
( ( sdtpldt0(sz00,W0_12) = W0_12 )
| ~ aInteger0(W0_12) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_1734,plain,
sdtpldt0(sz00,smndt0(xp)) = smndt0(xp),
inference(resolution,[status(thm)],[c_1695,c_18]) ).
tff(c_2345,plain,
! [W1_243,W0_244] :
( ( sdtpldt0(W1_243,W0_244) = sdtpldt0(W0_244,W1_243) )
| ~ aInteger0(W1_243)
| ~ aInteger0(W0_244) ),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_2609,plain,
! [W0_248] :
( ( sdtpldt0(sz10,W0_248) = sdtpldt0(W0_248,sz10) )
| ~ aInteger0(W0_248) ),
inference(resolution,[status(thm)],[c_6,c_2345]) ).
tff(c_2661,plain,
sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sz10,smndt0(sz10)),
inference(resolution,[status(thm)],[c_609,c_2609]) ).
tff(c_22,plain,
! [W0_13] :
( ( sdtpldt0(smndt0(W0_13),W0_13) = sz00 )
| ~ aInteger0(W0_13) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_2717,plain,
( ( sdtpldt0(sz10,smndt0(sz10)) = sz00 )
| ~ aInteger0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_2661,c_22]) ).
tff(c_2726,plain,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_2717]) ).
tff(c_2790,plain,
sdtpldt0(smndt0(sz10),sz10) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_2726,c_2661]) ).
tff(c_443,plain,
! [W0_187] :
( ( sdtpldt0(W0_187,sz00) = W0_187 )
| ~ aInteger0(W0_187) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_460,plain,
sdtpldt0(xp,sz00) = xp,
inference(resolution,[status(thm)],[c_286,c_443]) ).
tff(c_13809,plain,
! [W0_379,W1_380,W2_381] :
( ( sdtpldt0(sdtpldt0(W0_379,W1_380),W2_381) = sdtpldt0(W0_379,sdtpldt0(W1_380,W2_381)) )
| ~ aInteger0(W2_381)
| ~ aInteger0(W1_380)
| ~ aInteger0(W0_379) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_14041,plain,
! [W2_381] :
( ( sdtpldt0(smndt0(sz10),W2_381) = sdtpldt0(sz10,sdtpldt0(xp,W2_381)) )
| ~ aInteger0(W2_381)
| ~ aInteger0(xp)
| ~ aInteger0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_298,c_13809]) ).
tff(c_14382,plain,
! [W2_383] :
( ( sdtpldt0(smndt0(sz10),W2_383) = sdtpldt0(sz10,sdtpldt0(xp,W2_383)) )
| ~ aInteger0(W2_383) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_286,c_14041]) ).
tff(c_8,plain,
! [W0_2] :
( aInteger0(smndt0(W0_2))
| ~ aInteger0(W0_2) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_2467,plain,
! [W0_247] :
( ( sdtpldt0(xp,W0_247) = sdtpldt0(W0_247,xp) )
| ~ aInteger0(W0_247) ),
inference(resolution,[status(thm)],[c_286,c_2345]) ).
tff(c_2516,plain,
! [W0_2] :
( ( sdtpldt0(smndt0(W0_2),xp) = sdtpldt0(xp,smndt0(W0_2)) )
| ~ aInteger0(W0_2) ),
inference(resolution,[status(thm)],[c_8,c_2467]) ).
tff(c_14428,plain,
( ( sdtpldt0(xp,smndt0(sz10)) = sdtpldt0(sz10,sdtpldt0(xp,xp)) )
| ~ aInteger0(sz10)
| ~ aInteger0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_14382,c_2516]) ).
tff(c_14558,plain,
sdtpldt0(xp,smndt0(sz10)) = sdtpldt0(sz10,sdtpldt0(xp,xp)),
inference(demodulation,[status(thm),theory(equality)],[c_286,c_6,c_14428]) ).
tff(c_459,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(resolution,[status(thm)],[c_6,c_443]) ).
tff(c_296,plain,
sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10),
inference(cnfTransformation,[status(thm)],[f_453]) ).
tff(c_14029,plain,
! [W2_381] :
( ( sdtpldt0(sz10,sdtpldt0(smndt0(xp),W2_381)) = sdtpldt0(smndt0(sz10),W2_381) )
| ~ aInteger0(W2_381)
| ~ aInteger0(smndt0(xp))
| ~ aInteger0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_296,c_13809]) ).
tff(c_14919,plain,
! [W2_388] :
( ( sdtpldt0(sz10,sdtpldt0(smndt0(xp),W2_388)) = sdtpldt0(smndt0(sz10),W2_388) )
| ~ aInteger0(W2_388) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_1695,c_14029]) ).
tff(c_14984,plain,
( ( sdtpldt0(smndt0(sz10),xp) = sdtpldt0(sz10,sz00) )
| ~ aInteger0(xp)
| ~ aInteger0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_14919]) ).
tff(c_15018,plain,
sdtpldt0(smndt0(sz10),xp) = sz10,
inference(demodulation,[status(thm),theory(equality)],[c_286,c_286,c_459,c_14984]) ).
tff(c_15059,plain,
( ( sdtpldt0(xp,smndt0(sz10)) = sz10 )
| ~ aInteger0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_2516,c_15018]) ).
tff(c_15090,plain,
sdtpldt0(sz10,sdtpldt0(xp,xp)) = sz10,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_14558,c_15059]) ).
tff(c_15115,plain,
sdtpldt0(xp,smndt0(sz10)) = sz10,
inference(demodulation,[status(thm),theory(equality)],[c_15090,c_14558]) ).
tff(c_2503,plain,
sdtpldt0(xp,sz10) = sdtpldt0(sz10,xp),
inference(resolution,[status(thm)],[c_6,c_2467]) ).
tff(c_2520,plain,
sdtpldt0(xp,sz10) = smndt0(sz10),
inference(demodulation,[status(thm),theory(equality)],[c_298,c_2503]) ).
tff(c_13986,plain,
! [W2_381] :
( ( sdtpldt0(smndt0(sz10),W2_381) = sdtpldt0(xp,sdtpldt0(sz10,W2_381)) )
| ~ aInteger0(W2_381)
| ~ aInteger0(sz10)
| ~ aInteger0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_2520,c_13809]) ).
tff(c_26628,plain,
! [W2_474] :
( ( sdtpldt0(smndt0(sz10),W2_474) = sdtpldt0(xp,sdtpldt0(sz10,W2_474)) )
| ~ aInteger0(W2_474) ),
inference(demodulation,[status(thm),theory(equality)],[c_286,c_6,c_13986]) ).
tff(c_2379,plain,
! [W0_244] :
( ( sdtpldt0(smndt0(sz10),W0_244) = sdtpldt0(W0_244,smndt0(sz10)) )
| ~ aInteger0(W0_244) ),
inference(resolution,[status(thm)],[c_609,c_2345]) ).
tff(c_14517,plain,
! [W0_244] :
( ( sdtpldt0(sz10,sdtpldt0(xp,W0_244)) = sdtpldt0(W0_244,smndt0(sz10)) )
| ~ aInteger0(W0_244)
| ~ aInteger0(W0_244) ),
inference(superposition,[status(thm),theory(equality)],[c_2379,c_14382]) ).
tff(c_26656,plain,
( ( sdtpldt0(xp,sdtpldt0(sz10,smndt0(sz10))) = sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10))) )
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(smndt0(sz10)) ),
inference(superposition,[status(thm),theory(equality)],[c_26628,c_14517]) ).
tff(c_26837,plain,
sdtpldt0(sz10,sz10) = xp,
inference(demodulation,[status(thm),theory(equality)],[c_609,c_609,c_609,c_460,c_2726,c_15115,c_26656]) ).
tff(c_4,plain,
aInteger0(sz00),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_680,plain,
! [W0_200] :
( ( sdtasdt0(smndt0(sz10),W0_200) = smndt0(W0_200) )
| ~ aInteger0(W0_200) ),
inference(cnfTransformation,[status(thm)],[f_115]) ).
tff(c_469,plain,
! [W0_188] :
( ( sdtasdt0(W0_188,sz00) = sz00 )
| ~ aInteger0(W0_188) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_482,plain,
! [W0_2] :
( ( sdtasdt0(smndt0(W0_2),sz00) = sz00 )
| ~ aInteger0(W0_2) ),
inference(resolution,[status(thm)],[c_8,c_469]) ).
tff(c_690,plain,
( ( smndt0(sz00) = sz00 )
| ~ aInteger0(sz10)
| ~ aInteger0(sz00) ),
inference(superposition,[status(thm),theory(equality)],[c_680,c_482]) ).
tff(c_705,plain,
smndt0(sz00) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_4,c_6,c_690]) ).
tff(c_10,plain,
! [W0_3,W1_4] :
( aInteger0(sdtpldt0(W0_3,W1_4))
| ~ aInteger0(W1_4)
| ~ aInteger0(W0_3) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_14481,plain,
! [W2_383] :
( aInteger0(sdtpldt0(sz10,sdtpldt0(xp,W2_383)))
| ~ aInteger0(W2_383)
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(W2_383) ),
inference(superposition,[status(thm),theory(equality)],[c_14382,c_10]) ).
tff(c_14582,plain,
! [W2_383] :
( aInteger0(sdtpldt0(sz10,sdtpldt0(xp,W2_383)))
| ~ aInteger0(W2_383) ),
inference(demodulation,[status(thm),theory(equality)],[c_609,c_14481]) ).
tff(c_15149,plain,
( aInteger0(sdtpldt0(sz10,sz10))
| ~ aInteger0(smndt0(sz10)) ),
inference(superposition,[status(thm),theory(equality)],[c_15115,c_14582]) ).
tff(c_15180,plain,
aInteger0(sdtpldt0(sz10,sz10)),
inference(demodulation,[status(thm),theory(equality)],[c_609,c_15149]) ).
tff(c_40,plain,
! [W0_23] :
( ( sdtasdt0(W0_23,sz00) = sz00 )
| ~ aInteger0(W0_23) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_15252,plain,
sdtasdt0(sdtpldt0(sz10,sz10),sz00) = sz00,
inference(resolution,[status(thm)],[c_15180,c_40]) ).
tff(c_48,plain,
! [W1_33,W2_36] :
( aDivisorOf0(W1_33,sdtasdt0(W1_33,W2_36))
| ~ aInteger0(W2_36)
| ( sz00 = W1_33 )
| ~ aInteger0(W1_33)
| ~ aInteger0(sdtasdt0(W1_33,W2_36)) ),
inference(cnfTransformation,[status(thm)],[f_140]) ).
tff(c_15374,plain,
( aDivisorOf0(sdtpldt0(sz10,sz10),sz00)
| ~ aInteger0(sz00)
| ( sdtpldt0(sz10,sz10) = sz00 )
| ~ aInteger0(sdtpldt0(sz10,sz10))
| ~ aInteger0(sdtasdt0(sdtpldt0(sz10,sz10),sz00)) ),
inference(superposition,[status(thm),theory(equality)],[c_15252,c_48]) ).
tff(c_15401,plain,
( aDivisorOf0(sdtpldt0(sz10,sz10),sz00)
| ( sdtpldt0(sz10,sz10) = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_15252,c_15180,c_4,c_15374]) ).
tff(c_16484,plain,
sdtpldt0(sz10,sz10) = sz00,
inference(splitLeft,[status(thm)],[c_15401]) ).
tff(c_387,plain,
! [W0_184] :
( ( sdtasdt0(sz00,W0_184) = sz00 )
| ~ aInteger0(W0_184) ),
inference(cnfTransformation,[status(thm)],[f_109]) ).
tff(c_403,plain,
sdtasdt0(sz00,xp) = sz00,
inference(resolution,[status(thm)],[c_286,c_387]) ).
tff(c_1187,plain,
! [W0_221] :
( ( sdtasdt0(smndt0(sz10),W0_221) = sdtasdt0(W0_221,smndt0(sz10)) )
| ~ aInteger0(W0_221) ),
inference(resolution,[status(thm)],[c_609,c_1168]) ).
tff(c_6602,plain,
! [W0_221] :
( ( smndt0(sz10) = sz00 )
| ( sz00 = W0_221 )
| ( sdtasdt0(smndt0(sz10),W0_221) != sz00 )
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(W0_221)
| ~ aInteger0(W0_221) ),
inference(superposition,[status(thm),theory(equality)],[c_1187,c_6520]) ).
tff(c_6774,plain,
! [W0_221] :
( ( smndt0(sz10) = sz00 )
| ( sz00 = W0_221 )
| ( sdtasdt0(smndt0(sz10),W0_221) != sz00 )
| ~ aInteger0(W0_221) ),
inference(demodulation,[status(thm),theory(equality)],[c_609,c_6602]) ).
tff(c_6836,plain,
smndt0(sz10) = sz00,
inference(splitLeft,[status(thm)],[c_6774]) ).
tff(c_6874,plain,
sdtasdt0(sz00,xp) = smndt0(xp),
inference(demodulation,[status(thm),theory(equality)],[c_6836,c_1780]) ).
tff(c_6915,plain,
smndt0(xp) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_403,c_6874]) ).
tff(c_6917,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6835,c_6915]) ).
tff(c_6919,plain,
smndt0(sz10) != sz00,
inference(splitRight,[status(thm)],[c_6774]) ).
tff(c_6610,plain,
! [W0_24] :
( ( smndt0(sz10) = sz00 )
| ( sz00 = W0_24 )
| ( smndt0(W0_24) != sz00 )
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(W0_24)
| ~ aInteger0(W0_24) ),
inference(superposition,[status(thm),theory(equality)],[c_42,c_6520]) ).
tff(c_6782,plain,
! [W0_24] :
( ( smndt0(sz10) = sz00 )
| ( sz00 = W0_24 )
| ( smndt0(W0_24) != sz00 )
| ~ aInteger0(W0_24) ),
inference(demodulation,[status(thm),theory(equality)],[c_609,c_6610]) ).
tff(c_8311,plain,
! [W0_24] :
( ( sz00 = W0_24 )
| ( smndt0(W0_24) != sz00 )
| ~ aInteger0(W0_24) ),
inference(negUnitSimplification,[status(thm)],[c_6919,c_6782]) ).
tff(c_15243,plain,
( ( sdtpldt0(sz10,sz10) = sz00 )
| ( smndt0(sdtpldt0(sz10,sz10)) != sz00 ) ),
inference(resolution,[status(thm)],[c_15180,c_8311]) ).
tff(c_16483,plain,
smndt0(sdtpldt0(sz10,sz10)) != sz00,
inference(splitLeft,[status(thm)],[c_15243]) ).
tff(c_16492,plain,
smndt0(sz00) != sz00,
inference(demodulation,[status(thm),theory(equality)],[c_16484,c_16483]) ).
tff(c_16504,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_705,c_16492]) ).
tff(c_16506,plain,
sdtpldt0(sz10,sz10) != sz00,
inference(splitRight,[status(thm)],[c_15401]) ).
tff(c_1192,plain,
! [W0_221] :
( ( sdtasdt0(xp,W0_221) = sdtasdt0(W0_221,xp) )
| ~ aInteger0(W0_221) ),
inference(resolution,[status(thm)],[c_286,c_1168]) ).
tff(c_15248,plain,
sdtasdt0(sdtpldt0(sz10,sz10),xp) = sdtasdt0(xp,sdtpldt0(sz10,sz10)),
inference(resolution,[status(thm)],[c_15180,c_1192]) ).
tff(c_46,plain,
! [W1_26,W0_25] :
( ( sz00 = W1_26 )
| ( sz00 = W0_25 )
| ( sdtasdt0(W0_25,W1_26) != sz00 )
| ~ aInteger0(W1_26)
| ~ aInteger0(W0_25) ),
inference(cnfTransformation,[status(thm)],[f_125]) ).
tff(c_24000,plain,
( ( xp = sz00 )
| ( sdtpldt0(sz10,sz10) = sz00 )
| ( sdtasdt0(xp,sdtpldt0(sz10,sz10)) != sz00 )
| ~ aInteger0(xp)
| ~ aInteger0(sdtpldt0(sz10,sz10)) ),
inference(superposition,[status(thm),theory(equality)],[c_15248,c_46]) ).
tff(c_24022,plain,
( ( xp = sz00 )
| ( sdtpldt0(sz10,sz10) = sz00 )
| ( sdtasdt0(xp,sdtpldt0(sz10,sz10)) != sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_15180,c_286,c_24000]) ).
tff(c_24023,plain,
sdtasdt0(xp,sdtpldt0(sz10,sz10)) != sz00,
inference(negUnitSimplification,[status(thm)],[c_16506,c_284,c_24022]) ).
tff(c_26920,plain,
sdtasdt0(xp,xp) != sz00,
inference(demodulation,[status(thm),theory(equality)],[c_26837,c_24023]) ).
tff(c_2384,plain,
! [W0_244] :
( ( sdtpldt0(xp,W0_244) = sdtpldt0(W0_244,xp) )
| ~ aInteger0(W0_244) ),
inference(resolution,[status(thm)],[c_286,c_2345]) ).
tff(c_15245,plain,
sdtpldt0(sdtpldt0(sz10,sz10),xp) = sdtpldt0(xp,sdtpldt0(sz10,sz10)),
inference(resolution,[status(thm)],[c_15180,c_2384]) ).
tff(c_14,plain,
! [W0_7,W1_8,W2_9] :
( ( sdtpldt0(sdtpldt0(W0_7,W1_8),W2_9) = sdtpldt0(W0_7,sdtpldt0(W1_8,W2_9)) )
| ~ aInteger0(W2_9)
| ~ aInteger0(W1_8)
| ~ aInteger0(W0_7) ),
inference(cnfTransformation,[status(thm)],[f_55]) ).
tff(c_23695,plain,
( ( sdtpldt0(xp,sdtpldt0(sz10,sz10)) = sdtpldt0(sz10,sdtpldt0(sz10,xp)) )
| ~ aInteger0(xp)
| ~ aInteger0(sz10)
| ~ aInteger0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_15245,c_14]) ).
tff(c_23713,plain,
sdtpldt0(xp,sdtpldt0(sz10,sz10)) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_286,c_2726,c_298,c_23695]) ).
tff(c_26925,plain,
sdtpldt0(xp,xp) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_26837,c_23713]) ).
tff(c_416,plain,
! [W0_185] :
( ( sdtasdt0(W0_185,sz10) = W0_185 )
| ~ aInteger0(W0_185) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_434,plain,
sdtasdt0(xp,sz10) = xp,
inference(resolution,[status(thm)],[c_286,c_416]) ).
tff(c_24468,plain,
! [W0_466,W1_467,W2_468] :
( ( sdtpldt0(sdtasdt0(W0_466,W1_467),sdtasdt0(W0_466,W2_468)) = sdtasdt0(W0_466,sdtpldt0(W1_467,W2_468)) )
| ~ aInteger0(W2_468)
| ~ aInteger0(W1_467)
| ~ aInteger0(W0_466) ),
inference(cnfTransformation,[status(thm)],[f_103]) ).
tff(c_25151,plain,
! [W2_468] :
( ( sdtpldt0(xp,sdtasdt0(xp,W2_468)) = sdtasdt0(xp,sdtpldt0(sz10,W2_468)) )
| ~ aInteger0(W2_468)
| ~ aInteger0(sz10)
| ~ aInteger0(xp) ),
inference(superposition,[status(thm),theory(equality)],[c_434,c_24468]) ).
tff(c_65027,plain,
! [W2_735] :
( ( sdtpldt0(xp,sdtasdt0(xp,W2_735)) = sdtasdt0(xp,sdtpldt0(sz10,W2_735)) )
| ~ aInteger0(W2_735) ),
inference(demodulation,[status(thm),theory(equality)],[c_286,c_6,c_25151]) ).
tff(c_65181,plain,
( ( sdtasdt0(xp,sdtpldt0(sz10,sz10)) = sdtpldt0(xp,xp) )
| ~ aInteger0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_434,c_65027]) ).
tff(c_65226,plain,
sdtasdt0(xp,xp) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_26925,c_26837,c_65181]) ).
tff(c_65228,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_26920,c_65226]) ).
tff(c_65229,plain,
sdtpldt0(sz10,sz10) = sz00,
inference(splitRight,[status(thm)],[c_15243]) ).
tff(c_65251,plain,
! [W2_9] :
( ( sdtpldt0(sz10,sdtpldt0(sz10,W2_9)) = sdtpldt0(sz00,W2_9) )
| ~ aInteger0(W2_9)
| ~ aInteger0(sz10)
| ~ aInteger0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_65229,c_14]) ).
tff(c_73242,plain,
! [W2_790] :
( ( sdtpldt0(sz10,sdtpldt0(sz10,W2_790)) = sdtpldt0(sz00,W2_790) )
| ~ aInteger0(W2_790) ),
inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_65251]) ).
tff(c_2373,plain,
! [W0_244] :
( ( sdtpldt0(smndt0(xp),W0_244) = sdtpldt0(W0_244,smndt0(xp)) )
| ~ aInteger0(W0_244) ),
inference(resolution,[status(thm)],[c_1695,c_2345]) ).
tff(c_14947,plain,
! [W0_244] :
( ( sdtpldt0(sz10,sdtpldt0(W0_244,smndt0(xp))) = sdtpldt0(smndt0(sz10),W0_244) )
| ~ aInteger0(W0_244)
| ~ aInteger0(W0_244) ),
inference(superposition,[status(thm),theory(equality)],[c_2373,c_14919]) ).
tff(c_73258,plain,
( ( sdtpldt0(smndt0(sz10),sz10) = sdtpldt0(sz00,smndt0(xp)) )
| ~ aInteger0(sz10)
| ~ aInteger0(sz10)
| ~ aInteger0(smndt0(xp)) ),
inference(superposition,[status(thm),theory(equality)],[c_73242,c_14947]) ).
tff(c_73329,plain,
smndt0(xp) = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_1695,c_6,c_6,c_1734,c_2790,c_73258]) ).
tff(c_73331,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_6835,c_73329]) ).
tff(c_73332,plain,
smndt0(sz10) = sz00,
inference(splitRight,[status(thm)],[c_6753]) ).
tff(c_294,plain,
sdtpldt0(sz10,xp) != sz10,
inference(cnfTransformation,[status(thm)],[f_447]) ).
tff(c_299,plain,
smndt0(sz10) != sz10,
inference(demodulation,[status(thm),theory(equality)],[c_298,c_294]) ).
tff(c_73393,plain,
sz10 != sz00,
inference(demodulation,[status(thm),theory(equality)],[c_73332,c_299]) ).
tff(c_325,plain,
! [W0_182] :
( ( sdtpldt0(sz00,W0_182) = W0_182 )
| ~ aInteger0(W0_182) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_340,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(resolution,[status(thm)],[c_6,c_325]) ).
tff(c_73484,plain,
( ( sdtpldt0(sz00,sz10) = sz00 )
| ~ aInteger0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_73332,c_22]) ).
tff(c_73529,plain,
sz10 = sz00,
inference(demodulation,[status(thm),theory(equality)],[c_6,c_340,c_73484]) ).
tff(c_73553,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_73393,c_73529]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM454+1 : TPTP v8.1.2. Released v4.0.0.
% 0.15/0.14 % 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
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 3 14:56:04 EDT 2023
% 0.15/0.35 % CPUTime :
% 25.73/11.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.73/11.39
% 25.73/11.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.84/11.44
% 25.84/11.44 Inference rules
% 25.84/11.44 ----------------------
% 25.84/11.44 #Ref : 0
% 25.84/11.44 #Sup : 15172
% 25.84/11.44 #Fact : 0
% 25.84/11.44 #Define : 0
% 25.84/11.44 #Split : 10
% 25.84/11.44 #Chain : 0
% 25.84/11.44 #Close : 0
% 25.84/11.44
% 25.84/11.44 Ordering : KBO
% 25.84/11.44
% 25.84/11.44 Simplification rules
% 25.84/11.44 ----------------------
% 25.84/11.44 #Subsume : 2237
% 25.84/11.44 #Demod : 25957
% 25.84/11.44 #Tautology : 7533
% 25.84/11.44 #SimpNegUnit : 471
% 25.84/11.44 #BackRed : 447
% 25.84/11.44
% 25.84/11.44 #Partial instantiations: 0
% 25.84/11.44 #Strategies tried : 1
% 25.84/11.44
% 25.84/11.44 Timing (in seconds)
% 25.84/11.44 ----------------------
% 26.07/11.45 Preprocessing : 0.75
% 26.07/11.45 Parsing : 0.36
% 26.07/11.45 CNF conversion : 0.07
% 26.07/11.45 Main loop : 9.51
% 26.07/11.45 Inferencing : 2.02
% 26.07/11.45 Reduction : 4.33
% 26.07/11.45 Demodulation : 3.62
% 26.07/11.45 BG Simplification : 0.16
% 26.07/11.45 Subsumption : 2.54
% 26.07/11.45 Abstraction : 0.21
% 26.07/11.45 MUC search : 0.00
% 26.07/11.45 Cooper : 0.00
% 26.07/11.45 Total : 10.35
% 26.07/11.45 Index Insertion : 0.00
% 26.07/11.45 Index Deletion : 0.00
% 26.07/11.45 Index Matching : 0.00
% 26.07/11.45 BG Taut test : 0.00
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