TSTP Solution File: NUM447+5 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : NUM447+5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n023.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 : Thu Aug 31 11:30:32 EDT 2023
% Result : Theorem 43.59s 6.72s
% Output : CNFRefutation 43.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 31
% Syntax : Number of formulae : 279 ( 33 unt; 0 def)
% Number of atoms : 1395 ( 305 equ)
% Maximal formula atoms : 38 ( 5 avg)
% Number of connectives : 1766 ( 650 ~; 632 |; 433 &)
% ( 8 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 4 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 9 con; 0-2 aty)
% Number of variables : 450 ( 10 sgn; 228 !; 101 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(f9,axiom,
! [X0] :
( aInteger0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(f10,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(f15,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(f16,axiom,
! [X0] :
( aInteger0(X0)
=> ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& smndt0(X0) = sdtasdt0(smndt0(sz10),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulMinOne) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(f25,axiom,
! [X0] :
( aInteger0(X0)
=> ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
<=> ( smndt0(sz10) != X0
& sz10 != X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrimeDivisor) ).
fof(f35,axiom,
! [X0] :
( aSubsetOf0(X0,cS1395)
=> ( isOpen0(X0)
<=> ! [X1] :
( aElementOf0(X1,X0)
=> ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
& sz00 != X2
& aInteger0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mOpen) ).
fof(f42,axiom,
( xS = cS2043
& ! [X0] :
( ( ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
& isPrime0(X1)
& sz00 != X1
& aInteger0(X1) )
=> aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
=> ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& isPrime0(X1)
& sz00 != X1
& aInteger0(X1) ) ) )
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2046) ).
fof(f43,axiom,
aInteger0(xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2106) ).
fof(f44,conjecture,
( ( ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) )
=> ( aElementOf0(xn,sbsmnsldt0(xS))
| ? [X0] :
( aElementOf0(xn,X0)
& aElementOf0(X0,xS) ) ) )
& ( ( aElementOf0(xn,sbsmnsldt0(xS))
& ? [X0] :
( aElementOf0(xn,X0)
& aElementOf0(X0,xS) ) )
=> ? [X0] :
( isPrime0(X0)
& ( aDivisorOf0(X0,xn)
| ( ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ( ( ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) )
=> ( aElementOf0(xn,sbsmnsldt0(xS))
| ? [X0] :
( aElementOf0(xn,X0)
& aElementOf0(X0,xS) ) ) )
& ( ( aElementOf0(xn,sbsmnsldt0(xS))
& ? [X0] :
( aElementOf0(xn,X0)
& aElementOf0(X0,xS) ) )
=> ? [X0] :
( isPrime0(X0)
& ( aDivisorOf0(X0,xn)
| ( ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) ) ) ) ) ),
inference(negated_conjecture,[],[f44]) ).
fof(f52,plain,
( xS = cS2043
& ! [X0] :
( ( ? [X1] :
( ( ( ! [X2] :
( ( ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| ? [X3] :
( sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz00))
& aInteger0(X3) ) )
& aInteger0(X2) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
& ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
=> ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X4] :
( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
& aInteger0(X4) )
& aInteger0(X2) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0 )
& isPrime0(X1)
& sz00 != X1
& aInteger0(X1) )
=> aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
=> ? [X5] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
& ! [X6] :
( ( ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
| aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
| ? [X7] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X7)
& aInteger0(X7) ) )
& aInteger0(X6) )
=> aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
=> ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X8] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
& aInteger0(X8) )
& aInteger0(X6) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) ) ) )
& aSet0(xS) ),
inference(rectify,[],[f42]) ).
fof(f53,plain,
~ ( ( ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) )
=> ( aElementOf0(xn,sbsmnsldt0(xS))
| ? [X2] :
( aElementOf0(xn,X2)
& aElementOf0(X2,xS) ) ) )
& ( ( aElementOf0(xn,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(xn,X3)
& aElementOf0(X3,xS) ) )
=> ? [X4] :
( isPrime0(X4)
& ( aDivisorOf0(X4,xn)
| ( ? [X5] :
( xn = sdtasdt0(X4,X5)
& aInteger0(X5) )
& sz00 != X4
& aInteger0(X4) ) ) ) ) ),
inference(rectify,[],[f45]) ).
fof(f55,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f58,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(flattening,[],[f58]) ).
fof(f64,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f65,plain,
! [X0] :
( ( sz00 = sdtpldt0(smndt0(X0),X0)
& sz00 = sdtpldt0(X0,smndt0(X0)) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f73,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f74,plain,
! [X0] :
( ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& smndt0(X0) = sdtasdt0(smndt0(sz10),X0) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f88,plain,
! [X0] :
( ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
<=> ( smndt0(sz10) != X0
& sz10 != X0 ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f99,plain,
! [X0] :
( ( isOpen0(X0)
<=> ! [X1] :
( ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
& sz00 != X2
& aInteger0(X2) )
| ~ aElementOf0(X1,X0) ) )
| ~ aSubsetOf0(X0,cS1395) ),
inference(ennf_transformation,[],[f35]) ).
fof(f109,plain,
( xS = cS2043
& ! [X0] :
( ( aElementOf0(X0,xS)
| ! [X1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ! [X3] :
( sdtasdt0(X1,X3) != sdtpldt0(X2,smndt0(sz00))
| ~ aInteger0(X3) ) )
| ~ aInteger0(X2) )
& ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X4] :
( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
& aInteger0(X4) )
& aInteger0(X2) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ) )
& ( ? [X5] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X7] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X6) )
& ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X8] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
& aInteger0(X8) )
& aInteger0(X6) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f52]) ).
fof(f110,plain,
( xS = cS2043
& ! [X0] :
( ( aElementOf0(X0,xS)
| ! [X1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ! [X3] :
( sdtasdt0(X1,X3) != sdtpldt0(X2,smndt0(sz00))
| ~ aInteger0(X3) ) )
| ~ aInteger0(X2) )
& ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X4] :
( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
& aInteger0(X4) )
& aInteger0(X2) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ) )
& ( ? [X5] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
& ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X7] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X6) )
& ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X8] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
& aInteger0(X8) )
& aInteger0(X6) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(flattening,[],[f109]) ).
fof(f111,plain,
( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X2] :
( ~ aElementOf0(xn,X2)
| ~ aElementOf0(X2,xS) )
& ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) ) )
| ( ! [X4] :
( ~ isPrime0(X4)
| ( ~ aDivisorOf0(X4,xn)
& ( ! [X5] :
( xn != sdtasdt0(X4,X5)
| ~ aInteger0(X5) )
| sz00 = X4
| ~ aInteger0(X4) ) ) )
& aElementOf0(xn,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(xn,X3)
& aElementOf0(X3,xS) ) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f112,plain,
( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X2] :
( ~ aElementOf0(xn,X2)
| ~ aElementOf0(X2,xS) )
& ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) ) )
| ( ! [X4] :
( ~ isPrime0(X4)
| ( ~ aDivisorOf0(X4,xn)
& ( ! [X5] :
( xn != sdtasdt0(X4,X5)
| ~ aInteger0(X5) )
| sz00 = X4
| ~ aInteger0(X4) ) ) )
& aElementOf0(xn,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(xn,X3)
& aElementOf0(X3,xS) ) ) ),
inference(flattening,[],[f111]) ).
fof(f119,plain,
! [X0,X2] :
( sP4(X0,X2)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) ) )
& aSet0(X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f122,plain,
! [X5] :
( ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X7] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X6) )
& ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X8] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
& aInteger0(X8) )
& aInteger0(X6) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) ) )
| ~ sP6(X5) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f123,plain,
! [X1] :
( ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ! [X3] :
( sdtasdt0(X1,X3) != sdtpldt0(X2,smndt0(sz00))
| ~ aInteger0(X3) ) )
| ~ aInteger0(X2) )
& ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X4] :
( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
& aInteger0(X4) )
& aInteger0(X2) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
| ~ sP7(X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f124,plain,
( xS = cS2043
& ! [X0] :
( ( aElementOf0(X0,xS)
| ! [X1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
& sP7(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ) )
& ( ? [X5] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0
& sP6(X5)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(definition_folding,[],[f110,f123,f122]) ).
fof(f125,plain,
( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X2] :
( ~ aElementOf0(xn,X2)
| ~ aElementOf0(X2,xS) )
& ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) ) )
| ~ sP8 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f126,plain,
( sP8
| ( ! [X4] :
( ~ isPrime0(X4)
| ( ~ aDivisorOf0(X4,xn)
& ( ! [X5] :
( xn != sdtasdt0(X4,X5)
| ~ aInteger0(X5) )
| sz00 = X4
| ~ aInteger0(X4) ) ) )
& aElementOf0(xn,sbsmnsldt0(xS))
& ? [X3] :
( aElementOf0(xn,X3)
& aElementOf0(X3,xS) ) ) ),
inference(definition_folding,[],[f112,f125]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f77]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(flattening,[],[f127]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( ? [X3] :
( sdtasdt0(X1,X3) = X0
& aInteger0(X3) )
& sz00 != X1
& aInteger0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X1,X3) = X0
& aInteger0(X3) )
=> ( sdtasdt0(X1,sK9(X0,X1)) = X0
& aInteger0(sK9(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1) )
& ( ( sdtasdt0(X1,sK9(X0,X1)) = X0
& aInteger0(sK9(X0,X1))
& sz00 != X1
& aInteger0(X1) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f129,f130]) ).
fof(f133,plain,
! [X0] :
( ( ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
| smndt0(sz10) = X0
| sz10 = X0 )
& ( ( smndt0(sz10) != X0
& sz10 != X0 )
| ! [X1] :
( ~ isPrime0(X1)
| ~ aDivisorOf0(X1,X0) ) ) )
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f88]) ).
fof(f134,plain,
! [X0] :
( ( ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
| smndt0(sz10) = X0
| sz10 = X0 )
& ( ( smndt0(sz10) != X0
& sz10 != X0 )
| ! [X1] :
( ~ isPrime0(X1)
| ~ aDivisorOf0(X1,X0) ) ) )
| ~ aInteger0(X0) ),
inference(flattening,[],[f133]) ).
fof(f135,plain,
! [X0] :
( ( ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
| smndt0(sz10) = X0
| sz10 = X0 )
& ( ( smndt0(sz10) != X0
& sz10 != X0 )
| ! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0) ) ) )
| ~ aInteger0(X0) ),
inference(rectify,[],[f134]) ).
fof(f136,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
=> ( isPrime0(sK10(X0))
& aDivisorOf0(sK10(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f137,plain,
! [X0] :
( ( ( ( isPrime0(sK10(X0))
& aDivisorOf0(sK10(X0),X0) )
| smndt0(sz10) = X0
| sz10 = X0 )
& ( ( smndt0(sz10) != X0
& sz10 != X0 )
| ! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0) ) ) )
| ~ aInteger0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f135,f136]) ).
fof(f157,plain,
! [X0,X2] :
( ( sP4(X0,X2)
| ? [X3] :
( ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,X0) )
| ~ aInteger0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,X0) )
| ~ aInteger0(X3) )
& ( ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP4(X0,X2) ) ),
inference(nnf_transformation,[],[f119]) ).
fof(f158,plain,
! [X0,X2] :
( ( sP4(X0,X2)
| ? [X3] :
( ( ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,X0) )
| ~ aInteger0(X3)
| ~ aElementOf0(X3,X2) )
& ( ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) )
| aElementOf0(X3,X2) ) )
| ~ aSet0(X2) )
& ( ( ! [X3] :
( ( aElementOf0(X3,X2)
| ! [X4] :
( ~ aElementOf0(X3,X4)
| ~ aElementOf0(X4,X0) )
| ~ aInteger0(X3) )
& ( ( ? [X4] :
( aElementOf0(X3,X4)
& aElementOf0(X4,X0) )
& aInteger0(X3) )
| ~ aElementOf0(X3,X2) ) )
& aSet0(X2) )
| ~ sP4(X0,X2) ) ),
inference(flattening,[],[f157]) ).
fof(f159,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ aElementOf0(X2,X3)
| ~ aElementOf0(X3,X0) )
| ~ aInteger0(X2)
| ~ aElementOf0(X2,X1) )
& ( ( ? [X4] :
( aElementOf0(X2,X4)
& aElementOf0(X4,X0) )
& aInteger0(X2) )
| aElementOf0(X2,X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElementOf0(X5,X6)
| ~ aElementOf0(X6,X0) )
| ~ aInteger0(X5) )
& ( ( ? [X7] :
( aElementOf0(X5,X7)
& aElementOf0(X7,X0) )
& aInteger0(X5) )
| ~ aElementOf0(X5,X1) ) )
& aSet0(X1) )
| ~ sP4(X0,X1) ) ),
inference(rectify,[],[f158]) ).
fof(f160,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( ~ aElementOf0(X2,X3)
| ~ aElementOf0(X3,X0) )
| ~ aInteger0(X2)
| ~ aElementOf0(X2,X1) )
& ( ( ? [X4] :
( aElementOf0(X2,X4)
& aElementOf0(X4,X0) )
& aInteger0(X2) )
| aElementOf0(X2,X1) ) )
=> ( ( ! [X3] :
( ~ aElementOf0(sK14(X0,X1),X3)
| ~ aElementOf0(X3,X0) )
| ~ aInteger0(sK14(X0,X1))
| ~ aElementOf0(sK14(X0,X1),X1) )
& ( ( ? [X4] :
( aElementOf0(sK14(X0,X1),X4)
& aElementOf0(X4,X0) )
& aInteger0(sK14(X0,X1)) )
| aElementOf0(sK14(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
! [X0,X1] :
( ? [X4] :
( aElementOf0(sK14(X0,X1),X4)
& aElementOf0(X4,X0) )
=> ( aElementOf0(sK14(X0,X1),sK15(X0,X1))
& aElementOf0(sK15(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f162,plain,
! [X0,X5] :
( ? [X7] :
( aElementOf0(X5,X7)
& aElementOf0(X7,X0) )
=> ( aElementOf0(X5,sK16(X0,X5))
& aElementOf0(sK16(X0,X5),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f163,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ( ( ! [X3] :
( ~ aElementOf0(sK14(X0,X1),X3)
| ~ aElementOf0(X3,X0) )
| ~ aInteger0(sK14(X0,X1))
| ~ aElementOf0(sK14(X0,X1),X1) )
& ( ( aElementOf0(sK14(X0,X1),sK15(X0,X1))
& aElementOf0(sK15(X0,X1),X0)
& aInteger0(sK14(X0,X1)) )
| aElementOf0(sK14(X0,X1),X1) ) )
| ~ aSet0(X1) )
& ( ( ! [X5] :
( ( aElementOf0(X5,X1)
| ! [X6] :
( ~ aElementOf0(X5,X6)
| ~ aElementOf0(X6,X0) )
| ~ aInteger0(X5) )
& ( ( aElementOf0(X5,sK16(X0,X5))
& aElementOf0(sK16(X0,X5),X0)
& aInteger0(X5) )
| ~ aElementOf0(X5,X1) ) )
& aSet0(X1) )
| ~ sP4(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f159,f162,f161,f160]) ).
fof(f176,plain,
! [X0] :
( ( ( isOpen0(X0)
| ? [X1] :
( ! [X2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
| sz00 = X2
| ~ aInteger0(X2) )
& aElementOf0(X1,X0) ) )
& ( ! [X1] :
( ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
& sz00 != X2
& aInteger0(X2) )
| ~ aElementOf0(X1,X0) )
| ~ isOpen0(X0) ) )
| ~ aSubsetOf0(X0,cS1395) ),
inference(nnf_transformation,[],[f99]) ).
fof(f177,plain,
! [X0] :
( ( ( isOpen0(X0)
| ? [X1] :
( ! [X2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
| sz00 = X2
| ~ aInteger0(X2) )
& aElementOf0(X1,X0) ) )
& ( ! [X3] :
( ? [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),X0)
& sz00 != X4
& aInteger0(X4) )
| ~ aElementOf0(X3,X0) )
| ~ isOpen0(X0) ) )
| ~ aSubsetOf0(X0,cS1395) ),
inference(rectify,[],[f176]) ).
fof(f178,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
| sz00 = X2
| ~ aInteger0(X2) )
& aElementOf0(X1,X0) )
=> ( ! [X2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK20(X0),X2),X0)
| sz00 = X2
| ~ aInteger0(X2) )
& aElementOf0(sK20(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f179,plain,
! [X0,X3] :
( ? [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),X0)
& sz00 != X4
& aInteger0(X4) )
=> ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,sK21(X0,X3)),X0)
& sz00 != sK21(X0,X3)
& aInteger0(sK21(X0,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f180,plain,
! [X0] :
( ( ( isOpen0(X0)
| ( ! [X2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK20(X0),X2),X0)
| sz00 = X2
| ~ aInteger0(X2) )
& aElementOf0(sK20(X0),X0) ) )
& ( ! [X3] :
( ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,sK21(X0,X3)),X0)
& sz00 != sK21(X0,X3)
& aInteger0(sK21(X0,X3)) )
| ~ aElementOf0(X3,X0) )
| ~ isOpen0(X0) ) )
| ~ aSubsetOf0(X0,cS1395) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f177,f179,f178]) ).
fof(f184,plain,
! [X1] :
( ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ( ~ sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ! [X3] :
( sdtasdt0(X1,X3) != sdtpldt0(X2,smndt0(sz00))
| ~ aInteger0(X3) ) )
| ~ aInteger0(X2) )
& ( ( sdteqdtlpzmzozddtrp0(X2,sz00,X1)
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
& ? [X4] :
( sdtpldt0(X2,smndt0(sz00)) = sdtasdt0(X1,X4)
& aInteger0(X4) )
& aInteger0(X2) )
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ) )
| ~ sP7(X1) ),
inference(nnf_transformation,[],[f123]) ).
fof(f185,plain,
! [X0] :
( ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ( ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& ! [X2] :
( sdtasdt0(X0,X2) != sdtpldt0(X1,smndt0(sz00))
| ~ aInteger0(X2) ) )
| ~ aInteger0(X1) )
& ( ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& ? [X3] :
( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,X3)
& aInteger0(X3) )
& aInteger0(X1) )
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ) )
| ~ sP7(X0) ),
inference(rectify,[],[f184]) ).
fof(f186,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,X3)
& aInteger0(X3) )
=> ( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK23(X0,X1))
& aInteger0(sK23(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ( ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& ! [X2] :
( sdtasdt0(X0,X2) != sdtpldt0(X1,smndt0(sz00))
| ~ aInteger0(X2) ) )
| ~ aInteger0(X1) )
& ( ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK23(X0,X1))
& aInteger0(sK23(X0,X1))
& aInteger0(X1) )
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ) )
| ~ sP7(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f185,f186]) ).
fof(f188,plain,
! [X5] :
( ! [X6] :
( ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( ~ sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& ~ aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ! [X7] :
( sdtpldt0(X6,smndt0(sz00)) != sdtasdt0(X5,X7)
| ~ aInteger0(X7) ) )
| ~ aInteger0(X6) )
& ( ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X8] :
( sdtpldt0(X6,smndt0(sz00)) = sdtasdt0(X5,X8)
& aInteger0(X8) )
& aInteger0(X6) )
| ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5)) ) )
| ~ sP6(X5) ),
inference(nnf_transformation,[],[f122]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ( ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& ! [X2] :
( sdtasdt0(X0,X2) != sdtpldt0(X1,smndt0(sz00))
| ~ aInteger0(X2) ) )
| ~ aInteger0(X1) )
& ( ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& ? [X3] :
( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,X3)
& aInteger0(X3) )
& aInteger0(X1) )
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ) )
| ~ sP6(X0) ),
inference(rectify,[],[f188]) ).
fof(f190,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,X3)
& aInteger0(X3) )
=> ( sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK24(X0,X1))
& aInteger0(sK24(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f191,plain,
! [X0] :
( ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ( ~ sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& ~ aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& ! [X2] :
( sdtasdt0(X0,X2) != sdtpldt0(X1,smndt0(sz00))
| ~ aInteger0(X2) ) )
| ~ aInteger0(X1) )
& ( ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK24(X0,X1))
& aInteger0(sK24(X0,X1))
& aInteger0(X1) )
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ) )
| ~ sP6(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f189,f190]) ).
fof(f192,plain,
( xS = cS2043
& ! [X0] :
( ( aElementOf0(X0,xS)
| ! [X1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
& sP7(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ) )
& ( ? [X2] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X0
& sP6(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& isPrime0(X2)
& sz00 != X2
& aInteger0(X2) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(rectify,[],[f124]) ).
fof(f193,plain,
! [X0] :
( ? [X2] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X0
& sP6(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& isPrime0(X2)
& sz00 != X2
& aInteger0(X2) )
=> ( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0
& sP6(sK25(X0))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)))
& isPrime0(sK25(X0))
& sz00 != sK25(X0)
& aInteger0(sK25(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f194,plain,
( xS = cS2043
& ! [X0] :
( ( aElementOf0(X0,xS)
| ! [X1] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
& sP7(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1)) )
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ) )
& ( ( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0
& sP6(sK25(X0))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)))
& isPrime0(sK25(X0))
& sz00 != sK25(X0)
& aInteger0(sK25(X0)) )
| ~ aElementOf0(X0,xS) ) )
& aSet0(xS) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f192,f193]) ).
fof(f195,plain,
( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X2] :
( ~ aElementOf0(xn,X2)
| ~ aElementOf0(X2,xS) )
& ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& sz00 != X0
& aInteger0(X0) ) )
| ~ sP8 ),
inference(nnf_transformation,[],[f125]) ).
fof(f196,plain,
( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X0] :
( ~ aElementOf0(xn,X0)
| ~ aElementOf0(X0,xS) )
& ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,xn)
& ? [X2] :
( sdtasdt0(X1,X2) = xn
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) ) )
| ~ sP8 ),
inference(rectify,[],[f195]) ).
fof(f197,plain,
( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,xn)
& ? [X2] :
( sdtasdt0(X1,X2) = xn
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) )
=> ( isPrime0(sK26)
& aDivisorOf0(sK26,xn)
& ? [X2] :
( xn = sdtasdt0(sK26,X2)
& aInteger0(X2) )
& sz00 != sK26
& aInteger0(sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f198,plain,
( ? [X2] :
( xn = sdtasdt0(sK26,X2)
& aInteger0(X2) )
=> ( xn = sdtasdt0(sK26,sK27)
& aInteger0(sK27) ) ),
introduced(choice_axiom,[]) ).
fof(f199,plain,
( ( ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X0] :
( ~ aElementOf0(xn,X0)
| ~ aElementOf0(X0,xS) )
& isPrime0(sK26)
& aDivisorOf0(sK26,xn)
& xn = sdtasdt0(sK26,sK27)
& aInteger0(sK27)
& sz00 != sK26
& aInteger0(sK26) )
| ~ sP8 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f196,f198,f197]) ).
fof(f200,plain,
( sP8
| ( ! [X0] :
( ~ isPrime0(X0)
| ( ~ aDivisorOf0(X0,xn)
& ( ! [X1] :
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X1) )
| sz00 = X0
| ~ aInteger0(X0) ) ) )
& aElementOf0(xn,sbsmnsldt0(xS))
& ? [X2] :
( aElementOf0(xn,X2)
& aElementOf0(X2,xS) ) ) ),
inference(rectify,[],[f126]) ).
fof(f201,plain,
( ? [X2] :
( aElementOf0(xn,X2)
& aElementOf0(X2,xS) )
=> ( aElementOf0(xn,sK28)
& aElementOf0(sK28,xS) ) ),
introduced(choice_axiom,[]) ).
fof(f202,plain,
( sP8
| ( ! [X0] :
( ~ isPrime0(X0)
| ( ~ aDivisorOf0(X0,xn)
& ( ! [X1] :
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X1) )
| sz00 = X0
| ~ aInteger0(X0) ) ) )
& aElementOf0(xn,sbsmnsldt0(xS))
& aElementOf0(xn,sK28)
& aElementOf0(sK28,xS) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f200,f201]) ).
fof(f203,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f204,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f205,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f207,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f210,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f211,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f212,plain,
! [X0] :
( sz00 = sdtpldt0(X0,smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f220,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f223,plain,
! [X0] :
( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f74]) ).
fof(f227,plain,
! [X0,X1] :
( aInteger0(sK9(X0,X1))
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f228,plain,
! [X0,X1] :
( sdtasdt0(X1,sK9(X0,X1)) = X0
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f237,plain,
! [X2,X0] :
( sz10 != X0
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f238,plain,
! [X2,X0] :
( smndt0(sz10) != X0
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f239,plain,
! [X0] :
( aDivisorOf0(sK10(X0),X0)
| smndt0(sz10) = X0
| sz10 = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f240,plain,
! [X0] :
( isPrime0(sK10(X0))
| smndt0(sz10) = X0
| sz10 = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f273,plain,
! [X0,X1,X5] :
( aElementOf0(sK16(X0,X5),X0)
| ~ aElementOf0(X5,X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
fof(f275,plain,
! [X0,X1,X6,X5] :
( aElementOf0(X5,X1)
| ~ aElementOf0(X5,X6)
| ~ aElementOf0(X6,X0)
| ~ aInteger0(X5)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f163]) ).
fof(f299,plain,
! [X0] :
( isOpen0(X0)
| aElementOf0(sK20(X0),X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f180]) ).
fof(f312,plain,
! [X0,X1] :
( aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f314,plain,
! [X2,X0,X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| sdtasdt0(X0,X2) != sdtpldt0(X1,smndt0(sz00))
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f317,plain,
! [X0,X1] :
( aInteger0(X1)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f320,plain,
! [X0,X1] :
( aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f326,plain,
! [X0] :
( aInteger0(sK25(X0))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f194]) ).
fof(f327,plain,
! [X0] :
( sz00 != sK25(X0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f194]) ).
fof(f328,plain,
! [X0] :
( isPrime0(sK25(X0))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f194]) ).
fof(f330,plain,
! [X0] :
( sP6(sK25(X0))
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f194]) ).
fof(f331,plain,
! [X0] :
( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f194]) ).
fof(f332,plain,
! [X0,X1] :
( aElementOf0(X0,xS)
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f333,plain,
! [X0,X1] :
( aElementOf0(X0,xS)
| sP7(X1)
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f334,plain,
! [X0,X1] :
( aElementOf0(X0,xS)
| szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f335,plain,
xS = cS2043,
inference(cnf_transformation,[],[f194]) ).
fof(f336,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f43]) ).
fof(f337,plain,
( aInteger0(sK26)
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f338,plain,
( sz00 != sK26
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f339,plain,
( aInteger0(sK27)
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f340,plain,
( xn = sdtasdt0(sK26,sK27)
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f341,plain,
( aDivisorOf0(sK26,xn)
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f342,plain,
( isPrime0(sK26)
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f343,plain,
! [X0] :
( ~ aElementOf0(xn,X0)
| ~ aElementOf0(X0,xS)
| ~ sP8 ),
inference(cnf_transformation,[],[f199]) ).
fof(f345,plain,
( sP8
| aElementOf0(sK28,xS) ),
inference(cnf_transformation,[],[f202]) ).
fof(f346,plain,
( sP8
| aElementOf0(xn,sK28) ),
inference(cnf_transformation,[],[f202]) ).
fof(f348,plain,
! [X0,X1] :
( sP8
| ~ isPrime0(X0)
| sdtasdt0(X0,X1) != xn
| ~ aInteger0(X1)
| sz00 = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f349,plain,
! [X0] :
( sP8
| ~ isPrime0(X0)
| ~ aDivisorOf0(X0,xn) ),
inference(cnf_transformation,[],[f202]) ).
fof(f350,plain,
! [X0,X1] :
( aElementOf0(X0,cS2043)
| szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X0
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(definition_unfolding,[],[f334,f335]) ).
fof(f351,plain,
! [X0,X1] :
( aElementOf0(X0,cS2043)
| sP7(X1)
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(definition_unfolding,[],[f333,f335]) ).
fof(f352,plain,
! [X0,X1] :
( aElementOf0(X0,cS2043)
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(definition_unfolding,[],[f332,f335]) ).
fof(f353,plain,
! [X0] :
( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0
| ~ aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f331,f335]) ).
fof(f354,plain,
! [X0] :
( sP6(sK25(X0))
| ~ aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f330,f335]) ).
fof(f356,plain,
! [X0] :
( isPrime0(sK25(X0))
| ~ aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f328,f335]) ).
fof(f357,plain,
! [X0] :
( sz00 != sK25(X0)
| ~ aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f327,f335]) ).
fof(f358,plain,
! [X0] :
( aInteger0(sK25(X0))
| ~ aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f326,f335]) ).
fof(f361,plain,
! [X0] :
( ~ aElementOf0(xn,X0)
| ~ aElementOf0(X0,cS2043)
| ~ sP8 ),
inference(definition_unfolding,[],[f343,f335]) ).
fof(f363,plain,
( sP8
| aElementOf0(sK28,cS2043) ),
inference(definition_unfolding,[],[f345,f335]) ).
fof(f366,plain,
! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,smndt0(sz10))
| ~ aInteger0(smndt0(sz10)) ),
inference(equality_resolution,[],[f238]) ).
fof(f367,plain,
! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,sz10)
| ~ aInteger0(sz10) ),
inference(equality_resolution,[],[f237]) ).
fof(f379,plain,
! [X1] :
( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X1),cS2043)
| ~ isPrime0(X1)
| sz00 = X1
| ~ aInteger0(X1) ),
inference(equality_resolution,[],[f350]) ).
cnf(c_49,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f203]) ).
cnf(c_50,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f204]) ).
cnf(c_51,plain,
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[],[f205]) ).
cnf(c_53,plain,
( ~ aInteger0(X0)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f207]) ).
cnf(c_56,plain,
( ~ aInteger0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f211]) ).
cnf(c_57,plain,
( ~ aInteger0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f210]) ).
cnf(c_59,plain,
( ~ aInteger0(X0)
| sdtpldt0(X0,smndt0(X0)) = sz00 ),
inference(cnf_transformation,[],[f212]) ).
cnf(c_67,plain,
( ~ aInteger0(X0)
| sdtasdt0(X0,sz00) = sz00 ),
inference(cnf_transformation,[],[f220]) ).
cnf(c_68,plain,
( ~ aInteger0(X0)
| sdtasdt0(X0,smndt0(sz10)) = smndt0(X0) ),
inference(cnf_transformation,[],[f223]) ).
cnf(c_72,plain,
( ~ aDivisorOf0(X0,X1)
| ~ aInteger0(X1)
| sdtasdt0(X0,sK9(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f228]) ).
cnf(c_73,plain,
( ~ aDivisorOf0(X0,X1)
| ~ aInteger0(X1)
| aInteger0(sK9(X1,X0)) ),
inference(cnf_transformation,[],[f227]) ).
cnf(c_83,plain,
( ~ aInteger0(X0)
| smndt0(sz10) = X0
| X0 = sz10
| isPrime0(sK10(X0)) ),
inference(cnf_transformation,[],[f240]) ).
cnf(c_84,plain,
( ~ aInteger0(X0)
| smndt0(sz10) = X0
| X0 = sz10
| aDivisorOf0(sK10(X0),X0) ),
inference(cnf_transformation,[],[f239]) ).
cnf(c_85,plain,
( ~ aDivisorOf0(X0,smndt0(sz10))
| ~ aInteger0(smndt0(sz10))
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f366]) ).
cnf(c_86,plain,
( ~ aDivisorOf0(X0,sz10)
| ~ isPrime0(X0)
| ~ aInteger0(sz10) ),
inference(cnf_transformation,[],[f367]) ).
cnf(c_121,plain,
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,X2)
| ~ sP4(X2,X3)
| ~ aInteger0(X0)
| aElementOf0(X0,X3) ),
inference(cnf_transformation,[],[f275]) ).
cnf(c_123,plain,
( ~ aElementOf0(X0,X1)
| ~ sP4(X2,X1)
| aElementOf0(sK16(X2,X0),X2) ),
inference(cnf_transformation,[],[f273]) ).
cnf(c_143,plain,
( ~ aSubsetOf0(X0,cS1395)
| aElementOf0(sK20(X0),X0)
| isOpen0(X0) ),
inference(cnf_transformation,[],[f299]) ).
cnf(c_157,plain,
( sdtpldt0(X0,smndt0(sz00)) != sdtasdt0(X1,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X2)
| ~ sP7(X1)
| aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f314]) ).
cnf(c_159,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ sP7(X1)
| aDivisorOf0(X1,sdtpldt0(X0,smndt0(sz00))) ),
inference(cnf_transformation,[],[f312]) ).
cnf(c_167,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ sP6(X1)
| aDivisorOf0(X1,sdtpldt0(X0,smndt0(sz00))) ),
inference(cnf_transformation,[],[f320]) ).
cnf(c_170,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ sP6(X1)
| aInteger0(X0) ),
inference(cnf_transformation,[],[f317]) ).
cnf(c_171,plain,
( ~ aInteger0(X0)
| ~ isPrime0(X0)
| X0 = sz00
| aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X0),cS2043) ),
inference(cnf_transformation,[],[f379]) ).
cnf(c_172,plain,
( ~ aInteger0(X0)
| ~ isPrime0(X0)
| X0 = sz00
| aElementOf0(X1,cS2043)
| sP7(X0) ),
inference(cnf_transformation,[],[f351]) ).
cnf(c_173,plain,
( ~ aInteger0(X0)
| ~ isPrime0(X0)
| X0 = sz00
| aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| aElementOf0(X1,cS2043) ),
inference(cnf_transformation,[],[f352]) ).
cnf(c_174,plain,
( ~ aElementOf0(X0,cS2043)
| szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0 ),
inference(cnf_transformation,[],[f353]) ).
cnf(c_175,plain,
( ~ aElementOf0(X0,cS2043)
| sP6(sK25(X0)) ),
inference(cnf_transformation,[],[f354]) ).
cnf(c_177,plain,
( ~ aElementOf0(X0,cS2043)
| isPrime0(sK25(X0)) ),
inference(cnf_transformation,[],[f356]) ).
cnf(c_178,plain,
( sK25(X0) != sz00
| ~ aElementOf0(X0,cS2043) ),
inference(cnf_transformation,[],[f357]) ).
cnf(c_179,plain,
( ~ aElementOf0(X0,cS2043)
| aInteger0(sK25(X0)) ),
inference(cnf_transformation,[],[f358]) ).
cnf(c_181,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f336]) ).
cnf(c_183,plain,
( ~ aElementOf0(X0,cS2043)
| ~ aElementOf0(xn,X0)
| ~ sP8 ),
inference(cnf_transformation,[],[f361]) ).
cnf(c_184,plain,
( ~ sP8
| isPrime0(sK26) ),
inference(cnf_transformation,[],[f342]) ).
cnf(c_185,plain,
( ~ sP8
| aDivisorOf0(sK26,xn) ),
inference(cnf_transformation,[],[f341]) ).
cnf(c_186,plain,
( ~ sP8
| sdtasdt0(sK26,sK27) = xn ),
inference(cnf_transformation,[],[f340]) ).
cnf(c_187,plain,
( ~ sP8
| aInteger0(sK27) ),
inference(cnf_transformation,[],[f339]) ).
cnf(c_188,plain,
( sz00 != sK26
| ~ sP8 ),
inference(cnf_transformation,[],[f338]) ).
cnf(c_189,plain,
( ~ sP8
| aInteger0(sK26) ),
inference(cnf_transformation,[],[f337]) ).
cnf(c_190,negated_conjecture,
( ~ aDivisorOf0(X0,xn)
| ~ isPrime0(X0)
| sP8 ),
inference(cnf_transformation,[],[f349]) ).
cnf(c_191,negated_conjecture,
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ isPrime0(X0)
| X0 = sz00
| sP8 ),
inference(cnf_transformation,[],[f348]) ).
cnf(c_193,negated_conjecture,
( aElementOf0(xn,sK28)
| sP8 ),
inference(cnf_transformation,[],[f346]) ).
cnf(c_194,negated_conjecture,
( aElementOf0(sK28,cS2043)
| sP8 ),
inference(cnf_transformation,[],[f363]) ).
cnf(c_196,plain,
( ~ aInteger0(sz00)
| aInteger0(smndt0(sz00)) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_333,plain,
( ~ isPrime0(X0)
| ~ aDivisorOf0(X0,sz10) ),
inference(prop_impl_just,[status(thm)],[c_50,c_86]) ).
cnf(c_334,plain,
( ~ aDivisorOf0(X0,sz10)
| ~ isPrime0(X0) ),
inference(renaming,[status(thm)],[c_333]) ).
cnf(c_359,plain,
( ~ aElementOf0(X0,cS2043)
| sP6(sK25(X0)) ),
inference(prop_impl_just,[status(thm)],[c_175]) ).
cnf(c_373,plain,
( ~ sP8
| aDivisorOf0(sK26,xn) ),
inference(prop_impl_just,[status(thm)],[c_185]) ).
cnf(c_2881,plain,
( sK25(X0) != X1
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ aElementOf0(X0,cS2043)
| aInteger0(X2) ),
inference(resolution_lifted,[status(thm)],[c_170,c_359]) ).
cnf(c_2882,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X1)))
| ~ aElementOf0(X1,cS2043)
| aInteger0(X0) ),
inference(unflattening,[status(thm)],[c_2881]) ).
cnf(c_2916,plain,
( sK25(X0) != X1
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ aElementOf0(X0,cS2043)
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00))) ),
inference(resolution_lifted,[status(thm)],[c_167,c_359]) ).
cnf(c_2917,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X1)))
| ~ aElementOf0(X1,cS2043)
| aDivisorOf0(sK25(X1),sdtpldt0(X0,smndt0(sz00))) ),
inference(unflattening,[status(thm)],[c_2916]) ).
cnf(c_6340,plain,
( X0 != sK26
| X1 != xn
| ~ aInteger0(X1)
| ~ sP8
| aInteger0(sK9(X1,X0)) ),
inference(resolution_lifted,[status(thm)],[c_73,c_373]) ).
cnf(c_6341,plain,
( ~ aInteger0(xn)
| ~ sP8
| aInteger0(sK9(xn,sK26)) ),
inference(unflattening,[status(thm)],[c_6340]) ).
cnf(c_6778,plain,
( smndt0(sz10) != xn
| X0 != sK26
| ~ aInteger0(smndt0(sz10))
| ~ isPrime0(X0)
| ~ sP8 ),
inference(resolution_lifted,[status(thm)],[c_85,c_373]) ).
cnf(c_6779,plain,
( smndt0(sz10) != xn
| ~ aInteger0(smndt0(sz10))
| ~ isPrime0(sK26)
| ~ sP8 ),
inference(unflattening,[status(thm)],[c_6778]) ).
cnf(c_6780,plain,
( ~ aInteger0(smndt0(sz10))
| smndt0(sz10) != xn
| ~ sP8 ),
inference(global_subsumption_just,[status(thm)],[c_6779,c_184,c_6779]) ).
cnf(c_6781,plain,
( smndt0(sz10) != xn
| ~ aInteger0(smndt0(sz10))
| ~ sP8 ),
inference(renaming,[status(thm)],[c_6780]) ).
cnf(c_6825,plain,
( X0 != sK26
| sz10 != xn
| ~ isPrime0(X0)
| ~ sP8 ),
inference(resolution_lifted,[status(thm)],[c_334,c_373]) ).
cnf(c_6826,plain,
( sz10 != xn
| ~ isPrime0(sK26)
| ~ sP8 ),
inference(unflattening,[status(thm)],[c_6825]) ).
cnf(c_6827,plain,
( sz10 != xn
| ~ sP8 ),
inference(global_subsumption_just,[status(thm)],[c_6826,c_184,c_6826]) ).
cnf(c_13763,plain,
( aElementOf0(X0,cS2043)
| ~ sP0_iProver_split ),
inference(splitting,[splitting(split),new_symbols(definition,[sP0_iProver_split])],[c_173]) ).
cnf(c_13766,plain,
( sP7(X0)
| ~ isPrime0(X0)
| ~ aInteger0(X0)
| X0 = sz00
| ~ sP2_iProver_split ),
inference(splitting,[splitting(split),new_symbols(definition,[sP2_iProver_split])],[c_172]) ).
cnf(c_13767,plain,
( sP0_iProver_split
| sP2_iProver_split ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_172]) ).
cnf(c_17028,plain,
( ~ sP0_iProver_split
| isPrime0(sK25(X0)) ),
inference(superposition,[status(thm)],[c_13763,c_177]) ).
cnf(c_17029,plain,
( isPrime0(sK25(sK28))
| sP8 ),
inference(superposition,[status(thm)],[c_194,c_177]) ).
cnf(c_17040,plain,
( aInteger0(sK25(sK28))
| sP8 ),
inference(superposition,[status(thm)],[c_194,c_179]) ).
cnf(c_17128,plain,
sdtpldt0(xn,sz00) = xn,
inference(superposition,[status(thm)],[c_181,c_57]) ).
cnf(c_17706,plain,
sdtpldt0(sz00,smndt0(sz00)) = sz00,
inference(superposition,[status(thm)],[c_49,c_59]) ).
cnf(c_17946,plain,
( ~ aInteger0(sz10)
| aInteger0(smndt0(sz10)) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_17947,plain,
( ~ aDivisorOf0(sK25(X0),xn)
| ~ isPrime0(sK25(X0))
| sP8 ),
inference(instantiation,[status(thm)],[c_190]) ).
cnf(c_17949,plain,
( sK25(sK28) != sz00
| ~ aElementOf0(sK28,cS2043) ),
inference(instantiation,[status(thm)],[c_178]) ).
cnf(c_18146,plain,
( ~ aElementOf0(xn,X0)
| ~ sP8
| ~ sP0_iProver_split ),
inference(superposition,[status(thm)],[c_13763,c_183]) ).
cnf(c_18172,plain,
sdtasdt0(sz00,smndt0(sz10)) = smndt0(sz00),
inference(superposition,[status(thm)],[c_49,c_68]) ).
cnf(c_18814,plain,
( ~ aInteger0(sK25(sK28))
| ~ isPrime0(sK25(sK28))
| ~ sP2_iProver_split
| sK25(sK28) = sz00
| sP7(sK25(sK28)) ),
inference(instantiation,[status(thm)],[c_13766]) ).
cnf(c_19019,plain,
( ~ sP0_iProver_split
| szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0 ),
inference(superposition,[status(thm)],[c_13763,c_174]) ).
cnf(c_19020,plain,
( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(sK28)) = sK28
| sP8 ),
inference(superposition,[status(thm)],[c_194,c_174]) ).
cnf(c_19125,plain,
( ~ sP8
| ~ sP0_iProver_split ),
inference(superposition,[status(thm)],[c_13763,c_18146]) ).
cnf(c_19468,plain,
( ~ sP4(X0,cS2043)
| aElementOf0(sK16(X0,sK28),X0)
| sP8 ),
inference(superposition,[status(thm)],[c_194,c_123]) ).
cnf(c_19553,plain,
( ~ aInteger0(smndt0(sz10))
| ~ aInteger0(sz00)
| aInteger0(smndt0(sz00)) ),
inference(superposition,[status(thm)],[c_18172,c_53]) ).
cnf(c_19556,plain,
( ~ aInteger0(smndt0(sz10))
| aInteger0(smndt0(sz00)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19553,c_49]) ).
cnf(c_19559,plain,
aInteger0(smndt0(sz00)),
inference(global_subsumption_just,[status(thm)],[c_19556,c_49,c_196]) ).
cnf(c_19570,plain,
sdtpldt0(sz00,smndt0(sz00)) = smndt0(sz00),
inference(superposition,[status(thm)],[c_19559,c_56]) ).
cnf(c_19571,plain,
smndt0(sz00) = sz00,
inference(light_normalisation,[status(thm)],[c_19570,c_17706]) ).
cnf(c_24526,plain,
( ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ~ aInteger0(X0)
| ~ isPrime0(X0)
| ~ sP8
| X0 = sz00 ),
inference(superposition,[status(thm)],[c_171,c_183]) ).
cnf(c_24675,plain,
( ~ isPrime0(sK10(xn))
| ~ aInteger0(xn)
| smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(superposition,[status(thm)],[c_84,c_190]) ).
cnf(c_24680,plain,
( ~ isPrime0(sK10(xn))
| smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(forward_subsumption_resolution,[status(thm)],[c_24675,c_181]) ).
cnf(c_25227,plain,
( ~ aInteger0(xn)
| smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(superposition,[status(thm)],[c_83,c_24680]) ).
cnf(c_25228,plain,
( smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(forward_subsumption_resolution,[status(thm)],[c_25227,c_181]) ).
cnf(c_27763,plain,
( ~ aInteger0(sK16(X0,sK28))
| ~ aElementOf0(X0,X1)
| ~ sP4(X1,X2)
| ~ sP4(X0,cS2043)
| aElementOf0(sK16(X0,sK28),X2)
| sP8 ),
inference(superposition,[status(thm)],[c_19468,c_121]) ).
cnf(c_31963,plain,
( ~ aInteger0(sK16(xn,sK28))
| ~ sP4(sK28,X0)
| ~ sP4(xn,cS2043)
| aElementOf0(sK16(xn,sK28),X0)
| sP8 ),
inference(superposition,[status(thm)],[c_193,c_27763]) ).
cnf(c_33989,plain,
( ~ aInteger0(sK16(xn,sK28))
| ~ aElementOf0(X0,X1)
| ~ sP4(X1,X2)
| ~ sP4(sK28,X0)
| ~ sP4(xn,cS2043)
| aElementOf0(sK16(xn,sK28),X2)
| sP8 ),
inference(superposition,[status(thm)],[c_31963,c_121]) ).
cnf(c_41501,plain,
( sdtasdt0(X0,X1) != sdtpldt0(X2,sz00)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ sP7(X0)
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(light_normalisation,[status(thm)],[c_157,c_19571]) ).
cnf(c_41551,plain,
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X1)
| ~ sP7(X0)
| ~ aInteger0(xn)
| aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(superposition,[status(thm)],[c_17128,c_41501]) ).
cnf(c_41557,plain,
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X1)
| ~ sP7(X0)
| aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41551,c_181]) ).
cnf(c_48539,plain,
( ~ aDivisorOf0(sK25(sK28),xn)
| ~ isPrime0(sK25(sK28))
| sP8 ),
inference(instantiation,[status(thm)],[c_17947]) ).
cnf(c_97045,plain,
( X0 = sz00
| ~ isPrime0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| sdtasdt0(X0,X1) != xn ),
inference(global_subsumption_just,[status(thm)],[c_191,c_191,c_13766,c_13767,c_19125,c_24526,c_41557]) ).
cnf(c_97046,negated_conjecture,
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ isPrime0(X0)
| X0 = sz00 ),
inference(renaming,[status(thm)],[c_97045]) ).
cnf(c_97253,plain,
sdtpldt0(xn,sz00) = xn,
inference(superposition,[status(thm)],[c_181,c_57]) ).
cnf(c_97432,plain,
( ~ aInteger0(X0)
| sdtasdt0(smndt0(X0),sz00) = sz00 ),
inference(superposition,[status(thm)],[c_51,c_67]) ).
cnf(c_97702,plain,
sdtasdt0(smndt0(sz00),sz00) = sz00,
inference(superposition,[status(thm)],[c_49,c_97432]) ).
cnf(c_97729,plain,
( sz00 != xn
| ~ aInteger0(smndt0(sz00))
| ~ isPrime0(smndt0(sz00))
| ~ aInteger0(sz00)
| smndt0(sz00) = sz00 ),
inference(superposition,[status(thm)],[c_97702,c_97046]) ).
cnf(c_97730,plain,
( sz00 != xn
| ~ aInteger0(smndt0(sz00))
| ~ isPrime0(smndt0(sz00))
| smndt0(sz00) = sz00 ),
inference(forward_subsumption_resolution,[status(thm)],[c_97729,c_49]) ).
cnf(c_97792,plain,
smndt0(sz00) = sz00,
inference(global_subsumption_just,[status(thm)],[c_97730,c_19571]) ).
cnf(c_98081,plain,
( ~ aElementOf0(xn,sK20(cS2043))
| ~ aSubsetOf0(cS2043,cS1395)
| ~ sP8
| isOpen0(cS2043) ),
inference(superposition,[status(thm)],[c_143,c_183]) ).
cnf(c_98551,plain,
( szAzrzSzezqlpdtcmdtrp0(sz00,sK25(sK28)) = sK28
| sP8 ),
inference(superposition,[status(thm)],[c_194,c_174]) ).
cnf(c_100851,plain,
( ~ aInteger0(xn)
| ~ sP8
| sdtasdt0(sK26,sK9(xn,sK26)) = xn ),
inference(superposition,[status(thm)],[c_185,c_72]) ).
cnf(c_100852,plain,
( ~ sP8
| sdtasdt0(sK26,sK9(xn,sK26)) = xn ),
inference(forward_subsumption_resolution,[status(thm)],[c_100851,c_181]) ).
cnf(c_100875,plain,
( sdtasdt0(sK26,sK9(xn,sK26)) = xn
| szAzrzSzezqlpdtcmdtrp0(sz00,sK25(sK28)) = sK28 ),
inference(superposition,[status(thm)],[c_98551,c_100852]) ).
cnf(c_101657,plain,
( ~ aInteger0(sK9(xn,sK26))
| ~ aInteger0(sK26)
| ~ isPrime0(sK26)
| szAzrzSzezqlpdtcmdtrp0(sz00,sK25(sK28)) = sK28
| sz00 = sK26 ),
inference(superposition,[status(thm)],[c_100875,c_97046]) ).
cnf(c_101663,plain,
szAzrzSzezqlpdtcmdtrp0(sz00,sK25(sK28)) = sK28,
inference(global_subsumption_just,[status(thm)],[c_101657,c_181,c_189,c_184,c_188,c_6341,c_19020,c_101657]) ).
cnf(c_103770,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ sP7(X1)
| aDivisorOf0(X1,sdtpldt0(X0,sz00)) ),
inference(light_normalisation,[status(thm)],[c_159,c_97792]) ).
cnf(c_103788,plain,
( ~ aElementOf0(X0,sK28)
| ~ sP7(sK25(sK28))
| aDivisorOf0(sK25(sK28),sdtpldt0(X0,sz00)) ),
inference(superposition,[status(thm)],[c_101663,c_103770]) ).
cnf(c_103965,plain,
( ~ isPrime0(sK10(xn))
| ~ aInteger0(xn)
| smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(superposition,[status(thm)],[c_84,c_190]) ).
cnf(c_103970,plain,
( ~ isPrime0(sK10(xn))
| smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(forward_subsumption_resolution,[status(thm)],[c_103965,c_181]) ).
cnf(c_104395,plain,
( smndt0(sz10) = xn
| sz10 = xn
| sP8 ),
inference(global_subsumption_just,[status(thm)],[c_103970,c_25228]) ).
cnf(c_104409,plain,
( sdtasdt0(sK26,sK27) = xn
| smndt0(sz10) = xn
| sz10 = xn ),
inference(superposition,[status(thm)],[c_104395,c_186]) ).
cnf(c_104602,plain,
( ~ aInteger0(sK26)
| ~ aInteger0(sK27)
| ~ isPrime0(sK26)
| smndt0(sz10) = xn
| sz00 = sK26
| sz10 = xn ),
inference(superposition,[status(thm)],[c_104409,c_97046]) ).
cnf(c_105013,plain,
~ sP8,
inference(global_subsumption_just,[status(thm)],[c_98081,c_50,c_189,c_187,c_184,c_188,c_6781,c_6827,c_17946,c_104602]) ).
cnf(c_105085,plain,
aElementOf0(xn,sK28),
inference(backward_subsumption_resolution,[status(thm)],[c_193,c_105013]) ).
cnf(c_108398,plain,
( aElementOf0(sK16(xn,sK28),X2)
| ~ sP4(xn,cS2043)
| ~ sP4(sK28,X0)
| ~ sP4(X1,X2)
| ~ aElementOf0(X0,X1)
| ~ aInteger0(sK16(xn,sK28)) ),
inference(global_subsumption_just,[status(thm)],[c_33989,c_33989,c_105013]) ).
cnf(c_108399,plain,
( ~ aInteger0(sK16(xn,sK28))
| ~ aElementOf0(X0,X1)
| ~ sP4(X1,X2)
| ~ sP4(sK28,X0)
| ~ sP4(xn,cS2043)
| aElementOf0(sK16(xn,sK28),X2) ),
inference(renaming,[status(thm)],[c_108398]) ).
cnf(c_108440,plain,
( ~ aInteger0(sK16(xn,sK28))
| ~ sP4(sK28,X0)
| ~ sP4(xn,cS2043)
| ~ sP4(sK28,xn)
| aElementOf0(sK16(xn,sK28),X0)
| sP8 ),
inference(superposition,[status(thm)],[c_193,c_108399]) ).
cnf(c_109091,plain,
( aElementOf0(sK16(xn,sK28),X0)
| ~ aInteger0(sK16(xn,sK28))
| ~ sP4(sK28,X0)
| ~ sP4(xn,cS2043) ),
inference(global_subsumption_just,[status(thm)],[c_108440,c_31963,c_105013]) ).
cnf(c_109092,plain,
( ~ aInteger0(sK16(xn,sK28))
| ~ sP4(sK28,X0)
| ~ sP4(xn,cS2043)
| aElementOf0(sK16(xn,sK28),X0) ),
inference(renaming,[status(thm)],[c_109091]) ).
cnf(c_109122,plain,
( ~ aElementOf0(xn,sK16(xn,sK28))
| ~ aInteger0(sK16(xn,sK28))
| ~ sP4(xn,cS2043)
| ~ sP4(sK28,cS2043)
| ~ sP8 ),
inference(superposition,[status(thm)],[c_109092,c_183]) ).
cnf(c_111401,plain,
~ sP8,
inference(global_subsumption_just,[status(thm)],[c_109122,c_105013]) ).
cnf(c_111614,plain,
aElementOf0(xn,sK28),
inference(backward_subsumption_resolution,[status(thm)],[c_193,c_111401]) ).
cnf(c_111617,plain,
( ~ aDivisorOf0(X0,xn)
| ~ isPrime0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_190,c_111401]) ).
cnf(c_144749,plain,
( ~ aElementOf0(xn,sK28)
| ~ sP7(sK25(sK28))
| aDivisorOf0(sK25(sK28),xn) ),
inference(superposition,[status(thm)],[c_97253,c_103788]) ).
cnf(c_144752,plain,
( ~ sP7(sK25(sK28))
| aDivisorOf0(sK25(sK28),xn) ),
inference(forward_subsumption_resolution,[status(thm)],[c_144749,c_105085]) ).
cnf(c_195833,plain,
~ sP2_iProver_split,
inference(global_subsumption_just,[status(thm)],[c_13766,c_50,c_194,c_189,c_187,c_184,c_188,c_6781,c_6827,c_17029,c_17040,c_17946,c_17949,c_18814,c_48539,c_104602,c_144752]) ).
cnf(c_195835,plain,
sP0_iProver_split,
inference(backward_subsumption_resolution,[status(thm)],[c_13767,c_195833]) ).
cnf(c_195858,plain,
szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X0)) = X0,
inference(backward_subsumption_resolution,[status(thm)],[c_19019,c_195835]) ).
cnf(c_195871,plain,
isPrime0(sK25(X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_17028,c_195835]) ).
cnf(c_195872,plain,
aElementOf0(X0,cS2043),
inference(backward_subsumption_resolution,[status(thm)],[c_13763,c_195835]) ).
cnf(c_195905,plain,
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,cS2043)
| aInteger0(X0) ),
inference(demodulation,[status(thm)],[c_2882,c_195858]) ).
cnf(c_195913,plain,
( ~ aElementOf0(X0,X1)
| aInteger0(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_195905,c_195872]) ).
cnf(c_196873,plain,
aInteger0(X0),
inference(superposition,[status(thm)],[c_195872,c_195913]) ).
cnf(c_197033,plain,
sdtpldt0(X0,sz00) = X0,
inference(backward_subsumption_resolution,[status(thm)],[c_57,c_196873]) ).
cnf(c_241845,plain,
( ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,sK25(X1)))
| ~ aElementOf0(X1,cS2043)
| aDivisorOf0(sK25(X1),X0) ),
inference(light_normalisation,[status(thm)],[c_2917,c_19571,c_197033]) ).
cnf(c_241846,plain,
( ~ aElementOf0(X0,X1)
| ~ aElementOf0(X1,cS2043)
| aDivisorOf0(sK25(X1),X0) ),
inference(demodulation,[status(thm)],[c_241845,c_195858]) ).
cnf(c_241847,plain,
( ~ aElementOf0(X0,X1)
| aDivisorOf0(sK25(X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_241846,c_195872]) ).
cnf(c_241856,plain,
( ~ isPrime0(sK25(X0))
| ~ aElementOf0(xn,X0) ),
inference(superposition,[status(thm)],[c_241847,c_111617]) ).
cnf(c_241861,plain,
~ aElementOf0(xn,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_241856,c_195871]) ).
cnf(c_241875,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_111614,c_241861]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM447+5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 15:50:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 43.59/6.72 % SZS status Started for theBenchmark.p
% 43.59/6.72 % SZS status Theorem for theBenchmark.p
% 43.59/6.72
% 43.59/6.72 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 43.59/6.72
% 43.59/6.72 ------ iProver source info
% 43.59/6.72
% 43.59/6.72 git: date: 2023-05-31 18:12:56 +0000
% 43.59/6.72 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 43.59/6.72 git: non_committed_changes: false
% 43.59/6.72 git: last_make_outside_of_git: false
% 43.59/6.72
% 43.59/6.72 ------ Parsing...
% 43.59/6.72 ------ Clausification by vclausify_rel & Parsing by iProver...
% 43.59/6.72
% 43.59/6.72 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 43.59/6.72
% 43.59/6.72 ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e
% 43.59/6.72
% 43.59/6.72 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 43.59/6.72 ------ Proving...
% 43.59/6.72 ------ Problem Properties
% 43.59/6.72
% 43.59/6.72
% 43.59/6.72 clauses 146
% 43.59/6.72 conjectures 5
% 43.59/6.72 EPR 38
% 43.59/6.72 Horn 99
% 43.59/6.72 unary 4
% 43.59/6.72 binary 36
% 43.59/6.72 lits 516
% 43.59/6.72 lits eq 67
% 43.59/6.72 fd_pure 0
% 43.59/6.72 fd_pseudo 0
% 43.59/6.72 fd_cond 22
% 43.59/6.72 fd_pseudo_cond 9
% 43.59/6.72 AC symbols 0
% 43.59/6.72
% 43.59/6.72 ------ Schedule dynamic 5 is on
% 43.59/6.72
% 43.59/6.72 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 43.59/6.72
% 43.59/6.72
% 43.59/6.72 ------
% 43.59/6.72 Current options:
% 43.59/6.72 ------
% 43.59/6.72
% 43.59/6.72
% 43.59/6.72
% 43.59/6.72
% 43.59/6.72 ------ Proving...
% 43.59/6.72
% 43.59/6.72
% 43.59/6.72 % SZS status Theorem for theBenchmark.p
% 43.59/6.72
% 43.59/6.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 43.59/6.73
% 43.59/6.73
%------------------------------------------------------------------------------