%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM508+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:25:23 PM UTC 2026
% Result : Theorem 14.50s 2.70s
% Output : CNFRefutation 14.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 77 ( 22 unt; 2 def)
% Number of atoms : 417 ( 119 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 504 ( 164 ~; 164 |; 163 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 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 : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-2 aty)
% Number of variables : 128 ( 0 sgn 84 !; 44 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIH_03) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f40,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( ( doDivides0(X2,sdtasdt0(X0,X1))
| ? [X3] :
( sdtasdt0(X0,X1) = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) ) )
& ( isPrime0(X2)
| ( ! [X3] :
( ( doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3) )
=> ( X3 = X2
| X3 = sz10 ) )
& X2 != sz10
& X2 != sz00 ) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( doDivides0(X2,X1)
& ? [X3] :
( X1 = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) ) )
| ( doDivides0(X2,X0)
& ? [X3] :
( X0 = sdtasdt0(X2,X3)
& aNaturalNumber0(X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1799) ).
fof(f48,axiom,
( isPrime0(xr)
& ! [X0] :
( ( ( doDivides0(X0,xr)
| ? [X1] :
( xr = sdtasdt0(X0,X1)
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( X0 = xr
| X0 = sz10 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2342) ).
fof(f49,axiom,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& ? [X0] :
( sdtpldt0(xr,X0) = xk
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2362) ).
fof(f51,axiom,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& ? [X0] :
( sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),X0) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(X0) )
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2478) ).
fof(f52,conjecture,
( doDivides0(xr,xm)
| ? [X0] :
( xm = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
| doDivides0(xr,xn)
| ? [X0] :
( xn = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f53,negated_conjecture,
~ ( doDivides0(xr,xm)
| ? [X0] :
( xm = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
| doDivides0(xr,xn)
| ? [X0] :
( xn = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( ( doDivides0(X2,sdtasdt0(X0,X1))
| ? [X5] :
( sdtasdt0(X0,X1) = sdtasdt0(X2,X5)
& aNaturalNumber0(X5) ) )
& ( isPrime0(X2)
| ( ! [X3] :
( ( doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3) )
=> ( X3 = X2
| X3 = sz10 ) )
& X2 != sz10
& X2 != sz00 ) ) )
=> ( iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
=> ( ( doDivides0(X2,X1)
& ? [X7] :
( sdtasdt0(X2,X7) = X1
& aNaturalNumber0(X7) ) )
| ( doDivides0(X2,X0)
& ? [X6] :
( sdtasdt0(X2,X6) = X0
& aNaturalNumber0(X6) ) ) ) ) ) ),
inference(rectify,[],[f40]) ).
fof(f59,plain,
( isPrime0(xr)
& ! [X1] :
( ( ( doDivides0(X1,xr)
| ? [X2] :
( sdtasdt0(X1,X2) = xr
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( xr = X1
| sz10 = X1 ) )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
inference(rectify,[],[f48]) ).
fof(f60,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& ? [X1] :
( sdtasdt0(xn,xm) = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
& ? [X0] :
( sdtpldt0(xr,X0) = xk
& aNaturalNumber0(X0) ) ),
inference(rectify,[],[f49]) ).
fof(f61,plain,
~ ( doDivides0(xr,xm)
| ? [X1] :
( xm = sdtasdt0(xr,X1)
& aNaturalNumber0(X1) )
| doDivides0(xr,xn)
| ? [X0] :
( xn = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) ) ),
inference(rectify,[],[f53]) ).
fof(f62,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f62]) ).
fof(f106,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(flattening,[],[f106]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ~ doDivides0(X2,sdtasdt0(X0,X1))
& ! [X5] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X5)
| ~ aNaturalNumber0(X5) ) )
| ( ~ isPrime0(X2)
& ( ? [X3] :
( doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3)
& X2 != X3
& sz10 != X3 )
| sz10 = X2
| sz00 = X2 ) )
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( doDivides0(X2,X1)
& ? [X7] :
( sdtasdt0(X2,X7) = X1
& aNaturalNumber0(X7) ) )
| ( doDivides0(X2,X0)
& ? [X6] :
( sdtasdt0(X2,X6) = X0
& aNaturalNumber0(X6) ) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ~ doDivides0(X2,sdtasdt0(X0,X1))
& ! [X5] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X5)
| ~ aNaturalNumber0(X5) ) )
| ( ~ isPrime0(X2)
& ( ? [X3] :
( doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3)
& X2 != X3
& sz10 != X3 )
| sz10 = X2
| sz00 = X2 ) )
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( doDivides0(X2,X1)
& ? [X7] :
( sdtasdt0(X2,X7) = X1
& aNaturalNumber0(X7) ) )
| ( doDivides0(X2,X0)
& ? [X6] :
( sdtasdt0(X2,X6) = X0
& aNaturalNumber0(X6) ) ) ),
inference(flattening,[],[f126]) ).
fof(f133,plain,
( isPrime0(xr)
& ! [X1] :
( ( ~ doDivides0(X1,xr)
& ! [X2] :
( sdtasdt0(X1,X2) != xr
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| xr = X1
| sz10 = X1 )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
inference(ennf_transformation,[],[f59]) ).
fof(f134,plain,
( isPrime0(xr)
& ! [X1] :
( ( ~ doDivides0(X1,xr)
& ! [X2] :
( sdtasdt0(X1,X2) != xr
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| xr = X1
| sz10 = X1 )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& ? [X0] :
( xk = sdtasdt0(xr,X0)
& aNaturalNumber0(X0) )
& aNaturalNumber0(xr) ),
inference(flattening,[],[f133]) ).
fof(f135,plain,
( ~ doDivides0(xr,xm)
& ! [X1] :
( xm != sdtasdt0(xr,X1)
| ~ aNaturalNumber0(X1) )
& ~ doDivides0(xr,xn)
& ! [X0] :
( xn != sdtasdt0(xr,X0)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f61]) ).
fof(f154,plain,
! [X1,X2] :
( ~ sP1(X1,X2)
| ( doDivides0(X2,X1)
& ? [X7] :
( sdtasdt0(X2,X7) = X1
& aNaturalNumber0(X7) ) ) ),
inference(nnf_transformation,[],[f137]) ).
fof(f155,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) ) ) ),
inference(rectify,[],[f154]) ).
fof(f156,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ( doDivides0(X1,X0)
& sdtasdt0(X1,sK6(X0,X1)) = X0
& aNaturalNumber0(sK6(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f155]) ).
fof(f160,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ~ doDivides0(X2,sdtasdt0(X0,X1))
& ! [X4] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X4)
| ~ aNaturalNumber0(X4) ) )
| sP0(X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP1(X1,X2)
| ( doDivides0(X2,X0)
& ? [X3] :
( sdtasdt0(X2,X3) = X0
& aNaturalNumber0(X3) ) ) ),
inference(rectify,[],[f138]) ).
fof(f161,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ~ doDivides0(X2,sdtasdt0(X0,X1))
& ! [X4] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X4)
| ~ aNaturalNumber0(X4) ) )
| sP0(X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP1(X1,X2)
| ( doDivides0(X2,X0)
& sdtasdt0(X2,sK9(X0,X2)) = X0
& aNaturalNumber0(sK9(X0,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X3,sK9(X0,X2))],[f160]) ).
fof(f164,plain,
( isPrime0(xr)
& ! [X1] :
( ( ~ doDivides0(X1,xr)
& ! [X2] :
( sdtasdt0(X1,X2) != xr
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| xr = X1
| sz10 = X1 )
& xr != sz10
& xr != sz00
& doDivides0(xr,xk)
& xk = sdtasdt0(xr,sK13)
& aNaturalNumber0(sK13)
& aNaturalNumber0(xr) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f134]) ).
fof(f165,plain,
( doDivides0(xr,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xr,sK15)
& aNaturalNumber0(sK15)
& xk = sdtpldt0(xr,sK14)
& aNaturalNumber0(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,sK14),skolemize(X1,sK15)],[f60]) ).
fof(f167,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
& sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(xn,xm),xr),sK17)
& aNaturalNumber0(sK17)
& sdtpldt0(sdtpldt0(xn,xm),xr) != sdtpldt0(sdtpldt0(xn,xm),xp) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(X0,sK17)],[f51]) ).
fof(f171,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f214,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| iLess0(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f236,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f237,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f238,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f239,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| doDivides0(X1,X0) ),
inference(cnf_transformation,[],[f156]) ).
fof(f249,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X2,sdtasdt0(X0,X1))
| sP0(X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP1(X1,X2)
| doDivides0(X2,X0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f282,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f164]) ).
fof(f290,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f164]) ).
fof(f291,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f165]) ).
fof(f300,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f167]) ).
fof(f303,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xr),
inference(cnf_transformation,[],[f167]) ).
fof(f304,plain,
~ doDivides0(xr,xm),
inference(cnf_transformation,[],[f135]) ).
fof(f306,plain,
~ doDivides0(xr,xn),
inference(cnf_transformation,[],[f135]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( iLess0(X0,X1)
| ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f238]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f237]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f236]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i] :
( doDivides0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f239]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP0(X2)
| sP1(X1,X2)
| doDivides0(X2,X0)
| ~ 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,[],[f249]) ).
tcf(c_162,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f290]) ).
tcf(c_170,plain,
isPrime0(xr),
inference(cnf_transformation,[],[f282]) ).
tcf(c_175,plain,
doDivides0(xr,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f291]) ).
tcf(c_180,plain,
sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xn,xm),xr),
inference(cnf_transformation,[],[f303]) ).
tcf(c_183,plain,
sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)),
inference(cnf_transformation,[],[f300]) ).
tcf(c_185,negated_conjecture,
~ doDivides0(xr,xn),
inference(cnf_transformation,[],[f306]) ).
tcf(c_187,negated_conjecture,
~ doDivides0(xr,xm),
inference(cnf_transformation,[],[f304]) ).
tcf(c_11193,plain,
( doDivides0(xr,xm)
| ~ sP1(xm,xr) ),
inference(instantiation,[status(thm)],[c_121]) ).
tcf(c_12540,plain,
( iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xr) )
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(superposition,[status(thm)],[c_183,c_94]) ).
tcf(c_12643,plain,
( iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12540,c_180]) ).
tcf(c_12951,plain,
! [X0: $i] :
( sP0(xr)
| doDivides0(xr,xn)
| sP1(X0,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(xr,sdtasdt0(xn,X0))
| ~ iLess0(sdtpldt0(sdtpldt0(xn,X0),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(instantiation,[status(thm)],[c_134]) ).
tcf(c_13926,plain,
( sP0(xr)
| sP1(xm,xr)
| doDivides0(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ doDivides0(xr,sdtasdt0(xn,xm))
| ~ iLess0(sdtpldt0(sdtpldt0(xn,xm),xr),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(instantiation,[status(thm)],[c_12951]) ).
tcf(c_14390,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_34821,plain,
( aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_58434,plain,
( aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xr))
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
inference(instantiation,[status(thm)],[c_52]) ).
fof(f136,definition,
! [X2] :
( ~ sP0(X2)
| ( ~ isPrime0(X2)
& ( ? [X3] :
( doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3)
& X2 != X3
& sz10 != X3 )
| sz10 = X2
| sz00 = X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f137,definition,
! [X1,X2] :
( ~ sP1(X1,X2)
| ( doDivides0(X2,X1)
& ? [X7] :
( sdtasdt0(X2,X7) = X1
& aNaturalNumber0(X7) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ~ doDivides0(X2,sdtasdt0(X0,X1))
& ! [X5] :
( sdtasdt0(X0,X1) != sdtasdt0(X2,X5)
| ~ aNaturalNumber0(X5) ) )
| sP0(X2)
| ~ iLess0(sdtpldt0(sdtpldt0(X0,X1),X2),sdtpldt0(sdtpldt0(xn,xm),xp))
| sP1(X1,X2)
| ( doDivides0(X2,X0)
& ? [X6] :
( sdtasdt0(X2,X6) = X0
& aNaturalNumber0(X6) ) ) ),
inference(definition_folding,[],[f127,f137,f136]) ).
fof(f157,plain,
! [X2] :
( ~ sP0(X2)
| ( ~ isPrime0(X2)
& ( ? [X3] :
( doDivides0(X3,X2)
& ? [X4] :
( X2 = sdtasdt0(X3,X4)
& aNaturalNumber0(X4) )
& aNaturalNumber0(X3)
& X2 != X3
& sz10 != X3 )
| sz10 = X2
| sz00 = X2 ) ) ),
inference(nnf_transformation,[],[f136]) ).
fof(f158,plain,
! [X0] :
( ~ sP0(X0)
| ( ~ isPrime0(X0)
& ( ? [X1] :
( doDivides0(X1,X0)
& ? [X2] :
( sdtasdt0(X1,X2) = X0
& aNaturalNumber0(X2) )
& aNaturalNumber0(X1)
& X0 != X1
& sz10 != X1 )
| sz10 = X0
| sz00 = X0 ) ) ),
inference(rectify,[],[f157]) ).
fof(f159,plain,
! [X0] :
( ~ sP0(X0)
| ( ~ isPrime0(X0)
& ( ( doDivides0(sK7(X0),X0)
& sdtasdt0(sK7(X0),sK8(X0)) = X0
& aNaturalNumber0(sK8(X0))
& aNaturalNumber0(sK7(X0))
& sK7(X0) != X0
& sz10 != sK7(X0) )
| sz10 = X0
| sz00 = X0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X1,sK7(X0)),skolemize(X2,sK8(X0))],[f158]) ).
fof(f242,plain,
! [X0] :
( ~ sP0(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_128,plain,
! [X0: $i] :
( ~ sP0(X0)
| ~ isPrime0(X0) ),
inference(cnf_transformation,[],[f242]) ).
tcf(c_2253,plain,
! [X0: $i] :
( ~ sP0(X0)
| ( X0 != xr ) ),
inference(resolution_lifted,[status(thm)],[c_128,c_170]) ).
tcf(c_2254,plain,
~ sP0(xr),
inference(unflattening,[status(thm)],[c_2253]) ).
tcf(c_58435,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_58434,c_34821,c_14390,c_13926,c_12643,c_11193,c_2254,c_175,c_185,c_187,c_116,c_117,c_118,c_162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM508+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 04:20:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 14.50/2.70 % SZS status Started for theBenchmark.p
% 14.50/2.70 % SZS status Theorem for theBenchmark.p
% 14.50/2.70
% 14.50/2.70 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.50/2.70
% 14.50/2.70 % ------ iProver source info
% 14.50/2.70
% 14.50/2.70 % git: date: 2026-07-19 20:42:38 +0200
% 14.50/2.70 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.50/2.70 % git: non_committed_changes: false
% 14.50/2.70
% 14.50/2.70 % ------ Parsing...
% 14.50/2.70 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.50/2.70
% 14.50/2.70 % ------ Preprocessing... sup_sim: 5 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 14.50/2.70
% 14.50/2.70 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.50/2.70
% 14.50/2.70 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 14.50/2.70 % ------ Proving...
% 14.50/2.70 % ------ Problem Properties
% 14.50/2.70
% 14.50/2.70 %
% 14.50/2.70 % clauses 132
% 14.50/2.70 % conjectures 4
% 14.50/2.70 % EPR 50
% 14.50/2.70 % Horn 92
% 14.50/2.70 % unary 51
% 14.50/2.70 % binary 15
% 14.50/2.70 % lits 405
% 14.50/2.70 % lits eq 126
% 14.50/2.70 % fd_pure 0
% 14.50/2.70 % fd_pseudo 0
% 14.50/2.70 % fd_cond 24
% 14.50/2.70 % fd_pseudo_cond 11
% 14.50/2.70 % AC symbols 0
% 14.50/2.70
% 14.50/2.70 % ------ Schedule dynamic 5 is on
% 14.50/2.70
% 14.50/2.70 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 14.50/2.70
% 14.50/2.70
% 14.50/2.70 % ------
% 14.50/2.70 % Current options:
% 14.50/2.70 % ------
% 14.50/2.70
% 14.50/2.70
% 14.50/2.70 %
% 14.50/2.70
% 14.50/2.70 % ------ Proving...
% 14.50/2.70 %
% 14.50/2.70
% 14.50/2.70 % SZS status Theorem for theBenchmark.p
% 14.50/2.70
% 14.50/2.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.50/2.70
% 14.50/2.70
%------------------------------------------------------------------------------