%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM451+6 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n021.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 May 5 04:57:22 PM UTC 2026
% Result : Theorem 8.72s 5.91s
% Output : CNFRefutation 8.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 25
% Syntax : Number of formulae : 277 ( 90 unt; 0 def)
% Number of atoms : 917 ( 299 equ)
% Maximal formula atoms : 46 ( 3 avg)
% Number of connectives : 1031 ( 391 ~; 444 |; 153 &)
% ( 14 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 283 ( 0 sgn 119 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2171,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(mEquModRef,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModRef) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistrib) ).
fof(m__2079,hypothesis,
( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = sz10
| X1 = smndt0(sz10) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2079) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(m__,conjecture,
? [X1] :
( ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ~ ( ( X1 = sz10
| X1 = smndt0(sz10) )
& aElementOf0(X1,cS2200) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mArSeq,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ! [X3] :
( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aInteger0(X4)
& sdteqdtlpzmzozddtrp0(X4,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArSeq) ).
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(mEquModSym,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
=> sdteqdtlpzmzozddtrp0(X2,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModSym) ).
fof(mEquModTrn,axiom,
! [X1,X2,X3,X4] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00
& aInteger0(X4) )
=> ( ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
& sdteqdtlpzmzozddtrp0(X2,X4,X3) )
=> sdteqdtlpzmzozddtrp0(X1,X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModTrn) ).
fof(c_0_25,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(fof_simplification,[status(thm)],[m__2171]) ).
fof(c_0_26,plain,
! [X157,X158] :
( ~ aInteger0(X157)
| ~ aInteger0(X158)
| sdtasdt0(X157,X158) != sz00
| X157 = sz00
| X158 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])]) ).
fof(c_0_27,hypothesis,
! [X284,X286,X287,X288,X290,X291,X292,X293] :
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ( aInteger0(X284)
| ~ aElementOf0(X284,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aInteger0(esk26_1(X284))
| ~ aElementOf0(X284,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( sdtasdt0(xp,esk26_1(X284)) = sdtpldt0(X284,smndt0(sz10))
| ~ aElementOf0(X284,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aDivisorOf0(xp,sdtpldt0(X284,smndt0(sz10)))
| ~ aElementOf0(X284,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( sdteqdtlpzmzozddtrp0(X284,sz10,xp)
| ~ aElementOf0(X284,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aInteger0(X287)
| sdtasdt0(xp,X287) != sdtpldt0(X286,smndt0(sz10))
| ~ aInteger0(X286)
| aElementOf0(X286,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aDivisorOf0(xp,sdtpldt0(X286,smndt0(sz10)))
| ~ aInteger0(X286)
| aElementOf0(X286,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ sdteqdtlpzmzozddtrp0(X286,sz10,xp)
| ~ aInteger0(X286)
| aElementOf0(X286,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSet0(sbsmnsldt0(xS))
& ( aInteger0(X288)
| ~ aElementOf0(X288,sbsmnsldt0(xS)) )
& ( aElementOf0(esk27_1(X288),xS)
| ~ aElementOf0(X288,sbsmnsldt0(xS)) )
& ( aElementOf0(X288,esk27_1(X288))
| ~ aElementOf0(X288,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X290)
| ~ aElementOf0(X291,xS)
| ~ aElementOf0(X290,X291)
| aElementOf0(X290,sbsmnsldt0(xS)) )
& ( aInteger0(X292)
| ~ aElementOf0(X292,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X292,sbsmnsldt0(xS))
| ~ aElementOf0(X292,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X292)
| aElementOf0(X292,sbsmnsldt0(xS))
| aElementOf0(X292,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X293,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X293,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])])]) ).
fof(c_0_28,plain,
! [X167,X168] :
( ~ aInteger0(X167)
| ~ aInteger0(X168)
| X168 = sz00
| sdteqdtlpzmzozddtrp0(X167,X167,X168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModRef])]) ).
cnf(c_0_29,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_30,hypothesis,
( sdtasdt0(xp,esk26_1(X1)) = sdtpldt0(X1,smndt0(sz10))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,hypothesis,
( aInteger0(esk26_1(X1))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( X2 = sz00
| sdteqdtlpzmzozddtrp0(X1,X1,X2)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_35,plain,
! [X146,X147,X148] :
( ~ aInteger0(X146)
| ~ aInteger0(X147)
| ~ aInteger0(X148)
| sdtasdt0(X146,sdtasdt0(X147,X148)) = sdtasdt0(sdtasdt0(X146,X147),X148) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_36,plain,
! [X151] :
( ( sdtasdt0(X151,sz10) = X151
| ~ aInteger0(X151) )
& ( X151 = sdtasdt0(sz10,X151)
| ~ aInteger0(X151) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])]) ).
cnf(c_0_37,hypothesis,
( esk26_1(X1) = sz00
| sdtpldt0(X1,smndt0(sz10)) != sz00
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]),c_0_33]) ).
fof(c_0_38,plain,
! [X145] :
( ( sdtpldt0(X145,smndt0(X145)) = sz00
| ~ aInteger0(X145) )
& ( sz00 = sdtpldt0(smndt0(X145),X145)
| ~ aInteger0(X145) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
cnf(c_0_39,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_40,hypothesis,
( sdteqdtlpzmzozddtrp0(X1,X1,xp)
| ~ aInteger0(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_31]),c_0_32]) ).
cnf(c_0_41,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
fof(c_0_42,plain,
! [X152,X153,X154] :
( ( sdtasdt0(X152,sdtpldt0(X153,X154)) = sdtpldt0(sdtasdt0(X152,X153),sdtasdt0(X152,X154))
| ~ aInteger0(X152)
| ~ aInteger0(X153)
| ~ aInteger0(X154) )
& ( sdtasdt0(sdtpldt0(X152,X153),X154) = sdtpldt0(sdtasdt0(X152,X154),sdtasdt0(X153,X154))
| ~ aInteger0(X152)
| ~ aInteger0(X153)
| ~ aInteger0(X154) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
cnf(c_0_43,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_45,hypothesis,
( sdtpldt0(X1,smndt0(sz10)) = sdtasdt0(xp,sz00)
| sdtpldt0(X1,smndt0(sz10)) != sz00
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_46,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,hypothesis,
aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
fof(c_0_48,hypothesis,
( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = sz10
| X1 = smndt0(sz10) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(fof_simplification,[status(thm)],[m__2079]) ).
cnf(c_0_49,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
fof(c_0_50,plain,
! [X144] :
( ( sdtpldt0(X144,sz00) = X144
| ~ aInteger0(X144) )
& ( X144 = sdtpldt0(sz00,X144)
| ~ aInteger0(X144) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
cnf(c_0_51,plain,
( sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_41])]) ).
cnf(c_0_52,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_41])]) ).
cnf(c_0_53,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
fof(c_0_54,hypothesis,
! [X254,X256,X257,X258,X259] :
( aSet0(sbsmnsldt0(xS))
& ( aInteger0(X254)
| ~ aElementOf0(X254,sbsmnsldt0(xS)) )
& ( aElementOf0(esk19_1(X254),xS)
| ~ aElementOf0(X254,sbsmnsldt0(xS)) )
& ( aElementOf0(X254,esk19_1(X254))
| ~ aElementOf0(X254,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X256)
| ~ aElementOf0(X257,xS)
| ~ aElementOf0(X256,X257)
| aElementOf0(X256,sbsmnsldt0(xS)) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ( aInteger0(X258)
| ~ aElementOf0(X258,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X258,sbsmnsldt0(xS))
| ~ aElementOf0(X258,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X258)
| aElementOf0(X258,sbsmnsldt0(xS))
| aElementOf0(X258,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X259,stldt0(sbsmnsldt0(xS)))
| X259 = sz10
| X259 = smndt0(sz10) )
& ( X259 != sz10
| aElementOf0(X259,stldt0(sbsmnsldt0(xS))) )
& ( X259 != smndt0(sz10)
| aElementOf0(X259,stldt0(sbsmnsldt0(xS))) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])])])]) ).
cnf(c_0_55,plain,
( sdtasdt0(sz10,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(sz10,X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_41])]) ).
cnf(c_0_56,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_57,hypothesis,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_31])]) ).
cnf(c_0_58,hypothesis,
( aElementOf0(X1,sbsmnsldt0(xS))
| aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_59,hypothesis,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(split_conjunct,[status(thm)],[c_0_54]) ).
fof(c_0_60,plain,
! [X134] :
( ~ aInteger0(X134)
| aInteger0(smndt0(X134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_61,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_62,plain,
( sdtasdt0(sz10,X1) = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_53])]) ).
cnf(c_0_63,hypothesis,
( aElementOf0(X1,sbsmnsldt0(xS))
| aElementOf0(X1,cS2076)
| ~ aInteger0(X1) ),
inference(rw,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_65,plain,
! [X139,X140,X141] :
( ~ aInteger0(X139)
| ~ aInteger0(X140)
| ~ aInteger0(X141)
| sdtpldt0(X139,sdtpldt0(X140,X141)) = sdtpldt0(sdtpldt0(X139,X140),X141) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(c_0_66,plain,
! [X135,X136] :
( ~ aInteger0(X135)
| ~ aInteger0(X136)
| aInteger0(sdtpldt0(X135,X136)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
cnf(c_0_67,hypothesis,
( sdtasdt0(xp,sdtpldt0(sz00,X1)) = sdtpldt0(sz00,sdtasdt0(xp,X1))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_52]),c_0_53]),c_0_31])]) ).
cnf(c_0_68,plain,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_41])]) ).
cnf(c_0_69,hypothesis,
( aElementOf0(smndt0(X1),sbsmnsldt0(xS))
| aElementOf0(smndt0(X1),cS2076)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_71,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_72,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_73,hypothesis,
sdtpldt0(sz00,sdtasdt0(xp,sz10)) = sdtasdt0(xp,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_41])]) ).
cnf(c_0_74,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,sbsmnsldt0(xS)) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_75,hypothesis,
( aElementOf0(smndt0(xp),sbsmnsldt0(xS))
| aElementOf0(smndt0(xp),cS2076) ),
inference(spm,[status(thm)],[c_0_69,c_0_31]) ).
cnf(c_0_76,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,cS2076) ),
inference(rw,[status(thm)],[c_0_70,c_0_59]) ).
cnf(c_0_77,plain,
( sdtpldt0(X1,sdtpldt0(X2,smndt0(sdtpldt0(X1,X2)))) = sz00
| ~ aInteger0(smndt0(sdtpldt0(X1,X2)))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_71]),c_0_72]) ).
cnf(c_0_78,hypothesis,
sdtpldt0(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_61]),c_0_31])]) ).
cnf(c_0_79,hypothesis,
aInteger0(smndt0(xp)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]) ).
fof(c_0_80,plain,
! [X155] :
( ( sdtasdt0(X155,sz00) = sz00
| ~ aInteger0(X155) )
& ( sz00 = sdtasdt0(sz00,X155)
| ~ aInteger0(X155) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
fof(c_0_81,plain,
! [X156] :
( ( sdtasdt0(smndt0(sz10),X156) = smndt0(X156)
| ~ aInteger0(X156) )
& ( smndt0(X156) = sdtasdt0(X156,smndt0(sz10))
| ~ aInteger0(X156) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])]) ).
cnf(c_0_82,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_83,plain,
( sdtpldt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_56]),c_0_53])]) ).
cnf(c_0_84,hypothesis,
sdtpldt0(sz00,sdtpldt0(xp,smndt0(xp))) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]),c_0_31]),c_0_53])]) ).
cnf(c_0_85,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_86,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_87,hypothesis,
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| X1 != smndt0(sz10) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_88,plain,
( sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_82]),c_0_64]) ).
cnf(c_0_89,hypothesis,
sdtpldt0(xp,smndt0(xp)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_79]),c_0_31])]) ).
cnf(c_0_90,plain,
( sdtasdt0(sz10,sdtpldt0(X1,X2)) = sdtpldt0(X1,sdtasdt0(sz10,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_44]),c_0_41])]) ).
cnf(c_0_91,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
cnf(c_0_92,plain,
( smndt0(sz00) = sz00
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_53])]) ).
cnf(c_0_93,hypothesis,
aElementOf0(smndt0(sz10),cS2076),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_59])]) ).
cnf(c_0_94,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_95,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_61]),c_0_41])]) ).
cnf(c_0_96,hypothesis,
sdtpldt0(smndt0(xp),sz00) = sdtpldt0(sz00,smndt0(xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_79]),c_0_31])]) ).
cnf(c_0_97,hypothesis,
sdtasdt0(sz10,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_78]),c_0_57]),c_0_78]),c_0_31]),c_0_53])]) ).
cnf(c_0_98,plain,
( sdtasdt0(sz10,X1) = sdtpldt0(X1,sz00)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_57]),c_0_53])]) ).
cnf(c_0_99,hypothesis,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_76]),c_0_93])]) ).
fof(c_0_100,plain,
! [X149,X150] :
( ~ aInteger0(X149)
| ~ aInteger0(X150)
| sdtasdt0(X149,X150) = sdtasdt0(X150,X149) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_101,plain,
( sdtasdt0(smndt0(sz10),sdtasdt0(X1,X2)) = sdtasdt0(smndt0(X1),X2)
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_94]) ).
cnf(c_0_102,hypothesis,
sdtasdt0(xp,sz10) = xp,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_67]),c_0_52]),c_0_53]),c_0_31]),c_0_41])]),c_0_73]),c_0_78]) ).
cnf(c_0_103,hypothesis,
sdtpldt0(sz00,smndt0(xp)) = smndt0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_96]),c_0_79])]) ).
cnf(c_0_104,hypothesis,
sdtpldt0(xp,sz00) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_31])]) ).
cnf(c_0_105,hypothesis,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_99]),c_0_53])]) ).
cnf(c_0_106,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_107,hypothesis,
( sdtasdt0(smndt0(xp),sz10) = sdtasdt0(smndt0(sz10),xp)
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_41]),c_0_31])]) ).
cnf(c_0_108,hypothesis,
sdtasdt0(sz10,smndt0(xp)) = smndt0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_103]),c_0_57]),c_0_103]),c_0_79]),c_0_53])]) ).
cnf(c_0_109,hypothesis,
sdtpldt0(smndt0(xp),xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_104]),c_0_105]),c_0_53]),c_0_31])]) ).
cnf(c_0_110,hypothesis,
( sdtasdt0(smndt0(sz10),xp) = smndt0(xp)
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_41]),c_0_79])]) ).
cnf(c_0_111,hypothesis,
sdtpldt0(smndt0(smndt0(xp)),sz00) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_109]),c_0_78]),c_0_31]),c_0_79])]) ).
cnf(c_0_112,hypothesis,
( sdtasdt0(xp,smndt0(sz10)) = smndt0(xp)
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_110]),c_0_31])]) ).
cnf(c_0_113,hypothesis,
( smndt0(smndt0(xp)) = xp
| ~ aInteger0(smndt0(smndt0(xp))) ),
inference(spm,[status(thm)],[c_0_91,c_0_111]) ).
cnf(c_0_114,hypothesis,
( sdtasdt0(smndt0(xp),smndt0(sz10)) = sdtasdt0(smndt0(sz10),smndt0(xp))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_112]),c_0_31])]) ).
cnf(c_0_115,hypothesis,
smndt0(smndt0(xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_64]),c_0_79])]) ).
fof(c_0_116,plain,
! [X159,X160,X162,X163] :
( ( aInteger0(X160)
| ~ aDivisorOf0(X160,X159)
| ~ aInteger0(X159) )
& ( X160 != sz00
| ~ aDivisorOf0(X160,X159)
| ~ aInteger0(X159) )
& ( aInteger0(esk1_2(X159,X160))
| ~ aDivisorOf0(X160,X159)
| ~ aInteger0(X159) )
& ( sdtasdt0(X160,esk1_2(X159,X160)) = X159
| ~ aDivisorOf0(X160,X159)
| ~ aInteger0(X159) )
& ( ~ aInteger0(X162)
| X162 = sz00
| ~ aInteger0(X163)
| sdtasdt0(X162,X163) != X159
| aDivisorOf0(X162,X159)
| ~ aInteger0(X159) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivisor])])])])])]) ).
fof(c_0_117,plain,
! [X137,X138] :
( ~ aInteger0(X137)
| ~ aInteger0(X138)
| aInteger0(sdtasdt0(X137,X138)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_118,hypothesis,
( sdtasdt0(smndt0(sz10),smndt0(xp)) = xp
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_114]),c_0_115]),c_0_79])]) ).
fof(c_0_119,plain,
! [X142,X143] :
( ~ aInteger0(X142)
| ~ aInteger0(X143)
| sdtpldt0(X142,X143) = sdtpldt0(X143,X142) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_120,plain,
( X1 = sz00
| aDivisorOf0(X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X3
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_121,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_122,plain,
( sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_61]),c_0_41])]) ).
cnf(c_0_123,hypothesis,
( sdtasdt0(smndt0(sz10),sdtpldt0(smndt0(xp),sz10)) = sdtpldt0(xp,smndt0(sz10))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_118]),c_0_79])]) ).
cnf(c_0_124,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_125,plain,
( X1 = sz00
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_120]),c_0_121]) ).
cnf(c_0_126,hypothesis,
( sdtasdt0(smndt0(sz10),sdtpldt0(sz10,smndt0(xp))) = sdtpldt0(smndt0(sz10),xp)
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_118]),c_0_79])]) ).
cnf(c_0_127,hypothesis,
( sdtasdt0(smndt0(sz10),sdtpldt0(sz10,smndt0(xp))) = sdtpldt0(xp,smndt0(sz10))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_41]),c_0_79])]) ).
cnf(c_0_128,plain,
( X1 = sz00
| aDivisorOf0(X1,sdtasdt0(X1,sz10))
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_41]) ).
fof(c_0_129,negated_conjecture,
~ ? [X1] :
( ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ~ ( ( X1 = sz10
| X1 = smndt0(sz10) )
& aElementOf0(X1,cS2200) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_130,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_131,plain,
( sdtpldt0(X1,sdtpldt0(smndt0(X1),X2)) = sdtpldt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_46]),c_0_64]) ).
cnf(c_0_132,hypothesis,
( sdtpldt0(smndt0(sz10),xp) = sdtpldt0(xp,smndt0(sz10))
| ~ aInteger0(smndt0(sz10)) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_133,hypothesis,
aDivisorOf0(xp,sdtasdt0(xp,sz10)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_31]),c_0_32]) ).
fof(c_0_134,negated_conjecture,
! [X294,X295] :
( ( X294 = sz10
| X294 = smndt0(sz10)
| ~ aInteger0(X295)
| sdtasdt0(xp,X295) != sdtpldt0(X294,smndt0(sz10))
| ~ aInteger0(X294) )
& ( aElementOf0(X294,cS2200)
| ~ aInteger0(X295)
| sdtasdt0(xp,X295) != sdtpldt0(X294,smndt0(sz10))
| ~ aInteger0(X294) )
& ( X294 = sz10
| X294 = smndt0(sz10)
| ~ aDivisorOf0(xp,sdtpldt0(X294,smndt0(sz10)))
| ~ aInteger0(X294) )
& ( aElementOf0(X294,cS2200)
| ~ aDivisorOf0(xp,sdtpldt0(X294,smndt0(sz10)))
| ~ aInteger0(X294) )
& ( X294 = sz10
| X294 = smndt0(sz10)
| ~ sdteqdtlpzmzozddtrp0(X294,sz10,xp)
| ~ aInteger0(X294) )
& ( aElementOf0(X294,cS2200)
| ~ sdteqdtlpzmzozddtrp0(X294,sz10,xp)
| ~ aInteger0(X294) )
& ( X294 = sz10
| X294 = smndt0(sz10)
| ~ aElementOf0(X294,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X294,cS2200)
| ~ aElementOf0(X294,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_129])])])]) ).
cnf(c_0_135,hypothesis,
( aElementOf0(sdtpldt0(X1,X2),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aDivisorOf0(xp,sdtpldt0(X1,sdtpldt0(X2,smndt0(sz10))))
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_71]),c_0_72]) ).
cnf(c_0_136,hypothesis,
( sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10))) = xp
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_78]),c_0_31]),c_0_41])]) ).
cnf(c_0_137,hypothesis,
aDivisorOf0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_61]),c_0_31])]) ).
cnf(c_0_138,negated_conjecture,
( X1 = sz10
| X1 = smndt0(sz10)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_139,hypothesis,
( aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]),c_0_31]),c_0_41])]) ).
cnf(c_0_140,negated_conjecture,
( sdtpldt0(sz10,xp) = smndt0(sz10)
| sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(smndt0(sz10)) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
fof(c_0_141,plain,
! [X219,X220,X221,X222,X223,X224] :
( ( aSet0(X221)
| X221 != szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 )
& ( aInteger0(X222)
| ~ aElementOf0(X222,X221)
| X221 != szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 )
& ( sdteqdtlpzmzozddtrp0(X222,X219,X220)
| ~ aElementOf0(X222,X221)
| X221 != szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 )
& ( ~ aInteger0(X223)
| ~ sdteqdtlpzmzozddtrp0(X223,X219,X220)
| aElementOf0(X223,X221)
| X221 != szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 )
& ( ~ aElementOf0(esk11_3(X219,X220,X224),X224)
| ~ aInteger0(esk11_3(X219,X220,X224))
| ~ sdteqdtlpzmzozddtrp0(esk11_3(X219,X220,X224),X219,X220)
| ~ aSet0(X224)
| X224 = szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 )
& ( aInteger0(esk11_3(X219,X220,X224))
| aElementOf0(esk11_3(X219,X220,X224),X224)
| ~ aSet0(X224)
| X224 = szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 )
& ( sdteqdtlpzmzozddtrp0(esk11_3(X219,X220,X224),X219,X220)
| aElementOf0(esk11_3(X219,X220,X224),X224)
| ~ aSet0(X224)
| X224 = szAzrzSzezqlpdtcmdtrp0(X219,X220)
| ~ aInteger0(X219)
| ~ aInteger0(X220)
| X220 = sz00 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mArSeq])])])])])]) ).
cnf(c_0_142,hypothesis,
( sdtpldt0(sz10,xp) = smndt0(sz10)
| sdtpldt0(sz10,xp) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_76]),c_0_93])]) ).
cnf(c_0_143,plain,
sdtpldt0(sz10,sz00) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_98]),c_0_41])]) ).
cnf(c_0_144,plain,
( aInteger0(X1)
| X4 = sz00
| ~ aElementOf0(X1,X2)
| X2 != szAzrzSzezqlpdtcmdtrp0(X3,X4)
| ~ aInteger0(X3)
| ~ aInteger0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_145,hypothesis,
( sdtpldt0(sz10,xp) = sz10
| aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_142]),c_0_31]),c_0_41])]) ).
cnf(c_0_146,plain,
sdtpldt0(smndt0(sz10),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_143]),c_0_105]),c_0_53]),c_0_41])]) ).
cnf(c_0_147,plain,
( X1 = sz00
| aInteger0(X2)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X3) ),
inference(er,[status(thm)],[c_0_144]) ).
cnf(c_0_148,hypothesis,
( sdtasdt0(smndt0(sz10),sdtpldt0(sz10,xp)) = sdtpldt0(smndt0(sz10),smndt0(xp))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_110]),c_0_31])]) ).
cnf(c_0_149,hypothesis,
aInteger0(smndt0(sz10)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_145]),c_0_146]),c_0_78]),c_0_31]),c_0_41])]),c_0_32]) ).
cnf(c_0_150,hypothesis,
( aInteger0(sdtpldt0(sz10,xp))
| ~ aInteger0(smndt0(sz10)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_139]),c_0_31]),c_0_41])]),c_0_32]) ).
cnf(c_0_151,plain,
( sdtpldt0(smndt0(smndt0(sz10)),sz00) = sz10
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_146]),c_0_68]),c_0_41])]) ).
cnf(c_0_152,hypothesis,
sdtasdt0(smndt0(sz10),sdtpldt0(sz10,xp)) = sdtpldt0(smndt0(sz10),smndt0(xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_148,c_0_149])]) ).
cnf(c_0_153,hypothesis,
aInteger0(sdtpldt0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_150,c_0_149])]) ).
cnf(c_0_154,plain,
( smndt0(smndt0(sz10)) = sz10
| ~ aInteger0(smndt0(sz10)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_151]),c_0_64]) ).
cnf(c_0_155,plain,
( smndt0(X1) = sz00
| sdteqdtlpzmzozddtrp0(X2,X2,smndt0(X1))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_64]) ).
cnf(c_0_156,hypothesis,
sdtpldt0(smndt0(sz10),smndt0(xp)) = smndt0(sdtpldt0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_152]),c_0_153])]) ).
cnf(c_0_157,plain,
smndt0(smndt0(sz10)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_149])]) ).
fof(c_0_158,plain,
! [X164,X165,X166] :
( ( ~ sdteqdtlpzmzozddtrp0(X164,X165,X166)
| aDivisorOf0(X166,sdtpldt0(X164,smndt0(X165)))
| ~ aInteger0(X164)
| ~ aInteger0(X165)
| ~ aInteger0(X166)
| X166 = sz00 )
& ( ~ aDivisorOf0(X166,sdtpldt0(X164,smndt0(X165)))
| sdteqdtlpzmzozddtrp0(X164,X165,X166)
| ~ aInteger0(X164)
| ~ aInteger0(X165)
| ~ aInteger0(X166)
| X166 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
cnf(c_0_159,hypothesis,
( smndt0(X1) = sz00
| sdteqdtlpzmzozddtrp0(xp,xp,smndt0(X1))
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_155,c_0_31]) ).
cnf(c_0_160,hypothesis,
( sdtasdt0(smndt0(sz10),sdtpldt0(xp,sz10)) = sdtpldt0(smndt0(xp),smndt0(sz10))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_110]),c_0_31])]) ).
cnf(c_0_161,hypothesis,
sdtpldt0(sz10,smndt0(sdtpldt0(sz10,xp))) = smndt0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_156]),c_0_157]),c_0_103]),c_0_79]),c_0_149])]) ).
cnf(c_0_162,plain,
( aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2)))
| X3 = sz00
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_163,hypothesis,
( smndt0(sz10) = sz00
| sdteqdtlpzmzozddtrp0(xp,xp,smndt0(sz10)) ),
inference(spm,[status(thm)],[c_0_159,c_0_41]) ).
cnf(c_0_164,hypothesis,
( sdtasdt0(smndt0(sz10),sdtpldt0(sz10,xp)) = sdtpldt0(smndt0(xp),smndt0(sz10))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_124]),c_0_41]),c_0_31])]) ).
cnf(c_0_165,hypothesis,
( sdtpldt0(sz10,sz10) = smndt0(xp)
| sdtpldt0(sz10,xp) = sz10 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_142]),c_0_157]) ).
cnf(c_0_166,hypothesis,
sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10))) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_136,c_0_149])]) ).
cnf(c_0_167,hypothesis,
( smndt0(sz10) = sz00
| aDivisorOf0(smndt0(sz10),sdtpldt0(xp,smndt0(xp)))
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_31])]) ).
cnf(c_0_168,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_169,plain,
( X1 = sz00
| aDivisorOf0(X1,sdtasdt0(X1,smndt0(X2)))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(spm,[status(thm)],[c_0_125,c_0_64]) ).
cnf(c_0_170,hypothesis,
( sdtpldt0(smndt0(xp),smndt0(sz10)) = sdtpldt0(smndt0(sz10),smndt0(xp))
| ~ aInteger0(smndt0(sz10)) ),
inference(spm,[status(thm)],[c_0_164,c_0_148]) ).
cnf(c_0_171,hypothesis,
sdtpldt0(sz10,sz10) = smndt0(xp),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_165]),c_0_166]),c_0_149]),c_0_31]),c_0_41])]),c_0_32]) ).
cnf(c_0_172,hypothesis,
( smndt0(sz10) = sz00
| aDivisorOf0(smndt0(sz10),sdtpldt0(xp,smndt0(xp))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_76]),c_0_93])]) ).
cnf(c_0_173,hypothesis,
sdtasdt0(sz00,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_52]),c_0_53]),c_0_31])]) ).
cnf(c_0_174,hypothesis,
( sdtasdt0(xp,sdtasdt0(sz00,X1)) = sdtasdt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_52]),c_0_53]),c_0_31])]) ).
cnf(c_0_175,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_43]),c_0_53])]),c_0_121]) ).
cnf(c_0_176,plain,
( sdteqdtlpzmzozddtrp0(X2,X3,X1)
| X1 = sz00
| ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X3)))
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_177,plain,
( aInteger0(X1)
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_178,hypothesis,
( aDivisorOf0(xp,sdtasdt0(xp,smndt0(X1)))
| ~ aInteger0(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_31]),c_0_32]) ).
cnf(c_0_179,hypothesis,
sdtpldt0(smndt0(xp),smndt0(sz10)) = sdtpldt0(smndt0(sz10),smndt0(xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_149])]) ).
cnf(c_0_180,hypothesis,
smndt0(sdtpldt0(sz10,xp)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_171]),c_0_156]),c_0_68]),c_0_41])]) ).
cnf(c_0_181,hypothesis,
( smndt0(sz10) = sz00
| aDivisorOf0(smndt0(sz10),sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_46]),c_0_31])]) ).
cnf(c_0_182,hypothesis,
( sdtasdt0(sz00,sdtpldt0(X1,xp)) = sdtpldt0(sdtasdt0(sz00,X1),sz00)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_173]),c_0_31]),c_0_53])]) ).
cnf(c_0_183,hypothesis,
sdtasdt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_53]),c_0_31])]) ).
fof(c_0_184,plain,
! [X169,X170,X171] :
( ~ aInteger0(X169)
| ~ aInteger0(X170)
| ~ aInteger0(X171)
| X171 = sz00
| ~ sdteqdtlpzmzozddtrp0(X169,X170,X171)
| sdteqdtlpzmzozddtrp0(X170,X169,X171) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModSym])]) ).
cnf(c_0_185,plain,
( X1 = sz00
| sdteqdtlpzmzozddtrp0(sz00,X2,X1)
| ~ aDivisorOf0(X1,smndt0(X2))
| ~ aInteger0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_56]),c_0_53])]),c_0_177]),c_0_64]) ).
cnf(c_0_186,hypothesis,
aDivisorOf0(xp,smndt0(xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_86]),c_0_41]),c_0_31])]) ).
cnf(c_0_187,hypothesis,
sdtpldt0(smndt0(xp),smndt0(sz10)) = sz10,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_179,c_0_156]),c_0_180]) ).
cnf(c_0_188,hypothesis,
( smndt0(sz10) = sz00
| aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_181]),c_0_53])]) ).
cnf(c_0_189,hypothesis,
sdtpldt0(sdtasdt0(sz00,smndt0(xp)),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_82]),c_0_183]),c_0_79]),c_0_31])]) ).
cnf(c_0_190,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X3 = sz00
| ~ aElementOf0(X1,X4)
| X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
fof(c_0_191,plain,
! [X172,X173,X174,X175] :
( ~ aInteger0(X172)
| ~ aInteger0(X173)
| ~ aInteger0(X174)
| X174 = sz00
| ~ aInteger0(X175)
| ~ sdteqdtlpzmzozddtrp0(X172,X173,X174)
| ~ sdteqdtlpzmzozddtrp0(X173,X175,X174)
| sdteqdtlpzmzozddtrp0(X172,X175,X174) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModTrn])]) ).
cnf(c_0_192,plain,
( X3 = sz00
| sdteqdtlpzmzozddtrp0(X2,X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_184]) ).
cnf(c_0_193,hypothesis,
sdteqdtlpzmzozddtrp0(sz00,xp,xp),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_31])]),c_0_32]) ).
cnf(c_0_194,hypothesis,
sdtpldt0(sz00,smndt0(sz10)) = sdtpldt0(xp,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_187]),c_0_115]),c_0_149]),c_0_79])]) ).
cnf(c_0_195,plain,
( smndt0(sz10) = sz00
| X1 = sz00
| smndt0(X1) != sz00
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_94]),c_0_188]) ).
cnf(c_0_196,hypothesis,
( sdtasdt0(sz00,smndt0(xp)) = sz00
| ~ aInteger0(sdtasdt0(sz00,smndt0(xp))) ),
inference(spm,[status(thm)],[c_0_91,c_0_189]) ).
cnf(c_0_197,plain,
( X1 = sz00
| sdteqdtlpzmzozddtrp0(X2,X3,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X3) ),
inference(er,[status(thm)],[c_0_190]) ).
cnf(c_0_198,hypothesis,
( aElementOf0(smndt0(xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aDivisorOf0(xp,sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_187]),c_0_79])]) ).
cnf(c_0_199,plain,
( X3 = sz00
| sdteqdtlpzmzozddtrp0(X1,X4,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X4)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ sdteqdtlpzmzozddtrp0(X2,X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_191]) ).
cnf(c_0_200,hypothesis,
sdteqdtlpzmzozddtrp0(xp,sz00,xp),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_31]),c_0_53])]),c_0_32]) ).
cnf(c_0_201,hypothesis,
( sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_202,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_203,hypothesis,
sdtpldt0(xp,sz10) = smndt0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_194]),c_0_149])]) ).
cnf(c_0_204,hypothesis,
( sdtpldt0(sz10,xp) = sz10
| smndt0(sz10) != sz10 ),
inference(ef,[status(thm)],[c_0_142]) ).
cnf(c_0_205,plain,
( smndt0(sz10) = sz00
| sz10 != sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_154]),c_0_188]) ).
cnf(c_0_206,hypothesis,
sdtasdt0(sz00,smndt0(xp)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_121]),c_0_79]),c_0_53])]) ).
cnf(c_0_207,hypothesis,
( sdteqdtlpzmzozddtrp0(smndt0(xp),sz10,xp)
| ~ aDivisorOf0(xp,sz10) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_197,c_0_198]),c_0_31]),c_0_41])]),c_0_32]) ).
cnf(c_0_208,hypothesis,
( sdteqdtlpzmzozddtrp0(X1,sz00,xp)
| ~ sdteqdtlpzmzozddtrp0(X1,xp,xp)
| ~ aInteger0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_53]),c_0_31])]),c_0_32]) ).
cnf(c_0_209,hypothesis,
( sdteqdtlpzmzozddtrp0(sz10,X1,xp)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_201]),c_0_31]),c_0_41])]),c_0_32]),c_0_202]) ).
cnf(c_0_210,plain,
( sdtpldt0(smndt0(X1),sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(smndt0(sz10),X2))
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_86]) ).
cnf(c_0_211,hypothesis,
sdtasdt0(smndt0(sz10),smndt0(xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_149])]) ).
cnf(c_0_212,hypothesis,
( sdtpldt0(smndt0(sz10),smndt0(sz10)) = xp
| sdtpldt0(sz10,xp) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_142]),c_0_78]),c_0_31]),c_0_41])]) ).
cnf(c_0_213,hypothesis,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_203]),c_0_41]),c_0_31])]) ).
cnf(c_0_214,hypothesis,
smndt0(sz10) != sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_204]),c_0_146]),c_0_78]),c_0_31]),c_0_41])]),c_0_32]) ).
cnf(c_0_215,hypothesis,
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X1)
| sdtasdt0(xp,X1) != sdtpldt0(X2,smndt0(sz10))
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_216,negated_conjecture,
( X1 = sz10
| X1 = smndt0(sz10)
| ~ aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_217,hypothesis,
sdtpldt0(sz00,smndt0(sz10)) = smndt0(sz10),
inference(rw,[status(thm)],[c_0_194,c_0_203]) ).
cnf(c_0_218,hypothesis,
sz10 != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_205]),c_0_206]),c_0_53])]),c_0_32]) ).
cnf(c_0_219,hypothesis,
( sdteqdtlpzmzozddtrp0(sz10,smndt0(xp),xp)
| ~ aDivisorOf0(xp,sz10) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_207]),c_0_31]),c_0_41]),c_0_79])]),c_0_32]) ).
cnf(c_0_220,hypothesis,
( sdteqdtlpzmzozddtrp0(sz10,sz00,xp)
| ~ aElementOf0(xp,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_41])]) ).
cnf(c_0_221,plain,
( sdtpldt0(smndt0(X1),sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(smndt0(sz10),X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_210,c_0_149])]) ).
cnf(c_0_222,hypothesis,
sdtasdt0(smndt0(xp),smndt0(sz10)) = xp,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_149])]),c_0_211]) ).
cnf(c_0_223,hypothesis,
sdtpldt0(smndt0(sz10),smndt0(sz10)) = xp,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_212,c_0_213]),c_0_214]) ).
cnf(c_0_224,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtpldt0(X1,smndt0(sz10)) != smndt0(xp)
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_86]),c_0_31])]) ).
cnf(c_0_225,hypothesis,
sdtasdt0(smndt0(sz10),xp) = smndt0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_149])]) ).
cnf(c_0_226,hypothesis,
sdtpldt0(smndt0(sz10),xp) = sdtpldt0(xp,smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_149])]) ).
cnf(c_0_227,negated_conjecture,
( smndt0(sz10) = sz00
| ~ aDivisorOf0(xp,smndt0(sz10)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_217]),c_0_53])]),c_0_218]) ).
cnf(c_0_228,hypothesis,
( aDivisorOf0(xp,smndt0(sz10))
| ~ aDivisorOf0(xp,sz10) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_219]),c_0_115]),c_0_213]),c_0_31]),c_0_79]),c_0_41])]),c_0_32]) ).
cnf(c_0_229,hypothesis,
( aDivisorOf0(xp,sdtpldt0(sz10,sz00))
| ~ aElementOf0(xp,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_220]),c_0_99]),c_0_31]),c_0_53]),c_0_41])]),c_0_32]) ).
cnf(c_0_230,hypothesis,
( sdteqdtlpzmzozddtrp0(X1,xp,xp)
| ~ sdteqdtlpzmzozddtrp0(X1,sz00,xp)
| ~ aInteger0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_193]),c_0_31]),c_0_53])]),c_0_32]) ).
cnf(c_0_231,hypothesis,
sdtasdt0(smndt0(xp),xp) = sdtpldt0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_222]),c_0_115]),c_0_223]),c_0_149]),c_0_79])]) ).
cnf(c_0_232,plain,
( sdtasdt0(smndt0(sz10),sdtasdt0(X1,X2)) = sdtasdt0(smndt0(X1),X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_149])]) ).
cnf(c_0_233,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtpldt0(smndt0(sz10),X1) != smndt0(xp)
| ~ aInteger0(smndt0(sz10))
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_224,c_0_124]) ).
cnf(c_0_234,hypothesis,
sdtasdt0(smndt0(sz10),sdtpldt0(xp,smndt0(sz10))) = sdtpldt0(sz10,smndt0(xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_221,c_0_225]),c_0_157]),c_0_226]),c_0_31]),c_0_149])]) ).
cnf(c_0_235,hypothesis,
aInteger0(sdtpldt0(xp,smndt0(sz10))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_226]),c_0_31]),c_0_149])]) ).
cnf(c_0_236,negated_conjecture,
( smndt0(sz10) = sz00
| ~ aDivisorOf0(xp,sz10) ),
inference(spm,[status(thm)],[c_0_227,c_0_228]) ).
cnf(c_0_237,hypothesis,
( aDivisorOf0(xp,sz10)
| ~ aElementOf0(xp,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_229,c_0_91]),c_0_41])]) ).
cnf(c_0_238,plain,
( aElementOf0(X1,X4)
| X3 = sz00
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_239,hypothesis,
( sdteqdtlpzmzozddtrp0(xp,X1,xp)
| ~ sdteqdtlpzmzozddtrp0(X1,sz00,xp)
| ~ aInteger0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_230]),c_0_31])]),c_0_32]) ).
cnf(c_0_240,hypothesis,
sdtpldt0(sdtpldt0(xp,xp),smndt0(xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_231]),c_0_203]),c_0_222]),c_0_31]),c_0_79])]) ).
cnf(c_0_241,hypothesis,
aInteger0(sdtpldt0(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_231]),c_0_31]),c_0_79])]) ).
cnf(c_0_242,hypothesis,
sdtasdt0(smndt0(sz10),sdtpldt0(xp,xp)) = sdtasdt0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_231]),c_0_115]),c_0_31]),c_0_79])]) ).
cnf(c_0_243,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtpldt0(smndt0(sz10),X1) != smndt0(xp)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_233,c_0_149])]) ).
cnf(c_0_244,hypothesis,
sdtpldt0(smndt0(sz10),sdtpldt0(sz10,smndt0(xp))) = smndt0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_234]),c_0_166]),c_0_225]),c_0_235]),c_0_149])]) ).
cnf(c_0_245,hypothesis,
aInteger0(sdtpldt0(sz10,smndt0(xp))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_234]),c_0_235]),c_0_149])]) ).
cnf(c_0_246,hypothesis,
( smndt0(sz10) = sz00
| ~ aElementOf0(xp,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(spm,[status(thm)],[c_0_236,c_0_237]) ).
cnf(c_0_247,plain,
( X1 = sz00
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| ~ sdteqdtlpzmzozddtrp0(X2,X3,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X3)
| ~ aInteger0(X2) ),
inference(er,[status(thm)],[c_0_238]) ).
cnf(c_0_248,hypothesis,
( sdteqdtlpzmzozddtrp0(xp,sz10,xp)
| ~ aElementOf0(sz00,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_209]),c_0_41])]) ).
cnf(c_0_249,hypothesis,
sdtpldt0(smndt0(sdtpldt0(xp,xp)),xp) = smndt0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_240]),c_0_103]),c_0_79]),c_0_241])]) ).
cnf(c_0_250,hypothesis,
smndt0(sdtpldt0(xp,xp)) = sdtasdt0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_242]),c_0_241])]) ).
cnf(c_0_251,hypothesis,
aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_244]),c_0_245])]) ).
cnf(c_0_252,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtpldt0(X2,smndt0(sz10)) != sdtpldt0(X1,smndt0(sz10))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_215,c_0_30]),c_0_33]) ).
cnf(c_0_253,hypothesis,
~ aElementOf0(xp,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_246]),c_0_68]),c_0_41])]),c_0_218]) ).
cnf(c_0_254,hypothesis,
( aElementOf0(xp,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aElementOf0(sz00,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_248]),c_0_31]),c_0_41])]),c_0_32]) ).
cnf(c_0_255,hypothesis,
sdtpldt0(sdtasdt0(xp,xp),xp) = smndt0(xp),
inference(rw,[status(thm)],[c_0_249,c_0_250]) ).
cnf(c_0_256,hypothesis,
aInteger0(sdtasdt0(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_242]),c_0_241]),c_0_149])]) ).
cnf(c_0_257,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10)
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(spm,[status(thm)],[c_0_138,c_0_251]) ).
cnf(c_0_258,hypothesis,
sdtasdt0(sz10,sdtpldt0(xp,xp)) = sdtpldt0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_231]),c_0_31]),c_0_79])]) ).
cnf(c_0_259,plain,
( sdtasdt0(X1,X2) = sz00
| X3 = sz00
| sdtasdt0(X1,sdtasdt0(X2,X3)) != sz00
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_43]),c_0_121]) ).
cnf(c_0_260,hypothesis,
sdtasdt0(sz10,sdtasdt0(xp,xp)) = sdtasdt0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_242]),c_0_241]),c_0_149])]) ).
cnf(c_0_261,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtpldt0(X1,smndt0(sz10)) != sz00
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_252,c_0_46]),c_0_47]),c_0_41])]) ).
cnf(c_0_262,hypothesis,
~ aElementOf0(sz00,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(spm,[status(thm)],[c_0_253,c_0_254]) ).
cnf(c_0_263,hypothesis,
sdtasdt0(smndt0(xp),sz10) = smndt0(xp),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_107,c_0_149])]),c_0_225]) ).
cnf(c_0_264,hypothesis,
sdtpldt0(xp,sdtasdt0(xp,xp)) = smndt0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_255]),c_0_31]),c_0_256])]) ).
cnf(c_0_265,hypothesis,
sdtpldt0(sz00,sdtasdt0(xp,xp)) = sdtasdt0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_78]),c_0_31])]) ).
cnf(c_0_266,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = sz10
| smndt0(xp) = xp ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_257]),c_0_223]),c_0_103]),c_0_79]),c_0_41])]) ).
cnf(c_0_267,hypothesis,
sdtasdt0(smndt0(sz10),sdtasdt0(xp,xp)) = sdtpldt0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_242]),c_0_157]),c_0_258]),c_0_241]),c_0_149])]) ).
cnf(c_0_268,hypothesis,
sdtasdt0(xp,xp) != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_260]),c_0_97]),c_0_31]),c_0_41])]),c_0_32]) ).
cnf(c_0_269,hypothesis,
smndt0(sz10) != sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261,c_0_217]),c_0_53])]),c_0_262]) ).
cnf(c_0_270,hypothesis,
sdtasdt0(smndt0(xp),smndt0(xp)) = sdtpldt0(smndt0(xp),smndt0(xp)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_263]),c_0_41]),c_0_79])]),c_0_171]) ).
cnf(c_0_271,hypothesis,
sdtpldt0(smndt0(xp),smndt0(xp)) = sdtasdt0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_264]),c_0_265]),c_0_256]),c_0_31])]) ).
cnf(c_0_272,negated_conjecture,
( smndt0(xp) = xp
| smndt0(xp) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_266]),c_0_179]),c_0_156]),c_0_213]),c_0_157]),c_0_171]),c_0_149]),c_0_79]),c_0_41])]) ).
cnf(c_0_273,hypothesis,
sdtpldt0(xp,xp) != sz00,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_267]),c_0_256]),c_0_149])]),c_0_268]),c_0_269]) ).
cnf(c_0_274,hypothesis,
sdtasdt0(smndt0(xp),smndt0(xp)) = sdtasdt0(xp,xp),
inference(rw,[status(thm)],[c_0_270,c_0_271]) ).
cnf(c_0_275,negated_conjecture,
smndt0(xp) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_272]),c_0_31])]),c_0_273]) ).
cnf(c_0_276,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_274,c_0_275]),c_0_275]),c_0_183]),c_0_268]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM451+6 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n021.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:36:25 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 8.72/5.91 % Version : CSE_E---1.7
% 8.72/5.91 % Problem : theBenchmark.p
% 8.72/5.91 % SZS status Theorem for theBenchmark.p
% 8.72/5.91 % SZS output start CNFRefutation
% See solution above
% 8.72/5.94 % Total time : 4.373s
%------------------------------------------------------------------------------