%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM447+5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:57:22 PM UTC 2026
% Result : Theorem 76.21s 45.14s
% Output : CNFRefutation 76.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 22
% Syntax : Number of formulae : 189 ( 18 unt; 0 def)
% Number of atoms : 951 ( 253 equ)
% Maximal formula atoms : 125 ( 5 avg)
% Number of connectives : 1206 ( 444 ~; 560 |; 167 &)
% ( 4 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 261 ( 13 sgn 91 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(m__,conjecture,
( ( ( ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(xn,X1) )
& aElementOf0(xn,sbsmnsldt0(xS)) )
=> ? [X1] :
( ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = xn ) )
| aDivisorOf0(X1,xn) )
& isPrime0(X1) ) )
& ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = xn )
& aDivisorOf0(X1,xn)
& isPrime0(X1) )
=> ( ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(xn,X1) )
| aElementOf0(xn,sbsmnsldt0(xS)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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/sandbox/benchmark/theBenchmark.p',m__2046) ).
fof(m__2106,hypothesis,
aInteger0(xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2106) ).
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mEquModMul,axiom,
! [X1,X2,X3,X4] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00
& aInteger0(X4)
& X4 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,sdtasdt0(X3,X4))
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
& sdteqdtlpzmzozddtrp0(X1,X2,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModMul) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).
fof(mEquModRef,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModRef) ).
fof(mArSeq,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ! [X3] :
( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aInteger0(X4)
& sdteqdtlpzmzozddtrp0(X4,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mArSeq) ).
fof(mEquModSym,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
=> sdteqdtlpzmzozddtrp0(X2,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModSym) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDistrib) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(c_0_22,plain,
! [X119] :
( ( sdtpldt0(X119,sz00) = X119
| ~ aInteger0(X119) )
& ( X119 = sdtpldt0(sz00,X119)
| ~ aInteger0(X119) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(c_0_23,plain,
! [X120] :
( ( sdtpldt0(X120,smndt0(X120)) = sz00
| ~ aInteger0(X120) )
& ( sz00 = sdtpldt0(smndt0(X120),X120)
| ~ aInteger0(X120) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
fof(c_0_24,plain,
! [X134,X135,X137,X138] :
( ( aInteger0(X135)
| ~ aDivisorOf0(X135,X134)
| ~ aInteger0(X134) )
& ( X135 != sz00
| ~ aDivisorOf0(X135,X134)
| ~ aInteger0(X134) )
& ( aInteger0(esk1_2(X134,X135))
| ~ aDivisorOf0(X135,X134)
| ~ aInteger0(X134) )
& ( sdtasdt0(X135,esk1_2(X134,X135)) = X134
| ~ aDivisorOf0(X135,X134)
| ~ aInteger0(X134) )
& ( ~ aInteger0(X137)
| X137 = sz00
| ~ aInteger0(X138)
| sdtasdt0(X137,X138) != X134
| aDivisorOf0(X137,X134)
| ~ aInteger0(X134) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivisor])])])])])]) ).
fof(c_0_25,plain,
! [X112,X113] :
( ~ aInteger0(X112)
| ~ aInteger0(X113)
| aInteger0(sdtasdt0(X112,X113)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
cnf(c_0_26,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
fof(c_0_29,plain,
! [X109] :
( ~ aInteger0(X109)
| aInteger0(smndt0(X109)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(c_0_30,plain,
( X1 = sz00
| aDivisorOf0(X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X3
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_32,negated_conjecture,
~ ( ( ( ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(xn,X1) )
& aElementOf0(xn,sbsmnsldt0(xS)) )
=> ? [X1] :
( ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = xn ) )
| aDivisorOf0(X1,xn) )
& isPrime0(X1) ) )
& ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = xn )
& aDivisorOf0(X1,xn)
& isPrime0(X1) )
=> ( ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(xn,X1) )
| aElementOf0(xn,sbsmnsldt0(xS)) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_33,hypothesis,
! [X217,X219,X221,X222,X223,X224,X225,X227,X228] :
( aSet0(xS)
& ( aInteger0(esk16_1(X217))
| ~ aElementOf0(X217,xS) )
& ( esk16_1(X217) != sz00
| ~ aElementOf0(X217,xS) )
& ( isPrime0(esk16_1(X217))
| ~ aElementOf0(X217,xS) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X217)))
| ~ aElementOf0(X217,xS) )
& ( aInteger0(X219)
| ~ aElementOf0(X219,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X217)))
| ~ aElementOf0(X217,xS) )
& ( aInteger0(esk17_2(X217,X219))
| ~ aElementOf0(X219,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X217)))
| ~ aElementOf0(X217,xS) )
& ( sdtasdt0(esk16_1(X217),esk17_2(X217,X219)) = sdtpldt0(X219,smndt0(sz00))
| ~ aElementOf0(X219,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X217)))
| ~ aElementOf0(X217,xS) )
& ( aDivisorOf0(esk16_1(X217),sdtpldt0(X219,smndt0(sz00)))
| ~ aElementOf0(X219,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X217)))
| ~ aElementOf0(X217,xS) )
& ( sdteqdtlpzmzozddtrp0(X219,sz00,esk16_1(X217))
| ~ aElementOf0(X219,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X217)))
| ~ aElementOf0(X217,xS) )
& ( ~ aInteger0(X222)
| sdtasdt0(esk16_1(X217),X222) != sdtpldt0(X221,smndt0(sz00))
| ~ aInteger0(X221)
| aElementOf0(X221,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X217)))
| ~ aElementOf0(X217,xS) )
& ( ~ aDivisorOf0(esk16_1(X217),sdtpldt0(X221,smndt0(sz00)))
| ~ aInteger0(X221)
| aElementOf0(X221,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X217)))
| ~ aElementOf0(X217,xS) )
& ( ~ sdteqdtlpzmzozddtrp0(X221,sz00,esk16_1(X217))
| ~ aInteger0(X221)
| aElementOf0(X221,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X217)))
| ~ aElementOf0(X217,xS) )
& ( szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X217)) = X217
| ~ aElementOf0(X217,xS) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X224))
| ~ aInteger0(X224)
| X224 = sz00
| ~ isPrime0(X224)
| aElementOf0(X223,xS) )
& ( aInteger0(X225)
| ~ aElementOf0(X225,szAzrzSzezqlpdtcmdtrp0(sz00,X224))
| ~ aInteger0(X224)
| X224 = sz00
| ~ isPrime0(X224)
| aElementOf0(X223,xS) )
& ( aInteger0(esk18_3(X223,X224,X225))
| ~ aElementOf0(X225,szAzrzSzezqlpdtcmdtrp0(sz00,X224))
| ~ aInteger0(X224)
| X224 = sz00
| ~ isPrime0(X224)
| aElementOf0(X223,xS) )
& ( sdtasdt0(X224,esk18_3(X223,X224,X225)) = sdtpldt0(X225,smndt0(sz00))
| ~ aElementOf0(X225,szAzrzSzezqlpdtcmdtrp0(sz00,X224))
| ~ aInteger0(X224)
| X224 = sz00
| ~ isPrime0(X224)
| aElementOf0(X223,xS) )
& ( aDivisorOf0(X224,sdtpldt0(X225,smndt0(sz00)))
| ~ aElementOf0(X225,szAzrzSzezqlpdtcmdtrp0(sz00,X224))
| ~ aInteger0(X224)
| X224 = sz00
| ~ isPrime0(X224)
| aElementOf0(X223,xS) )
& ( sdteqdtlpzmzozddtrp0(X225,sz00,X224)
| ~ aElementOf0(X225,szAzrzSzezqlpdtcmdtrp0(sz00,X224))
| ~ aInteger0(X224)
| X224 = sz00
| ~ isPrime0(X224)
| aElementOf0(X223,xS) )
& ( ~ aInteger0(X228)
| sdtasdt0(X224,X228) != sdtpldt0(X227,smndt0(sz00))
| ~ aInteger0(X227)
| aElementOf0(X227,szAzrzSzezqlpdtcmdtrp0(sz00,X224))
| ~ aInteger0(X224)
| X224 = sz00
| ~ isPrime0(X224)
| aElementOf0(X223,xS) )
& ( ~ aDivisorOf0(X224,sdtpldt0(X227,smndt0(sz00)))
| ~ aInteger0(X227)
| aElementOf0(X227,szAzrzSzezqlpdtcmdtrp0(sz00,X224))
| ~ aInteger0(X224)
| X224 = sz00
| ~ isPrime0(X224)
| aElementOf0(X223,xS) )
& ( ~ sdteqdtlpzmzozddtrp0(X227,sz00,X224)
| ~ aInteger0(X227)
| aElementOf0(X227,szAzrzSzezqlpdtcmdtrp0(sz00,X224))
| ~ aInteger0(X224)
| X224 = sz00
| ~ isPrime0(X224)
| aElementOf0(X223,xS) )
& ( szAzrzSzezqlpdtcmdtrp0(sz00,X224) != X223
| ~ aInteger0(X224)
| X224 = sz00
| ~ isPrime0(X224)
| aElementOf0(X223,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])])])])])]) ).
cnf(c_0_34,plain,
( smndt0(sz00) = sz00
| ~ aInteger0(smndt0(sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_35,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( X1 = sz00
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_30]),c_0_31]) ).
fof(c_0_37,negated_conjecture,
! [X230,X231,X234] :
( ( aInteger0(esk20_0)
| aElementOf0(esk19_0,xS) )
& ( esk20_0 != sz00
| aElementOf0(esk19_0,xS) )
& ( aInteger0(esk21_0)
| aElementOf0(esk19_0,xS) )
& ( sdtasdt0(esk20_0,esk21_0) = xn
| aElementOf0(esk19_0,xS) )
& ( aDivisorOf0(esk20_0,xn)
| aElementOf0(esk19_0,xS) )
& ( isPrime0(esk20_0)
| aElementOf0(esk19_0,xS) )
& ( ~ aElementOf0(X234,xS)
| ~ aElementOf0(xn,X234)
| aElementOf0(esk19_0,xS) )
& ( ~ aElementOf0(xn,sbsmnsldt0(xS))
| aElementOf0(esk19_0,xS) )
& ( aInteger0(esk20_0)
| aElementOf0(xn,esk19_0) )
& ( esk20_0 != sz00
| aElementOf0(xn,esk19_0) )
& ( aInteger0(esk21_0)
| aElementOf0(xn,esk19_0) )
& ( sdtasdt0(esk20_0,esk21_0) = xn
| aElementOf0(xn,esk19_0) )
& ( aDivisorOf0(esk20_0,xn)
| aElementOf0(xn,esk19_0) )
& ( isPrime0(esk20_0)
| aElementOf0(xn,esk19_0) )
& ( ~ aElementOf0(X234,xS)
| ~ aElementOf0(xn,X234)
| aElementOf0(xn,esk19_0) )
& ( ~ aElementOf0(xn,sbsmnsldt0(xS))
| aElementOf0(xn,esk19_0) )
& ( aInteger0(esk20_0)
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( esk20_0 != sz00
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( aInteger0(esk21_0)
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( sdtasdt0(esk20_0,esk21_0) = xn
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( aDivisorOf0(esk20_0,xn)
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( isPrime0(esk20_0)
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( ~ aElementOf0(X234,xS)
| ~ aElementOf0(xn,X234)
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( ~ aElementOf0(xn,sbsmnsldt0(xS))
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( aInteger0(esk20_0)
| ~ aInteger0(X230)
| X230 = sz00
| ~ aInteger0(X231)
| sdtasdt0(X230,X231) != xn
| ~ isPrime0(X230) )
& ( esk20_0 != sz00
| ~ aInteger0(X230)
| X230 = sz00
| ~ aInteger0(X231)
| sdtasdt0(X230,X231) != xn
| ~ isPrime0(X230) )
& ( aInteger0(esk21_0)
| ~ aInteger0(X230)
| X230 = sz00
| ~ aInteger0(X231)
| sdtasdt0(X230,X231) != xn
| ~ isPrime0(X230) )
& ( sdtasdt0(esk20_0,esk21_0) = xn
| ~ aInteger0(X230)
| X230 = sz00
| ~ aInteger0(X231)
| sdtasdt0(X230,X231) != xn
| ~ isPrime0(X230) )
& ( aDivisorOf0(esk20_0,xn)
| ~ aInteger0(X230)
| X230 = sz00
| ~ aInteger0(X231)
| sdtasdt0(X230,X231) != xn
| ~ isPrime0(X230) )
& ( isPrime0(esk20_0)
| ~ aInteger0(X230)
| X230 = sz00
| ~ aInteger0(X231)
| sdtasdt0(X230,X231) != xn
| ~ isPrime0(X230) )
& ( ~ aElementOf0(X234,xS)
| ~ aElementOf0(xn,X234)
| ~ aInteger0(X230)
| X230 = sz00
| ~ aInteger0(X231)
| sdtasdt0(X230,X231) != xn
| ~ isPrime0(X230) )
& ( ~ aElementOf0(xn,sbsmnsldt0(xS))
| ~ aInteger0(X230)
| X230 = sz00
| ~ aInteger0(X231)
| sdtasdt0(X230,X231) != xn
| ~ isPrime0(X230) )
& ( aInteger0(esk20_0)
| ~ aDivisorOf0(X230,xn)
| ~ isPrime0(X230) )
& ( esk20_0 != sz00
| ~ aDivisorOf0(X230,xn)
| ~ isPrime0(X230) )
& ( aInteger0(esk21_0)
| ~ aDivisorOf0(X230,xn)
| ~ isPrime0(X230) )
& ( sdtasdt0(esk20_0,esk21_0) = xn
| ~ aDivisorOf0(X230,xn)
| ~ isPrime0(X230) )
& ( aDivisorOf0(esk20_0,xn)
| ~ aDivisorOf0(X230,xn)
| ~ isPrime0(X230) )
& ( isPrime0(esk20_0)
| ~ aDivisorOf0(X230,xn)
| ~ isPrime0(X230) )
& ( ~ aElementOf0(X234,xS)
| ~ aElementOf0(xn,X234)
| ~ aDivisorOf0(X230,xn)
| ~ isPrime0(X230) )
& ( ~ aElementOf0(xn,sbsmnsldt0(xS))
| ~ aDivisorOf0(X230,xn)
| ~ isPrime0(X230) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])])])]) ).
cnf(c_0_38,hypothesis,
( sdtasdt0(esk16_1(X1),esk17_2(X1,X2)) = sdtpldt0(X2,smndt0(sz00))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_28])]) ).
cnf(c_0_40,plain,
( X1 = sz00
| aDivisorOf0(X1,sdtasdt0(X1,smndt0(X2)))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_41,hypothesis,
aInteger0(xn),
inference(split_conjunct,[status(thm)],[m__2106]) ).
cnf(c_0_42,negated_conjecture,
( aDivisorOf0(esk20_0,xn)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != xn
| ~ isPrime0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,hypothesis,
( sdtasdt0(esk16_1(X1),esk17_2(X1,X2)) = sdtpldt0(X2,sz00)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
| ~ aElementOf0(X1,xS) ),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,hypothesis,
( aInteger0(esk16_1(X1))
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_45,hypothesis,
( aInteger0(esk17_2(X1,X2))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_46,hypothesis,
( isPrime0(esk16_1(X1))
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_47,hypothesis,
( esk16_1(X1) != sz00
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_48,negated_conjecture,
( isPrime0(esk20_0)
| X1 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != xn
| ~ isPrime0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_49,plain,
! [X139,X140,X141] :
( ( ~ sdteqdtlpzmzozddtrp0(X139,X140,X141)
| aDivisorOf0(X141,sdtpldt0(X139,smndt0(X140)))
| ~ aInteger0(X139)
| ~ aInteger0(X140)
| ~ aInteger0(X141)
| X141 = sz00 )
& ( ~ aDivisorOf0(X141,sdtpldt0(X139,smndt0(X140)))
| sdteqdtlpzmzozddtrp0(X139,X140,X141)
| ~ aInteger0(X139)
| ~ aInteger0(X140)
| ~ aInteger0(X141)
| X141 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
cnf(c_0_50,hypothesis,
( xn = sz00
| aDivisorOf0(xn,sdtasdt0(xn,smndt0(X1)))
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_51,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
fof(c_0_52,plain,
! [X131] :
( ( sdtasdt0(smndt0(sz10),X131) = smndt0(X131)
| ~ aInteger0(X131) )
& ( smndt0(X131) = sdtasdt0(X131,smndt0(sz10))
| ~ aInteger0(X131) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])]) ).
cnf(c_0_53,negated_conjecture,
( aDivisorOf0(esk20_0,xn)
| sdtpldt0(X1,sz00) != xn
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
| ~ aElementOf0(X2,xS) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45]),c_0_46]),c_0_47]) ).
cnf(c_0_54,hypothesis,
( szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)) = X1
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_55,negated_conjecture,
( isPrime0(esk20_0)
| sdtpldt0(X1,sz00) != xn
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
| ~ aElementOf0(X2,xS) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_43]),c_0_44]),c_0_45]),c_0_46]),c_0_47]) ).
fof(c_0_56,plain,
! [X151,X152,X153,X154] :
( ( sdteqdtlpzmzozddtrp0(X151,X152,X153)
| ~ sdteqdtlpzmzozddtrp0(X151,X152,sdtasdt0(X153,X154))
| ~ aInteger0(X151)
| ~ aInteger0(X152)
| ~ aInteger0(X153)
| X153 = sz00
| ~ aInteger0(X154)
| X154 = sz00 )
& ( sdteqdtlpzmzozddtrp0(X151,X152,X154)
| ~ sdteqdtlpzmzozddtrp0(X151,X152,sdtasdt0(X153,X154))
| ~ aInteger0(X151)
| ~ aInteger0(X152)
| ~ aInteger0(X153)
| X153 = sz00
| ~ aInteger0(X154)
| X154 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModMul])])]) ).
cnf(c_0_57,plain,
( sdteqdtlpzmzozddtrp0(X2,X3,X1)
| X1 = sz00
| ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X3)))
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_58,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_59,plain,
( aInteger0(X1)
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_60,hypothesis,
( xn = sz00
| aDivisorOf0(xn,sdtasdt0(xn,smndt0(sz10))) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_61,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_62,plain,
! [X132,X133] :
( ~ aInteger0(X132)
| ~ aInteger0(X133)
| sdtasdt0(X132,X133) != sz00
| X132 = sz00
| X133 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])]) ).
cnf(c_0_63,hypothesis,
( aDivisorOf0(esk20_0,xn)
| sdtpldt0(X1,sz00) != xn
| ~ aElementOf0(X2,xS)
| ~ aElementOf0(X1,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_64,hypothesis,
( isPrime0(esk20_0)
| sdtpldt0(X1,sz00) != xn
| ~ aElementOf0(X2,xS)
| ~ aElementOf0(X1,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_54]) ).
cnf(c_0_65,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X3 = sz00
| X4 = sz00
| ~ sdteqdtlpzmzozddtrp0(X1,X2,sdtasdt0(X3,X4))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_66,negated_conjecture,
( sdtasdt0(esk20_0,esk21_0) = xn
| aElementOf0(esk19_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_67,negated_conjecture,
( aInteger0(esk20_0)
| aElementOf0(esk19_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_68,negated_conjecture,
( aInteger0(esk21_0)
| aElementOf0(esk19_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_69,negated_conjecture,
( aElementOf0(esk19_0,xS)
| esk20_0 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_70,plain,
( X1 = sz00
| sdteqdtlpzmzozddtrp0(sz00,X2,X1)
| ~ aDivisorOf0(X1,smndt0(X2))
| ~ aInteger0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_28])]),c_0_59]),c_0_35]) ).
cnf(c_0_71,hypothesis,
( xn = sz00
| aDivisorOf0(xn,smndt0(xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_41])]) ).
cnf(c_0_72,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_73,hypothesis,
( aDivisorOf0(esk20_0,xn)
| ~ aElementOf0(X1,xS)
| ~ aElementOf0(xn,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_26])]),c_0_41])]) ).
cnf(c_0_74,negated_conjecture,
( aDivisorOf0(esk20_0,xn)
| aElementOf0(xn,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_75,hypothesis,
( isPrime0(esk20_0)
| ~ aElementOf0(X1,xS)
| ~ aElementOf0(xn,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_26])]),c_0_41])]) ).
cnf(c_0_76,negated_conjecture,
( isPrime0(esk20_0)
| aElementOf0(xn,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_77,hypothesis,
( X1 = sz00
| aElementOf0(X2,xS)
| szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X2
| ~ aInteger0(X1)
| ~ isPrime0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_78,negated_conjecture,
( sdtasdt0(esk20_0,esk21_0) = xn
| aElementOf0(xn,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_79,negated_conjecture,
( aInteger0(esk20_0)
| aElementOf0(xn,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_80,negated_conjecture,
( aInteger0(esk21_0)
| aElementOf0(xn,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_81,negated_conjecture,
( aElementOf0(xn,esk19_0)
| esk20_0 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_82,plain,
! [X121,X122,X123] :
( ~ aInteger0(X121)
| ~ aInteger0(X122)
| ~ aInteger0(X123)
| sdtasdt0(X121,sdtasdt0(X122,X123)) = sdtasdt0(sdtasdt0(X121,X122),X123) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_83,plain,
! [X126] :
( ( sdtasdt0(X126,sz10) = X126
| ~ aInteger0(X126) )
& ( X126 = sdtasdt0(sz10,X126)
| ~ aInteger0(X126) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])]) ).
fof(c_0_84,plain,
! [X142,X143] :
( ~ aInteger0(X142)
| ~ aInteger0(X143)
| X143 = sz00
| sdteqdtlpzmzozddtrp0(X142,X142,X143) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModRef])]) ).
fof(c_0_85,plain,
! [X194,X195,X196,X197,X198,X199] :
( ( aSet0(X196)
| X196 != szAzrzSzezqlpdtcmdtrp0(X194,X195)
| ~ aInteger0(X194)
| ~ aInteger0(X195)
| X195 = sz00 )
& ( aInteger0(X197)
| ~ aElementOf0(X197,X196)
| X196 != szAzrzSzezqlpdtcmdtrp0(X194,X195)
| ~ aInteger0(X194)
| ~ aInteger0(X195)
| X195 = sz00 )
& ( sdteqdtlpzmzozddtrp0(X197,X194,X195)
| ~ aElementOf0(X197,X196)
| X196 != szAzrzSzezqlpdtcmdtrp0(X194,X195)
| ~ aInteger0(X194)
| ~ aInteger0(X195)
| X195 = sz00 )
& ( ~ aInteger0(X198)
| ~ sdteqdtlpzmzozddtrp0(X198,X194,X195)
| aElementOf0(X198,X196)
| X196 != szAzrzSzezqlpdtcmdtrp0(X194,X195)
| ~ aInteger0(X194)
| ~ aInteger0(X195)
| X195 = sz00 )
& ( ~ aElementOf0(esk11_3(X194,X195,X199),X199)
| ~ aInteger0(esk11_3(X194,X195,X199))
| ~ sdteqdtlpzmzozddtrp0(esk11_3(X194,X195,X199),X194,X195)
| ~ aSet0(X199)
| X199 = szAzrzSzezqlpdtcmdtrp0(X194,X195)
| ~ aInteger0(X194)
| ~ aInteger0(X195)
| X195 = sz00 )
& ( aInteger0(esk11_3(X194,X195,X199))
| aElementOf0(esk11_3(X194,X195,X199),X199)
| ~ aSet0(X199)
| X199 = szAzrzSzezqlpdtcmdtrp0(X194,X195)
| ~ aInteger0(X194)
| ~ aInteger0(X195)
| X195 = sz00 )
& ( sdteqdtlpzmzozddtrp0(esk11_3(X194,X195,X199),X194,X195)
| aElementOf0(esk11_3(X194,X195,X199),X199)
| ~ aSet0(X199)
| X199 = szAzrzSzezqlpdtcmdtrp0(X194,X195)
| ~ aInteger0(X194)
| ~ aInteger0(X195)
| X195 = 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_86,plain,
! [X144,X145,X146] :
( ~ aInteger0(X144)
| ~ aInteger0(X145)
| ~ aInteger0(X146)
| X146 = sz00
| ~ sdteqdtlpzmzozddtrp0(X144,X145,X146)
| sdteqdtlpzmzozddtrp0(X145,X144,X146) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModSym])]) ).
cnf(c_0_87,negated_conjecture,
( esk21_0 = sz00
| aElementOf0(esk19_0,xS)
| sdteqdtlpzmzozddtrp0(X1,X2,esk20_0)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,xn)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_67]),c_0_68]),c_0_69]) ).
cnf(c_0_88,hypothesis,
( xn = sz00
| sdteqdtlpzmzozddtrp0(sz00,xn,xn) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_41])]) ).
cnf(c_0_89,negated_conjecture,
( esk21_0 = sz00
| aElementOf0(esk19_0,xS)
| xn != sz00 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_66]),c_0_67]),c_0_68]),c_0_69]) ).
cnf(c_0_90,negated_conjecture,
( esk20_0 != sz00
| ~ aDivisorOf0(X1,xn)
| ~ isPrime0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_91,negated_conjecture,
( aDivisorOf0(esk20_0,xn)
| esk20_0 != sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_69]),c_0_74]) ).
cnf(c_0_92,negated_conjecture,
( isPrime0(esk20_0)
| esk20_0 != sz00 ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_69]),c_0_76]) ).
cnf(c_0_93,hypothesis,
( X1 = sz00
| aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X1),xS)
| ~ isPrime0(X1)
| ~ aInteger0(X1) ),
inference(er,[status(thm)],[c_0_77]) ).
cnf(c_0_94,negated_conjecture,
( isPrime0(esk20_0)
| aElementOf0(esk19_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_95,negated_conjecture,
( esk21_0 = sz00
| aElementOf0(xn,esk19_0)
| sdteqdtlpzmzozddtrp0(X1,X2,esk20_0)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,xn)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_78]),c_0_79]),c_0_80]),c_0_81]) ).
cnf(c_0_96,negated_conjecture,
( esk21_0 = sz00
| aElementOf0(xn,esk19_0)
| xn != sz00 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_78]),c_0_79]),c_0_80]),c_0_81]) ).
cnf(c_0_97,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_98,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
fof(c_0_99,plain,
! [X130] :
( ( sdtasdt0(X130,sz00) = sz00
| ~ aInteger0(X130) )
& ( sz00 = sdtasdt0(sz00,X130)
| ~ aInteger0(X130) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
cnf(c_0_100,plain,
( X2 = sz00
| sdteqdtlpzmzozddtrp0(X1,X1,X2)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_101,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_85]) ).
cnf(c_0_102,plain,
( X3 = sz00
| sdteqdtlpzmzozddtrp0(X2,X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_103,negated_conjecture,
( esk21_0 = sz00
| aElementOf0(esk19_0,xS)
| sdteqdtlpzmzozddtrp0(sz00,xn,esk20_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_41]),c_0_28])]),c_0_89]) ).
cnf(c_0_104,negated_conjecture,
esk20_0 != sz00,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]) ).
cnf(c_0_105,negated_conjecture,
( aElementOf0(esk19_0,xS)
| ~ aElementOf0(X1,xS)
| ~ aElementOf0(xn,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_106,negated_conjecture,
( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0),xS)
| aElementOf0(esk19_0,xS) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_67]),c_0_69]) ).
cnf(c_0_107,negated_conjecture,
( esk21_0 = sz00
| aElementOf0(xn,esk19_0)
| sdteqdtlpzmzozddtrp0(sz00,xn,esk20_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_88]),c_0_41]),c_0_28])]),c_0_96]) ).
cnf(c_0_108,negated_conjecture,
( aElementOf0(xn,esk19_0)
| ~ aElementOf0(X1,xS)
| ~ aElementOf0(xn,X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_109,negated_conjecture,
( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0),xS)
| aElementOf0(xn,esk19_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_76]),c_0_79]),c_0_81]) ).
cnf(c_0_110,plain,
( sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_51])]) ).
cnf(c_0_111,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_112,plain,
( sdtasdt0(X1,esk1_2(X2,X1)) = X2
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_113,hypothesis,
( xn = sz00
| sdteqdtlpzmzozddtrp0(X1,X1,xn)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_41]) ).
cnf(c_0_114,plain,
( X1 = sz00
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| ~ sdteqdtlpzmzozddtrp0(X2,X3,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X3)
| ~ aInteger0(X2) ),
inference(er,[status(thm)],[c_0_101]) ).
cnf(c_0_115,negated_conjecture,
( esk21_0 = sz00
| aElementOf0(esk19_0,xS)
| sdteqdtlpzmzozddtrp0(xn,sz00,esk20_0) ),
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_102,c_0_103]),c_0_41]),c_0_28])]),c_0_104]),c_0_67]) ).
cnf(c_0_116,negated_conjecture,
( aElementOf0(esk19_0,xS)
| ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0)) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_117,negated_conjecture,
( esk21_0 = sz00
| aElementOf0(xn,esk19_0)
| sdteqdtlpzmzozddtrp0(xn,sz00,esk20_0) ),
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_102,c_0_107]),c_0_41]),c_0_28])]),c_0_104]),c_0_79]) ).
cnf(c_0_118,negated_conjecture,
( aElementOf0(xn,esk19_0)
| ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0)) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
fof(c_0_119,plain,
! [X127,X128,X129] :
( ( sdtasdt0(X127,sdtpldt0(X128,X129)) = sdtpldt0(sdtasdt0(X127,X128),sdtasdt0(X127,X129))
| ~ aInteger0(X127)
| ~ aInteger0(X128)
| ~ aInteger0(X129) )
& ( sdtasdt0(sdtpldt0(X127,X128),X129) = sdtpldt0(sdtasdt0(X127,X129),sdtasdt0(X128,X129))
| ~ aInteger0(X127)
| ~ aInteger0(X128)
| ~ aInteger0(X129) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
fof(c_0_120,plain,
! [X124,X125] :
( ~ aInteger0(X124)
| ~ aInteger0(X125)
| sdtasdt0(X124,X125) = sdtasdt0(X125,X124) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_121,plain,
( sdtasdt0(sz10,sz00) = sz00
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_28])]) ).
cnf(c_0_122,plain,
( esk1_2(sz00,X1) = sz00
| X1 = sz00
| ~ aDivisorOf0(X1,sz00)
| ~ aInteger0(esk1_2(sz00,X1))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_112])]),c_0_28])]) ).
cnf(c_0_123,plain,
( aInteger0(esk1_2(X1,X2))
| ~ aDivisorOf0(X2,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_124,plain,
( aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2)))
| X3 = sz00
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_125,hypothesis,
( xn = sz00
| sdteqdtlpzmzozddtrp0(sz00,sz00,xn) ),
inference(spm,[status(thm)],[c_0_113,c_0_28]) ).
cnf(c_0_126,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_39]),c_0_28])]) ).
cnf(c_0_127,negated_conjecture,
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(xn,X1)
| ~ aDivisorOf0(X2,xn)
| ~ isPrime0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_128,negated_conjecture,
( esk21_0 = sz00
| aElementOf0(esk19_0,xS) ),
inference(csr,[status(thm)],[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_114,c_0_115]),c_0_28]),c_0_41])]),c_0_104]),c_0_67]),c_0_116]) ).
cnf(c_0_129,negated_conjecture,
( esk21_0 = sz00
| aElementOf0(xn,esk19_0) ),
inference(csr,[status(thm)],[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_114,c_0_117]),c_0_28]),c_0_41])]),c_0_104]),c_0_79]),c_0_118]) ).
cnf(c_0_130,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_131,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_132,hypothesis,
sdtasdt0(sz10,sz00) = sz00,
inference(spm,[status(thm)],[c_0_121,c_0_41]) ).
cnf(c_0_133,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
| ~ sdteqdtlpzmzozddtrp0(X1,sz00,esk16_1(X2))
| ~ aInteger0(X1)
| ~ aElementOf0(X2,xS) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_134,hypothesis,
( sdteqdtlpzmzozddtrp0(X1,X1,esk16_1(X2))
| ~ aElementOf0(X2,xS)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_44]),c_0_47]) ).
cnf(c_0_135,plain,
( esk1_2(sz00,X1) = sz00
| X1 = sz00
| ~ aDivisorOf0(X1,sz00)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_28])]) ).
cnf(c_0_136,hypothesis,
( xn = sz00
| aDivisorOf0(xn,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_125]),c_0_39]),c_0_126]),c_0_41]),c_0_28])]) ).
cnf(c_0_137,negated_conjecture,
( esk21_0 = sz00
| ~ isPrime0(X1)
| ~ aDivisorOf0(X1,xn) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]) ).
cnf(c_0_138,hypothesis,
( esk21_0 = sz00
| aDivisorOf0(esk20_0,xn) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_128]),c_0_129]) ).
cnf(c_0_139,hypothesis,
( esk21_0 = sz00
| isPrime0(esk20_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_128]),c_0_76]) ).
cnf(c_0_140,plain,
( sdtpldt0(sdtasdt0(sz00,X1),sz00) = sdtasdt0(sz00,sdtpldt0(X1,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_111]),c_0_28])]) ).
cnf(c_0_141,plain,
( sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_111]),c_0_28])]) ).
cnf(c_0_142,hypothesis,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_28]),c_0_51])]) ).
cnf(c_0_143,hypothesis,
( aElementOf0(sz00,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
| ~ aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_28])]) ).
cnf(c_0_144,hypothesis,
( esk1_2(sz00,xn) = sz00
| xn = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_41])]) ).
cnf(c_0_145,negated_conjecture,
( sdtasdt0(esk20_0,esk21_0) = xn
| ~ aDivisorOf0(X1,xn)
| ~ isPrime0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_146,negated_conjecture,
esk21_0 = sz00,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139]) ).
cnf(c_0_147,hypothesis,
( isPrime0(esk20_0)
| sdtasdt0(sz00,sdtpldt0(X1,X2)) != xn
| ~ aElementOf0(sdtasdt0(sz00,X1),X3)
| ~ aElementOf0(X3,xS)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_140]) ).
cnf(c_0_148,hypothesis,
sdtasdt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_142]),c_0_51]),c_0_28])]) ).
cnf(c_0_149,hypothesis,
( aElementOf0(sz00,X1)
| ~ aElementOf0(X1,xS) ),
inference(spm,[status(thm)],[c_0_143,c_0_54]) ).
cnf(c_0_150,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(X3,sdtasdt0(X1,X2))
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_97]),c_0_31]) ).
cnf(c_0_151,hypothesis,
( sdtasdt0(xn,sz00) = sz00
| xn = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_144]),c_0_28])]),c_0_136]) ).
cnf(c_0_152,negated_conjecture,
( sdtasdt0(esk20_0,sz00) = xn
| ~ isPrime0(X1)
| ~ aDivisorOf0(X1,xn) ),
inference(rw,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_153,negated_conjecture,
( aDivisorOf0(esk20_0,xn)
| aElementOf0(esk19_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_154,hypothesis,
( isPrime0(esk20_0)
| sdtasdt0(sz00,X1) != xn
| ~ aElementOf0(X2,xS)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_58]),c_0_148]),c_0_28])]),c_0_149]) ).
cnf(c_0_155,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_156,hypothesis,
( sdtasdt0(xn,sdtasdt0(sz00,X1)) = sdtasdt0(X1,sz00)
| xn = sz00
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_151]),c_0_28]),c_0_41])]) ).
cnf(c_0_157,negated_conjecture,
( sdtasdt0(esk20_0,sz00) = xn
| aElementOf0(esk19_0,xS) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_94]) ).
cnf(c_0_158,negated_conjecture,
( sdtasdt0(esk20_0,sz00) = xn
| aElementOf0(xn,esk19_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_74]),c_0_76]) ).
cnf(c_0_159,hypothesis,
( isPrime0(esk20_0)
| sdtasdt0(X1,sdtasdt0(sz00,X2)) != xn
| ~ aElementOf0(X3,xS)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_150]),c_0_28])]),c_0_31]) ).
cnf(c_0_160,plain,
( sdtasdt0(X1,sdtasdt0(sz00,X2)) = sdtasdt0(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_155]),c_0_28])]) ).
cnf(c_0_161,hypothesis,
( sdtasdt0(xn,sdtasdt0(sz00,xn)) = sdtasdt0(xn,sz00)
| xn = sz00 ),
inference(spm,[status(thm)],[c_0_156,c_0_41]) ).
cnf(c_0_162,negated_conjecture,
( xn = sz00
| aElementOf0(esk19_0,xS) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_157]),c_0_67]) ).
cnf(c_0_163,negated_conjecture,
( xn = sz00
| aElementOf0(xn,esk19_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_158]),c_0_79]) ).
cnf(c_0_164,hypothesis,
( isPrime0(esk20_0)
| sdtasdt0(X1,sdtasdt0(X2,sz00)) != xn
| ~ aElementOf0(X3,xS)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_131]),c_0_28])]) ).
cnf(c_0_165,hypothesis,
( sdtasdt0(xn,sz00) = sdtasdt0(sz00,xn)
| xn = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_41])]) ).
cnf(c_0_166,hypothesis,
( isPrime0(esk20_0)
| xn != sz00
| ~ aElementOf0(X1,xS) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_143]),c_0_126]) ).
cnf(c_0_167,negated_conjecture,
( xn = sz00
| ~ isPrime0(X1)
| ~ aDivisorOf0(X1,xn) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_162]),c_0_163]) ).
cnf(c_0_168,hypothesis,
( xn = sz00
| aDivisorOf0(esk20_0,xn) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_162]),c_0_163]) ).
cnf(c_0_169,hypothesis,
( xn = sz00
| isPrime0(esk20_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_162]),c_0_76]) ).
cnf(c_0_170,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X3 = sz00
| ~ aElementOf0(X1,X4)
| X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_171,hypothesis,
( isPrime0(esk20_0)
| sdtasdt0(X1,sdtasdt0(sz00,xn)) != xn
| ~ aElementOf0(X2,xS)
| ~ aInteger0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_41])]),c_0_166]) ).
cnf(c_0_172,negated_conjecture,
xn = sz00,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_169]) ).
cnf(c_0_173,plain,
( X1 = sz00
| sdteqdtlpzmzozddtrp0(X2,X3,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X3) ),
inference(er,[status(thm)],[c_0_170]) ).
cnf(c_0_174,negated_conjecture,
( aElementOf0(sz00,szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0))
| aElementOf0(esk19_0,xS) ),
inference(spm,[status(thm)],[c_0_149,c_0_106]) ).
cnf(c_0_175,hypothesis,
( isPrime0(esk20_0)
| sdtasdt0(xn,sdtasdt0(X1,sz00)) != xn
| ~ aElementOf0(X2,xS)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_150]),c_0_41]),c_0_28])]) ).
cnf(c_0_176,negated_conjecture,
( ~ aElementOf0(X1,xS)
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,sz00) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_172]),c_0_172]),c_0_149]) ).
cnf(c_0_177,negated_conjecture,
( aElementOf0(esk19_0,xS)
| sdteqdtlpzmzozddtrp0(sz00,sz00,esk20_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_28])]),c_0_67]),c_0_69]) ).
cnf(c_0_178,hypothesis,
( isPrime0(esk20_0)
| sdtasdt0(xn,sdtasdt0(sz00,xn)) != xn
| ~ aElementOf0(X1,xS) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_165]),c_0_41])]),c_0_166]) ).
cnf(c_0_179,hypothesis,
( aDivisorOf0(esk20_0,xn)
| xn != sz00
| ~ aElementOf0(X1,xS) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_143]),c_0_126]) ).
cnf(c_0_180,negated_conjecture,
( ~ isPrime0(X1)
| ~ aDivisorOf0(X1,sz00) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_106]),c_0_176]) ).
cnf(c_0_181,negated_conjecture,
( aElementOf0(esk19_0,xS)
| aDivisorOf0(esk20_0,sz00) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[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_177]),c_0_39]),c_0_126]),c_0_28])]),c_0_67]),c_0_69]) ).
cnf(c_0_182,hypothesis,
( isPrime0(esk20_0)
| sdtasdt0(sz00,sdtasdt0(xn,xn)) != xn
| ~ aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_150]),c_0_41]),c_0_28])]) ).
cnf(c_0_183,hypothesis,
( aDivisorOf0(esk20_0,sz00)
| ~ aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_179,c_0_172]),c_0_172])]) ).
cnf(c_0_184,negated_conjecture,
aElementOf0(esk19_0,xS),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_94]) ).
cnf(c_0_185,hypothesis,
( isPrime0(esk20_0)
| ~ aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_182,c_0_172]),c_0_172]),c_0_148]),c_0_148]),c_0_172])]) ).
cnf(c_0_186,hypothesis,
aDivisorOf0(esk20_0,sz00),
inference(spm,[status(thm)],[c_0_183,c_0_184]) ).
cnf(c_0_187,hypothesis,
isPrime0(esk20_0),
inference(spm,[status(thm)],[c_0_185,c_0_184]) ).
cnf(c_0_188,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_186]),c_0_187])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM447+5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n007.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 00:33:23 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 76.21/45.14 % Version : CSE_E---1.7
% 76.21/45.14 % Problem : theBenchmark.p
% 76.21/45.14 % SZS status Theorem for theBenchmark.p
% 76.21/45.14 % SZS output start CNFRefutation
% See solution above
% 76.49/45.45 % Total time : 33.707s
%------------------------------------------------------------------------------