%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM447+5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n013.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 : Fri Sep 25 02:24:29 PM UTC 2026
% Result : Theorem 63.16s 12.39s
% Output : CNFRefutation 82.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 17
% Syntax : Number of formulae : 264 ( 39 unt; 3 def)
% Number of atoms : 1165 ( 290 equ)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 1439 ( 538 ~; 515 |; 350 &)
% ( 6 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 4 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-2 aty)
% Number of variables : 357 ( 0 sgn 283 !; 74 ?; 109 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(f3,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X1)
& aInteger0(X0) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(f9,axiom,
! [X0] :
( aInteger0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(f10,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtpldt0(smndt0(X0),X0)
& sdtpldt0(X0,smndt0(X0)) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(f15,axiom,
! [X0] :
( aInteger0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(f16,axiom,
! [X0] :
( aInteger0(X0)
=> ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),X0) = smndt0(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(f25,axiom,
! [X0] :
( aInteger0(X0)
=> ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
<=> ( X0 != smndt0(sz10)
& X0 != sz10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimeDivisor) ).
fof(f35,axiom,
! [X0] :
( aSubsetOf0(X0,cS1395)
=> ( isOpen0(X0)
<=> ! [X1] :
( aElementOf0(X1,X0)
=> ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
& X2 != sz00
& aInteger0(X2) ) ) ) ),
file('/export/starexec/sandbox2/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)
& X1 != sz00
& 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)
& X1 != sz00
& aInteger0(X1) ) ) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2046) ).
fof(f43,axiom,
aInteger0(xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2106) ).
fof(f44,conjecture,
( ( ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& X0 != sz00
& 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) )
& X0 != sz00
& aInteger0(X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f45,negated_conjecture,
~ ( ( ? [X0] :
( isPrime0(X0)
& aDivisorOf0(X0,xn)
& ? [X1] :
( sdtasdt0(X0,X1) = xn
& aInteger0(X1) )
& X0 != sz00
& 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) )
& X0 != sz00
& aInteger0(X0) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f46,plain,
( xS = cS2043
& ! [X0] :
( ( ? [X5] :
( ( ( ! [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)) )
& ( aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
=> ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X7] :
( sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00))
& aInteger0(X7) )
& aInteger0(X6) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5)) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X5) = X0 )
& isPrime0(X5)
& sz00 != X5
& aInteger0(X5) )
=> aElementOf0(X0,xS) )
& ( aElementOf0(X0,xS)
=> ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& ! [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)) )
& ( 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)
& X1 != sz00
& aInteger0(X1) ) ) )
& aSet0(xS) ),
inference(rectify,[],[f42]) ).
fof(f47,plain,
~ ( ( ? [X3] :
( isPrime0(X3)
& aDivisorOf0(X3,xn)
& ? [X4] :
( xn = sdtasdt0(X3,X4)
& aInteger0(X4) )
& sz00 != X3
& aInteger0(X3) )
=> ( aElementOf0(xn,sbsmnsldt0(xS))
| ? [X5] :
( aElementOf0(xn,X5)
& aElementOf0(X5,xS) ) ) )
& ( ( 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) ) ) ) ) ),
inference(rectify,[],[f45]) ).
fof(f54,plain,
( xS = cS2043
& ! [X0] :
( ( ! [X5] :
( ( ! [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)) )
& ( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X7] :
( sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00))
& aInteger0(X7) )
& aInteger0(X6) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& szAzrzSzezqlpdtcmdtrp0(sz00,X5) != X0 )
| ~ isPrime0(X5)
| sz00 = X5
| ~ aInteger0(X5) )
| aElementOf0(X0,xS) )
& ( ~ aElementOf0(X0,xS)
| ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& ! [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)) )
& ( ~ 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)
& X1 != sz00
& aInteger0(X1) ) ) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f46]) ).
fof(f55,plain,
( xS = cS2043
& ! [X0] :
( ( ! [X5] :
( ( ! [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)) )
& ( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X7] :
( sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00))
& aInteger0(X7) )
& aInteger0(X6) ) ) )
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& szAzrzSzezqlpdtcmdtrp0(sz00,X5) != X0 )
| ~ isPrime0(X5)
| sz00 = X5
| ~ aInteger0(X5) )
| aElementOf0(X0,xS) )
& ( ~ aElementOf0(X0,xS)
| ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& ! [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)) )
& ( ~ 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)
& X1 != sz00
& aInteger0(X1) ) ) )
& aSet0(xS) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ( ? [X3] :
( isPrime0(X3)
& aDivisorOf0(X3,xn)
& ? [X4] :
( xn = sdtasdt0(X3,X4)
& aInteger0(X4) )
& sz00 != X3
& aInteger0(X3) )
& ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X5] :
( ~ aElementOf0(xn,X5)
| ~ aElementOf0(X5,xS) ) )
| ( 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) ) ) ) ) ),
inference(ennf_transformation,[],[f47]) ).
fof(f57,plain,
( ( ? [X3] :
( isPrime0(X3)
& aDivisorOf0(X3,xn)
& ? [X4] :
( xn = sdtasdt0(X3,X4)
& aInteger0(X4) )
& sz00 != X3
& aInteger0(X3) )
& ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X5] :
( ~ aElementOf0(xn,X5)
| ~ aElementOf0(X5,xS) ) )
| ( 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) ) ) ) ) ),
inference(flattening,[],[f56]) ).
fof(f60,plain,
! [X0] :
( ~ aInteger0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f61,plain,
! [X0] :
( ~ aInteger0(X0)
| ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) )
<=> ( X0 != smndt0(sz10)
& X0 != sz10 ) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f64,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f65,plain,
! [X0] :
( ~ aInteger0(X0)
| ( smndt0(X0) = sdtasdt0(X0,smndt0(sz10))
& sdtasdt0(smndt0(sz10),X0) = smndt0(X0) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f66,plain,
! [X0] :
( ~ aInteger0(X0)
| ( sz00 = sdtpldt0(smndt0(X0),X0)
& sdtpldt0(X0,smndt0(X0)) = sz00 ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f67,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f78,plain,
! [X0] :
( ~ aInteger0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f89,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f90,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f89]) ).
fof(f94,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ( isOpen0(X0)
<=> ! [X1] :
( ~ aElementOf0(X1,X0)
| ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
& X2 != sz00
& aInteger0(X2) ) ) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f110,plain,
! [X1] :
( ~ sP1(X1)
| ! [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)) )
& ( ~ 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) ) ) ) ),
inference(nnf_transformation,[],[f103]) ).
fof(f111,plain,
! [X0] :
( ~ sP1(X0)
| ! [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)) )
& ( ~ 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) ) ) ) ),
inference(rectify,[],[f110]) ).
fof(f112,plain,
! [X0] :
( ~ sP1(X0)
| ! [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)) )
& ( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK5(X0,X1))
& aInteger0(sK5(X0,X1))
& aInteger0(X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f111]) ).
fof(f116,plain,
( xS = cS2043
& ! [X0] :
( ( ! [X2] :
( ( sP0(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0 )
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2) )
| aElementOf0(X0,xS) )
& ( ~ aElementOf0(X0,xS)
| ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& sP1(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& isPrime0(X1)
& X1 != sz00
& aInteger0(X1) ) ) )
& aSet0(xS) ),
inference(rectify,[],[f104]) ).
fof(f117,plain,
( xS = cS2043
& ! [X0] :
( ( ! [X2] :
( ( sP0(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0 )
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2) )
| aElementOf0(X0,xS) )
& ( ~ aElementOf0(X0,xS)
| ( szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X0)) = X0
& sP1(sK7(X0))
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X0)))
& isPrime0(sK7(X0))
& sz00 != sK7(X0)
& aInteger0(sK7(X0)) ) ) )
& aSet0(xS) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X1,sK7(X0))],[f116]) ).
fof(f121,plain,
( sP2
| ( 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) ) ) ) ) ),
inference(rectify,[],[f106]) ).
fof(f122,plain,
( sP2
| ( aElementOf0(xn,sbsmnsldt0(xS))
& aElementOf0(xn,sK10)
& aElementOf0(sK10,xS)
& ! [X0] :
( ~ isPrime0(X0)
| ( ~ aDivisorOf0(X0,xn)
& ( ! [X1] :
( sdtasdt0(X0,X1) != xn
| ~ aInteger0(X1) )
| sz00 = X0
| ~ aInteger0(X0) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10)],[f121]) ).
fof(f123,plain,
! [X0] :
( ~ aInteger0(X0)
| ( ( ! [X1] :
( ~ isPrime0(X1)
| ~ aDivisorOf0(X1,X0) )
| ( X0 != smndt0(sz10)
& X0 != sz10 ) )
& ( smndt0(sz10) = X0
| sz10 = X0
| ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f124,plain,
! [X0] :
( ~ aInteger0(X0)
| ( ( ! [X1] :
( ~ isPrime0(X1)
| ~ aDivisorOf0(X1,X0) )
| ( X0 != smndt0(sz10)
& X0 != sz10 ) )
& ( smndt0(sz10) = X0
| sz10 = X0
| ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) ) ) ) ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
! [X0] :
( ~ aInteger0(X0)
| ( ( ! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0) )
| ( X0 != smndt0(sz10)
& X0 != sz10 ) )
& ( smndt0(sz10) = X0
| sz10 = X0
| ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,X0) ) ) ) ),
inference(rectify,[],[f124]) ).
fof(f126,plain,
! [X0] :
( ~ aInteger0(X0)
| ( ( ! [X2] :
( ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0) )
| ( X0 != smndt0(sz10)
& X0 != sz10 ) )
& ( smndt0(sz10) = X0
| sz10 = X0
| ( isPrime0(sK11(X0))
& aDivisorOf0(sK11(X0),X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X1,sK11(X0))],[f125]) ).
fof(f128,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f129,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( ? [X2] :
( sdtasdt0(X1,X2) = X0
& aInteger0(X2) )
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(flattening,[],[f128]) ).
fof(f130,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( ? [X3] :
( sdtasdt0(X1,X3) = X0
& aInteger0(X3) )
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(rectify,[],[f129]) ).
fof(f131,plain,
! [X0] :
( ~ aInteger0(X0)
| ! [X1] :
( ( ~ aDivisorOf0(X1,X0)
| ( sdtasdt0(X1,sK12(X0,X1)) = X0
& aInteger0(sK12(X0,X1))
& X1 != sz00
& aInteger0(X1) ) )
& ( ! [X2] :
( sdtasdt0(X1,X2) != X0
| ~ aInteger0(X2) )
| sz00 = X1
| ~ aInteger0(X1)
| aDivisorOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X3,sK12(X0,X1))],[f130]) ).
fof(f136,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ( ( ~ isOpen0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| ? [X2] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
& X2 != sz00
& aInteger0(X2) ) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ! [X2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
| sz00 = X2
| ~ aInteger0(X2) ) )
| isOpen0(X0) ) ) ),
inference(nnf_transformation,[],[f94]) ).
fof(f137,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ( ( ~ isOpen0(X0)
| ! [X3] :
( ~ aElementOf0(X3,X0)
| ? [X4] :
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,X4),X0)
& sz00 != X4
& aInteger0(X4) ) ) )
& ( ? [X1] :
( aElementOf0(X1,X0)
& ! [X2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),X0)
| sz00 = X2
| ~ aInteger0(X2) ) )
| isOpen0(X0) ) ) ),
inference(rectify,[],[f136]) ).
fof(f138,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| ( ( ~ isOpen0(X0)
| ! [X3] :
( ~ aElementOf0(X3,X0)
| ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X3,sK15(X0,X3)),X0)
& sz00 != sK15(X0,X3)
& aInteger0(sK15(X0,X3)) ) ) )
& ( ( aElementOf0(sK14(X0),X0)
& ! [X2] :
( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sK14(X0),X2),X0)
| sz00 = X2
| ~ aInteger0(X2) ) )
| isOpen0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X1,sK14(X0)),skolemize(X4,sK15(X0,X3))],[f137]) ).
fof(f155,plain,
! [X0,X1] :
( ~ sP1(X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00))) ),
inference(cnf_transformation,[],[f112]) ).
fof(f158,plain,
! [X0,X1] :
( ~ sP1(X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| aInteger0(X1) ),
inference(cnf_transformation,[],[f112]) ).
fof(f167,plain,
xS = cS2043,
inference(cnf_transformation,[],[f117]) ).
fof(f168,plain,
! [X2,X0] :
( sP0(X2)
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f117]) ).
fof(f170,plain,
! [X2,X0] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2)
| aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f117]) ).
fof(f171,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X0)) = X0 ),
inference(cnf_transformation,[],[f117]) ).
fof(f172,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| sP1(sK7(X0)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f174,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| isPrime0(sK7(X0)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f175,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| sz00 != sK7(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f176,plain,
! [X0] :
( ~ aElementOf0(X0,xS)
| aInteger0(sK7(X0)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f178,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f43]) ).
fof(f187,plain,
( sP2
| aElementOf0(xn,sbsmnsldt0(xS)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f188,plain,
( sP2
| aElementOf0(xn,sK10) ),
inference(cnf_transformation,[],[f122]) ).
fof(f189,plain,
( sP2
| aElementOf0(sK10,xS) ),
inference(cnf_transformation,[],[f122]) ).
fof(f190,plain,
! [X0] :
( sP2
| ~ isPrime0(X0)
| ~ aDivisorOf0(X0,xn) ),
inference(cnf_transformation,[],[f122]) ).
fof(f191,plain,
! [X0,X1] :
( sP2
| ~ isPrime0(X0)
| sdtasdt0(X0,X1) != xn
| ~ aInteger0(X1)
| sz00 = X0
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f194,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f60]) ).
fof(f195,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f196,plain,
! [X2,X0] :
( ~ aInteger0(X0)
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0)
| smndt0(sz10) != X0 ),
inference(cnf_transformation,[],[f126]) ).
fof(f197,plain,
! [X2,X0] :
( ~ aInteger0(X0)
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,X0)
| sz10 != X0 ),
inference(cnf_transformation,[],[f126]) ).
fof(f198,plain,
! [X0] :
( ~ aInteger0(X0)
| smndt0(sz10) = X0
| sz10 = X0
| isPrime0(sK11(X0)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f199,plain,
! [X0] :
( ~ aInteger0(X0)
| smndt0(sz10) = X0
| sz10 = X0
| aDivisorOf0(sK11(X0),X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f202,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| sdtasdt0(X1,sK12(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f131]) ).
fof(f203,plain,
! [X0,X1] :
( ~ aInteger0(X0)
| ~ aDivisorOf0(X1,X0)
| aInteger0(sK12(X0,X1)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f208,plain,
! [X0] :
( ~ aInteger0(X0)
| smndt0(X0) = sdtasdt0(smndt0(sz10),X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f209,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtpldt0(smndt0(X0),X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f210,plain,
! [X0] :
( ~ aInteger0(X0)
| sz00 = sdtpldt0(X0,smndt0(X0)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f211,plain,
! [X0] :
( ~ aInteger0(X0)
| aInteger0(smndt0(X0)) ),
inference(cnf_transformation,[],[f67]) ).
fof(f219,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f78]) ).
fof(f220,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtpldt0(X0,sz00) = X0 ),
inference(cnf_transformation,[],[f78]) ).
fof(f226,plain,
! [X0,X1] :
( ~ aInteger0(X1)
| ~ aInteger0(X0)
| aInteger0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f235,plain,
! [X0] :
( ~ aSubsetOf0(X0,cS1395)
| aElementOf0(sK14(X0),X0)
| isOpen0(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f261,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f263,plain,
! [X0] :
( ~ aElementOf0(X0,cS2043)
| aInteger0(sK7(X0)) ),
inference(definition_unfolding,[],[f176,f167]) ).
fof(f264,plain,
! [X0] :
( ~ aElementOf0(X0,cS2043)
| sz00 != sK7(X0) ),
inference(definition_unfolding,[],[f175,f167]) ).
fof(f265,plain,
! [X0] :
( ~ aElementOf0(X0,cS2043)
| isPrime0(sK7(X0)) ),
inference(definition_unfolding,[],[f174,f167]) ).
fof(f267,plain,
! [X0] :
( ~ aElementOf0(X0,cS2043)
| sP1(sK7(X0)) ),
inference(definition_unfolding,[],[f172,f167]) ).
fof(f268,plain,
! [X0] :
( ~ aElementOf0(X0,cS2043)
| szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X0)) = X0 ),
inference(definition_unfolding,[],[f171,f167]) ).
fof(f269,plain,
! [X2,X0] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X2) != X0
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2)
| aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f170,f167]) ).
fof(f271,plain,
! [X2,X0] :
( sP0(X2)
| ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2)
| aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f168,f167]) ).
fof(f274,plain,
( sP2
| aElementOf0(sK10,cS2043) ),
inference(definition_unfolding,[],[f189,f167]) ).
fof(f275,plain,
( sP2
| aElementOf0(xn,sbsmnsldt0(cS2043)) ),
inference(definition_unfolding,[],[f187,f167]) ).
fof(f276,plain,
! [X2] :
( ~ isPrime0(X2)
| sz00 = X2
| ~ aInteger0(X2)
| aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X2),cS2043) ),
inference(equality_resolution,[],[f269]) ).
fof(f277,plain,
! [X2] :
( ~ aInteger0(sz10)
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,sz10) ),
inference(equality_resolution,[],[f197]) ).
fof(f278,plain,
! [X2] :
( ~ aInteger0(smndt0(sz10))
| ~ isPrime0(X2)
| ~ aDivisorOf0(X2,smndt0(sz10)) ),
inference(equality_resolution,[],[f196]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aInteger0(X0)
| ~ sP1(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X1,sdtpldt0(X0,smndt0(sz00)))
| ~ sP1(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_66,plain,
! [X0: $i] :
( aInteger0(sK7(X0))
| ~ aElementOf0(X0,cS2043) ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_67,plain,
! [X0: $i] :
( ~ aElementOf0(X0,cS2043)
| ( sK7(X0) != sz00 ) ),
inference(cnf_transformation,[],[f264]) ).
tcf(c_68,plain,
! [X0: $i] :
( isPrime0(sK7(X0))
| ~ aElementOf0(X0,cS2043) ),
inference(cnf_transformation,[],[f265]) ).
tcf(c_70,plain,
! [X0: $i] :
( sP1(sK7(X0))
| ~ aElementOf0(X0,cS2043) ),
inference(cnf_transformation,[],[f267]) ).
tcf(c_71,plain,
! [X0: $i] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X0)) = X0 )
| ~ aElementOf0(X0,cS2043) ),
inference(cnf_transformation,[],[f268]) ).
tcf(c_72,plain,
! [X0: $i] :
( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X0),cS2043)
| ( X0 = sz00 )
| ~ isPrime0(X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f276]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( sP0(X0)
| aElementOf0(X1,cS2043)
| ( X0 = sz00 )
| ~ isPrime0(X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f271]) ).
tcf(c_75,plain,
aInteger0(xn),
inference(cnf_transformation,[],[f178]) ).
tcf(c_84,negated_conjecture,
! [X0: $i,X1: $i] :
( sP2
| ( X0 = sz00 )
| ~ isPrime0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdtasdt0(X0,X1) != xn ) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_85,negated_conjecture,
! [X0: $i] :
( sP2
| ~ isPrime0(X0)
| ~ aDivisorOf0(X0,xn) ),
inference(cnf_transformation,[],[f190]) ).
tcf(c_86,negated_conjecture,
( sP2
| aElementOf0(sK10,cS2043) ),
inference(cnf_transformation,[],[f274]) ).
tcf(c_87,negated_conjecture,
( sP2
| aElementOf0(xn,sK10) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_88,negated_conjecture,
( sP2
| aElementOf0(xn,sbsmnsldt0(cS2043)) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_90,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f194]) ).
tcf(c_92,plain,
aInteger0(sz00),
inference(cnf_transformation,[],[f195]) ).
tcf(c_93,plain,
! [X0: $i] :
( aDivisorOf0(sK11(X0),X0)
| ( X0 = sz10 )
| ( smndt0(sz10) = X0 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_94,plain,
! [X0: $i] :
( isPrime0(sK11(X0))
| ( X0 = sz10 )
| ( smndt0(sz10) = X0 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_95,plain,
! [X0: $i] :
( ~ aInteger0(sz10)
| ~ isPrime0(X0)
| ~ aDivisorOf0(X0,sz10) ),
inference(cnf_transformation,[],[f277]) ).
tcf(c_96,plain,
! [X0: $i] :
( ~ isPrime0(X0)
| ~ aInteger0(smndt0(sz10))
| ~ aDivisorOf0(X0,smndt0(sz10)) ),
inference(cnf_transformation,[],[f278]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( aInteger0(sK12(X1,X0))
| ~ aInteger0(X1)
| ~ aDivisorOf0(X0,X1) ),
inference(cnf_transformation,[],[f203]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,sK12(X1,X0)) = X1 )
| ~ aInteger0(X1)
| ~ aDivisorOf0(X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_104,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(sz10),X0) = smndt0(X0) )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_106,plain,
! [X0: $i] :
( ( sdtpldt0(X0,smndt0(X0)) = sz00 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_107,plain,
! [X0: $i] :
( ( sdtpldt0(smndt0(X0),X0) = sz00 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_108,plain,
! [X0: $i] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_116,plain,
! [X0: $i] :
( ( sdtpldt0(X0,sz00) = X0 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_117,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_123,plain,
! [X0: $i,X1: $i] :
( aInteger0(sdtasdt0(X1,X0))
| ~ aInteger0(X1)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_130,plain,
! [X0: $i] :
( isOpen0(X0)
| aElementOf0(sK14(X0),X0)
| ~ aSubsetOf0(X0,cS1395) ),
inference(cnf_transformation,[],[f235]) ).
tcf(c_158,plain,
aInteger0(sz10),
inference(cnf_transformation,[],[f261]) ).
tcf(c_160,plain,
( aInteger0(smndt0(sz00))
| ~ aInteger0(sz00) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_277,plain,
! [X0: $i] :
( sP1(sK7(X0))
| ~ aElementOf0(X0,cS2043) ),
inference(prop_impl_just,[status(thm)],[c_70]) ).
tcf(c_283,plain,
! [X0: $i] :
( ~ aDivisorOf0(X0,sz10)
| ~ isPrime0(X0) ),
inference(prop_impl_just,[status(thm)],[c_158,c_95]) ).
tcf(c_284,plain,
! [X0: $i] :
( ~ isPrime0(X0)
| ~ aDivisorOf0(X0,sz10) ),
inference(renaming,[status(thm)],[c_283]) ).
tcf(c_2168,plain,
! [X0: $i,X1: $i,X2: $i] :
( aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz00)))
| ~ aElementOf0(X0,cS2043)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ( sK7(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_277]) ).
tcf(c_2169,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(sK7(X1),sdtpldt0(X0,smndt0(sz00)))
| ~ aElementOf0(X1,cS2043)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X1))) ),
inference(unflattening,[status(thm)],[c_2168]) ).
tcf(c_2204,plain,
! [X0: $i,X1: $i,X2: $i] :
( aInteger0(X2)
| ~ aElementOf0(X0,cS2043)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ( sK7(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_277]) ).
tcf(c_2205,plain,
! [X0: $i,X1: $i] :
( aInteger0(X0)
| ~ aElementOf0(X1,cS2043)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X1))) ),
inference(unflattening,[status(thm)],[c_2204]) ).
tcf(c_9814,plain,
! [X0: $i] :
( ~ iPr_def_10
| aElementOf0(X0,cS2043) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_74]) ).
tcf(c_9815,plain,
! [X0: $i] :
( ~ iPr_def_11
| ( X0 = sz00 )
| ~ aInteger0(X0)
| sP0(X0)
| ~ isPrime0(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_74]) ).
tcf(c_9816,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_74]) ).
tcf(c_11094,plain,
! [X0: $i] :
( ~ iPr_def_10
| aElementOf0(X0,cS2043) ),
inference(prop_impl_just,[status(thm)],[c_9814]) ).
tcf(c_11095,plain,
! [X0: $i] :
( aElementOf0(X0,cS2043)
| ~ iPr_def_10 ),
inference(renaming,[status(thm)],[c_11094]) ).
tcf(c_12341,plain,
( sP2
| aInteger0(sK7(sK10)) ),
inference(superposition,[status(thm)],[c_86,c_66]) ).
tcf(c_12359,plain,
! [X0: $i] :
( isPrime0(sK7(X0))
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_9814,c_68]) ).
tcf(c_12360,plain,
( sP2
| isPrime0(sK7(sK10)) ),
inference(superposition,[status(thm)],[c_86,c_68]) ).
tcf(c_12431,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(X0),sz00) = sz00 )
| ~ aInteger0(X0) ),
inference(superposition,[status(thm)],[c_108,c_90]) ).
tcf(c_12551,plain,
sdtpldt0(xn,sz00) = xn,
inference(superposition,[status(thm)],[c_75,c_116]) ).
tcf(c_12907,plain,
sdtpldt0(smndt0(sz00),sz00) = sz00,
inference(superposition,[status(thm)],[c_92,c_107]) ).
tcf(c_13052,plain,
( ~ aElementOf0(sK10,cS2043)
| ( sK7(sK10) != sz00 ) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_13055,plain,
( aInteger0(smndt0(sz10))
| ~ aInteger0(sz10) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_13387,plain,
! [X0: $i] :
( ( szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X0)) = X0 )
| ~ iPr_def_10 ),
inference(superposition,[status(thm)],[c_9814,c_71]) ).
tcf(c_13388,plain,
( sP2
| ( szAzrzSzezqlpdtcmdtrp0(sz00,sK7(sK10)) = sK10 ) ),
inference(superposition,[status(thm)],[c_86,c_71]) ).
tcf(c_13611,plain,
( sP0(sK7(sK10))
| ( sK7(sK10) = sz00 )
| ~ iPr_def_11
| ~ isPrime0(sK7(sK10))
| ~ aInteger0(sK7(sK10)) ),
inference(instantiation,[status(thm)],[c_9815]) ).
tcf(c_13756,plain,
sdtasdt0(smndt0(sz10),sz00) = smndt0(sz00),
inference(superposition,[status(thm)],[c_92,c_104]) ).
tcf(c_16745,plain,
( aInteger0(smndt0(sz00))
| ~ aInteger0(sz00)
| ~ aInteger0(smndt0(sz10)) ),
inference(superposition,[status(thm)],[c_13756,c_123]) ).
tcf(c_16748,plain,
( aInteger0(smndt0(sz00))
| ~ aInteger0(smndt0(sz10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16745,c_92]) ).
tcf(c_17349,plain,
aInteger0(smndt0(sz00)),
inference(global_subsumption_just,[status(thm)],[c_16748,c_92,c_160]) ).
tcf(c_17361,plain,
sdtpldt0(smndt0(sz00),sz00) = smndt0(sz00),
inference(superposition,[status(thm)],[c_17349,c_116]) ).
tcf(c_17364,plain,
smndt0(sz00) = sz00,
inference(light_normalisation,[status(thm)],[c_17361,c_12907]) ).
tcf(c_19348,plain,
( sP2
| ( xn = sz10 )
| ( smndt0(sz10) = xn )
| ~ aInteger0(xn)
| ~ isPrime0(sK11(xn)) ),
inference(superposition,[status(thm)],[c_93,c_85]) ).
tcf(c_19357,plain,
( sP2
| ( xn = sz10 )
| ( smndt0(sz10) = xn )
| ~ isPrime0(sK11(xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19348,c_75]) ).
tcf(c_19754,plain,
( sP2
| ( xn = sz10 )
| ( smndt0(sz10) = xn )
| ~ aInteger0(xn) ),
inference(superposition,[status(thm)],[c_94,c_19357]) ).
tcf(c_19755,plain,
( sP2
| ( xn = sz10 )
| ( smndt0(sz10) = xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19754,c_75]) ).
tcf(c_30788,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(smndt0(X0)),sz00) = sz00 )
| ~ aInteger0(X0) ),
inference(superposition,[status(thm)],[c_108,c_12431]) ).
tcf(c_64671,plain,
! [X0: $i] :
( ( sdtasdt0(smndt0(X0),sz00) = sz00 )
| ~ aInteger0(X0) ),
inference(superposition,[status(thm)],[c_108,c_90]) ).
tcf(c_64717,plain,
sdtasdt0(smndt0(sz00),sz00) = sz00,
inference(superposition,[status(thm)],[c_92,c_64671]) ).
tcf(c_64765,plain,
sdtpldt0(xn,sz00) = xn,
inference(superposition,[status(thm)],[c_75,c_116]) ).
tcf(c_65613,plain,
( sP2
| ( szAzrzSzezqlpdtcmdtrp0(sz00,sK7(sK10)) = sK10 ) ),
inference(superposition,[status(thm)],[c_86,c_71]) ).
tcf(c_65922,plain,
! [X0: $i] :
( ~ isPrime0(X0)
| ~ aDivisorOf0(X0,smndt0(sz10)) ),
inference(global_subsumption_just,[status(thm)],[c_96,c_158,c_96,c_13055]) ).
tcf(c_69083,plain,
( sP2
| ( xn = sz10 )
| ( smndt0(sz10) = xn )
| ~ aInteger0(xn)
| ~ isPrime0(sK11(xn)) ),
inference(superposition,[status(thm)],[c_93,c_85]) ).
tcf(c_69092,plain,
( sP2
| ( xn = sz10 )
| ( smndt0(sz10) = xn )
| ~ isPrime0(sK11(xn)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_69083,c_75]) ).
tcf(c_69886,plain,
( sP2
| ( xn = sz10 )
| ( smndt0(sz10) = xn ) ),
inference(global_subsumption_just,[status(thm)],[c_69092,c_19755]) ).
fof(f102,definition,
! [X5] :
( ~ sP0(X5)
| ! [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)) )
& ( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X7] :
( sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00))
& aInteger0(X7) )
& aInteger0(X6) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f103,definition,
! [X1] :
( ~ sP1(X1)
| ! [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)) )
& ( ~ 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) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f104,plain,
( xS = cS2043
& ! [X0] :
( ( ! [X5] :
( ( sP0(X5)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X5))
& szAzrzSzezqlpdtcmdtrp0(sz00,X5) != X0 )
| ~ isPrime0(X5)
| sz00 = X5
| ~ aInteger0(X5) )
| aElementOf0(X0,xS) )
& ( ~ aElementOf0(X0,xS)
| ? [X1] :
( szAzrzSzezqlpdtcmdtrp0(sz00,X1) = X0
& sP1(X1)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X1))
& isPrime0(X1)
& X1 != sz00
& aInteger0(X1) ) ) )
& aSet0(xS) ),
inference(definition_folding,[],[f55,f103,f102]) ).
fof(f105,definition,
( ~ sP2
| ( ? [X3] :
( isPrime0(X3)
& aDivisorOf0(X3,xn)
& ? [X4] :
( xn = sdtasdt0(X3,X4)
& aInteger0(X4) )
& sz00 != X3
& aInteger0(X3) )
& ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X5] :
( ~ aElementOf0(xn,X5)
| ~ aElementOf0(X5,xS) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f106,plain,
( sP2
| ( 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) ) ) ) ) ),
inference(definition_folding,[],[f57,f105]) ).
fof(f113,plain,
! [X5] :
( ~ sP0(X5)
| ! [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)) )
& ( ~ aElementOf0(X6,szAzrzSzezqlpdtcmdtrp0(sz00,X5))
| ( sdteqdtlpzmzozddtrp0(X6,sz00,X5)
& aDivisorOf0(X5,sdtpldt0(X6,smndt0(sz00)))
& ? [X7] :
( sdtasdt0(X5,X7) = sdtpldt0(X6,smndt0(sz00))
& aInteger0(X7) )
& aInteger0(X6) ) ) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f114,plain,
! [X0] :
( ~ sP0(X0)
| ! [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)) )
& ( ~ 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) ) ) ) ),
inference(rectify,[],[f113]) ).
fof(f115,plain,
! [X0] :
( ~ sP0(X0)
| ! [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)) )
& ( ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ( sdteqdtlpzmzozddtrp0(X1,sz00,X0)
& aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00)))
& sdtpldt0(X1,smndt0(sz00)) = sdtasdt0(X0,sK6(X0,X1))
& aInteger0(sK6(X0,X1))
& aInteger0(X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f114]) ).
fof(f118,plain,
( ~ sP2
| ( ? [X3] :
( isPrime0(X3)
& aDivisorOf0(X3,xn)
& ? [X4] :
( xn = sdtasdt0(X3,X4)
& aInteger0(X4) )
& sz00 != X3
& aInteger0(X3) )
& ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X5] :
( ~ aElementOf0(xn,X5)
| ~ aElementOf0(X5,xS) ) ) ),
inference(nnf_transformation,[],[f105]) ).
fof(f119,plain,
( ~ sP2
| ( ? [X1] :
( isPrime0(X1)
& aDivisorOf0(X1,xn)
& ? [X2] :
( sdtasdt0(X1,X2) = xn
& aInteger0(X2) )
& sz00 != X1
& aInteger0(X1) )
& ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X0] :
( ~ aElementOf0(xn,X0)
| ~ aElementOf0(X0,xS) ) ) ),
inference(rectify,[],[f118]) ).
fof(f120,plain,
( ~ sP2
| ( isPrime0(sK8)
& aDivisorOf0(sK8,xn)
& xn = sdtasdt0(sK8,sK9)
& aInteger0(sK9)
& sz00 != sK8
& aInteger0(sK8)
& ~ aElementOf0(xn,sbsmnsldt0(xS))
& ! [X0] :
( ~ aElementOf0(xn,X0)
| ~ aElementOf0(X0,xS) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X1,sK8),skolemize(X2,sK9)],[f119]) ).
fof(f161,plain,
! [X3,X0,X1] :
( ~ sP0(X0)
| sdtpldt0(X1,smndt0(sz00)) != sdtasdt0(X0,X3)
| ~ aInteger0(X3)
| ~ aInteger0(X1)
| aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f163,plain,
! [X0,X1] :
( ~ sP0(X0)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| aDivisorOf0(X0,sdtpldt0(X1,smndt0(sz00))) ),
inference(cnf_transformation,[],[f115]) ).
fof(f179,plain,
( ~ sP2
| isPrime0(sK8) ),
inference(cnf_transformation,[],[f120]) ).
fof(f180,plain,
( ~ sP2
| aDivisorOf0(sK8,xn) ),
inference(cnf_transformation,[],[f120]) ).
fof(f181,plain,
( ~ sP2
| xn = sdtasdt0(sK8,sK9) ),
inference(cnf_transformation,[],[f120]) ).
fof(f182,plain,
( ~ sP2
| aInteger0(sK9) ),
inference(cnf_transformation,[],[f120]) ).
fof(f183,plain,
( ~ sP2
| sz00 != sK8 ),
inference(cnf_transformation,[],[f120]) ).
fof(f184,plain,
( ~ sP2
| aInteger0(sK8) ),
inference(cnf_transformation,[],[f120]) ).
fof(f186,plain,
! [X0] :
( ~ sP2
| ~ aElementOf0(xn,X0)
| ~ aElementOf0(X0,xS) ),
inference(cnf_transformation,[],[f120]) ).
fof(f272,plain,
! [X0] :
( ~ sP2
| ~ aElementOf0(xn,X0)
| ~ aElementOf0(X0,cS2043) ),
inference(definition_unfolding,[],[f186,f167]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X1,sdtpldt0(X0,smndt0(sz00)))
| ~ sP0(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1))
| ~ sP0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X0)
| ( sdtpldt0(X0,smndt0(sz00)) != sdtasdt0(X1,X2) ) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_76,plain,
! [X0: $i] :
( ~ sP2
| ~ aElementOf0(xn,X0)
| ~ aElementOf0(X0,cS2043) ),
inference(cnf_transformation,[],[f272]) ).
tcf(c_78,plain,
( aInteger0(sK8)
| ~ sP2 ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_79,plain,
( ~ sP2
| ( sz00 != sK8 ) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_80,plain,
( aInteger0(sK9)
| ~ sP2 ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_81,plain,
( ( sdtasdt0(sK8,sK9) = xn )
| ~ sP2 ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_82,plain,
( aDivisorOf0(sK8,xn)
| ~ sP2 ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_83,plain,
( isPrime0(sK8)
| ~ sP2 ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_293,plain,
( aDivisorOf0(sK8,xn)
| ~ sP2 ),
inference(prop_impl_just,[status(thm)],[c_82]) ).
tcf(c_4273,plain,
! [X0: $i] :
( ~ sP2
| ~ isPrime0(X0)
| ( xn != sz10 )
| ( X0 != sK8 ) ),
inference(resolution_lifted,[status(thm)],[c_293,c_284]) ).
tcf(c_4274,plain,
( ~ sP2
| ~ isPrime0(sK8)
| ( xn != sz10 ) ),
inference(unflattening,[status(thm)],[c_4273]) ).
tcf(c_4275,plain,
( ~ sP2
| ( xn != sz10 ) ),
inference(global_subsumption_just,[status(thm)],[c_4274,c_83,c_4274]) ).
tcf(c_4330,plain,
! [X0: $i,X1: $i] :
( aInteger0(sK12(X0,X1))
| ~ sP2
| ~ aInteger0(X0)
| ( X1 != sK8 )
| ( X0 != xn ) ),
inference(resolution_lifted,[status(thm)],[c_293,c_102]) ).
tcf(c_4331,plain,
( aInteger0(sK12(xn,sK8))
| ~ sP2
| ~ aInteger0(xn) ),
inference(unflattening,[status(thm)],[c_4330]) ).
tcf(c_12858,plain,
! [X0: $i] :
( ~ iPr_def_10
| ~ sP2
| ~ aElementOf0(xn,X0) ),
inference(superposition,[status(thm)],[c_9814,c_76]) ).
tcf(c_15849,plain,
( ~ iPr_def_10
| ~ sP2 ),
inference(superposition,[status(thm)],[c_9814,c_12858]) ).
tcf(c_17015,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ~ sP2
| ~ isPrime0(X0)
| ~ aInteger0(X0)
| ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,X0)) ),
inference(superposition,[status(thm)],[c_72,c_76]) ).
tcf(c_25442,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ~ sP0(X0)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ( sdtasdt0(X0,X1) != sdtpldt0(X2,sz00) ) ),
inference(light_normalisation,[status(thm)],[c_62,c_17364]) ).
tcf(c_25479,plain,
! [X0: $i,X1: $i] :
( aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ~ aInteger0(xn)
| ~ sP0(X0)
| ~ aInteger0(X1)
| ( sdtasdt0(X0,X1) != xn ) ),
inference(superposition,[status(thm)],[c_12551,c_25442]) ).
tcf(c_25489,plain,
! [X0: $i,X1: $i] :
( aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,X0))
| ~ sP0(X0)
| ~ aInteger0(X1)
| ( sdtasdt0(X0,X1) != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25479,c_75]) ).
tcf(c_64132,plain,
( ( sdtasdt0(smndt0(smndt0(sK8)),sz00) = sz00 )
| ~ sP2 ),
inference(superposition,[status(thm)],[c_78,c_30788]) ).
tcf(c_64514,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,X1) != xn )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ isPrime0(X0)
| ( X0 = sz00 ) ),
inference(global_subsumption_just,[status(thm)],[c_84,c_84,c_9815,c_9816,c_15849,c_17015,c_25489]) ).
tcf(c_64515,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X0 = sz00 )
| ~ isPrime0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X0)
| ( sdtasdt0(X0,X1) != xn ) ),
inference(renaming,[status(thm)],[c_64514]) ).
tcf(c_64804,plain,
( ( smndt0(sz00) = sz00 )
| ~ aInteger0(sz00)
| ~ isPrime0(smndt0(sz00))
| ~ aInteger0(smndt0(sz00))
| ( sz00 != xn ) ),
inference(superposition,[status(thm)],[c_64717,c_64515]) ).
tcf(c_64805,plain,
( ( smndt0(sz00) = sz00 )
| ~ isPrime0(smndt0(sz00))
| ~ aInteger0(smndt0(sz00))
| ( sz00 != xn ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_64804,c_92]) ).
tcf(c_64875,plain,
smndt0(sz00) = sz00,
inference(global_subsumption_just,[status(thm)],[c_64805,c_17364]) ).
tcf(c_65401,plain,
( isOpen0(cS2043)
| ~ sP2
| ~ aSubsetOf0(cS2043,cS1395)
| ~ aElementOf0(xn,sK14(cS2043)) ),
inference(superposition,[status(thm)],[c_130,c_76]) ).
tcf(c_67430,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(X1,sdtpldt0(X0,sz00))
| ~ sP0(X1)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,X1)) ),
inference(light_normalisation,[status(thm)],[c_60,c_64875]) ).
tcf(c_67579,plain,
( ( sdtasdt0(sK8,sK12(xn,sK8)) = xn )
| ~ sP2
| ~ aInteger0(xn) ),
inference(superposition,[status(thm)],[c_82,c_103]) ).
tcf(c_67580,plain,
( ( sdtasdt0(sK8,sK12(xn,sK8)) = xn )
| ~ sP2 ),
inference(forward_subsumption_resolution,[status(thm)],[c_67579,c_75]) ).
tcf(c_67592,plain,
( ( szAzrzSzezqlpdtcmdtrp0(sz00,sK7(sK10)) = sK10 )
| ( sdtasdt0(sK8,sK12(xn,sK8)) = xn ) ),
inference(superposition,[status(thm)],[c_65613,c_67580]) ).
tcf(c_68605,plain,
( ( sz00 = sK8 )
| ( szAzrzSzezqlpdtcmdtrp0(sz00,sK7(sK10)) = sK10 )
| ~ isPrime0(sK8)
| ~ aInteger0(sK8)
| ~ aInteger0(sK12(xn,sK8)) ),
inference(superposition,[status(thm)],[c_67592,c_64515]) ).
tcf(c_68611,plain,
szAzrzSzezqlpdtcmdtrp0(sz00,sK7(sK10)) = sK10,
inference(global_subsumption_just,[status(thm)],[c_68605,c_75,c_83,c_78,c_79,c_4331,c_13388,c_68605]) ).
tcf(c_68614,plain,
! [X0: $i] :
( aDivisorOf0(sK7(sK10),sdtpldt0(X0,sz00))
| ~ sP0(sK7(sK10))
| ~ aElementOf0(X0,sK10) ),
inference(superposition,[status(thm)],[c_68611,c_67430]) ).
tcf(c_68618,plain,
( aElementOf0(sK10,cS2043)
| ( sK7(sK10) = sz00 )
| ~ isPrime0(sK7(sK10))
| ~ aInteger0(sK7(sK10)) ),
inference(superposition,[status(thm)],[c_68611,c_72]) ).
tcf(c_69904,plain,
( ( xn = sz10 )
| ( smndt0(sz10) = xn )
| ( sdtasdt0(sK8,sK9) = xn ) ),
inference(superposition,[status(thm)],[c_69886,c_81]) ).
tcf(c_70201,plain,
( ( xn = sz10 )
| ( sz00 = sK8 )
| ( smndt0(sz10) = xn )
| ~ isPrime0(sK8)
| ~ aInteger0(sK9)
| ~ aInteger0(sK8) ),
inference(superposition,[status(thm)],[c_69904,c_64515]) ).
tcf(c_70416,plain,
( ( xn = sz10 )
| ( smndt0(sz10) = xn ) ),
inference(global_subsumption_just,[status(thm)],[c_70201,c_83,c_80,c_78,c_79,c_19755,c_70201]) ).
tcf(c_70423,plain,
! [X0: $i] :
( ( xn = sz10 )
| ~ isPrime0(X0)
| ~ aDivisorOf0(X0,xn) ),
inference(superposition,[status(thm)],[c_70416,c_65922]) ).
tcf(c_70434,plain,
! [X0: $i] :
( ~ aDivisorOf0(X0,xn)
| ~ isPrime0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_70423,c_85,c_4275,c_70423]) ).
tcf(c_70435,plain,
! [X0: $i] :
( ~ isPrime0(X0)
| ~ aDivisorOf0(X0,xn) ),
inference(renaming,[status(thm)],[c_70434]) ).
tcf(c_70441,plain,
( ~ sP2
| ~ isPrime0(sK8) ),
inference(superposition,[status(thm)],[c_82,c_70435]) ).
tcf(c_71461,plain,
aElementOf0(sK10,cS2043),
inference(global_subsumption_just,[status(thm)],[c_68618,c_86,c_83,c_70441]) ).
tcf(c_71466,plain,
isPrime0(sK7(sK10)),
inference(superposition,[status(thm)],[c_71461,c_68]) ).
tcf(c_72873,plain,
~ sP2,
inference(global_subsumption_just,[status(thm)],[c_64132,c_83,c_70441]) ).
tcf(c_93082,plain,
~ sP2,
inference(global_subsumption_just,[status(thm)],[c_65401,c_83,c_70441]) ).
tcf(c_93120,plain,
aElementOf0(xn,sK10),
inference(backward_subsumption_resolution,[status(thm)],[c_87,c_93082]) ).
tcf(c_100634,plain,
( aDivisorOf0(sK7(sK10),xn)
| ~ sP0(sK7(sK10))
| ~ aElementOf0(xn,sK10) ),
inference(superposition,[status(thm)],[c_64765,c_68614]) ).
tcf(c_100636,plain,
( aDivisorOf0(sK7(sK10),xn)
| ~ sP0(sK7(sK10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_100634,c_93120]) ).
tcf(c_101302,plain,
( ~ isPrime0(sK7(sK10))
| ~ sP0(sK7(sK10)) ),
inference(superposition,[status(thm)],[c_100636,c_70435]) ).
tcf(c_101305,plain,
~ sP0(sK7(sK10)),
inference(forward_subsumption_resolution,[status(thm)],[c_101302,c_71466]) ).
tcf(c_171101,plain,
! [X0: $i] : aElementOf0(X0,cS2043),
inference(global_subsumption_just,[status(thm)],[c_9814,c_86,c_83,c_9814,c_9816,c_12341,c_12360,c_13052,c_13611,c_70441,c_101305]) ).
tcf(c_171603,plain,
! [X0: $i,X1: $i] :
( aInteger0(X0)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2205,c_171101]) ).
tcf(c_171646,plain,
! [X0: $i] : szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_71,c_86,c_83,c_9816,c_12341,c_12360,c_13052,c_13387,c_13611,c_70441,c_101305]) ).
tcf(c_171650,plain,
! [X0: $i,X1: $i] :
( aInteger0(X0)
| ~ aElementOf0(X0,X1) ),
inference(demodulation,[status(thm)],[c_171603,c_171646]) ).
tcf(c_171694,plain,
! [X0: $i] : aInteger0(X0),
inference(superposition,[status(thm)],[c_171101,c_171650]) ).
tcf(c_174421,negated_conjecture,
aElementOf0(xn,sbsmnsldt0(cS2043)),
inference(global_subsumption_just,[status(thm)],[c_88,c_88,c_72873]) ).
tcf(c_174423,plain,
! [X0: $i] :
( ~ aDivisorOf0(X0,xn)
| ~ isPrime0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_85,c_4275,c_70423]) ).
tcf(c_174424,negated_conjecture,
! [X0: $i] :
( ~ isPrime0(X0)
| ~ aDivisorOf0(X0,xn) ),
inference(renaming,[status(thm)],[c_174423]) ).
tcf(c_174531,plain,
! [X0: $i] : isPrime0(sK7(X0)),
inference(global_subsumption_just,[status(thm)],[c_68,c_86,c_83,c_9816,c_12341,c_12360,c_12359,c_13052,c_13611,c_70441,c_101305]) ).
tcf(c_174642,plain,
! [X0: $i] : sdtpldt0(X0,sz00) = X0,
inference(global_subsumption_just,[status(thm)],[c_116,c_116,c_171694]) ).
tcf(c_174644,plain,
! [X0: $i] : sdtpldt0(sz00,X0) = X0,
inference(global_subsumption_just,[status(thm)],[c_117,c_117,c_171694]) ).
tcf(c_174981,plain,
! [X0: $i] : sdtpldt0(X0,smndt0(X0)) = sz00,
inference(global_subsumption_just,[status(thm)],[c_106,c_106,c_171694]) ).
tcf(c_174983,plain,
smndt0(sz00) = sz00,
inference(superposition,[status(thm)],[c_174644,c_174981]) ).
tcf(c_175029,plain,
! [X0: $i] : szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X0)) = X0,
inference(global_subsumption_just,[status(thm)],[c_71,c_86,c_83,c_9816,c_12341,c_12360,c_13052,c_13387,c_13611,c_70441,c_101305]) ).
tcf(c_179564,plain,
! [X0: $i] : aElementOf0(X0,cS2043),
inference(global_subsumption_just,[status(thm)],[c_11095,c_86,c_83,c_9814,c_9816,c_12341,c_12360,c_13052,c_13611,c_70441,c_101305]) ).
tcf(c_179581,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(sK7(X1),sdtpldt0(X0,smndt0(sz00)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2169,c_179564]) ).
tcf(c_179974,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(sK7(X1),sdtpldt0(X0,smndt0(sz00)))
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_2169,c_179581]) ).
tcf(c_179976,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(sK7(X1),X0)
| ~ aElementOf0(X0,szAzrzSzezqlpdtcmdtrp0(sz00,sK7(X1))) ),
inference(light_normalisation,[status(thm)],[c_179974,c_174983,c_174642]) ).
tcf(c_179977,plain,
! [X0: $i,X1: $i] :
( aDivisorOf0(sK7(X1),X0)
| ~ aElementOf0(X0,X1) ),
inference(demodulation,[status(thm)],[c_179976,c_175029]) ).
tcf(c_179984,plain,
! [X0: $i] :
( ~ isPrime0(sK7(X0))
| ~ aElementOf0(xn,X0) ),
inference(superposition,[status(thm)],[c_179977,c_174424]) ).
tcf(c_179989,plain,
! [X0: $i] : ~ aElementOf0(xn,X0),
inference(forward_subsumption_resolution,[status(thm)],[c_179984,c_174531]) ).
tcf(c_179991,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_174421,c_179989]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM447+5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 04:01:08 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 63.16/12.39 % SZS status Started for theBenchmark.p
% 63.16/12.39 % SZS status Theorem for theBenchmark.p
% 63.16/12.39
% 63.16/12.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 63.16/12.39
% 63.16/12.39 % ------ iProver source info
% 63.16/12.39
% 63.16/12.39 % git: date: 2026-07-19 20:42:38 +0200
% 63.16/12.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 63.16/12.39 % git: non_committed_changes: false
% 63.16/12.39
% 63.16/12.39 % ------ Parsing...
% 63.16/12.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 63.16/12.39
% 63.16/12.39 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 63.16/12.39
% 63.16/12.39 % ------ Preprocessing... gs_s sp: 4 0s gs_e snvd_s sp: 0 0s snvd_e %
% 63.16/12.39
% 63.16/12.39 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 63.16/12.39 % ------ Proving...
% 63.16/12.39 % ------ Problem Properties
% 63.16/12.39
% 63.16/12.39 %
% 63.16/12.39 % clauses 112
% 63.16/12.39 % conjectures 5
% 63.16/12.39 % EPR 28
% 63.16/12.39 % Horn 76
% 63.16/12.39 % unary 4
% 63.16/12.39 % binary 33
% 63.16/12.39 % lits 384
% 63.16/12.39 % lits eq 61
% 63.16/12.39 % fd_pure 0
% 63.16/12.39 % fd_pseudo 0
% 63.16/12.39 % fd_cond 21
% 63.16/12.39 % fd_pseudo_cond 4
% 63.16/12.39 % AC symbols 0
% 63.16/12.39
% 63.16/12.39 % ------ Schedule dynamic 5 is on
% 63.16/12.39
% 63.16/12.39 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 63.16/12.39
% 63.16/12.39
% 63.16/12.39 % ------
% 63.16/12.39 % Current options:
% 63.16/12.39 % ------
% 63.16/12.39
% 63.16/12.39
% 63.16/12.39 %
% 63.16/12.39
% 63.16/12.39 % ------ Proving...
% 63.16/12.39 % Proof_search_loop: time out after: 7483 full_loop iterations
% 63.16/12.39
% 63.16/12.39 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 63.16/12.39
% 63.16/12.39
% 63.16/12.39 % ------
% 63.16/12.39 % Current options:
% 63.16/12.39 % ------
% 63.16/12.39
% 63.16/12.39
% 63.16/12.39 %
% 63.16/12.39
% 63.16/12.39 % ------ Proving...
% 63.16/12.39 %
% 63.16/12.39
% 63.16/12.39 % SZS status Theorem for theBenchmark.p
% 63.16/12.39
% 63.16/12.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 82.48/12.40
% 82.48/12.40
%------------------------------------------------------------------------------