%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM451+6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:55:04 PM UTC 2026
% Result : Theorem 0.12s 5.97s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 24
% Syntax : Number of formulae : 262 ( 80 unt; 0 def)
% Number of atoms : 1033 ( 325 equ)
% Maximal formula atoms : 102 ( 3 avg)
% Number of connectives : 1182 ( 411 ~; 478 |; 232 &)
% ( 16 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 300 ( 1 sgn 131 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__2171,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( ( ( ( sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| ? [X2] :
( sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10))
& aInteger0(X2) ) )
& aInteger0(X1) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( sdteqdtlpzmzozddtrp0(X1,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& ? [X2] :
( sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10))
& aInteger0(X2) )
& aInteger0(X1) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2171) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtpldt0(smndt0(X1),X1)
& sdtpldt0(X1,smndt0(X1)) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mArSeq,axiom,
! [X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1) )
=> ! [X3] :
( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( sdteqdtlpzmzozddtrp0(X4,X1,X2)
& aInteger0(X4) ) )
& aSet0(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArSeq) ).
fof(mEquModSym,axiom,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
=> sdteqdtlpzmzozddtrp0(X2,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModSym) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).
fof(m__2079,hypothesis,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = smndt0(sz10)
| X1 = sz10 ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2079) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
& sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistrib) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
& sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).
fof(m__,conjecture,
? [X1] :
( ~ ( aElementOf0(X1,cS2200)
& ( X1 = smndt0(sz10)
| X1 = sz10 ) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ( sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| ? [X2] :
( sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10))
& aInteger0(X2) ) )
& aInteger0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
fof(m__2046,hypothesis,
( xS = cS2043
& ! [X1] :
( ( ? [X2] :
( ( ( ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 )
& isPrime0(X2)
& X2 != sz00
& aInteger0(X2) )
=> aElementOf0(X1,xS) )
& ( aElementOf0(X1,xS)
=> ? [X2] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1
& ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& isPrime0(X2)
& X2 != sz00
& aInteger0(X2) ) ) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2046) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(mEquModRef,axiom,
! [X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1) )
=> sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModRef) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aInteger0(X3) )
& X2 != sz00
& aInteger0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(c_0_24,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( ( ( ( sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| ? [X2] :
( sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10))
& aInteger0(X2) ) )
& aInteger0(X1) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( sdteqdtlpzmzozddtrp0(X1,sz10,xp)
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& ? [X2] :
( sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10))
& aInteger0(X2) )
& aInteger0(X1) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(fof_simplification,[status(thm)],[m__2171]) ).
fof(c_0_25,hypothesis,
! [X161,X163,X164,X165,X167,X168,X169,X170] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& ( aElementOf0(X170,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X170,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aElementOf0(X169,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X169,sbsmnsldt0(xS))
| ~ aInteger0(X169) )
& ( ~ aElementOf0(X169,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X169,sbsmnsldt0(xS)) )
& ( ~ aElementOf0(X169,stldt0(sbsmnsldt0(xS)))
| aInteger0(X169) )
& ( aElementOf0(X167,sbsmnsldt0(xS))
| ~ aElementOf0(X167,X168)
| ~ aElementOf0(X168,xS)
| ~ aInteger0(X167) )
& ( ~ aElementOf0(X165,sbsmnsldt0(xS))
| aElementOf0(X165,esk27_1(X165)) )
& ( ~ aElementOf0(X165,sbsmnsldt0(xS))
| aElementOf0(esk27_1(X165),xS) )
& ( ~ aElementOf0(X165,sbsmnsldt0(xS))
| aInteger0(X165) )
& aSet0(sbsmnsldt0(xS))
& ( aElementOf0(X163,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X163)
| ~ sdteqdtlpzmzozddtrp0(X163,sz10,xp) )
& ( aElementOf0(X163,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X163)
| ~ aDivisorOf0(xp,sdtpldt0(X163,smndt0(sz10))) )
& ( aElementOf0(X163,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ~ aInteger0(X163)
| sdtasdt0(xp,X164) != sdtpldt0(X163,smndt0(sz10))
| ~ aInteger0(X164) )
& ( ~ aElementOf0(X161,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdteqdtlpzmzozddtrp0(X161,sz10,xp) )
& ( ~ aElementOf0(X161,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aDivisorOf0(xp,sdtpldt0(X161,smndt0(sz10))) )
& ( ~ aElementOf0(X161,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtasdt0(xp,esk26_1(X161)) = sdtpldt0(X161,smndt0(sz10)) )
& ( ~ aElementOf0(X161,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(esk26_1(X161)) )
& ( ~ aElementOf0(X161,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(X161) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& xp != sz00
& aInteger0(xp) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_24])])])])])])]) ).
fof(c_0_26,plain,
! [X17] :
( ( ~ aInteger0(X17)
| sz00 = sdtpldt0(smndt0(X17),X17) )
& ( ~ aInteger0(X17)
| sdtpldt0(X17,smndt0(X17)) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])])]) ).
fof(c_0_27,plain,
! [X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1) )
=> ! [X3] :
( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
<=> ( ! [X4] :
( aElementOf0(X4,X3)
<=> ( sdteqdtlpzmzozddtrp0(X4,X1,X2)
& aInteger0(X4) ) )
& aSet0(X3) ) ) ),
inference(fof_simplification,[status(thm)],[mArSeq]) ).
fof(c_0_28,plain,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
=> sdteqdtlpzmzozddtrp0(X2,X1,X3) ) ),
inference(fof_simplification,[status(thm)],[mEquModSym]) ).
cnf(c_0_29,hypothesis,
( ~ aInteger0(X2)
| sdtasdt0(xp,X1) != sdtpldt0(X2,smndt0(sz10))
| ~ aInteger0(X1)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,smndt0(X1)) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
fof(c_0_32,plain,
! [X27] :
( ( ~ aInteger0(X27)
| sz00 = sdtasdt0(sz00,X27) )
& ( ~ aInteger0(X27)
| sdtasdt0(X27,sz00) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])])]) ).
fof(c_0_33,plain,
! [X96,X97,X98,X99,X100,X101] :
( ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aSet0(X101)
| aElementOf0(esk11_3(X96,X97,X101),X101)
| sdteqdtlpzmzozddtrp0(esk11_3(X96,X97,X101),X96,X97) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aSet0(X101)
| aElementOf0(esk11_3(X96,X97,X101),X101)
| aInteger0(esk11_3(X96,X97,X101)) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X101 = szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aSet0(X101)
| ~ sdteqdtlpzmzozddtrp0(esk11_3(X96,X97,X101),X96,X97)
| ~ aInteger0(esk11_3(X96,X97,X101))
| ~ aElementOf0(esk11_3(X96,X97,X101),X101) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| aElementOf0(X100,X98)
| ~ sdteqdtlpzmzozddtrp0(X100,X96,X97)
| ~ aInteger0(X100) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aElementOf0(X99,X98)
| sdteqdtlpzmzozddtrp0(X99,X96,X97) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| ~ aElementOf0(X99,X98)
| aInteger0(X99) )
& ( X97 = sz00
| ~ aInteger0(X97)
| ~ aInteger0(X96)
| X98 != szAzrzSzezqlpdtcmdtrp0(X96,X97)
| aSet0(X98) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_27])])])])])])]) ).
fof(c_0_34,plain,
! [X41,X42,X43] :
( sdteqdtlpzmzozddtrp0(X42,X41,X43)
| ~ sdteqdtlpzmzozddtrp0(X41,X42,X43)
| X43 = sz00
| ~ aInteger0(X43)
| ~ aInteger0(X42)
| ~ aInteger0(X41) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
cnf(c_0_35,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtasdt0(xp,esk26_1(X1)) = sdtpldt0(X1,smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_36,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(esk26_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,hypothesis,
( ~ aInteger0(X1)
| sdtasdt0(xp,X1) != sz00
| aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_38,plain,
( ~ aInteger0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_40,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_41,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X1)
| X3 = sz00
| aElementOf0(X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
( ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdteqdtlpzmzozddtrp0(X2,X1,X3)
| X3 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_43,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdteqdtlpzmzozddtrp0(X1,sz10,xp) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_44,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_45,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_46,hypothesis,
( ~ aInteger0(X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtpldt0(X2,smndt0(sz10)) != sdtpldt0(X1,smndt0(sz10))
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_35]),c_0_36]) ).
cnf(c_0_47,hypothesis,
aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40])]) ).
fof(c_0_48,plain,
! [X29,X30] :
( X30 = sz00
| X29 = sz00
| sdtasdt0(X29,X30) != sz00
| ~ aInteger0(X30)
| ~ aInteger0(X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])])]) ).
cnf(c_0_49,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X2,X3,X1)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_50,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdteqdtlpzmzozddtrp0(sz10,X1,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_42,c_0_43]),c_0_40]),c_0_31])]),c_0_44]),c_0_45]) ).
cnf(c_0_51,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(sz10,smndt0(sz10)) != sdtpldt0(X1,smndt0(sz10))
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_53,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(X1,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_49,c_0_50]),c_0_40]),c_0_31])]),c_0_44]),c_0_45]) ).
cnf(c_0_54,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(X1,smndt0(sz10)) != sz00
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_30]),c_0_31])]) ).
cnf(c_0_55,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtpldt0(X1,smndt0(sz10)) != sz00
| esk26_1(X1) = sz00 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_35]),c_0_40])]),c_0_44]),c_0_36]) ).
cnf(c_0_56,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(X1,smndt0(sz10)) != sz00
| aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(X1,xp)) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,hypothesis,
( sdtpldt0(sz10,smndt0(sz10)) != sz00
| esk26_1(sz10) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_31])]) ).
fof(c_0_58,hypothesis,
( stldt0(sbsmnsldt0(xS)) = cS2076
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = smndt0(sz10)
| X1 = sz10 ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( ~ aElementOf0(X1,sbsmnsldt0(xS))
& aInteger0(X1) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( ? [X2] :
( aElementOf0(X1,X2)
& aElementOf0(X2,xS) )
& aInteger0(X1) ) )
& aSet0(sbsmnsldt0(xS)) ),
inference(fof_simplification,[status(thm)],[m__2079]) ).
cnf(c_0_59,hypothesis,
esk26_1(sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_30]),c_0_31])]) ).
fof(c_0_60,hypothesis,
! [X131,X133,X134,X135,X136] :
( stldt0(sbsmnsldt0(xS)) = cS2076
& ( aElementOf0(X136,stldt0(sbsmnsldt0(xS)))
| X136 != smndt0(sz10) )
& ( aElementOf0(X136,stldt0(sbsmnsldt0(xS)))
| X136 != sz10 )
& ( X136 = smndt0(sz10)
| X136 = sz10
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( aElementOf0(X135,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X135,sbsmnsldt0(xS))
| ~ aInteger0(X135) )
& ( ~ aElementOf0(X135,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X135,sbsmnsldt0(xS)) )
& ( ~ aElementOf0(X135,stldt0(sbsmnsldt0(xS)))
| aInteger0(X135) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ( aElementOf0(X133,sbsmnsldt0(xS))
| ~ aElementOf0(X133,X134)
| ~ aElementOf0(X134,xS)
| ~ aInteger0(X133) )
& ( ~ aElementOf0(X131,sbsmnsldt0(xS))
| aElementOf0(X131,esk19_1(X131)) )
& ( ~ aElementOf0(X131,sbsmnsldt0(xS))
| aElementOf0(esk19_1(X131),xS) )
& ( ~ aElementOf0(X131,sbsmnsldt0(xS))
| aInteger0(X131) )
& aSet0(sbsmnsldt0(xS)) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_58])])])])])])]) ).
cnf(c_0_61,hypothesis,
sdtpldt0(sz10,smndt0(sz10)) = sdtasdt0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_59]),c_0_47])]) ).
cnf(c_0_62,hypothesis,
( X1 != smndt0(sz10)
| aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
fof(c_0_63,plain,
! [X11,X12,X13] :
( sdtpldt0(X11,sdtpldt0(X12,X13)) = sdtpldt0(sdtpldt0(X11,X12),X13)
| ~ aInteger0(X13)
| ~ aInteger0(X12)
| ~ aInteger0(X11) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
cnf(c_0_64,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_61]),c_0_31])]) ).
cnf(c_0_65,hypothesis,
( ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_66,hypothesis,
aElementOf0(smndt0(sz10),stldt0(sbsmnsldt0(xS))),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_67,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_68,hypothesis,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(rw,[status(thm)],[c_0_61,c_0_64]) ).
cnf(c_0_69,hypothesis,
aInteger0(smndt0(sz10)),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
fof(c_0_70,plain,
! [X16] :
( ( ~ aInteger0(X16)
| X16 = sdtpldt0(sz00,X16) )
& ( ~ aInteger0(X16)
| sdtpldt0(X16,sz00) = X16 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).
cnf(c_0_71,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(sz10,sdtpldt0(smndt0(sz10),X1)) = sdtpldt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_31])]) ).
cnf(c_0_72,plain,
( ~ aInteger0(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_73,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10))) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_74,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_75,hypothesis,
sdtpldt0(sz10,sz00) = sdtpldt0(sz00,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_31])]) ).
cnf(c_0_76,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(X1,smndt0(sz10)) != sz00
| esk26_1(X1) = sz00 ),
inference(spm,[status(thm)],[c_0_55,c_0_54]) ).
cnf(c_0_77,hypothesis,
( ~ aInteger0(X1)
| ~ aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_78,hypothesis,
( ~ aElementOf0(sz10,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aDivisorOf0(xp,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_30]),c_0_31])]) ).
cnf(c_0_79,hypothesis,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_31])]) ).
cnf(c_0_80,hypothesis,
( ~ aInteger0(smndt0(smndt0(sz10)))
| esk26_1(smndt0(smndt0(sz10))) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_72]),c_0_69])]) ).
cnf(c_0_81,hypothesis,
( ~ aInteger0(smndt0(smndt0(sz10)))
| ~ aDivisorOf0(xp,sz00)
| aElementOf0(smndt0(smndt0(sz10)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_72]),c_0_69])]) ).
cnf(c_0_82,hypothesis,
aDivisorOf0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_47])]) ).
cnf(c_0_83,hypothesis,
sdtpldt0(sz10,sz00) = sz10,
inference(rw,[status(thm)],[c_0_75,c_0_79]) ).
fof(c_0_84,plain,
! [X14,X15] :
( sdtpldt0(X14,X15) = sdtpldt0(X15,X14)
| ~ aInteger0(X15)
| ~ aInteger0(X14) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
cnf(c_0_85,hypothesis,
( ~ aElementOf0(smndt0(smndt0(sz10)),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| sdtpldt0(smndt0(smndt0(sz10)),smndt0(sz10)) = sz00 ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_80]),c_0_64]),c_0_45]) ).
cnf(c_0_86,hypothesis,
( ~ aInteger0(smndt0(smndt0(sz10)))
| aElementOf0(smndt0(smndt0(sz10)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82])]) ).
cnf(c_0_87,plain,
( ~ aInteger0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_88,hypothesis,
( ~ aInteger0(smndt0(smndt0(sz10)))
| sdtpldt0(sz00,smndt0(smndt0(sz10))) = sz10 ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_30]),c_0_69])]),c_0_83]) ).
fof(c_0_89,plain,
! [X6] :
( aInteger0(smndt0(X6))
| ~ aInteger0(X6) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).
cnf(c_0_90,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_91,hypothesis,
( ~ aInteger0(smndt0(smndt0(sz10)))
| sdtpldt0(smndt0(smndt0(sz10)),smndt0(sz10)) = sz00 ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_92,hypothesis,
( ~ aInteger0(smndt0(smndt0(sz10)))
| smndt0(smndt0(sz10)) = sz10 ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_93,plain,
( ~ aInteger0(X1)
| aInteger0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_94,hypothesis,
( ~ aInteger0(smndt0(smndt0(sz10)))
| sdtpldt0(smndt0(sz10),smndt0(smndt0(sz10))) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_69])]) ).
cnf(c_0_95,hypothesis,
smndt0(smndt0(sz10)) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_69])]) ).
fof(c_0_96,plain,
! [X24,X25,X26] :
( ( ~ aInteger0(X26)
| ~ aInteger0(X25)
| ~ aInteger0(X24)
| sdtasdt0(sdtpldt0(X24,X25),X26) = sdtpldt0(sdtasdt0(X24,X26),sdtasdt0(X25,X26)) )
& ( ~ aInteger0(X26)
| ~ aInteger0(X25)
| ~ aInteger0(X24)
| sdtasdt0(X24,sdtpldt0(X25,X26)) = sdtpldt0(sdtasdt0(X24,X25),sdtasdt0(X24,X26)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])])]) ).
fof(c_0_97,plain,
! [X23] :
( ( ~ aInteger0(X23)
| X23 = sdtasdt0(sz10,X23) )
& ( ~ aInteger0(X23)
| sdtasdt0(X23,sz10) = X23 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])])]) ).
cnf(c_0_98,hypothesis,
sdtpldt0(smndt0(sz10),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_95]),c_0_95]),c_0_31])]) ).
cnf(c_0_99,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_100,plain,
( ~ aInteger0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
fof(c_0_101,plain,
! [X28] :
( ( ~ aInteger0(X28)
| smndt0(X28) = sdtasdt0(X28,smndt0(sz10)) )
& ( ~ aInteger0(X28)
| sdtasdt0(smndt0(sz10),X28) = smndt0(X28) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])])]) ).
cnf(c_0_102,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(smndt0(sz10),sdtpldt0(sz10,X1)) = sdtpldt0(sz00,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_98]),c_0_31]),c_0_69])]) ).
fof(c_0_103,negated_conjecture,
~ ? [X1] :
( ~ ( aElementOf0(X1,cS2200)
& ( X1 = smndt0(sz10)
| X1 = sz10 ) )
& ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| ( ( sdteqdtlpzmzozddtrp0(X1,sz10,xp)
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| ? [X2] :
( sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10))
& aInteger0(X2) ) )
& aInteger0(X1) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_104,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_31])]) ).
cnf(c_0_105,plain,
( ~ aInteger0(X1)
| smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_106,hypothesis,
sdtpldt0(smndt0(sz10),sz00) = sdtpldt0(sz00,smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_30]),c_0_69]),c_0_31])]) ).
fof(c_0_107,negated_conjecture,
! [X171,X172] :
( ( ~ aElementOf0(X171,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X171,cS2200) )
& ( ~ aElementOf0(X171,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| X171 = smndt0(sz10)
| X171 = sz10 )
& ( ~ aInteger0(X171)
| ~ sdteqdtlpzmzozddtrp0(X171,sz10,xp)
| aElementOf0(X171,cS2200) )
& ( ~ aInteger0(X171)
| ~ sdteqdtlpzmzozddtrp0(X171,sz10,xp)
| X171 = smndt0(sz10)
| X171 = sz10 )
& ( ~ aInteger0(X171)
| ~ aDivisorOf0(xp,sdtpldt0(X171,smndt0(sz10)))
| aElementOf0(X171,cS2200) )
& ( ~ aInteger0(X171)
| ~ aDivisorOf0(xp,sdtpldt0(X171,smndt0(sz10)))
| X171 = smndt0(sz10)
| X171 = sz10 )
& ( ~ aInteger0(X171)
| sdtasdt0(xp,X172) != sdtpldt0(X171,smndt0(sz10))
| ~ aInteger0(X172)
| aElementOf0(X171,cS2200) )
& ( ~ aInteger0(X171)
| sdtasdt0(xp,X172) != sdtpldt0(X171,smndt0(sz10))
| ~ aInteger0(X172)
| X171 = smndt0(sz10)
| X171 = sz10 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_103])])])])]) ).
fof(c_0_108,plain,
! [X18,X19,X20] :
( sdtasdt0(X18,sdtasdt0(X19,X20)) = sdtasdt0(sdtasdt0(X18,X19),X20)
| ~ aInteger0(X20)
| ~ aInteger0(X19)
| ~ aInteger0(X18) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).
cnf(c_0_109,hypothesis,
sdtasdt0(xp,sz10) = sdtpldt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_64]),c_0_79]),c_0_39]),c_0_40])]) ).
cnf(c_0_110,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(sdtasdt0(X1,X2),smndt0(X1)) = sdtasdt0(X1,sdtpldt0(X2,smndt0(sz10))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_105]),c_0_69])]) ).
cnf(c_0_111,hypothesis,
sdtpldt0(sz00,smndt0(sz10)) = smndt0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_106]),c_0_69])]) ).
fof(c_0_112,plain,
! [X21,X22] :
( sdtasdt0(X21,X22) = sdtasdt0(X22,X21)
| ~ aInteger0(X22)
| ~ aInteger0(X21) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).
cnf(c_0_113,negated_conjecture,
( ~ aInteger0(X1)
| ~ aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| X1 = smndt0(sz10)
| X1 = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
fof(c_0_114,plain,
! [X7,X8] :
( aInteger0(sdtpldt0(X7,X8))
| ~ aInteger0(X8)
| ~ aInteger0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])])]) ).
cnf(c_0_115,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_116,plain,
( ~ aInteger0(X1)
| sdtasdt0(smndt0(sz10),X1) = smndt0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_117,hypothesis,
sdtpldt0(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_109]),c_0_40])]) ).
cnf(c_0_118,hypothesis,
sdtasdt0(xp,smndt0(sz10)) = sdtpldt0(sz00,smndt0(xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_64]),c_0_111]),c_0_39]),c_0_40])]) ).
cnf(c_0_119,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_120,plain,
( ~ aInteger0(X1)
| sz00 = sdtasdt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_121,hypothesis,
( xS = cS2043
& ! [X1] :
( ( ? [X2] :
( ( ( ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 )
& isPrime0(X2)
& X2 != sz00
& aInteger0(X2) )
=> aElementOf0(X1,xS) )
& ( aElementOf0(X1,xS)
=> ? [X2] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1
& ! [X3] :
( ( ( ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) ) )
& aInteger0(X3) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) )
& ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( sdteqdtlpzmzozddtrp0(X3,sz00,X2)
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& ? [X4] :
( sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00))
& aInteger0(X4) )
& aInteger0(X3) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& isPrime0(X2)
& X2 != sz00
& aInteger0(X2) ) ) )
& aSet0(xS) ),
inference(fof_simplification,[status(thm)],[m__2046]) ).
cnf(c_0_122,negated_conjecture,
( ~ aInteger0(smndt0(smndt0(sz10)))
| ~ aDivisorOf0(xp,sz00)
| smndt0(smndt0(sz10)) = sz10
| smndt0(smndt0(sz10)) = smndt0(sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_72]),c_0_69])]) ).
cnf(c_0_123,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_124,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(smndt0(sz10),sdtasdt0(X1,X2)) = sdtasdt0(smndt0(X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_69])]) ).
cnf(c_0_125,hypothesis,
sdtasdt0(xp,sz10) = xp,
inference(rw,[status(thm)],[c_0_109,c_0_117]) ).
fof(c_0_126,plain,
! [X9,X10] :
( aInteger0(sdtasdt0(X9,X10))
| ~ aInteger0(X10)
| ~ aInteger0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])])]) ).
cnf(c_0_127,hypothesis,
sdtpldt0(sz00,smndt0(xp)) = smndt0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_118]),c_0_40])]) ).
cnf(c_0_128,hypothesis,
sdtasdt0(sz00,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_64]),c_0_39]),c_0_40])]) ).
cnf(c_0_129,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_105]),c_0_69]),c_0_39])]) ).
fof(c_0_130,hypothesis,
! [X119,X121,X123,X124,X125,X126,X127,X129,X130] :
( xS = cS2043
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| szAzrzSzezqlpdtcmdtrp0(sz00,X126) != X125 )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| aElementOf0(X129,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X129)
| ~ sdteqdtlpzmzozddtrp0(X129,sz00,X126) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| aElementOf0(X129,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X129)
| ~ aDivisorOf0(X126,sdtpldt0(X129,smndt0(sz00))) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| aElementOf0(X129,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| ~ aInteger0(X129)
| sdtasdt0(X126,X130) != sdtpldt0(X129,smndt0(sz00))
| ~ aInteger0(X130) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| sdteqdtlpzmzozddtrp0(X127,sz00,X126) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| aDivisorOf0(X126,sdtpldt0(X127,smndt0(sz00))) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| sdtasdt0(X126,esk18_3(X125,X126,X127)) = sdtpldt0(X127,smndt0(sz00)) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| aInteger0(esk18_3(X125,X126,X127)) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| ~ aElementOf0(X127,szAzrzSzezqlpdtcmdtrp0(sz00,X126))
| aInteger0(X127) )
& ( aElementOf0(X125,xS)
| ~ isPrime0(X126)
| X126 = sz00
| ~ aInteger0(X126)
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X126)) )
& ( ~ aElementOf0(X119,xS)
| szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)) = X119 )
& ( ~ aElementOf0(X119,xS)
| aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aInteger0(X123)
| ~ sdteqdtlpzmzozddtrp0(X123,sz00,esk16_1(X119)) )
& ( ~ aElementOf0(X119,xS)
| aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aInteger0(X123)
| ~ aDivisorOf0(esk16_1(X119),sdtpldt0(X123,smndt0(sz00))) )
& ( ~ aElementOf0(X119,xS)
| aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| ~ aInteger0(X123)
| sdtasdt0(esk16_1(X119),X124) != sdtpldt0(X123,smndt0(sz00))
| ~ aInteger0(X124) )
& ( ~ aElementOf0(X119,xS)
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| sdteqdtlpzmzozddtrp0(X121,sz00,esk16_1(X119)) )
& ( ~ aElementOf0(X119,xS)
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| aDivisorOf0(esk16_1(X119),sdtpldt0(X121,smndt0(sz00))) )
& ( ~ aElementOf0(X119,xS)
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| sdtasdt0(esk16_1(X119),esk17_2(X119,X121)) = sdtpldt0(X121,smndt0(sz00)) )
& ( ~ aElementOf0(X119,xS)
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| aInteger0(esk17_2(X119,X121)) )
& ( ~ aElementOf0(X119,xS)
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119)))
| aInteger0(X121) )
& ( ~ aElementOf0(X119,xS)
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X119))) )
& ( ~ aElementOf0(X119,xS)
| isPrime0(esk16_1(X119)) )
& ( ~ aElementOf0(X119,xS)
| esk16_1(X119) != sz00 )
& ( ~ aElementOf0(X119,xS)
| aInteger0(esk16_1(X119)) )
& aSet0(xS) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_121])])])])])])]) ).
fof(c_0_131,plain,
! [X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1) )
=> sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
inference(fof_simplification,[status(thm)],[mEquModRef]) ).
cnf(c_0_132,negated_conjecture,
( ~ aInteger0(smndt0(smndt0(sz10)))
| smndt0(smndt0(sz10)) = sz10
| smndt0(smndt0(sz10)) = smndt0(sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_122,c_0_82])]) ).
cnf(c_0_133,hypothesis,
( ~ aInteger0(X1)
| ~ aInteger0(sdtpldt0(smndt0(sz10),X1))
| aInteger0(sdtpldt0(sz00,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_71]),c_0_31])]) ).
cnf(c_0_134,hypothesis,
sdtasdt0(smndt0(xp),sz10) = sdtasdt0(smndt0(sz10),xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_31]),c_0_40])]) ).
cnf(c_0_135,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_136,hypothesis,
sdtasdt0(xp,smndt0(sz10)) = smndt0(xp),
inference(rw,[status(thm)],[c_0_118,c_0_127]) ).
cnf(c_0_137,plain,
( ~ aInteger0(X1)
| X1 = sdtasdt0(sz10,X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_138,hypothesis,
sdtasdt0(smndt0(sz10),sz00) = sz00,
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_124,c_0_128]),c_0_129]),c_0_128]),c_0_40]),c_0_39])]) ).
cnf(c_0_139,hypothesis,
( ~ aElementOf0(X2,xS)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
| aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_140,hypothesis,
( ~ aElementOf0(X1,xS)
| szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
fof(c_0_141,plain,
! [X39,X40] :
( sdteqdtlpzmzozddtrp0(X39,X39,X40)
| X40 = sz00
| ~ aInteger0(X40)
| ~ aInteger0(X39) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_131])])]) ).
cnf(c_0_142,negated_conjecture,
( smndt0(smndt0(sz10)) = sz10
| smndt0(smndt0(sz10)) = smndt0(sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_93]),c_0_69])]) ).
cnf(c_0_143,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(sz10,sdtpldt0(sz00,X1)) = sdtpldt0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_83]),c_0_39]),c_0_31])]) ).
cnf(c_0_144,hypothesis,
( ~ aInteger0(X1)
| aInteger0(sdtpldt0(sz00,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_123]),c_0_69])]) ).
cnf(c_0_145,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| aInteger0(sdtpldt0(X1,sdtpldt0(X2,X3))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_67]),c_0_123]) ).
cnf(c_0_146,hypothesis,
( ~ aInteger0(smndt0(xp))
| sdtasdt0(smndt0(sz10),xp) = smndt0(xp) ),
inference(spm,[status(thm)],[c_0_100,c_0_134]) ).
cnf(c_0_147,hypothesis,
aInteger0(smndt0(xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_69]),c_0_40])]) ).
cnf(c_0_148,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(sz10,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(sz10,X1),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_137]),c_0_31])]) ).
cnf(c_0_149,hypothesis,
sdtasdt0(sz10,sz00) = sz00,
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_124,c_0_138]),c_0_138]),c_0_95]),c_0_39]),c_0_69])]) ).
cnf(c_0_150,hypothesis,
( ~ aElementOf0(X1,X2)
| ~ aElementOf0(X2,xS)
| aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_151,hypothesis,
( ~ aElementOf0(X1,sbsmnsldt0(xS))
| aElementOf0(esk27_1(X1),xS) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_152,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdteqdtlpzmzozddtrp0(X1,X1,X2)
| X2 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_153,negated_conjecture,
( smndt0(smndt0(sz10)) = sz10
| sdtpldt0(smndt0(sz10),smndt0(sz10)) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_142]),c_0_69])]) ).
cnf(c_0_154,hypothesis,
( ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| X1 = smndt0(sz10)
| X1 = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_155,hypothesis,
( ~ aInteger0(X1)
| aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| aElementOf0(X1,sbsmnsldt0(xS)) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_156,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(sz00,sdtpldt0(sz10,X1)) = sdtpldt0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_79]),c_0_31]),c_0_39])]) ).
cnf(c_0_157,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(sz10,sdtpldt0(X1,sz00)) = sdtpldt0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_90]),c_0_39])]) ).
cnf(c_0_158,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_67]),c_0_123]) ).
cnf(c_0_159,hypothesis,
( ~ aInteger0(X1)
| aInteger0(sdtpldt0(sz10,X1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_143]),c_0_31])]),c_0_144]) ).
cnf(c_0_160,hypothesis,
( ~ aInteger0(X1)
| aInteger0(sdtpldt0(X1,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_117]),c_0_40]),c_0_39])]) ).
cnf(c_0_161,hypothesis,
sdtasdt0(smndt0(sz10),xp) = smndt0(xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_146,c_0_147])]) ).
cnf(c_0_162,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_148,c_0_117]),c_0_149]),c_0_117]),c_0_40]),c_0_39])]) ).
cnf(c_0_163,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(smndt0(X1),sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(smndt0(sz10),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_105]),c_0_69])]) ).
cnf(c_0_164,hypothesis,
( ~ aElementOf0(X1,X2)
| ~ aElementOf0(X2,xS)
| ~ aInteger0(X1)
| aElementOf0(X1,sbsmnsldt0(xS)) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_165,hypothesis,
( ~ aElementOf0(X1,esk27_1(X2))
| ~ aElementOf0(X2,sbsmnsldt0(xS))
| aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_166,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X2,X1))
| X1 = sz00 ),
inference(spm,[status(thm)],[c_0_49,c_0_152]) ).
cnf(c_0_167,hypothesis,
( ~ aElementOf0(X1,xS)
| aInteger0(esk16_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_168,hypothesis,
( ~ aElementOf0(X1,xS)
| esk16_1(X1) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_169,negated_conjecture,
( smndt0(smndt0(sz10)) = sz10
| sdtpldt0(sz00,smndt0(sz10)) = sz10 ),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_153]),c_0_69])]),c_0_83]) ).
cnf(c_0_170,hypothesis,
( ~ aInteger0(X1)
| aElementOf0(X1,sbsmnsldt0(xS))
| X1 = sz10
| X1 = smndt0(sz10) ),
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_171,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(sz00,sdtpldt0(X1,sz10)) = sdtpldt0(X1,sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_90]),c_0_31])]) ).
cnf(c_0_172,hypothesis,
( ~ aInteger0(X1)
| sdtpldt0(X1,sz10) = sdtpldt0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_158]),c_0_79]),c_0_31]),c_0_39])]) ).
cnf(c_0_173,hypothesis,
( ~ aInteger0(X1)
| aInteger0(sdtpldt0(X1,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_90]),c_0_31])]) ).
cnf(c_0_174,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_31])]) ).
cnf(c_0_175,hypothesis,
( ~ aInteger0(X1)
| aInteger0(sdtpldt0(xp,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_90]),c_0_40])]) ).
cnf(c_0_176,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| aInteger0(sdtasdt0(X1,sdtpldt0(X2,X3))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_99]),c_0_135]),c_0_135]) ).
cnf(c_0_177,hypothesis,
sdtasdt0(smndt0(sz10),sdtpldt0(xp,sz10)) = sdtpldt0(smndt0(xp),smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_161]),c_0_40]),c_0_69])]) ).
cnf(c_0_178,hypothesis,
( ~ aInteger0(smndt0(xp))
| sdtasdt0(smndt0(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_124,c_0_146]),c_0_95]),c_0_162]),c_0_40]),c_0_69])]) ).
cnf(c_0_179,hypothesis,
sdtasdt0(smndt0(sz10),sdtpldt0(smndt0(sz10),xp)) = sdtpldt0(sz10,smndt0(xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_161]),c_0_95]),c_0_40]),c_0_69])]) ).
cnf(c_0_180,hypothesis,
sdtasdt0(smndt0(sz10),sdtpldt0(xp,smndt0(sz10))) = sdtpldt0(smndt0(xp),sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_161]),c_0_95]),c_0_40]),c_0_69])]) ).
fof(c_0_181,plain,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aInteger0(X3) )
& X2 != sz00
& aInteger0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[mDivisor]) ).
cnf(c_0_182,hypothesis,
( ~ aElementOf0(X1,esk27_1(X2))
| ~ aElementOf0(X2,sbsmnsldt0(xS))
| aElementOf0(X1,sbsmnsldt0(xS)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_151]),c_0_165]) ).
cnf(c_0_183,hypothesis,
( ~ aElementOf0(X1,xS)
| aElementOf0(sz00,X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_140]),c_0_39])]),c_0_167]),c_0_168]) ).
cnf(c_0_184,plain,
( ~ aInteger0(X1)
| smndt0(X1) != sz00
| X1 = sz00
| smndt0(sz10) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_116]),c_0_69])]) ).
cnf(c_0_185,negated_conjecture,
( smndt0(sz10) = sz10
| smndt0(smndt0(sz10)) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_169]),c_0_69])]) ).
cnf(c_0_186,hypothesis,
( aElementOf0(sz00,sbsmnsldt0(xS))
| sz10 = sz00
| smndt0(sz10) = sz00 ),
inference(spm,[status(thm)],[c_0_170,c_0_39]) ).
cnf(c_0_187,hypothesis,
sdtpldt0(sz00,sdtpldt0(sz10,sz10)) = sdtpldt0(sz10,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_31])]) ).
cnf(c_0_188,hypothesis,
aInteger0(sdtpldt0(sz10,sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_172]),c_0_31])]) ).
cnf(c_0_189,hypothesis,
sdtasdt0(smndt0(sz10),sdtpldt0(sz10,xp)) = sdtpldt0(smndt0(sz10),smndt0(xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_161]),c_0_40]),c_0_69])]) ).
cnf(c_0_190,hypothesis,
aInteger0(sdtpldt0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_172]),c_0_31]),c_0_40])]) ).
cnf(c_0_191,hypothesis,
aInteger0(sdtpldt0(smndt0(xp),smndt0(sz10))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_177]),c_0_31]),c_0_40]),c_0_69])]) ).
cnf(c_0_192,hypothesis,
sdtasdt0(smndt0(sz10),smndt0(xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_178,c_0_147])]) ).
cnf(c_0_193,hypothesis,
sdtpldt0(smndt0(xp),sz10) = sdtpldt0(sz10,smndt0(xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_90]),c_0_180]),c_0_40]),c_0_69])]) ).
fof(c_0_194,plain,
! [X31,X32,X34,X35] :
( ( ~ aInteger0(X31)
| aDivisorOf0(X34,X31)
| sdtasdt0(X34,X35) != X31
| ~ aInteger0(X35)
| X34 = sz00
| ~ aInteger0(X34) )
& ( ~ aInteger0(X31)
| ~ aDivisorOf0(X32,X31)
| sdtasdt0(X32,esk1_2(X31,X32)) = X31 )
& ( ~ aInteger0(X31)
| ~ aDivisorOf0(X32,X31)
| aInteger0(esk1_2(X31,X32)) )
& ( ~ aInteger0(X31)
| ~ aDivisorOf0(X32,X31)
| X32 != sz00 )
& ( ~ aInteger0(X31)
| ~ aDivisorOf0(X32,X31)
| aInteger0(X32) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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_181])])])])])])]) ).
cnf(c_0_195,hypothesis,
( ~ aInteger0(X1)
| sdtasdt0(xp,X1) != smndt0(sz10)
| aElementOf0(sz00,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_87]),c_0_39]),c_0_69])]) ).
cnf(c_0_196,hypothesis,
( ~ aElementOf0(X1,sbsmnsldt0(xS))
| aElementOf0(sz00,sbsmnsldt0(xS)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_183]),c_0_151]) ).
cnf(c_0_197,hypothesis,
( aElementOf0(xp,sbsmnsldt0(xS))
| xp = sz10
| smndt0(sz10) = xp ),
inference(spm,[status(thm)],[c_0_170,c_0_40]) ).
cnf(c_0_198,negated_conjecture,
( sz10 != sz00
| smndt0(sz10) = sz00
| smndt0(sz10) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_185]),c_0_69])]) ).
cnf(c_0_199,hypothesis,
( aElementOf0(sz00,sbsmnsldt0(xS))
| sz10 = sz00
| sdtpldt0(sz00,sz10) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_186]),c_0_31])]) ).
cnf(c_0_200,hypothesis,
( ~ aInteger0(X1)
| aInteger0(sdtpldt0(X1,sdtpldt0(sz10,sz10))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_187]),c_0_188]),c_0_39])]) ).
cnf(c_0_201,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_72]),c_0_93]) ).
cnf(c_0_202,hypothesis,
sdtpldt0(smndt0(sz10),smndt0(xp)) = smndt0(sdtpldt0(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_189]),c_0_190])]) ).
cnf(c_0_203,hypothesis,
aInteger0(sdtpldt0(smndt0(sz10),smndt0(xp))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_191,c_0_90]),c_0_69]),c_0_147])]) ).
cnf(c_0_204,hypothesis,
sdtasdt0(smndt0(sz10),sdtpldt0(sz10,smndt0(xp))) = sdtpldt0(xp,smndt0(sz10)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_192]),c_0_147]),c_0_69])]),c_0_193]) ).
cnf(c_0_205,plain,
( ~ aInteger0(X3)
| sdtasdt0(X1,X2) != X3
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| aDivisorOf0(X1,X3)
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_194]) ).
cnf(c_0_206,hypothesis,
( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_207,hypothesis,
( smndt0(sz10) != sz00
| aElementOf0(sz00,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_38]),c_0_39]),c_0_40])]) ).
cnf(c_0_208,hypothesis,
( aElementOf0(sz00,sbsmnsldt0(xS))
| xp = sz10
| smndt0(sz10) = xp ),
inference(spm,[status(thm)],[c_0_196,c_0_197]) ).
cnf(c_0_209,negated_conjecture,
( sz10 != sz00
| smndt0(sz10) = sz00 ),
inference(ef,[status(thm)],[c_0_198]) ).
cnf(c_0_210,hypothesis,
( aElementOf0(sz00,sbsmnsldt0(xS))
| sz10 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_199]),c_0_31])]) ).
cnf(c_0_211,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_212,hypothesis,
( ~ aInteger0(X1)
| aInteger0(sdtpldt0(sz10,sdtpldt0(sz10,X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_158]),c_0_31])]) ).
cnf(c_0_213,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_201,c_0_202]),c_0_95]),c_0_127]),c_0_147]),c_0_69])]) ).
cnf(c_0_214,hypothesis,
aInteger0(smndt0(sdtpldt0(sz10,xp))),
inference(rw,[status(thm)],[c_0_203,c_0_202]) ).
cnf(c_0_215,hypothesis,
sdtpldt0(smndt0(sz10),xp) = sdtpldt0(xp,smndt0(sz10)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_192]),c_0_147]),c_0_69])]),c_0_204]) ).
cnf(c_0_216,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| X1 = sz00 ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_205]),c_0_135]) ).
cnf(c_0_217,hypothesis,
sdtasdt0(smndt0(sz10),smndt0(sz10)) = sz10,
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_110,c_0_138]),c_0_95]),c_0_79]),c_0_111]),c_0_39]),c_0_69])]) ).
cnf(c_0_218,hypothesis,
sdtasdt0(sz10,smndt0(sz10)) = smndt0(sz10),
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_148,c_0_111]),c_0_149]),c_0_111]),c_0_69]),c_0_39])]) ).
cnf(c_0_219,hypothesis,
( ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X1,sbsmnsldt0(xS)) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_220,hypothesis,
( smndt0(sz10) != sz00
| aElementOf0(sz00,stldt0(sbsmnsldt0(xS))) ),
inference(spm,[status(thm)],[c_0_206,c_0_207]) ).
cnf(c_0_221,hypothesis,
( aElementOf0(sz00,sbsmnsldt0(xS))
| xp = sz10 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_44]),c_0_210]) ).
cnf(c_0_222,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(sdtasdt0(X1,X2),smndt0(X2)) = sdtasdt0(sdtpldt0(X1,smndt0(sz10)),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_116]),c_0_69])]) ).
cnf(c_0_223,hypothesis,
aInteger0(sdtpldt0(sz10,smndt0(xp))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_214])]) ).
cnf(c_0_224,negated_conjecture,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aDivisorOf0(xp,sdtpldt0(X1,sdtpldt0(X2,smndt0(sz10))))
| sdtpldt0(X1,X2) = sz10
| sdtpldt0(X1,X2) = smndt0(sz10) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_67]),c_0_69])]),c_0_123]) ).
cnf(c_0_225,hypothesis,
sdtpldt0(sz10,sdtpldt0(xp,smndt0(sz10))) = 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_201,c_0_215]),c_0_95]),c_0_117]),c_0_40]),c_0_69])]) ).
cnf(c_0_226,hypothesis,
aDivisorOf0(xp,xp),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_125]),c_0_31]),c_0_40])]),c_0_44]) ).
cnf(c_0_227,hypothesis,
sdtasdt0(smndt0(sz10),sz10) = smndt0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_217]),c_0_95]),c_0_218]),c_0_69])]) ).
cnf(c_0_228,hypothesis,
( ~ aElementOf0(sz00,sbsmnsldt0(xS))
| smndt0(sz10) != sz00 ),
inference(spm,[status(thm)],[c_0_219,c_0_220]) ).
cnf(c_0_229,hypothesis,
aElementOf0(sz00,sbsmnsldt0(xS)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_221]),c_0_210]) ).
cnf(c_0_230,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,sdtasdt0(X2,X1)) = sdtasdt0(sdtpldt0(sz10,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_211,c_0_137]),c_0_31])]) ).
cnf(c_0_231,hypothesis,
sdtasdt0(sdtpldt0(xp,smndt0(sz10)),smndt0(sz10)) = sdtpldt0(sz10,smndt0(xp)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_222,c_0_136]),c_0_95]),c_0_69]),c_0_40])]),c_0_193]) ).
cnf(c_0_232,hypothesis,
aInteger0(sdtpldt0(xp,smndt0(sz10))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_204]),c_0_223]),c_0_69])]) ).
cnf(c_0_233,negated_conjecture,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,xp) = smndt0(sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_224,c_0_225]),c_0_226]),c_0_40]),c_0_31])]) ).
cnf(c_0_234,hypothesis,
sdtasdt0(smndt0(sz10),sdtpldt0(sz10,sz10)) = sdtpldt0(smndt0(sz10),smndt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_227]),c_0_31]),c_0_69])]) ).
cnf(c_0_235,hypothesis,
( ~ aInteger0(smndt0(xp))
| smndt0(smndt0(xp)) = xp ),
inference(spm,[status(thm)],[c_0_116,c_0_178]) ).
cnf(c_0_236,hypothesis,
smndt0(sz10) != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_228,c_0_229])]) ).
cnf(c_0_237,negated_conjecture,
( ~ aInteger0(X1)
| ~ aDivisorOf0(xp,sdtpldt0(smndt0(sz10),X1))
| X1 = sz10
| X1 = smndt0(sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_90]),c_0_69])]) ).
cnf(c_0_238,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_231]),c_0_225]),c_0_118]),c_0_127]),c_0_69]),c_0_232])]) ).
cnf(c_0_239,hypothesis,
aDivisorOf0(xp,smndt0(xp)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_136]),c_0_69]),c_0_40])]),c_0_44]) ).
cnf(c_0_240,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(smndt0(sdtpldt0(X1,X2)))
| sdtpldt0(X1,sdtpldt0(X2,smndt0(sdtpldt0(X1,X2)))) = sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_67]),c_0_123]) ).
cnf(c_0_241,hypothesis,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,sz10) = smndt0(xp) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_233]),c_0_95]) ).
cnf(c_0_242,hypothesis,
sdtpldt0(smndt0(sz10),smndt0(sz10)) = smndt0(sdtpldt0(sz10,sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_234]),c_0_188])]) ).
cnf(c_0_243,hypothesis,
sdtasdt0(smndt0(xp),smndt0(sz10)) = xp,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_136]),c_0_69]),c_0_40])]),c_0_192]) ).
cnf(c_0_244,hypothesis,
smndt0(smndt0(xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_235,c_0_147])]) ).
cnf(c_0_245,hypothesis,
aInteger0(sdtpldt0(smndt0(sz10),smndt0(sz10))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_234]),c_0_188]),c_0_69])]) ).
cnf(c_0_246,hypothesis,
( ~ aInteger0(smndt0(xp))
| smndt0(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_52,c_0_146]),c_0_40]),c_0_69])]),c_0_44]),c_0_236]) ).
cnf(c_0_247,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = sz10
| sdtpldt0(sz10,smndt0(xp)) = smndt0(sz10) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_238]),c_0_239]),c_0_223])]) ).
cnf(c_0_248,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_240,c_0_241]),c_0_225]),c_0_69]),c_0_40]),c_0_31])]),c_0_44]) ).
cnf(c_0_249,hypothesis,
sdtasdt0(smndt0(sz10),sdtpldt0(sz10,xp)) = smndt0(sdtpldt0(sz10,xp)),
inference(rw,[status(thm)],[c_0_189,c_0_202]) ).
cnf(c_0_250,hypothesis,
sdtpldt0(sz10,smndt0(sdtpldt0(sz10,sz10))) = smndt0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_242]),c_0_95]),c_0_111]),c_0_69])]) ).
cnf(c_0_251,hypothesis,
sdtasdt0(smndt0(xp),smndt0(sdtpldt0(sz10,sz10))) = 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_110,c_0_243]),c_0_244]),c_0_242]),c_0_69]),c_0_147])]) ).
cnf(c_0_252,hypothesis,
aInteger0(smndt0(sdtpldt0(sz10,sz10))),
inference(rw,[status(thm)],[c_0_245,c_0_242]) ).
cnf(c_0_253,hypothesis,
smndt0(xp) != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_246,c_0_93]),c_0_40])]) ).
cnf(c_0_254,negated_conjecture,
( smndt0(xp) = xp
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
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(spm,[status(thm)],[c_0_201,c_0_247]),c_0_242]),c_0_248]),c_0_244]),c_0_127]),c_0_147]),c_0_31])]) ).
cnf(c_0_255,hypothesis,
sdtpldt0(smndt0(xp),smndt0(sz10)) = smndt0(sdtpldt0(sz10,xp)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_177,c_0_90]),c_0_31]),c_0_40])]),c_0_249]) ).
cnf(c_0_256,hypothesis,
sdtpldt0(sz10,xp) = smndt0(sz10),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_248]),c_0_244]) ).
cnf(c_0_257,hypothesis,
( sdtpldt0(xp,xp) != sz00
| smndt0(sdtpldt0(sz10,sz10)) = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_251]),c_0_252]),c_0_147])]),c_0_253]) ).
cnf(c_0_258,hypothesis,
sdtpldt0(smndt0(xp),xp) = sz00,
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_163,c_0_125]),c_0_98]),c_0_64]),c_0_31]),c_0_40])]) ).
cnf(c_0_259,negated_conjecture,
smndt0(xp) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_240,c_0_254]),c_0_255]),c_0_256]),c_0_95]),c_0_248]),c_0_69]),c_0_147]),c_0_31])]),c_0_253]) ).
cnf(c_0_260,hypothesis,
sdtpldt0(xp,xp) != sz00,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_257,c_0_248]),c_0_244]),c_0_44]) ).
cnf(c_0_261,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_258,c_0_259]),c_0_260]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM451+6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/5.36 % Computer : n005.cluster.edu
% 0.11/5.36 % Model : x86_64 x86_64
% 0.11/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.36 % Memory : 8046.5625MB
% 0.11/5.36 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Mon Sep 21 02:30:08 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/5.41 Running first-order theorem proving
% 0.12/5.41 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.97 % Version: 3.5.1
% 0.12/5.97 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/5.97 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/5.97 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/5.97 % Starting new_bool_3 with 300s (1) cores
% 0.12/5.97 % Starting new_bool_1 with 300s (1) cores
% 0.12/5.97 % Starting sh5l with 300s (1) cores
% 0.12/5.97 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2354763 completed with status 0
% 0.12/5.97 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.12/5.97 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/5.97 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/5.97 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/5.97 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/5.97 % No SInE strategy applied
% 0.12/5.97 % Search class: FGHSF-FSLM31-SFFFFFNN
% 0.12/5.97 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/5.97 % Starting SubtermCWHack with 136s (1) cores
% 0.12/5.97 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.12/5.97 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 198s (1) cores
% 0.12/5.97 % Starting new_bool_3 with 194s (1) cores
% 0.12/5.97 % Starting new_bool_1 with 188s (1) cores
% 0.12/5.97 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 2354771 completed with status 0
% 0.12/5.97 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.12/5.97 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.12/5.97 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.12/5.97 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.12/5.97 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.12/5.97 % No SInE strategy applied
% 0.12/5.97 % Search class: FGHSF-FSLM31-SFFFFFNN
% 0.12/5.97 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.12/5.97 % Starting SubtermCWHack with 136s (1) cores
% 0.12/5.97 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.12/5.97 % Preprocessing time : 0.003 s
% 0.12/5.97 % Presaturation interreduction done
% 0.12/5.97
% 0.12/5.97 % Proof found!
% 0.12/5.97 % SZS status Theorem
% 0.12/5.97 % SZS output start CNFRefutation
% See solution above
% 0.12/5.97 % Parsed axioms : 47
% 0.12/5.97 % Removed by relevancy pruning/SinE : 0
% 0.12/5.97 % Initial clauses : 224
% 0.12/5.97 % Removed in clause preprocessing : 5
% 0.12/5.97 % Initial clauses in saturation : 219
% 0.12/5.97 % Processed clauses : 6464
% 0.12/5.97 % ...of these trivial : 220
% 0.12/5.97 % ...subsumed : 4214
% 0.12/5.97 % ...remaining for further processing : 2030
% 0.12/5.97 % Other redundant clauses eliminated : 108
% 0.12/5.97 % Clauses deleted for lack of memory : 0
% 0.12/5.97 % Backward-subsumed : 243
% 0.12/5.97 % Backward-rewritten : 432
% 0.12/5.97 % Generated clauses : 34347
% 0.12/5.97 % ...of the previous two non-redundant : 30524
% 0.12/5.97 % ...aggressively subsumed : 0
% 0.12/5.97 % Contextual simplify-reflections : 354
% 0.12/5.97 % Paramodulations : 34206
% 0.12/5.97 % Factorizations : 16
% 0.12/5.97 % NegExts : 0
% 0.12/5.97 % Equation resolutions : 119
% 0.12/5.97 % Disequality decompositions : 0
% 0.12/5.97 % Total rewrite steps : 39308
% 0.12/5.97 % ...of those cached : 39012
% 0.12/5.97 % Propositional unsat checks : 0
% 0.12/5.97 % Propositional check models : 0
% 0.12/5.97 % Propositional check unsatisfiable : 0
% 0.12/5.97 % Propositional clauses : 0
% 0.12/5.97 % Propositional clauses after purity: 0
% 0.12/5.97 % Propositional unsat core size : 0
% 0.12/5.97 % Propositional preprocessing time : 0.000
% 0.12/5.97 % Propositional encoding time : 0.000
% 0.12/5.97 % Propositional solver time : 0.000
% 0.12/5.97 % Success case prop preproc time : 0.000
% 0.12/5.97 % Success case prop encoding time : 0.000
% 0.12/5.97 % Success case prop solver time : 0.000
% 0.12/5.97 % Current number of processed clauses : 1113
% 0.12/5.97 % Positive orientable unit clauses : 203
% 0.12/5.97 % Positive unorientable unit clauses: 0
% 0.12/5.97 % Negative unit clauses : 86
% 0.12/5.97 % Non-unit-clauses : 824
% 0.12/5.97 % Current number of unprocessed clauses: 23927
% 0.12/5.97 % ...number of literals in the above : 113577
% 0.12/5.97 % Current number of archived formulas : 0
% 0.12/5.97 % Current number of archived clauses : 882
% 0.12/5.97 % Clause-clause subsumption calls (NU) : 147018
% 0.12/5.97 % Rec. Clause-clause subsumption calls : 61512
% 0.12/5.97 % Non-unit clause-clause subsumptions : 2520
% 0.12/5.97 % Unit Clause-clause subsumption calls : 62787
% 0.12/5.97 % Rewrite failures with RHS unbound : 0
% 0.12/5.97 % BW rewrite match attempts : 137
% 0.12/5.97 % BW rewrite match successes : 60
% 0.12/5.97 % Condensation attempts : 0
% 0.12/5.97 % Condensation successes : 0
% 0.12/5.97 % Termbank termtop insertions : 698637
% 0.12/5.97 % Search garbage collected termcells : 3853
% 0.12/5.97
% 0.12/5.97 % -------------------------------------------------
% 0.12/5.97 % User time : 0.502 s
% 0.12/5.97 % System time : 0.022 s
% 0.12/5.97 % Total time : 0.524 s
% 0.12/5.97 % Maximum resident set size: 3968 pages
% 0.12/5.97
% 0.12/5.97 % -------------------------------------------------
% 0.12/5.97 % User time : 2.492 s
% 0.12/5.97 % System time : 0.088 s
% 0.12/5.97 % Total time : 2.581 s
% 0.12/5.97 % Maximum resident set size: 4608 pages
% 0.12/5.97 % E exiting
%------------------------------------------------------------------------------