%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM447+5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 01:49:07 PM UTC 2026
% Result : Theorem 98.56s 19.84s
% Output : CNFRefutation 98.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 127 ( 22 unt; 0 def)
% Number of atoms : 786 ( 192 equ)
% Maximal formula atoms : 125 ( 6 avg)
% Number of connectives : 1006 ( 347 ~; 411 |; 203 &)
% ( 8 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 5 avg)
% Maximal term depth : 5 ( 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 : 205 ( 2 sgn 79 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtpldt0(smndt0(X1),X1)
& sdtpldt0(X1,smndt0(X1)) = sz00 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',mArSeq) ).
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/sandbox/benchmark/theBenchmark.p',m__2046) ).
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] :
( isPrime0(X1)
& aDivisorOf0(X1,xn)
& ? [X2] :
( sdtasdt0(X1,X2) = xn
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) )
=> ( aElementOf0(xn,sbsmnsldt0(xS))
| ? [X1] :
( aElementOf0(xn,X1)
& aElementOf0(X1,xS) ) ) )
& ( ( aElementOf0(xn,sbsmnsldt0(xS))
& ? [X1] :
( aElementOf0(xn,X1)
& aElementOf0(X1,xS) ) )
=> ? [X1] :
( isPrime0(X1)
& ( aDivisorOf0(X1,xn)
| ( ? [X2] :
( sdtasdt0(X1,X2) = xn
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mEquModRef,axiom,
! [X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1) )
=> sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquModRef) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtasdt0(sz00,X1)
& sdtasdt0(X1,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aInteger0(X3) )
& X2 != sz00
& aInteger0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(m__2106,hypothesis,
aInteger0(xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2106) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
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/sandbox/benchmark/theBenchmark.p',mDistrib) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtasdt0(sz10,X1)
& sdtasdt0(X1,sz10) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulOne) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(c_0_17,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])])])]) ).
fof(c_0_18,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_19,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_20,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_21,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,plain,
( ~ aInteger0(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
fof(c_0_24,plain,
! [X6] :
( aInteger0(smndt0(X6))
| ~ aInteger0(X6) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).
fof(c_0_25,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_19])])])])])])]) ).
fof(c_0_26,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_20])])])])])])]) ).
cnf(c_0_27,plain,
( ~ aInteger0(smndt0(sz00))
| smndt0(sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_28,plain,
( ~ aInteger0(X1)
| aInteger0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
| ~ aElementOf0(X1,X4)
| X3 = sz00
| sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_30,negated_conjecture,
~ ( ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,xn)
& ? [X2] :
( sdtasdt0(X1,X2) = xn
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) )
=> ( aElementOf0(xn,sbsmnsldt0(xS))
| ? [X1] :
( aElementOf0(xn,X1)
& aElementOf0(X1,xS) ) ) )
& ( ( aElementOf0(xn,sbsmnsldt0(xS))
& ? [X1] :
( aElementOf0(xn,X1)
& aElementOf0(X1,xS) ) )
=> ? [X1] :
( isPrime0(X1)
& ( aDivisorOf0(X1,xn)
| ( ? [X2] :
( sdtasdt0(X1,X2) = xn
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) ) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_31,hypothesis,
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
| aDivisorOf0(esk16_1(X1),sdtpldt0(X2,smndt0(sz00))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_23])]) ).
cnf(c_0_33,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| sdteqdtlpzmzozddtrp0(X2,X3,X1)
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_34,hypothesis,
( ~ aElementOf0(X1,xS)
| szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,hypothesis,
( ~ aElementOf0(X1,xS)
| aInteger0(esk16_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,hypothesis,
( ~ aElementOf0(X1,xS)
| esk16_1(X1) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,hypothesis,
( ~ aElementOf0(X2,xS)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
| aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_38,negated_conjecture,
~ ( ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,xn)
& ? [X2] :
( sdtasdt0(X1,X2) = xn
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) )
=> ( aElementOf0(xn,sbsmnsldt0(xS))
| ? [X1] :
( aElementOf0(xn,X1)
& aElementOf0(X1,xS) ) ) )
& ( ( aElementOf0(xn,sbsmnsldt0(xS))
& ? [X1] :
( aElementOf0(xn,X1)
& aElementOf0(X1,xS) ) )
=> ? [X1] :
( isPrime0(X1)
& ( aDivisorOf0(X1,xn)
| ( ? [X2] :
( sdtasdt0(X1,X2) = xn
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_30]) ).
cnf(c_0_39,hypothesis,
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
| aDivisorOf0(esk16_1(X1),sdtpldt0(X2,sz00)) ),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,hypothesis,
( ~ aElementOf0(X2,xS)
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,sz00,esk16_1(X2))
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_41,hypothesis,
( ~ aElementOf0(X1,X2)
| ~ aElementOf0(X2,xS)
| sdteqdtlpzmzozddtrp0(X1,sz00,esk16_1(X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_23])]),c_0_35]),c_0_36]) ).
cnf(c_0_42,hypothesis,
( ~ aElementOf0(X1,X2)
| ~ aElementOf0(X2,xS)
| aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_34]) ).
cnf(c_0_43,hypothesis,
( ~ isPrime0(X1)
| ~ aInteger0(X1)
| szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X2
| aElementOf0(X2,xS)
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_44,negated_conjecture,
! [X132,X133,X136] :
( ( ~ isPrime0(X132)
| ~ aDivisorOf0(X132,xn)
| ~ aElementOf0(xn,sbsmnsldt0(xS)) )
& ( ~ isPrime0(X132)
| ~ aDivisorOf0(X132,xn)
| ~ aElementOf0(xn,X136)
| ~ aElementOf0(X136,xS) )
& ( ~ isPrime0(X132)
| ~ aDivisorOf0(X132,xn)
| isPrime0(esk20_0) )
& ( ~ isPrime0(X132)
| ~ aDivisorOf0(X132,xn)
| aDivisorOf0(esk20_0,xn) )
& ( ~ isPrime0(X132)
| ~ aDivisorOf0(X132,xn)
| sdtasdt0(esk20_0,esk21_0) = xn )
& ( ~ isPrime0(X132)
| ~ aDivisorOf0(X132,xn)
| aInteger0(esk21_0) )
& ( ~ isPrime0(X132)
| ~ aDivisorOf0(X132,xn)
| esk20_0 != sz00 )
& ( ~ isPrime0(X132)
| ~ aDivisorOf0(X132,xn)
| aInteger0(esk20_0) )
& ( ~ isPrime0(X132)
| sdtasdt0(X132,X133) != xn
| ~ aInteger0(X133)
| X132 = sz00
| ~ aInteger0(X132)
| ~ aElementOf0(xn,sbsmnsldt0(xS)) )
& ( ~ isPrime0(X132)
| sdtasdt0(X132,X133) != xn
| ~ aInteger0(X133)
| X132 = sz00
| ~ aInteger0(X132)
| ~ aElementOf0(xn,X136)
| ~ aElementOf0(X136,xS) )
& ( ~ isPrime0(X132)
| sdtasdt0(X132,X133) != xn
| ~ aInteger0(X133)
| X132 = sz00
| ~ aInteger0(X132)
| isPrime0(esk20_0) )
& ( ~ isPrime0(X132)
| sdtasdt0(X132,X133) != xn
| ~ aInteger0(X133)
| X132 = sz00
| ~ aInteger0(X132)
| aDivisorOf0(esk20_0,xn) )
& ( ~ isPrime0(X132)
| sdtasdt0(X132,X133) != xn
| ~ aInteger0(X133)
| X132 = sz00
| ~ aInteger0(X132)
| sdtasdt0(esk20_0,esk21_0) = xn )
& ( ~ isPrime0(X132)
| sdtasdt0(X132,X133) != xn
| ~ aInteger0(X133)
| X132 = sz00
| ~ aInteger0(X132)
| aInteger0(esk21_0) )
& ( ~ isPrime0(X132)
| sdtasdt0(X132,X133) != xn
| ~ aInteger0(X133)
| X132 = sz00
| ~ aInteger0(X132)
| esk20_0 != sz00 )
& ( ~ isPrime0(X132)
| sdtasdt0(X132,X133) != xn
| ~ aInteger0(X133)
| X132 = sz00
| ~ aInteger0(X132)
| aInteger0(esk20_0) )
& ( aElementOf0(xn,sbsmnsldt0(xS))
| ~ aElementOf0(xn,sbsmnsldt0(xS)) )
& ( aElementOf0(xn,sbsmnsldt0(xS))
| ~ aElementOf0(xn,X136)
| ~ aElementOf0(X136,xS) )
& ( aElementOf0(xn,sbsmnsldt0(xS))
| isPrime0(esk20_0) )
& ( aElementOf0(xn,sbsmnsldt0(xS))
| aDivisorOf0(esk20_0,xn) )
& ( aElementOf0(xn,sbsmnsldt0(xS))
| sdtasdt0(esk20_0,esk21_0) = xn )
& ( aElementOf0(xn,sbsmnsldt0(xS))
| aInteger0(esk21_0) )
& ( aElementOf0(xn,sbsmnsldt0(xS))
| esk20_0 != sz00 )
& ( aElementOf0(xn,sbsmnsldt0(xS))
| aInteger0(esk20_0) )
& ( aElementOf0(xn,esk19_0)
| ~ aElementOf0(xn,sbsmnsldt0(xS)) )
& ( aElementOf0(xn,esk19_0)
| ~ aElementOf0(xn,X136)
| ~ aElementOf0(X136,xS) )
& ( aElementOf0(xn,esk19_0)
| isPrime0(esk20_0) )
& ( aElementOf0(xn,esk19_0)
| aDivisorOf0(esk20_0,xn) )
& ( aElementOf0(xn,esk19_0)
| sdtasdt0(esk20_0,esk21_0) = xn )
& ( aElementOf0(xn,esk19_0)
| aInteger0(esk21_0) )
& ( aElementOf0(xn,esk19_0)
| esk20_0 != sz00 )
& ( aElementOf0(xn,esk19_0)
| aInteger0(esk20_0) )
& ( aElementOf0(esk19_0,xS)
| ~ aElementOf0(xn,sbsmnsldt0(xS)) )
& ( aElementOf0(esk19_0,xS)
| ~ aElementOf0(xn,X136)
| ~ aElementOf0(X136,xS) )
& ( aElementOf0(esk19_0,xS)
| isPrime0(esk20_0) )
& ( aElementOf0(esk19_0,xS)
| aDivisorOf0(esk20_0,xn) )
& ( aElementOf0(esk19_0,xS)
| sdtasdt0(esk20_0,esk21_0) = xn )
& ( aElementOf0(esk19_0,xS)
| aInteger0(esk21_0) )
& ( aElementOf0(esk19_0,xS)
| esk20_0 != sz00 )
& ( aElementOf0(esk19_0,xS)
| aInteger0(esk20_0) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_38])])])])])]) ).
cnf(c_0_45,hypothesis,
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
| aDivisorOf0(esk16_1(X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_21]),c_0_37]) ).
cnf(c_0_46,hypothesis,
( ~ aElementOf0(X1,X2)
| ~ aElementOf0(X2,xS)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_47,hypothesis,
( ~ aElementOf0(X2,xS)
| ~ aInteger0(X3)
| sdtasdt0(esk16_1(X2),X1) != sdtpldt0(X3,smndt0(sz00))
| ~ aInteger0(X1)
| aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_48,hypothesis,
( ~ aInteger0(X1)
| ~ isPrime0(X1)
| aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X1),xS)
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_43]) ).
cnf(c_0_49,hypothesis,
( ~ aElementOf0(X1,xS)
| isPrime0(esk16_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_50,plain,
! [X1,X2] :
( ( X2 != sz00
& aInteger0(X2)
& aInteger0(X1) )
=> sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
inference(fof_simplification,[status(thm)],[mEquModRef]) ).
cnf(c_0_51,negated_conjecture,
( ~ isPrime0(X1)
| ~ aDivisorOf0(X1,xn)
| ~ aElementOf0(xn,sbsmnsldt0(xS)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,hypothesis,
( ~ aElementOf0(X2,X1)
| ~ aElementOf0(X1,xS)
| aDivisorOf0(esk16_1(X1),X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_53,negated_conjecture,
( ~ aElementOf0(xn,X1)
| ~ aElementOf0(X1,xS)
| aElementOf0(xn,sbsmnsldt0(xS)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_54,hypothesis,
( ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ aElementOf0(X2,xS)
| sdtasdt0(esk16_1(X2),X3) != sdtpldt0(X1,sz00)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2))) ),
inference(rw,[status(thm)],[c_0_47,c_0_32]) ).
cnf(c_0_55,hypothesis,
( ~ aElementOf0(X1,xS)
| aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)),xS) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_35]),c_0_36]) ).
fof(c_0_56,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_57,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_50])])]) ).
cnf(c_0_58,negated_conjecture,
( ~ aElementOf0(xn,X1)
| ~ aElementOf0(X1,xS) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_49]),c_0_53]) ).
cnf(c_0_59,hypothesis,
( ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ aElementOf0(X2,xS)
| sdtasdt0(esk16_1(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2))),X3) != sdtpldt0(X1,sz00)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2))))) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,plain,
( ~ aInteger0(X1)
| sdtasdt0(X1,sz00) = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
fof(c_0_61,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]) ).
fof(c_0_62,plain,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
inference(fof_simplification,[status(thm)],[mEquMod]) ).
cnf(c_0_63,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdteqdtlpzmzozddtrp0(X1,X1,X2)
| X2 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,hypothesis,
aInteger0(xn),
inference(split_conjunct,[status(thm)],[m__2106]) ).
cnf(c_0_65,hypothesis,
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1))) ),
inference(spm,[status(thm)],[c_0_58,c_0_55]) ).
cnf(c_0_66,hypothesis,
( ~ aInteger0(X1)
| ~ aInteger0(esk16_1(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2))))
| ~ aElementOf0(X2,xS)
| sdtpldt0(X1,sz00) != sz00
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2))))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_23])]) ).
fof(c_0_67,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])])]) ).
fof(c_0_68,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_61])])])])])])]) ).
fof(c_0_69,plain,
! [X36,X37,X38] :
( ( X38 = sz00
| ~ aInteger0(X38)
| ~ aInteger0(X37)
| ~ aInteger0(X36)
| sdteqdtlpzmzozddtrp0(X36,X37,X38)
| ~ aDivisorOf0(X38,sdtpldt0(X36,smndt0(X37))) )
& ( X38 = sz00
| ~ aInteger0(X38)
| ~ aInteger0(X37)
| ~ aInteger0(X36)
| aDivisorOf0(X38,sdtpldt0(X36,smndt0(X37)))
| ~ sdteqdtlpzmzozddtrp0(X36,X37,X38) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])]) ).
cnf(c_0_70,hypothesis,
( ~ aInteger0(X1)
| sdteqdtlpzmzozddtrp0(X1,X1,xn)
| xn = sz00 ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,hypothesis,
( ~ aElementOf0(X1,xS)
| sdtpldt0(xn,sz00) != sz00 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_64])]),c_0_35]),c_0_55]) ).
cnf(c_0_72,negated_conjecture,
( aElementOf0(esk19_0,xS)
| isPrime0(esk20_0) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_73,negated_conjecture,
( aElementOf0(esk19_0,xS)
| aInteger0(esk20_0) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_74,negated_conjecture,
( esk20_0 != sz00
| aElementOf0(esk19_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_75,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_76,plain,
( ~ aInteger0(X2)
| ~ aDivisorOf0(X1,X2)
| sdtasdt0(X1,esk1_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_77,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X3 = sz00
| aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_78,hypothesis,
( sdteqdtlpzmzozddtrp0(sz00,sz00,xn)
| xn = sz00 ),
inference(spm,[status(thm)],[c_0_70,c_0_23]) ).
cnf(c_0_79,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_32]),c_0_23])]) ).
cnf(c_0_80,hypothesis,
( ~ aElementOf0(X1,xS)
| xn != sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_21]),c_0_64])]) ).
cnf(c_0_81,negated_conjecture,
( aElementOf0(esk19_0,xS)
| aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0),xS) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_72]),c_0_73]),c_0_74]) ).
cnf(c_0_82,plain,
( ~ aInteger0(X1)
| ~ aInteger0(esk1_2(sz00,X1))
| ~ aDivisorOf0(X1,sz00)
| X1 = sz00
| esk1_2(sz00,X1) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76])]),c_0_23])]) ).
cnf(c_0_83,plain,
( ~ aInteger0(X1)
| ~ aDivisorOf0(X2,X1)
| aInteger0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_84,hypothesis,
( aDivisorOf0(xn,sz00)
| 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_77,c_0_78]),c_0_32]),c_0_79]),c_0_64]),c_0_23])]) ).
cnf(c_0_85,negated_conjecture,
xn != sz00,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_80]) ).
fof(c_0_86,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_87,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_88,plain,
( ~ aInteger0(X1)
| ~ aDivisorOf0(X1,sz00)
| X1 = sz00
| esk1_2(sz00,X1) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_23])]) ).
cnf(c_0_89,hypothesis,
aDivisorOf0(xn,sz00),
inference(sr,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_90,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_86]) ).
cnf(c_0_91,plain,
( ~ aInteger0(X1)
| sdtasdt0(X1,sz10) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_92,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_93,hypothesis,
esk1_2(sz00,xn) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_64])]),c_0_85]) ).
cnf(c_0_94,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_90,c_0_91]),c_0_92])]) ).
cnf(c_0_95,hypothesis,
sdtasdt0(xn,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_93]),c_0_89]),c_0_23])]) ).
cnf(c_0_96,hypothesis,
sdtasdt0(xn,sdtpldt0(sz00,sz10)) = sdtpldt0(sz00,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_23]),c_0_64])]) ).
cnf(c_0_97,plain,
( ~ aInteger0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_98,hypothesis,
sdtpldt0(sz00,xn) = sdtasdt0(xn,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_92])]) ).
cnf(c_0_99,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_90,c_0_91]),c_0_92])]) ).
fof(c_0_100,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_101,hypothesis,
sdtasdt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_64])]) ).
cnf(c_0_102,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X3)))
| X1 = sz00
| sdteqdtlpzmzozddtrp0(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_103,hypothesis,
sdtasdt0(xn,sdtpldt0(sz10,sz00)) = sdtpldt0(xn,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_95]),c_0_23]),c_0_64])]) ).
cnf(c_0_104,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_105,hypothesis,
sdtasdt0(xn,sdtpldt0(sz00,sz10)) = xn,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_98]),c_0_101]) ).
cnf(c_0_106,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aDivisorOf0(X1,sdtpldt0(X2,sz00))
| sdteqdtlpzmzozddtrp0(X2,sz00,X1)
| X1 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_32]),c_0_23])]) ).
cnf(c_0_107,hypothesis,
sdtpldt0(xn,sz00) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_105]),c_0_23]),c_0_92])]) ).
cnf(c_0_108,negated_conjecture,
( esk20_0 != sz00
| aElementOf0(xn,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_109,negated_conjecture,
( aElementOf0(xn,esk19_0)
| isPrime0(esk20_0) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_110,negated_conjecture,
( aElementOf0(xn,esk19_0)
| aInteger0(esk20_0) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_111,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_25]) ).
cnf(c_0_112,hypothesis,
( ~ aInteger0(X1)
| ~ aDivisorOf0(X1,xn)
| sdteqdtlpzmzozddtrp0(xn,sz00,X1)
| X1 = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_64])]) ).
cnf(c_0_113,negated_conjecture,
( aElementOf0(esk19_0,xS)
| aDivisorOf0(esk20_0,xn) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_114,negated_conjecture,
esk20_0 != sz00,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_74]),c_0_108]) ).
cnf(c_0_115,negated_conjecture,
( ~ aElementOf0(xn,X1)
| ~ aElementOf0(X1,xS)
| aElementOf0(esk19_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_116,negated_conjecture,
( aElementOf0(xn,esk19_0)
| aDivisorOf0(esk20_0,xn) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_117,negated_conjecture,
( ~ aElementOf0(xn,X1)
| ~ aElementOf0(X1,xS)
| aElementOf0(xn,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_118,negated_conjecture,
( aElementOf0(xn,esk19_0)
| aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0),xS) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_109]),c_0_110]),c_0_108]) ).
cnf(c_0_119,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X2,X3,X1)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| X1 = sz00 ),
inference(er,[status(thm)],[c_0_111]) ).
cnf(c_0_120,negated_conjecture,
( sdteqdtlpzmzozddtrp0(xn,sz00,esk20_0)
| aElementOf0(esk19_0,xS) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_114]),c_0_73]) ).
cnf(c_0_121,negated_conjecture,
( ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0))
| aElementOf0(esk19_0,xS) ),
inference(spm,[status(thm)],[c_0_115,c_0_81]) ).
cnf(c_0_122,negated_conjecture,
( sdteqdtlpzmzozddtrp0(xn,sz00,esk20_0)
| aElementOf0(xn,esk19_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_116]),c_0_114]),c_0_110]) ).
cnf(c_0_123,negated_conjecture,
( ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0))
| aElementOf0(xn,esk19_0) ),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_124,negated_conjecture,
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_119,c_0_120]),c_0_23]),c_0_64])]),c_0_114]),c_0_73]),c_0_121]) ).
cnf(c_0_125,negated_conjecture,
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_119,c_0_122]),c_0_23]),c_0_64])]),c_0_114]),c_0_110]),c_0_123]) ).
cnf(c_0_126,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_124]),c_0_125])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM447+5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/5.38 % Computer : n017.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 02:26:03 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 98.56/19.84 % Version: 3.5.1
% 98.56/19.84 % Preprocessing class: FSLSSMSSSSSNFFN.
% 98.56/19.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 98.56/19.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 98.56/19.84 % Starting new_bool_3 with 300s (1) cores
% 98.56/19.84 % Starting new_bool_1 with 300s (1) cores
% 98.56/19.84 % Starting sh5l with 300s (1) cores
% 98.56/19.84 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 1224919 completed with status 0
% 98.56/19.84 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 98.56/19.84 % Preprocessing class: FSLSSMSSSSSNFFN.
% 98.56/19.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 98.56/19.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 98.56/19.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 98.56/19.84 % No SInE strategy applied
% 98.56/19.84 % Search class: FGHSF-FSLM31-SFFFFFNN
% 98.56/19.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 98.56/19.84 % Starting SubtermCWHack with 136s (1) cores
% 98.56/19.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 98.56/19.84 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 198s (1) cores
% 98.56/19.84 % Starting new_bool_3 with 194s (1) cores
% 98.56/19.84 % Starting new_bool_1 with 188s (1) cores
% 98.56/19.84 % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1224928 completed with status 0
% 98.56/19.84 % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 98.56/19.84 % Preprocessing class: FSLSSMSSSSSNFFN.
% 98.56/19.84 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 98.56/19.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 98.56/19.84 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 98.56/19.84 % No SInE strategy applied
% 98.56/19.84 % Search class: FGHSF-FSLM31-SFFFFFNN
% 98.56/19.84 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 98.56/19.84 % Starting SubtermCWHack with 136s (1) cores
% 98.56/19.84 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 98.56/19.84 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 198s (1) cores
% 98.56/19.84 % Preprocessing time : 0.004 s
% 98.56/19.84 % Presaturation interreduction done
% 98.56/19.84
% 98.56/19.84 % Proof found!
% 98.56/19.84 % SZS status Theorem
% 98.56/19.84 % SZS output start CNFRefutation
% See solution above
% 98.56/19.84 % Parsed axioms : 44
% 98.56/19.84 % Removed by relevancy pruning/SinE : 0
% 98.56/19.84 % Initial clauses : 178
% 98.56/19.84 % Removed in clause preprocessing : 6
% 98.56/19.84 % Initial clauses in saturation : 172
% 98.56/19.84 % Processed clauses : 33243
% 98.56/19.84 % ...of these trivial : 166
% 98.56/19.84 % ...subsumed : 26856
% 98.56/19.84 % ...remaining for further processing : 6221
% 98.56/19.84 % Other redundant clauses eliminated : 245
% 98.56/19.84 % Clauses deleted for lack of memory : 0
% 98.56/19.84 % Backward-subsumed : 456
% 98.56/19.84 % Backward-rewritten : 3689
% 98.56/19.84 % Generated clauses : 571968
% 98.56/19.84 % ...of the previous two non-redundant : 556125
% 98.56/19.84 % ...aggressively subsumed : 0
% 98.56/19.84 % Contextual simplify-reflections : 1665
% 98.56/19.84 % Paramodulations : 571662
% 98.56/19.84 % Factorizations : 0
% 98.56/19.84 % NegExts : 0
% 98.56/19.84 % Equation resolutions : 245
% 98.56/19.84 % Disequality decompositions : 0
% 98.56/19.84 % Total rewrite steps : 174006
% 98.56/19.84 % ...of those cached : 173883
% 98.56/19.84 % Propositional unsat checks : 1
% 98.56/19.84 % Propositional check models : 0
% 98.56/19.84 % Propositional check unsatisfiable : 0
% 98.56/19.84 % Propositional clauses : 0
% 98.56/19.84 % Propositional clauses after purity: 0
% 98.56/19.84 % Propositional unsat core size : 0
% 98.56/19.84 % Propositional preprocessing time : 0.000
% 98.56/19.84 % Propositional encoding time : 0.597
% 98.56/19.84 % Propositional solver time : 0.159
% 98.56/19.84 % Success case prop preproc time : 0.000
% 98.56/19.84 % Success case prop encoding time : 0.000
% 98.56/19.84 % Success case prop solver time : 0.000
% 98.56/19.84 % Current number of processed clauses : 1810
% 98.56/19.84 % Positive orientable unit clauses : 125
% 98.56/19.84 % Positive unorientable unit clauses: 0
% 98.56/19.84 % Negative unit clauses : 6
% 98.56/19.84 % Non-unit-clauses : 1679
% 98.56/19.84 % Current number of unprocessed clauses: 519838
% 98.56/19.84 % ...number of literals in the above : 2275596
% 98.56/19.84 % Current number of archived formulas : 0
% 98.56/19.84 % Current number of archived clauses : 4378
% 98.56/19.84 % Clause-clause subsumption calls (NU) : 4075876
% 98.56/19.84 % Rec. Clause-clause subsumption calls : 1525363
% 98.56/19.84 % Non-unit clause-clause subsumptions : 25036
% 98.56/19.84 % Unit Clause-clause subsumption calls : 114772
% 98.56/19.84 % Rewrite failures with RHS unbound : 0
% 98.56/19.84 % BW rewrite match attempts : 163
% 98.56/19.84 % BW rewrite match successes : 33
% 98.56/19.84 % Condensation attempts : 0
% 98.56/19.84 % Condensation successes : 0
% 98.56/19.84 % Termbank termtop insertions : 16154545
% 98.56/19.84 % Search garbage collected termcells : 3077
% 98.56/19.84
% 98.56/19.84 % -------------------------------------------------
% 98.56/19.84 % User time : 13.398 s
% 98.56/19.84 % System time : 0.581 s
% 98.56/19.84 % Total time : 13.979 s
% 98.56/19.84 % Maximum resident set size: 3952 pages
% 98.56/19.84
% 98.56/19.84 % -------------------------------------------------
% 98.56/19.84 % User time : 67.845 s
% 98.56/19.84 % System time : 2.623 s
% 98.56/19.84 % Total time : 70.468 s
% 98.56/19.84 % Maximum resident set size: 4864 pages
% 98.56/19.84 % E exiting
%------------------------------------------------------------------------------