%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM517+1 : 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 : n012.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 02:25:47 PM UTC 2026
% Result : Theorem 18.57s 3.19s
% Output : CNFRefutation 18.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 96 ( 31 unt; 0 def)
% Number of atoms : 361 ( 111 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 452 ( 187 ~; 187 |; 59 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 94 !; 3 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(X0,X1) = sz00
=> ( X1 = sz00
& X0 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH_03) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& X0 != sz00 )
=> ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X1 = X0
| X1 = sz10 ) )
& X0 != sz10
& X0 != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X2,sdtasdt0(X0,X1))
& isPrime0(X2) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( doDivides0(X2,X1)
| doDivides0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1799) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(f48,axiom,
( isPrime0(xr)
& doDivides0(xr,xk)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(f52,axiom,
doDivides0(xr,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(f54,axiom,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2529) ).
fof(f55,axiom,
( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2686) ).
fof(f56,conjecture,
( doDivides0(xp,xm)
| doDivides0(xp,sdtsldt0(xn,xr)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f57,negated_conjecture,
~ ( doDivides0(xp,xm)
| doDivides0(xp,sdtsldt0(xn,xr)) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f60,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f61,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f60]) ).
fof(f68,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f81,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f82,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f81]) ).
fof(f104,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f105,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(flattening,[],[f104]) ).
fof(f108,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f109,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( X2 = sdtsldt0(X1,X0)
<=> ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f108]) ).
fof(f120,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f121,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( isPrime0(X0)
<=> ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) ) ),
inference(flattening,[],[f120]) ).
fof(f124,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X2,X1)
| doDivides0(X2,X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f125,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X2,X1)
| doDivides0(X2,X0) ),
inference(flattening,[],[f124]) ).
fof(f127,plain,
( ~ doDivides0(xp,xm)
& ~ doDivides0(xp,sdtsldt0(xn,xr)) ),
inference(ennf_transformation,[],[f57]) ).
fof(f136,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ( sdtsldt0(X1,X0) != X2
| ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f109]) ).
fof(f137,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ! [X2] :
( ( sdtsldt0(X1,X0) != X2
| ( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtsldt0(X1,X0) ) ) ),
inference(flattening,[],[f136]) ).
fof(f138,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(nnf_transformation,[],[f121]) ).
fof(f139,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X1] :
( ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1)
| X1 = X0
| X1 = sz10 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(flattening,[],[f138]) ).
fof(f140,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X2] :
( ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sz10 = X2 )
& X0 != sz10
& X0 != sz00 ) )
& ( ? [X1] :
( doDivides0(X1,X0)
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(rectify,[],[f139]) ).
fof(f141,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( ( ~ isPrime0(X0)
| ( ! [X2] :
( ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| X0 = X2
| sz10 = X2 )
& X0 != sz10
& X0 != sz00 ) )
& ( ( doDivides0(sK2(X0),X0)
& aNaturalNumber0(sK2(X0))
& sK2(X0) != X0
& sz10 != sK2(X0) )
| sz10 = X0
| sz00 = X0
| isPrime0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f140]) ).
fof(f143,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f146,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f150,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f68]) ).
fof(f164,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f82]) ).
fof(f189,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f194,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f137]) ).
fof(f203,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ~ isPrime0(X0)
| sz00 != X0 ),
inference(cnf_transformation,[],[f141]) ).
fof(f211,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f212,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f213,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f214,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ isPrime0(X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| doDivides0(X2,X1)
| doDivides0(X2,X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f216,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f41]) ).
fof(f228,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f230,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f48]) ).
fof(f236,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f52]) ).
fof(f239,plain,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(cnf_transformation,[],[f54]) ).
fof(f240,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f55]) ).
fof(f241,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),
inference(cnf_transformation,[],[f55]) ).
fof(f242,plain,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f127]) ).
fof(f243,plain,
~ doDivides0(xp,sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f127]) ).
fof(f252,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f194]) ).
fof(f254,plain,
( ~ aNaturalNumber0(sz00)
| ~ isPrime0(sz00) ),
inference(equality_resolution,[],[f203]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f143]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f252]) ).
tcf(c_110,negated_conjecture,
( ~ isPrime0(sz00)
| ~ aNaturalNumber0(sz00) ),
inference(cnf_transformation,[],[f254]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f213]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f212]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f211]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X2,X1)
| doDivides0(X2,X0)
| ~ isPrime0(X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_120,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f216]) ).
tcf(c_133,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f230]) ).
tcf(c_135,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f228]) ).
tcf(c_141,plain,
doDivides0(xr,xn),
inference(cnf_transformation,[],[f236]) ).
tcf(c_144,plain,
doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm)),
inference(cnf_transformation,[],[f239]) ).
tcf(c_145,negated_conjecture,
sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xp),
inference(cnf_transformation,[],[f241]) ).
tcf(c_146,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f240]) ).
tcf(c_147,negated_conjecture,
~ doDivides0(xp,sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f243]) ).
tcf(c_148,negated_conjecture,
~ doDivides0(xp,xm),
inference(cnf_transformation,[],[f242]) ).
tcf(c_153,plain,
( ( sdtpldt0(sz00,sz00) = sz00 )
| ~ aNaturalNumber0(sz00) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_171,plain,
( ( sz00 = sz00 )
| ~ aNaturalNumber0(sz00)
| ( sdtpldt0(sz00,sz00) != sz00 ) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_263,plain,
! [X0: $i,X1: $i] :
( isPrime0(X0)
| ~ isPrime0(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_278,plain,
! [X0: $i] :
( isPrime0(X0)
| ~ isPrime0(xr)
| ( X0 != xr ) ),
inference(instantiation,[status(thm)],[c_263]) ).
tcf(c_279,plain,
( isPrime0(sz00)
| ~ isPrime0(xr)
| ( sz00 != xr ) ),
inference(instantiation,[status(thm)],[c_278]) ).
tcf(c_579,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_1610,plain,
! [X0: $i,X1: $i] :
( ( X0 = xr )
| ( xr != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_252]) ).
tcf(c_1611,plain,
( ( sz00 = xr )
| ( xr != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_1610]) ).
tcf(c_2503,plain,
( aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_2883,plain,
( iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(resolution,[status(thm)],[c_94,c_145]) ).
tcf(c_5310,plain,
( iLess0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ),
inference(global_subsumption_just,[status(thm)],[c_2883,c_118,c_117,c_116,c_146,c_579,c_2503,c_2883]) ).
tcf(c_5656,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_8991,plain,
( aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_13007,plain,
( doDivides0(xp,xm)
| doDivides0(xp,sdtsldt0(xn,xr))
| ~ isPrime0(xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp)) ),
inference(resolution,[status(thm)],[c_119,c_5310]) ).
tcf(c_13028,plain,
~ aNaturalNumber0(sdtsldt0(xn,xr)),
inference(global_subsumption_just,[status(thm)],[c_13007,c_120,c_118,c_117,c_148,c_147,c_144,c_5656,c_8991,c_13007]) ).
tcf(c_13034,plain,
( ( xr = sz00 )
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,xn) ),
inference(resolution,[status(thm)],[c_13028,c_99]) ).
tcf(c_13035,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_13034,c_1611,c_279,c_171,c_153,c_110,c_141,c_49,c_116,c_133,c_135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM517+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Thu Sep 24 04:23:50 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.02/0.33 Running first-order theorem proving
% 0.02/0.33 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
% 0.02/0.34
% 0.02/0.34 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.34
% 0.02/0.34 % Detected problem language: tptp
% 0.02/0.35 % Proving...
% 18.57/3.19 % SZS status Started for theBenchmark.p
% 18.57/3.19 % SZS status Theorem for theBenchmark.p
% 18.57/3.19
% 18.57/3.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.57/3.19
% 18.57/3.19 % ------ iProver source info
% 18.57/3.19
% 18.57/3.19 % git: date: 2026-07-19 20:42:38 +0200
% 18.57/3.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.57/3.19 % git: non_committed_changes: false
% 18.57/3.19
% 18.57/3.19 % ------ Parsing...
% 18.57/3.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.57/3.19
% 18.57/3.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e %
% 18.57/3.19
% 18.57/3.19 % ------ Preprocessing...%
% 18.57/3.19
% 18.57/3.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.57/3.19 % ------ Proving...
% 18.57/3.19 % ------ Problem Properties
% 18.57/3.19
% 18.57/3.19 %
% 18.57/3.19 % clauses 92
% 18.57/3.19 % conjectures 14
% 18.57/3.19 % EPR 34
% 18.57/3.19 % Horn 67
% 18.57/3.19 % unary 34
% 18.57/3.19 % binary 7
% 18.57/3.19 % lits 287
% 18.57/3.19 % lits eq 79
% 18.57/3.19 % fd_pure 0
% 18.57/3.19 % fd_pseudo 0
% 18.57/3.19 % fd_cond 15
% 18.57/3.19 % fd_pseudo_cond 11
% 18.57/3.19 % AC symbols 0
% 18.57/3.19
% 18.57/3.19 % ------ Input Options Time Limit: Unbounded
% 18.57/3.19
% 18.57/3.19
% 18.57/3.19 % ------
% 18.57/3.19 % Current options:
% 18.57/3.19 % ------
% 18.57/3.19
% 18.57/3.19
% 18.57/3.19 %
% 18.57/3.19
% 18.57/3.19 % ------ Proving...
% 18.57/3.19 %
% 18.57/3.19
% 18.57/3.19 % SZS status Theorem for theBenchmark.p
% 18.57/3.19
% 18.57/3.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.57/3.19
% 18.57/3.19
%------------------------------------------------------------------------------