TSTP Solution File: NUM463+2 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : NUM463+2 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n002.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 10:51:45 EDT 2023
% Result : Theorem 217.95s 173.93s
% Output : CNFRefutation 218.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 31
% Syntax : Number of formulae : 194 ( 64 unt; 10 typ; 1 def)
% Number of atoms : 564 ( 216 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 669 ( 289 ~; 320 |; 33 &)
% ( 1 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 6 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 150 (; 148 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ sdtlseqdt0 > aNaturalNumber0 > sdtpldt0 > sdtmndt0 > sdtasdt0 > #nlpp > xn > xm > sz10 > sz00 > #skF_1
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(sdtasdt0,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sz10,type,
sz10: $i ).
tff(sdtmndt0,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(sdtlseqdt0,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sz00,type,
sz00: $i ).
tff(sdtpldt0,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(aNaturalNumber0,type,
aNaturalNumber0: $i > $o ).
tff(xm,type,
xm: $i ).
tff(xn,type,
xn: $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i ) > $i ).
tff(f_272,hypothesis,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__987) ).
tff(f_67,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
tff(f_31,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
tff(f_162,definition,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
tff(f_87,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
tff(f_93,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
tff(f_35,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
tff(f_282,negated_conjecture,
~ ( ( xm != sz00 )
=> ( ? [W0] :
( aNaturalNumber0(W0)
& ( sdtpldt0(xn,W0) = sdtasdt0(xn,xm) ) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(f_212,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
| ( ( W1 != W0 )
& sdtlseqdt0(W1,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
tff(f_201,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W2) )
=> sdtlseqdt0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
tff(f_269,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( W0 = sz00 )
| ( W0 = sz10 )
| ( ( sz10 != W0 )
& sdtlseqdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
tff(f_189,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
tff(f_81,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
tff(f_47,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
tff(f_131,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1,W2] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
tff(f_258,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( W0 != sz00 )
& ( W1 != W2 )
& sdtlseqdt0(W1,W2) )
=> ( ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2) )
& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))
& ( sdtasdt0(W1,W0) != sdtasdt0(W2,W0) )
& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
tff(f_73,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(f_53,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
tff(f_141,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtpldt0(W0,W1) = sz00 )
=> ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
tff(f_41,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(f_151,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtasdt0(W0,W1) = sz00 )
=> ( ( W0 = sz00 )
| ( W1 = sz00 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
tff(c_95,plain,
aNaturalNumber0(xn),
inference(cnfTransformation,[status(thm)],[f_272]) ).
tff(c_248,plain,
! [W0_66] :
( ( sdtpldt0(W0_66,sz00) = W0_66 )
| ~ aNaturalNumber0(W0_66) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_264,plain,
sdtpldt0(xn,sz00) = xn,
inference(resolution,[status(thm)],[c_95,c_248]) ).
tff(c_4,plain,
aNaturalNumber0(sz00),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_2888,plain,
! [W0_119,W2_120] :
( sdtlseqdt0(W0_119,sdtpldt0(W0_119,W2_120))
| ~ aNaturalNumber0(W2_120)
| ~ aNaturalNumber0(sdtpldt0(W0_119,W2_120))
| ~ aNaturalNumber0(W0_119) ),
inference(cnfTransformation,[status(thm)],[f_162]) ).
tff(c_2932,plain,
( sdtlseqdt0(xn,xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xn,sz00))
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_264,c_2888]) ).
tff(c_2975,plain,
sdtlseqdt0(xn,xn),
inference(demodulation,[status(thm),theory(equality)],[c_95,c_95,c_264,c_4,c_2932]) ).
tff(c_279,plain,
! [W0_67] :
( ( sdtasdt0(sz10,W0_67) = W0_67 )
| ~ aNaturalNumber0(W0_67) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_296,plain,
sdtasdt0(sz10,xn) = xn,
inference(resolution,[status(thm)],[c_95,c_279]) ).
tff(c_97,plain,
aNaturalNumber0(xm),
inference(cnfTransformation,[status(thm)],[f_272]) ).
tff(c_105,plain,
! [W0_61] :
( ( sdtasdt0(W0_61,sz00) = sz00 )
| ~ aNaturalNumber0(W0_61) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_121,plain,
sdtasdt0(xm,sz00) = sz00,
inference(resolution,[status(thm)],[c_97,c_105]) ).
tff(c_8,plain,
aNaturalNumber0(sz10),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_172,plain,
! [W0_64] :
( ( sdtasdt0(W0_64,sz10) = W0_64 )
| ~ aNaturalNumber0(W0_64) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_186,plain,
sdtasdt0(sz10,sz10) = sz10,
inference(resolution,[status(thm)],[c_8,c_172]) ).
tff(c_103,plain,
xm != sz00,
inference(cnfTransformation,[status(thm)],[f_282]) ).
tff(c_265,plain,
sdtpldt0(xm,sz00) = xm,
inference(resolution,[status(thm)],[c_97,c_248]) ).
tff(c_2935,plain,
( sdtlseqdt0(xm,xm)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xm,sz00))
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_265,c_2888]) ).
tff(c_2977,plain,
sdtlseqdt0(xm,xm),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_97,c_265,c_4,c_2935]) ).
tff(c_70,plain,
! [W1_50,W0_49] :
( sdtlseqdt0(W1_50,W0_49)
| sdtlseqdt0(W0_49,W1_50)
| ~ aNaturalNumber0(W1_50)
| ~ aNaturalNumber0(W0_49) ),
inference(cnfTransformation,[status(thm)],[f_212]) ).
tff(c_3569,plain,
! [W0_127,W2_128,W1_129] :
( sdtlseqdt0(W0_127,W2_128)
| ~ sdtlseqdt0(W1_129,W2_128)
| ~ sdtlseqdt0(W0_127,W1_129)
| ~ aNaturalNumber0(W2_128)
| ~ aNaturalNumber0(W1_129)
| ~ aNaturalNumber0(W0_127) ),
inference(cnfTransformation,[status(thm)],[f_201]) ).
tff(c_18118,plain,
! [W0_270,W1_271,W0_272] :
( sdtlseqdt0(W0_270,W1_271)
| ~ sdtlseqdt0(W0_270,W0_272)
| ~ aNaturalNumber0(W0_270)
| sdtlseqdt0(W1_271,W0_272)
| ~ aNaturalNumber0(W1_271)
| ~ aNaturalNumber0(W0_272) ),
inference(resolution,[status(thm)],[c_70,c_3569]) ).
tff(c_18196,plain,
! [W1_271] :
( sdtlseqdt0(xm,W1_271)
| sdtlseqdt0(W1_271,xm)
| ~ aNaturalNumber0(W1_271)
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[c_2977,c_18118]) ).
tff(c_18701,plain,
! [W1_279] :
( sdtlseqdt0(xm,W1_279)
| sdtlseqdt0(W1_279,xm)
| ~ aNaturalNumber0(W1_279) ),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_18196]) ).
tff(c_90,plain,
! [W0_58] :
( sdtlseqdt0(sz10,W0_58)
| ( sz10 = W0_58 )
| ( sz00 = W0_58 )
| ~ aNaturalNumber0(W0_58) ),
inference(cnfTransformation,[status(thm)],[f_269]) ).
tff(c_1657,plain,
! [W1_102,W0_103] :
( ( W1_102 = W0_103 )
| ~ sdtlseqdt0(W1_102,W0_103)
| ~ sdtlseqdt0(W0_103,W1_102)
| ~ aNaturalNumber0(W1_102)
| ~ aNaturalNumber0(W0_103) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_1663,plain,
! [W0_58] :
( ~ sdtlseqdt0(W0_58,sz10)
| ~ aNaturalNumber0(sz10)
| ( sz10 = W0_58 )
| ( sz00 = W0_58 )
| ~ aNaturalNumber0(W0_58) ),
inference(resolution,[status(thm)],[c_90,c_1657]) ).
tff(c_1670,plain,
! [W0_58] :
( ~ sdtlseqdt0(W0_58,sz10)
| ( sz10 = W0_58 )
| ( sz00 = W0_58 )
| ~ aNaturalNumber0(W0_58) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_1663]) ).
tff(c_18719,plain,
( ( xm = sz10 )
| ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(sz10) ),
inference(resolution,[status(thm)],[c_18701,c_1670]) ).
tff(c_18749,plain,
( ( xm = sz10 )
| ( xm = sz00 )
| sdtlseqdt0(sz10,xm) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_97,c_18719]) ).
tff(c_18750,plain,
( ( xm = sz10 )
| sdtlseqdt0(sz10,xm) ),
inference(negUnitSimplification,[status(thm)],[c_103,c_18749]) ).
tff(c_18766,plain,
sdtlseqdt0(sz10,xm),
inference(splitLeft,[status(thm)],[c_18750]) ).
tff(c_297,plain,
sdtasdt0(sz10,xm) = xm,
inference(resolution,[status(thm)],[c_97,c_279]) ).
tff(c_188,plain,
sdtasdt0(xm,sz10) = xm,
inference(resolution,[status(thm)],[c_97,c_172]) ).
tff(c_3758,plain,
! [W0_131,W1_132,W2_133] :
( ( sdtasdt0(sdtasdt0(W0_131,W1_132),W2_133) = sdtasdt0(W0_131,sdtasdt0(W1_132,W2_133)) )
| ~ aNaturalNumber0(W2_133)
| ~ aNaturalNumber0(W1_132)
| ~ aNaturalNumber0(W0_131) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_3890,plain,
! [W2_133] :
( ( sdtasdt0(xm,sdtasdt0(sz10,W2_133)) = sdtasdt0(xm,W2_133) )
| ~ aNaturalNumber0(W2_133)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_188,c_3758]) ).
tff(c_3977,plain,
! [W2_133] :
( ( sdtasdt0(xm,sdtasdt0(sz10,W2_133)) = sdtasdt0(xm,W2_133) )
| ~ aNaturalNumber0(W2_133) ),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_8,c_3890]) ).
tff(c_12,plain,
! [W0_4,W1_5] :
( aNaturalNumber0(sdtasdt0(W0_4,W1_5))
| ~ aNaturalNumber0(W1_5)
| ~ aNaturalNumber0(W0_4) ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_31952,plain,
! [W0_374,W1_375,W2_376] :
( aNaturalNumber0(sdtasdt0(W0_374,sdtasdt0(W1_375,W2_376)))
| ~ aNaturalNumber0(W2_376)
| ~ aNaturalNumber0(sdtasdt0(W0_374,W1_375))
| ~ aNaturalNumber0(W2_376)
| ~ aNaturalNumber0(W1_375)
| ~ aNaturalNumber0(W0_374) ),
inference(superposition,[status(thm),theory(equality)],[c_3758,c_12]) ).
tff(c_32212,plain,
! [W2_133] :
( aNaturalNumber0(sdtasdt0(xm,W2_133))
| ~ aNaturalNumber0(W2_133)
| ~ aNaturalNumber0(sdtasdt0(xm,sz10))
| ~ aNaturalNumber0(W2_133)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(W2_133) ),
inference(superposition,[status(thm),theory(equality)],[c_3977,c_31952]) ).
tff(c_32514,plain,
! [W2_133] :
( aNaturalNumber0(sdtasdt0(xm,W2_133))
| ~ aNaturalNumber0(W2_133) ),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_8,c_97,c_188,c_32212]) ).
tff(c_4532,plain,
! [W0_140,W2_141,W1_142] :
( ( sdtasdt0(W0_140,W2_141) != sdtasdt0(W0_140,W1_142) )
| ( W2_141 = W1_142 )
| ~ aNaturalNumber0(W2_141)
| ~ aNaturalNumber0(W1_142)
| ( sz00 = W0_140 )
| ~ aNaturalNumber0(W0_140) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_4668,plain,
! [W2_141] :
( ( sdtasdt0(xm,W2_141) != sz00 )
| ( sz00 = W2_141 )
| ~ aNaturalNumber0(W2_141)
| ~ aNaturalNumber0(sz00)
| ( xm = sz00 )
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_121,c_4532]) ).
tff(c_4859,plain,
! [W2_141] :
( ( sdtasdt0(xm,W2_141) != sz00 )
| ( sz00 = W2_141 )
| ~ aNaturalNumber0(W2_141)
| ( xm = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_4,c_4668]) ).
tff(c_4998,plain,
! [W2_145] :
( ( sdtasdt0(xm,W2_145) != sz00 )
| ( sz00 = W2_145 )
| ~ aNaturalNumber0(W2_145) ),
inference(negUnitSimplification,[status(thm)],[c_103,c_4859]) ).
tff(c_5037,plain,
( ( sdtasdt0(xm,xm) != sz00 )
| ( xm = sz00 ) ),
inference(resolution,[status(thm)],[c_97,c_4998]) ).
tff(c_5065,plain,
sdtasdt0(xm,xm) != sz00,
inference(negUnitSimplification,[status(thm)],[c_103,c_5037]) ).
tff(c_6,plain,
sz10 != sz00,
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_155,plain,
! [W0_63] :
( ( sdtpldt0(sz00,W0_63) = W0_63 )
| ~ aNaturalNumber0(W0_63) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_169,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(resolution,[status(thm)],[c_8,c_155]) ).
tff(c_2941,plain,
( sdtlseqdt0(sz00,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(sdtpldt0(sz00,sz10))
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm),theory(equality)],[c_169,c_2888]) ).
tff(c_2981,plain,
sdtlseqdt0(sz00,sz10),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_8,c_169,c_8,c_2941]) ).
tff(c_7603,plain,
! [W0_176,W1_177,W2_178] :
( sdtlseqdt0(sdtasdt0(W0_176,W1_177),sdtasdt0(W0_176,W2_178))
| ~ sdtlseqdt0(W1_177,W2_178)
| ( W2_178 = W1_177 )
| ( sz00 = W0_176 )
| ~ aNaturalNumber0(W2_178)
| ~ aNaturalNumber0(W1_177)
| ~ aNaturalNumber0(W0_176) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_7787,plain,
! [W1_177] :
( sdtlseqdt0(sdtasdt0(xm,W1_177),xm)
| ~ sdtlseqdt0(W1_177,sz10)
| ( sz10 = W1_177 )
| ( xm = sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(W1_177)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_188,c_7603]) ).
tff(c_7986,plain,
! [W1_177] :
( sdtlseqdt0(sdtasdt0(xm,W1_177),xm)
| ~ sdtlseqdt0(W1_177,sz10)
| ( sz10 = W1_177 )
| ( xm = sz00 )
| ~ aNaturalNumber0(W1_177) ),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_8,c_7787]) ).
tff(c_7987,plain,
! [W1_177] :
( sdtlseqdt0(sdtasdt0(xm,W1_177),xm)
| ~ sdtlseqdt0(W1_177,sz10)
| ( sz10 = W1_177 )
| ~ aNaturalNumber0(W1_177) ),
inference(negUnitSimplification,[status(thm)],[c_103,c_7986]) ).
tff(c_24,plain,
! [W0_14,W1_15,W2_16] :
( ( sdtasdt0(sdtasdt0(W0_14,W1_15),W2_16) = sdtasdt0(W0_14,sdtasdt0(W1_15,W2_16)) )
| ~ aNaturalNumber0(W2_16)
| ~ aNaturalNumber0(W1_15)
| ~ aNaturalNumber0(W0_14) ),
inference(cnfTransformation,[status(thm)],[f_81]) ).
tff(c_32893,plain,
! [W2_378] :
( aNaturalNumber0(sdtasdt0(xm,W2_378))
| ~ aNaturalNumber0(W2_378) ),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_8,c_97,c_188,c_32212]) ).
tff(c_32,plain,
! [W0_18] :
( ( sdtasdt0(W0_18,sz00) = sz00 )
| ~ aNaturalNumber0(W0_18) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_33520,plain,
! [W2_381] :
( ( sdtasdt0(sdtasdt0(xm,W2_381),sz00) = sz00 )
| ~ aNaturalNumber0(W2_381) ),
inference(resolution,[status(thm)],[c_32893,c_32]) ).
tff(c_33649,plain,
! [W1_15] :
( ( sdtasdt0(xm,sdtasdt0(W1_15,sz00)) = sz00 )
| ~ aNaturalNumber0(W1_15)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(W1_15)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_33520]) ).
tff(c_38426,plain,
! [W1_406] :
( ( sdtasdt0(xm,sdtasdt0(W1_406,sz00)) = sz00 )
| ~ aNaturalNumber0(W1_406) ),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_4,c_33649]) ).
tff(c_86,plain,
! [W0_55,W1_56,W2_57] :
( sdtlseqdt0(sdtasdt0(W0_55,W1_56),sdtasdt0(W0_55,W2_57))
| ~ sdtlseqdt0(W1_56,W2_57)
| ( W2_57 = W1_56 )
| ( sz00 = W0_55 )
| ~ aNaturalNumber0(W2_57)
| ~ aNaturalNumber0(W1_56)
| ~ aNaturalNumber0(W0_55) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_38530,plain,
! [W2_57,W1_406] :
( sdtlseqdt0(sz00,sdtasdt0(xm,W2_57))
| ~ sdtlseqdt0(sdtasdt0(W1_406,sz00),W2_57)
| ( sdtasdt0(W1_406,sz00) = W2_57 )
| ( xm = sz00 )
| ~ aNaturalNumber0(W2_57)
| ~ aNaturalNumber0(sdtasdt0(W1_406,sz00))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(W1_406) ),
inference(superposition,[status(thm),theory(equality)],[c_38426,c_86]) ).
tff(c_38711,plain,
! [W2_57,W1_406] :
( sdtlseqdt0(sz00,sdtasdt0(xm,W2_57))
| ~ sdtlseqdt0(sdtasdt0(W1_406,sz00),W2_57)
| ( sdtasdt0(W1_406,sz00) = W2_57 )
| ( xm = sz00 )
| ~ aNaturalNumber0(W2_57)
| ~ aNaturalNumber0(sdtasdt0(W1_406,sz00))
| ~ aNaturalNumber0(W1_406) ),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_38530]) ).
tff(c_40948,plain,
! [W2_427,W1_428] :
( sdtlseqdt0(sz00,sdtasdt0(xm,W2_427))
| ~ sdtlseqdt0(sdtasdt0(W1_428,sz00),W2_427)
| ( sdtasdt0(W1_428,sz00) = W2_427 )
| ~ aNaturalNumber0(W2_427)
| ~ aNaturalNumber0(sdtasdt0(W1_428,sz00))
| ~ aNaturalNumber0(W1_428) ),
inference(negUnitSimplification,[status(thm)],[c_103,c_38711]) ).
tff(c_41133,plain,
( sdtlseqdt0(sz00,sdtasdt0(xm,xm))
| ( sdtasdt0(xm,sz00) = xm )
| ~ aNaturalNumber0(sdtasdt0(xm,sz00))
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sz00,sz10)
| ( sz10 = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(resolution,[status(thm)],[c_7987,c_40948]) ).
tff(c_41298,plain,
( sdtlseqdt0(sz00,sdtasdt0(xm,xm))
| ( xm = sz00 )
| ( sz10 = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_2981,c_97,c_4,c_121,c_121,c_41133]) ).
tff(c_41299,plain,
sdtlseqdt0(sz00,sdtasdt0(xm,xm)),
inference(negUnitSimplification,[status(thm)],[c_6,c_103,c_41298]) ).
tff(c_66,plain,
! [W1_45,W0_44] :
( ( W1_45 = W0_44 )
| ~ sdtlseqdt0(W1_45,W0_44)
| ~ sdtlseqdt0(W0_44,W1_45)
| ~ aNaturalNumber0(W1_45)
| ~ aNaturalNumber0(W0_44) ),
inference(cnfTransformation,[status(thm)],[f_189]) ).
tff(c_41337,plain,
( ( sdtasdt0(xm,xm) = sz00 )
| ~ sdtlseqdt0(sdtasdt0(xm,xm),sz00)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(resolution,[status(thm)],[c_41299,c_66]) ).
tff(c_41348,plain,
( ( sdtasdt0(xm,xm) = sz00 )
| ~ sdtlseqdt0(sdtasdt0(xm,xm),sz00)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_41337]) ).
tff(c_41349,plain,
( ~ sdtlseqdt0(sdtasdt0(xm,xm),sz00)
| ~ aNaturalNumber0(sdtasdt0(xm,xm)) ),
inference(negUnitSimplification,[status(thm)],[c_5065,c_41348]) ).
tff(c_41578,plain,
~ aNaturalNumber0(sdtasdt0(xm,xm)),
inference(splitLeft,[status(thm)],[c_41349]) ).
tff(c_41581,plain,
~ aNaturalNumber0(xm),
inference(resolution,[status(thm)],[c_32514,c_41578]) ).
tff(c_41588,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_97,c_41581]) ).
tff(c_41590,plain,
aNaturalNumber0(sdtasdt0(xm,xm)),
inference(splitRight,[status(thm)],[c_41349]) ).
tff(c_26,plain,
! [W0_17] :
( ( sdtasdt0(sz10,W0_17) = W0_17 )
| ~ aNaturalNumber0(W0_17) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_41851,plain,
sdtasdt0(sz10,sdtasdt0(xm,xm)) = sdtasdt0(xm,xm),
inference(resolution,[status(thm)],[c_41590,c_26]) ).
tff(c_8203,plain,
! [W1_182,W0_183,W2_184] :
( sdtlseqdt0(sdtasdt0(W1_182,W0_183),sdtasdt0(W2_184,W0_183))
| ~ sdtlseqdt0(W1_182,W2_184)
| ( W2_184 = W1_182 )
| ( sz00 = W0_183 )
| ~ aNaturalNumber0(W2_184)
| ~ aNaturalNumber0(W1_182)
| ~ aNaturalNumber0(W0_183) ),
inference(cnfTransformation,[status(thm)],[f_258]) ).
tff(c_116059,plain,
! [W1_790,W2_791,W0_792,W1_793] :
( sdtlseqdt0(sdtasdt0(W1_790,W2_791),sdtasdt0(W0_792,sdtasdt0(W1_793,W2_791)))
| ~ sdtlseqdt0(W1_790,sdtasdt0(W0_792,W1_793))
| ( sdtasdt0(W0_792,W1_793) = W1_790 )
| ( sz00 = W2_791 )
| ~ aNaturalNumber0(sdtasdt0(W0_792,W1_793))
| ~ aNaturalNumber0(W1_790)
| ~ aNaturalNumber0(W2_791)
| ~ aNaturalNumber0(W2_791)
| ~ aNaturalNumber0(W1_793)
| ~ aNaturalNumber0(W0_792) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_8203]) ).
tff(c_116278,plain,
! [W1_790] :
( sdtlseqdt0(sdtasdt0(W1_790,xm),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(W1_790,sdtasdt0(sz10,xm))
| ( sdtasdt0(sz10,xm) = W1_790 )
| ( xm = sz00 )
| ~ aNaturalNumber0(sdtasdt0(sz10,xm))
| ~ aNaturalNumber0(W1_790)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_41851,c_116059]) ).
tff(c_117142,plain,
! [W1_790] :
( sdtlseqdt0(sdtasdt0(W1_790,xm),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(W1_790,xm)
| ( xm = W1_790 )
| ( xm = sz00 )
| ~ aNaturalNumber0(W1_790) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_97,c_97,c_97,c_97,c_297,c_297,c_297,c_116278]) ).
tff(c_117635,plain,
! [W1_794] :
( sdtlseqdt0(sdtasdt0(W1_794,xm),sdtasdt0(xm,xm))
| ~ sdtlseqdt0(W1_794,xm)
| ( xm = W1_794 )
| ~ aNaturalNumber0(W1_794) ),
inference(negUnitSimplification,[status(thm)],[c_103,c_117142]) ).
tff(c_117687,plain,
( sdtlseqdt0(xm,sdtasdt0(xm,xm))
| ~ sdtlseqdt0(sz10,xm)
| ( xm = sz10 )
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_297,c_117635]) ).
tff(c_117729,plain,
( sdtlseqdt0(xm,sdtasdt0(xm,xm))
| ( xm = sz10 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_18766,c_117687]) ).
tff(c_117733,plain,
xm = sz10,
inference(splitLeft,[status(thm)],[c_117729]) ).
tff(c_545,plain,
! [W1_79,W0_80] :
( ( sdtasdt0(W1_79,W0_80) = sdtasdt0(W0_80,W1_79) )
| ~ aNaturalNumber0(W1_79)
| ~ aNaturalNumber0(W0_80) ),
inference(cnfTransformation,[status(thm)],[f_73]) ).
tff(c_558,plain,
! [W0_4,W1_5,W0_80] :
( ( sdtasdt0(sdtasdt0(W0_4,W1_5),W0_80) = sdtasdt0(W0_80,sdtasdt0(W0_4,W1_5)) )
| ~ aNaturalNumber0(W0_80)
| ~ aNaturalNumber0(W1_5)
| ~ aNaturalNumber0(W0_4) ),
inference(resolution,[status(thm)],[c_12,c_545]) ).
tff(c_4062,plain,
! [W2_135,W0_136,W1_137] :
( ( sdtasdt0(W2_135,W0_136) != sdtasdt0(W1_137,W0_136) )
| ( W2_135 = W1_137 )
| ~ aNaturalNumber0(W2_135)
| ~ aNaturalNumber0(W1_137)
| ( sz00 = W0_136 )
| ~ aNaturalNumber0(W0_136) ),
inference(cnfTransformation,[status(thm)],[f_131]) ).
tff(c_4160,plain,
! [W1_137] :
( ( sdtasdt0(W1_137,xm) != xm )
| ( sz10 = W1_137 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(W1_137)
| ( xm = sz00 )
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_297,c_4062]) ).
tff(c_4334,plain,
! [W1_137] :
( ( sdtasdt0(W1_137,xm) != xm )
| ( sz10 = W1_137 )
| ~ aNaturalNumber0(W1_137)
| ( xm = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_8,c_4160]) ).
tff(c_4463,plain,
! [W1_139] :
( ( sdtasdt0(W1_139,xm) != xm )
| ( sz10 = W1_139 )
| ~ aNaturalNumber0(W1_139) ),
inference(negUnitSimplification,[status(thm)],[c_103,c_4334]) ).
tff(c_4525,plain,
( ( sdtasdt0(xm,xm) != xm )
| ( xm = sz10 ) ),
inference(resolution,[status(thm)],[c_97,c_4463]) ).
tff(c_4527,plain,
sdtasdt0(xm,xm) != xm,
inference(splitLeft,[status(thm)],[c_4525]) ).
tff(c_59644,plain,
! [W1_545,W2_546,W0_547,W1_548] :
( ( sdtasdt0(W1_545,W2_546) != sdtasdt0(W0_547,sdtasdt0(W1_548,W2_546)) )
| ( sdtasdt0(W0_547,W1_548) = W1_545 )
| ~ aNaturalNumber0(sdtasdt0(W0_547,W1_548))
| ~ aNaturalNumber0(W1_545)
| ( sz00 = W2_546 )
| ~ aNaturalNumber0(W2_546)
| ~ aNaturalNumber0(W2_546)
| ~ aNaturalNumber0(W1_548)
| ~ aNaturalNumber0(W0_547) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_4062]) ).
tff(c_59684,plain,
! [W1_545] :
( ( sdtasdt0(xm,xm) != sdtasdt0(W1_545,xm) )
| ( sdtasdt0(sz10,xm) = W1_545 )
| ~ aNaturalNumber0(sdtasdt0(sz10,xm))
| ~ aNaturalNumber0(W1_545)
| ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10) ),
inference(superposition,[status(thm),theory(equality)],[c_41851,c_59644]) ).
tff(c_60090,plain,
! [W1_545] :
( ( sdtasdt0(xm,xm) != sdtasdt0(W1_545,xm) )
| ( xm = W1_545 )
| ~ aNaturalNumber0(W1_545)
| ( xm = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_97,c_97,c_97,c_97,c_297,c_297,c_59684]) ).
tff(c_60957,plain,
! [W1_549] :
( ( sdtasdt0(xm,xm) != sdtasdt0(W1_549,xm) )
| ( xm = W1_549 )
| ~ aNaturalNumber0(W1_549) ),
inference(negUnitSimplification,[status(thm)],[c_103,c_60090]) ).
tff(c_60975,plain,
( ( sdtasdt0(sdtasdt0(xm,xm),xm) != sdtasdt0(xm,xm) )
| ( sdtasdt0(xm,xm) = xm ) ),
inference(resolution,[status(thm)],[c_41590,c_60957]) ).
tff(c_61054,plain,
sdtasdt0(sdtasdt0(xm,xm),xm) != sdtasdt0(xm,xm),
inference(negUnitSimplification,[status(thm)],[c_4527,c_60975]) ).
tff(c_69950,plain,
( ( sdtasdt0(xm,sdtasdt0(xm,xm)) != sdtasdt0(xm,xm) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_558,c_61054]) ).
tff(c_69955,plain,
sdtasdt0(xm,sdtasdt0(xm,xm)) != sdtasdt0(xm,xm),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_97,c_97,c_69950]) ).
tff(c_117870,plain,
sdtasdt0(sz10,sdtasdt0(sz10,sz10)) != sdtasdt0(sz10,sz10),
inference(demodulation,[status(thm),theory(equality)],[c_117733,c_117733,c_117733,c_117733,c_117733,c_69955]) ).
tff(c_118336,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_186,c_117870]) ).
tff(c_118338,plain,
xm != sz10,
inference(splitRight,[status(thm)],[c_117729]) ).
tff(c_185,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(resolution,[status(thm)],[c_4,c_172]) ).
tff(c_263,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(resolution,[status(thm)],[c_8,c_248]) ).
tff(c_4158,plain,
! [W2_135] :
( ( sdtasdt0(W2_135,xn) != xn )
| ( sz10 = W2_135 )
| ~ aNaturalNumber0(W2_135)
| ~ aNaturalNumber0(sz10)
| ( xn = sz00 )
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_296,c_4062]) ).
tff(c_4332,plain,
! [W2_135] :
( ( sdtasdt0(W2_135,xn) != xn )
| ( sz10 = W2_135 )
| ~ aNaturalNumber0(W2_135)
| ( xn = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_95,c_8,c_4158]) ).
tff(c_12007,plain,
xn = sz00,
inference(splitLeft,[status(thm)],[c_4332]) ).
tff(c_743,plain,
! [W1_86,W0_87] :
( ( sdtpldt0(W1_86,W0_87) = sdtpldt0(W0_87,W1_86) )
| ~ aNaturalNumber0(W1_86)
| ~ aNaturalNumber0(W0_87) ),
inference(cnfTransformation,[status(thm)],[f_53]) ).
tff(c_813,plain,
! [W0_89] :
( ( sdtpldt0(sz10,W0_89) = sdtpldt0(W0_89,sz10) )
| ~ aNaturalNumber0(W0_89) ),
inference(resolution,[status(thm)],[c_8,c_743]) ).
tff(c_842,plain,
sdtpldt0(xn,sz10) = sdtpldt0(sz10,xn),
inference(resolution,[status(thm)],[c_95,c_813]) ).
tff(c_46,plain,
! [W1_31,W0_30] :
( ( sz00 = W1_31 )
| ( sdtpldt0(W0_30,W1_31) != sz00 )
| ~ aNaturalNumber0(W1_31)
| ~ aNaturalNumber0(W0_30) ),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_849,plain,
( ( sz10 = sz00 )
| ( sdtpldt0(sz10,xn) != sz00 )
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_842,c_46]) ).
tff(c_858,plain,
( ( sz10 = sz00 )
| ( sdtpldt0(sz10,xn) != sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_95,c_8,c_849]) ).
tff(c_859,plain,
sdtpldt0(sz10,xn) != sz00,
inference(negUnitSimplification,[status(thm)],[c_6,c_858]) ).
tff(c_10,plain,
! [W0_2,W1_3] :
( aNaturalNumber0(sdtpldt0(W0_2,W1_3))
| ~ aNaturalNumber0(W1_3)
| ~ aNaturalNumber0(W0_2) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_852,plain,
( aNaturalNumber0(sdtpldt0(sz10,xn))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_842,c_10]) ).
tff(c_861,plain,
aNaturalNumber0(sdtpldt0(sz10,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_95,c_8,c_852]) ).
tff(c_562,plain,
! [W0_80] :
( ( sdtasdt0(xn,W0_80) = sdtasdt0(W0_80,xn) )
| ~ aNaturalNumber0(W0_80) ),
inference(resolution,[status(thm)],[c_95,c_545]) ).
tff(c_903,plain,
sdtasdt0(sdtpldt0(sz10,xn),xn) = sdtasdt0(xn,sdtpldt0(sz10,xn)),
inference(resolution,[status(thm)],[c_861,c_562]) ).
tff(c_50,plain,
! [W1_33,W0_32] :
( ( sz00 = W1_33 )
| ( sz00 = W0_32 )
| ( sdtasdt0(W0_32,W1_33) != sz00 )
| ~ aNaturalNumber0(W1_33)
| ~ aNaturalNumber0(W0_32) ),
inference(cnfTransformation,[status(thm)],[f_151]) ).
tff(c_2867,plain,
( ( xn = sz00 )
| ( sdtpldt0(sz10,xn) = sz00 )
| ( sdtasdt0(xn,sdtpldt0(sz10,xn)) != sz00 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtpldt0(sz10,xn)) ),
inference(superposition,[status(thm),theory(equality)],[c_903,c_50]) ).
tff(c_2881,plain,
( ( xn = sz00 )
| ( sdtpldt0(sz10,xn) = sz00 )
| ( sdtasdt0(xn,sdtpldt0(sz10,xn)) != sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_861,c_95,c_2867]) ).
tff(c_2882,plain,
( ( xn = sz00 )
| ( sdtasdt0(xn,sdtpldt0(sz10,xn)) != sz00 ) ),
inference(negUnitSimplification,[status(thm)],[c_859,c_2881]) ).
tff(c_10570,plain,
sdtasdt0(xn,sdtpldt0(sz10,xn)) != sz00,
inference(splitLeft,[status(thm)],[c_2882]) ).
tff(c_12051,plain,
sdtasdt0(sz00,sdtpldt0(sz10,sz00)) != sz00,
inference(demodulation,[status(thm),theory(equality)],[c_12007,c_12007,c_10570]) ).
tff(c_12185,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_185,c_263,c_12051]) ).
tff(c_12187,plain,
xn != sz00,
inference(splitRight,[status(thm)],[c_4332]) ).
tff(c_8348,plain,
! [W2_184] :
( sdtlseqdt0(xn,sdtasdt0(W2_184,xn))
| ~ sdtlseqdt0(sz10,W2_184)
| ( sz10 = W2_184 )
| ( xn = sz00 )
| ~ aNaturalNumber0(W2_184)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_296,c_8203]) ).
tff(c_8547,plain,
! [W2_184] :
( sdtlseqdt0(xn,sdtasdt0(W2_184,xn))
| ~ sdtlseqdt0(sz10,W2_184)
| ( sz10 = W2_184 )
| ( xn = sz00 )
| ~ aNaturalNumber0(W2_184) ),
inference(demodulation,[status(thm),theory(equality)],[c_95,c_8,c_8348]) ).
tff(c_435788,plain,
! [W2_1348] :
( sdtlseqdt0(xn,sdtasdt0(W2_1348,xn))
| ~ sdtlseqdt0(sz10,W2_1348)
| ( sz10 = W2_1348 )
| ~ aNaturalNumber0(W2_1348) ),
inference(negUnitSimplification,[status(thm)],[c_12187,c_8547]) ).
tff(c_622,plain,
! [W0_83] :
( ( sdtasdt0(xn,W0_83) = sdtasdt0(W0_83,xn) )
| ~ aNaturalNumber0(W0_83) ),
inference(resolution,[status(thm)],[c_95,c_545]) ).
tff(c_649,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(resolution,[status(thm)],[c_97,c_622]) ).
tff(c_99,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(cnfTransformation,[status(thm)],[f_282]) ).
tff(c_692,plain,
~ sdtlseqdt0(xn,sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_649,c_99]) ).
tff(c_435833,plain,
( ~ sdtlseqdt0(sz10,xm)
| ( xm = sz10 )
| ~ aNaturalNumber0(xm) ),
inference(resolution,[status(thm)],[c_435788,c_692]) ).
tff(c_435955,plain,
xm = sz10,
inference(demodulation,[status(thm),theory(equality)],[c_97,c_18766,c_435833]) ).
tff(c_435957,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_118338,c_435955]) ).
tff(c_435958,plain,
xm = sz10,
inference(splitRight,[status(thm)],[c_18750]) ).
tff(c_122,plain,
! [W0_62] :
( ( sdtpldt0(xn,W0_62) != sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(W0_62) ),
inference(cnfTransformation,[status(thm)],[f_282]) ).
tff(c_135,plain,
sdtpldt0(xn,sz00) != sdtasdt0(xn,xm),
inference(resolution,[status(thm)],[c_4,c_122]) ).
tff(c_274,plain,
sdtasdt0(xn,xm) != xn,
inference(demodulation,[status(thm),theory(equality)],[c_264,c_135]) ).
tff(c_689,plain,
sdtasdt0(xm,xn) != xn,
inference(demodulation,[status(thm),theory(equality)],[c_649,c_274]) ).
tff(c_696,plain,
( aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(superposition,[status(thm),theory(equality)],[c_649,c_12]) ).
tff(c_700,plain,
aNaturalNumber0(sdtasdt0(xm,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_95,c_97,c_696]) ).
tff(c_4152,plain,
! [W1_137] :
( ( sdtasdt0(xm,xn) != sdtasdt0(W1_137,xm) )
| ( xn = W1_137 )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(W1_137)
| ( xm = sz00 )
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_649,c_4062]) ).
tff(c_4324,plain,
! [W1_137] :
( ( sdtasdt0(xm,xn) != sdtasdt0(W1_137,xm) )
| ( xn = W1_137 )
| ~ aNaturalNumber0(W1_137)
| ( xm = sz00 ) ),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_95,c_4152]) ).
tff(c_6630,plain,
! [W1_166] :
( ( sdtasdt0(xm,xn) != sdtasdt0(W1_166,xm) )
| ( xn = W1_166 )
| ~ aNaturalNumber0(W1_166) ),
inference(negUnitSimplification,[status(thm)],[c_103,c_4324]) ).
tff(c_6651,plain,
( ( sdtasdt0(sdtasdt0(xm,xn),xm) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) = xn ) ),
inference(resolution,[status(thm)],[c_700,c_6630]) ).
tff(c_6682,plain,
sdtasdt0(sdtasdt0(xm,xn),xm) != sdtasdt0(xm,xn),
inference(negUnitSimplification,[status(thm)],[c_689,c_6651]) ).
tff(c_10163,plain,
( ( sdtasdt0(xm,sdtasdt0(xn,xm)) != sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm),theory(equality)],[c_24,c_6682]) ).
tff(c_10165,plain,
sdtasdt0(xm,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn),
inference(demodulation,[status(thm),theory(equality)],[c_97,c_95,c_97,c_649,c_10163]) ).
tff(c_436004,plain,
sdtasdt0(sz10,sdtasdt0(sz10,xn)) != sdtasdt0(sz10,xn),
inference(demodulation,[status(thm),theory(equality)],[c_435958,c_435958,c_435958,c_10165]) ).
tff(c_436153,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_296,c_436004]) ).
tff(c_436154,plain,
xn = sz00,
inference(splitRight,[status(thm)],[c_2882]) ).
tff(c_436159,plain,
sdtasdt0(xm,sdtasdt0(xm,sz00)) != sdtasdt0(xm,sz00),
inference(demodulation,[status(thm),theory(equality)],[c_436154,c_436154,c_10165]) ).
tff(c_436284,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_121,c_436159]) ).
tff(c_436285,plain,
xm = sz10,
inference(splitRight,[status(thm)],[c_4525]) ).
tff(c_436348,plain,
~ sdtlseqdt0(xn,sdtasdt0(sz10,xn)),
inference(demodulation,[status(thm),theory(equality)],[c_436285,c_692]) ).
tff(c_436398,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2975,c_296,c_436348]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM463+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 15:12:31 EDT 2023
% 0.15/0.36 % CPUTime :
% 217.95/173.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 217.95/173.96
% 217.95/173.96 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 218.15/174.01
% 218.15/174.01 Inference rules
% 218.15/174.01 ----------------------
% 218.15/174.01 #Ref : 16
% 218.15/174.01 #Sup : 90550
% 218.15/174.01 #Fact : 12
% 218.15/174.01 #Define : 0
% 218.15/174.01 #Split : 42
% 218.15/174.01 #Chain : 0
% 218.15/174.01 #Close : 0
% 218.15/174.01
% 218.15/174.01 Ordering : KBO
% 218.15/174.01
% 218.15/174.01 Simplification rules
% 218.15/174.01 ----------------------
% 218.15/174.01 #Subsume : 20593
% 218.15/174.01 #Demod : 177343
% 218.15/174.01 #Tautology : 18539
% 218.15/174.01 #SimpNegUnit : 8561
% 218.15/174.01 #BackRed : 2244
% 218.15/174.01
% 218.15/174.01 #Partial instantiations: 0
% 218.15/174.01 #Strategies tried : 1
% 218.15/174.01
% 218.15/174.01 Timing (in seconds)
% 218.15/174.01 ----------------------
% 218.15/174.01 Preprocessing : 0.60
% 218.15/174.01 Parsing : 0.30
% 218.15/174.01 CNF conversion : 0.04
% 218.15/174.01 Main loop : 172.36
% 218.15/174.01 Inferencing : 10.63
% 218.15/174.01 Reduction : 93.07
% 218.15/174.01 Demodulation : 72.02
% 218.15/174.01 BG Simplification : 0.81
% 218.15/174.01 Subsumption : 57.31
% 218.15/174.01 Abstraction : 1.45
% 218.15/174.01 MUC search : 0.00
% 218.15/174.01 Cooper : 0.00
% 218.15/174.01 Total : 173.05
% 218.15/174.01 Index Insertion : 0.00
% 218.15/174.01 Index Deletion : 0.00
% 218.15/174.01 Index Matching : 0.00
% 218.15/174.01 BG Taut test : 0.00
%------------------------------------------------------------------------------