%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM453+6 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 04:57:23 PM UTC 2026
% Result : Theorem 1.86s 1.94s
% Output : CNFRefutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 128 ( 41 unt; 0 def)
% Number of atoms : 614 ( 196 equ)
% Maximal formula atoms : 102 ( 4 avg)
% Number of connectives : 703 ( 217 ~; 270 |; 179 &)
% ( 12 <=>; 25 =>; 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; 8 con; 0-3 aty)
% Number of variables : 139 ( 0 sgn 81 !; 16 ?)
% 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/sandbox2/benchmark/theBenchmark.p',m__2171) ).
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/sandbox2/benchmark/theBenchmark.p',mArSeq) ).
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/sandbox2/benchmark/theBenchmark.p',m__2079) ).
fof(m__2046,hypothesis,
( aSet0(xS)
& ! [X1] :
( ( aElementOf0(X1,xS)
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& isPrime0(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) )
& szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
& ( ? [X2] :
( aInteger0(X2)
& X2 != sz00
& isPrime0(X2)
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) ) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
=> aElementOf0(X1,xS) ) )
& xS = cS2043 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2046) ).
fof(m__,conjecture,
( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(mEquModRef,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModRef) ).
fof(m__2232,hypothesis,
( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xp,X1) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2232) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(c_0_18,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_19,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])])])])])]) ).
fof(c_0_20,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]) ).
fof(c_0_21,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_18])])])])])]) ).
cnf(c_0_22,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_19]) ).
fof(c_0_23,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_20])])])])])]) ).
fof(c_0_24,hypothesis,
! [X242,X244,X246,X247,X248,X249,X250,X252,X253] :
( aSet0(xS)
& ( aInteger0(esk16_1(X242))
| ~ aElementOf0(X242,xS) )
& ( esk16_1(X242) != sz00
| ~ aElementOf0(X242,xS) )
& ( isPrime0(esk16_1(X242))
| ~ aElementOf0(X242,xS) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( aInteger0(X244)
| ~ aElementOf0(X244,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( aInteger0(esk17_2(X242,X244))
| ~ aElementOf0(X244,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( sdtasdt0(esk16_1(X242),esk17_2(X242,X244)) = sdtpldt0(X244,smndt0(sz00))
| ~ aElementOf0(X244,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( aDivisorOf0(esk16_1(X242),sdtpldt0(X244,smndt0(sz00)))
| ~ aElementOf0(X244,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( sdteqdtlpzmzozddtrp0(X244,sz00,esk16_1(X242))
| ~ aElementOf0(X244,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( ~ aInteger0(X247)
| sdtasdt0(esk16_1(X242),X247) != sdtpldt0(X246,smndt0(sz00))
| ~ aInteger0(X246)
| aElementOf0(X246,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( ~ aDivisorOf0(esk16_1(X242),sdtpldt0(X246,smndt0(sz00)))
| ~ aInteger0(X246)
| aElementOf0(X246,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( ~ sdteqdtlpzmzozddtrp0(X246,sz00,esk16_1(X242))
| ~ aInteger0(X246)
| aElementOf0(X246,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)))
| ~ aElementOf0(X242,xS) )
& ( szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X242)) = X242
| ~ aElementOf0(X242,xS) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( aInteger0(X250)
| ~ aElementOf0(X250,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( aInteger0(esk18_3(X248,X249,X250))
| ~ aElementOf0(X250,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( sdtasdt0(X249,esk18_3(X248,X249,X250)) = sdtpldt0(X250,smndt0(sz00))
| ~ aElementOf0(X250,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( aDivisorOf0(X249,sdtpldt0(X250,smndt0(sz00)))
| ~ aElementOf0(X250,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( sdteqdtlpzmzozddtrp0(X250,sz00,X249)
| ~ aElementOf0(X250,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( ~ aInteger0(X253)
| sdtasdt0(X249,X253) != sdtpldt0(X252,smndt0(sz00))
| ~ aInteger0(X252)
| aElementOf0(X252,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( ~ aDivisorOf0(X249,sdtpldt0(X252,smndt0(sz00)))
| ~ aInteger0(X252)
| aElementOf0(X252,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( ~ sdteqdtlpzmzozddtrp0(X252,sz00,X249)
| ~ aInteger0(X252)
| aElementOf0(X252,szAzrzSzezqlpdtcmdtrp0(sz00,X249))
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& ( szAzrzSzezqlpdtcmdtrp0(sz00,X249) != X248
| ~ aInteger0(X249)
| X249 = sz00
| ~ isPrime0(X249)
| aElementOf0(X248,xS) )
& xS = cS2043 ),
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)],[m__2046])])])])])]) ).
fof(c_0_25,negated_conjecture,
~ ( sdtpldt0(sz10,xp) != sz10
& sdtpldt0(sz10,smndt0(xp)) != sz10 ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_26,hypothesis,
( sdtasdt0(xp,esk26_1(X1)) = sdtpldt0(X1,smndt0(sz10))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
( X1 = sz00
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| ~ sdteqdtlpzmzozddtrp0(X2,X3,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X3)
| ~ aInteger0(X2) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_28,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_30,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_31,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_32,hypothesis,
( aInteger0(esk26_1(X1))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_33,hypothesis,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,hypothesis,
xS = cS2043,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_35,hypothesis,
( aInteger0(esk28_0)
& sdtasdt0(xp,esk28_0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10))
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,xp),sz10,xp)
& aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& aInteger0(esk29_0)
& sdtasdt0(xp,esk29_0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10))
& aDivisorOf0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(sdtpldt0(sz10,smndt0(xp)),sz10,xp)
& aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2232])]) ).
fof(c_0_36,negated_conjecture,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(fof_nnf,[status(thm)],[c_0_25]) ).
fof(c_0_37,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])]) ).
cnf(c_0_38,hypothesis,
( sdtasdt0(xp,esk26_1(X1)) = sdtpldt0(X1,smndt0(sz10))
| ~ sdteqdtlpzmzozddtrp0(X1,sz10,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_26,c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_39,plain,
( X2 = sz00
| sdteqdtlpzmzozddtrp0(X1,X1,X2)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,hypothesis,
( aInteger0(esk26_1(X1))
| ~ sdteqdtlpzmzozddtrp0(X1,sz10,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_32,c_0_27]),c_0_28]),c_0_29])]),c_0_30]) ).
cnf(c_0_41,hypothesis,
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_42,hypothesis,
stldt0(sbsmnsldt0(cS2043)) = cS2076,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
fof(c_0_43,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_44,hypothesis,
sdtasdt0(xp,esk29_0) = sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_45,negated_conjecture,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,smndt0(xp)) = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_46,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_47,hypothesis,
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| X1 != smndt0(sz10) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_48,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_49,hypothesis,
sdtasdt0(xp,esk26_1(sz10)) = sdtpldt0(sz10,smndt0(sz10)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_29]),c_0_28])]),c_0_30]) ).
cnf(c_0_50,hypothesis,
aInteger0(esk26_1(sz10)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_39]),c_0_29]),c_0_28])]),c_0_30]) ).
cnf(c_0_51,hypothesis,
( X1 = sz10
| X1 = smndt0(sz10)
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_52,hypothesis,
( aElementOf0(X1,cS2076)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_34]),c_0_42]) ).
cnf(c_0_53,hypothesis,
aElementOf0(sdtpldt0(sz10,xp),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_54,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_55,negated_conjecture,
( sdtpldt0(sz10,smndt0(sz10)) = sdtasdt0(xp,esk29_0)
| sdtpldt0(sz10,xp) = sz10 ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_56,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_57,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_58,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,cS2076) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_34]),c_0_42]) ).
cnf(c_0_59,hypothesis,
aElementOf0(smndt0(sz10),cS2076),
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_34]),c_0_42])]) ).
fof(c_0_60,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_61,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_62,hypothesis,
( esk26_1(sz10) = sz00
| sdtpldt0(sz10,smndt0(sz10)) != sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_28])]),c_0_30]) ).
cnf(c_0_63,hypothesis,
( X1 = smndt0(sz10)
| X1 = sz10
| ~ aElementOf0(X1,cS2076) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_34]),c_0_42]) ).
cnf(c_0_64,hypothesis,
aElementOf0(sdtpldt0(sz10,xp),cS2076),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_65,negated_conjecture,
( sdtpldt0(sz10,xp) = sz10
| sdtasdt0(xp,esk29_0) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_29])]) ).
cnf(c_0_66,hypothesis,
aInteger0(esk29_0),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_67,hypothesis,
sdtasdt0(xp,esk28_0) = sdtpldt0(sdtpldt0(sz10,xp),smndt0(sz10)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_68,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_69,hypothesis,
aInteger0(sdtpldt0(sz10,xp)),
inference(spm,[status(thm)],[c_0_57,c_0_53]) ).
cnf(c_0_70,hypothesis,
aInteger0(smndt0(sz10)),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
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_60]) ).
cnf(c_0_72,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_73,hypothesis,
esk26_1(sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_54]),c_0_29])]) ).
cnf(c_0_74,hypothesis,
( sdtpldt0(sz10,xp) = smndt0(sz10)
| sdtpldt0(sz10,xp) = sz10 ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_75,negated_conjecture,
( sdtpldt0(sz10,xp) = sz10
| esk29_0 = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_65]),c_0_66]),c_0_28])]),c_0_30]) ).
cnf(c_0_76,hypothesis,
sdtpldt0(smndt0(sz10),sdtpldt0(sz10,xp)) = sdtasdt0(xp,esk28_0),
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_70])]) ).
cnf(c_0_77,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(X3,sdtpldt0(X1,X2))
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_71]),c_0_72]) ).
cnf(c_0_78,hypothesis,
sdtpldt0(sz10,smndt0(sz10)) = sdtasdt0(xp,sz00),
inference(rw,[status(thm)],[c_0_49,c_0_73]) ).
cnf(c_0_79,hypothesis,
( sdtpldt0(sz10,sdtpldt0(smndt0(xp),smndt0(sz10))) = sdtasdt0(xp,esk29_0)
| ~ aInteger0(smndt0(xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_71]),c_0_29])]),c_0_70])]) ).
cnf(c_0_80,hypothesis,
( sdtpldt0(sz10,sdtpldt0(xp,X1)) = sdtpldt0(smndt0(sz10),X1)
| sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_74]),c_0_28]),c_0_29])]) ).
cnf(c_0_81,hypothesis,
( sdtpldt0(sz10,smndt0(sz10)) = sdtasdt0(xp,esk28_0)
| esk29_0 = sz00 ),
inference(spm,[status(thm)],[c_0_67,c_0_75]) ).
cnf(c_0_82,hypothesis,
sdtpldt0(xp,sdtpldt0(smndt0(sz10),sz10)) = sdtasdt0(xp,esk28_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_28]),c_0_29]),c_0_70])]) ).
cnf(c_0_83,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_78]),c_0_29])]) ).
cnf(c_0_84,hypothesis,
( sdtpldt0(sz10,sdtpldt0(smndt0(sz10),smndt0(xp))) = sdtasdt0(xp,esk29_0)
| ~ aInteger0(smndt0(xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_68]),c_0_70])]) ).
cnf(c_0_85,hypothesis,
( sdtpldt0(smndt0(sz10),smndt0(xp)) = sdtpldt0(sz10,sz00)
| sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(smndt0(xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_54]),c_0_28])]) ).
fof(c_0_86,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_87,hypothesis,
( sdtasdt0(xp,esk28_0) = sz00
| esk29_0 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_81]),c_0_29])]) ).
cnf(c_0_88,hypothesis,
sdtasdt0(xp,esk28_0) = sdtpldt0(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_82,c_0_68]),c_0_78]),c_0_83]),c_0_29]),c_0_70])]) ).
fof(c_0_89,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_90,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_91,hypothesis,
( sdtpldt0(sz10,sdtpldt0(sz10,sz00)) = sdtasdt0(xp,esk29_0)
| sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(smndt0(xp)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_92,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
fof(c_0_93,plain,
! [X134] :
( ~ aInteger0(X134)
| aInteger0(smndt0(X134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_94,hypothesis,
( sdtpldt0(xp,sz00) = sz00
| esk29_0 = sz00 ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_95,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_96,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_97,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
cnf(c_0_98,hypothesis,
( sdtasdt0(xp,esk29_0) = sdtpldt0(sz10,sz10)
| sdtpldt0(sz10,xp) = sz10
| ~ aInteger0(smndt0(xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_29])]) ).
cnf(c_0_99,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_100,hypothesis,
esk29_0 = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_94]),c_0_28])]),c_0_30]) ).
cnf(c_0_101,plain,
( smndt0(sz00) = sz00
| ~ aInteger0(smndt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97])]) ).
cnf(c_0_102,hypothesis,
aElementOf0(sdtpldt0(sz10,smndt0(xp)),szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_103,hypothesis,
( sdtasdt0(xp,esk29_0) = sdtpldt0(sz10,sz10)
| sdtpldt0(sz10,xp) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_28])]) ).
cnf(c_0_104,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_54,c_0_71]),c_0_72]) ).
cnf(c_0_105,hypothesis,
sdtpldt0(sdtpldt0(sz10,smndt0(xp)),smndt0(sz10)) = sz00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_100]),c_0_83]) ).
cnf(c_0_106,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_99]),c_0_29])]) ).
cnf(c_0_107,hypothesis,
aInteger0(sdtpldt0(sz10,smndt0(xp))),
inference(spm,[status(thm)],[c_0_57,c_0_102]) ).
cnf(c_0_108,negated_conjecture,
( sdtpldt0(sz10,sz10) = sz00
| sdtpldt0(sz10,xp) = sz10 ),
inference(spm,[status(thm)],[c_0_65,c_0_103]) ).
cnf(c_0_109,hypothesis,
sdtpldt0(sz10,smndt0(sz10)) = sz00,
inference(rw,[status(thm)],[c_0_78,c_0_83]) ).
cnf(c_0_110,hypothesis,
sdtpldt0(sdtpldt0(sz10,smndt0(xp)),sdtpldt0(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_106]),c_0_106]),c_0_97]),c_0_70]),c_0_107])]) ).
cnf(c_0_111,hypothesis,
( sdtpldt0(smndt0(sz10),sz00) = sdtpldt0(sz10,xp)
| sdtpldt0(sz10,xp) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_92]),c_0_97]),c_0_28])]) ).
cnf(c_0_112,hypothesis,
( sdtpldt0(sz10,sz10) = sz00
| sdtasdt0(xp,esk28_0) = sz00 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_108]),c_0_78]),c_0_83]) ).
cnf(c_0_113,hypothesis,
sdtpldt0(sz10,sdtpldt0(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_109]),c_0_106]),c_0_106]),c_0_97]),c_0_70]),c_0_29])]) ).
cnf(c_0_114,hypothesis,
( sdtpldt0(sdtpldt0(sz10,smndt0(xp)),sdtpldt0(sz10,xp)) = sz00
| sdtpldt0(sz10,xp) = sz10 ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_115,hypothesis,
( sdtpldt0(xp,sz00) = sz00
| sdtpldt0(sz10,sz10) = sz00 ),
inference(spm,[status(thm)],[c_0_112,c_0_88]) ).
cnf(c_0_116,hypothesis,
sdtpldt0(sz10,sdtpldt0(sz00,smndt0(sz10))) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_68]),c_0_97]),c_0_70])]) ).
cnf(c_0_117,hypothesis,
( sdtpldt0(xp,sdtpldt0(sdtpldt0(sz10,smndt0(xp)),sz10)) = sz00
| 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_77,c_0_114]),c_0_28]),c_0_29]),c_0_107])]) ).
cnf(c_0_118,hypothesis,
sdtpldt0(sz10,sz10) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_115]),c_0_28])]),c_0_30]) ).
cnf(c_0_119,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_120,hypothesis,
sdtpldt0(sz00,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_116,c_0_77]),c_0_29]),c_0_70]),c_0_97])]) ).
cnf(c_0_121,negated_conjecture,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(xp,sz00) = sz00 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_45]),c_0_118]) ).
cnf(c_0_122,hypothesis,
( sdtpldt0(smndt0(sz10),sz10) = sz00
| ~ aInteger0(sdtpldt0(smndt0(sz10),sz10)) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_123,hypothesis,
sdtpldt0(smndt0(sz10),sdtpldt0(sz10,xp)) = sdtpldt0(xp,sz00),
inference(rw,[status(thm)],[c_0_76,c_0_88]) ).
cnf(c_0_124,negated_conjecture,
sdtpldt0(sz10,xp) = sz10,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_121]),c_0_28])]),c_0_30]) ).
cnf(c_0_125,hypothesis,
sdtpldt0(smndt0(sz10),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_72]),c_0_29]),c_0_70])]) ).
cnf(c_0_126,hypothesis,
sdtpldt0(xp,sz00) = sz00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124]),c_0_125]) ).
cnf(c_0_127,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_126]),c_0_28])]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM453+6 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n018.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 00:35:17 EDT 2026
% 0.14/0.34 % CPUTime :
% 0.18/0.35 % start to proof: theBenchmark
% 1.86/1.94 % Version : CSE_E---1.7
% 1.86/1.94 % Problem : theBenchmark.p
% 1.86/1.94 % SZS status Theorem for theBenchmark.p
% 1.86/1.94 % SZS output start CNFRefutation
% See solution above
% 1.86/1.94 % Total time : 1.372s
%------------------------------------------------------------------------------