%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM469+1 : 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 : n015.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 02:24:44 PM UTC 2026
% Result : Theorem 17.24s 4.79s
% Output : CNFRefutation 17.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 16
% Syntax : Number of formulae : 131 ( 34 unt; 1 def)
% Number of atoms : 485 ( 107 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 515 ( 215 ~; 232 |; 44 &)
% ( 9 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 153 ( 0 sgn 143 !; 10 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( X0 != sz00
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
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/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(f33,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).
fof(f34,axiom,
( doDivides0(xl,xn)
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).
fof(f35,axiom,
( xl != sz00
=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1298) ).
fof(f36,conjecture,
doDivides0(xl,sdtpldt0(xm,xn)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f37,negated_conjecture,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f40,plain,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(flattening,[],[f37]) ).
fof(f42,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f43,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f45,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f44]) ).
fof(f50,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f56,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f67,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f67]) ).
fof(f72,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f21]) ).
fof(f73,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f72]) ).
fof(f84,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f87,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f86]) ).
fof(f88,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(f89,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,[],[f88]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(flattening,[],[f90]) ).
fof(f92,plain,
( sz00 = xl
| sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
inference(ennf_transformation,[],[f35]) ).
fof(f93,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f94,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ sdtlseqdt0(X0,X1)
| ( sdtpldt0(X0,sK0(X0,X1)) = X1
& aNaturalNumber0(sK0(X0,X1)) ) )
& ( ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| sdtlseqdt0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f94]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f87]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(rectify,[],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( ( ~ doDivides0(X0,X1)
| ( sdtasdt0(X0,sK1(X0,X1)) = X1
& aNaturalNumber0(sK1(X0,X1)) ) )
& ( ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
| doDivides0(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f99]) ).
fof(f101,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,[],[f89]) ).
fof(f102,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,[],[f101]) ).
fof(f103,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f106,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f43]) ).
fof(f107,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f110,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f50]) ).
fof(f117,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) ),
inference(cnf_transformation,[],[f56]) ).
fof(f129,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f134,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f148,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 = X0
| sdtlseqdt0(X1,sdtasdt0(X1,X0)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f149,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sdtasdt0(X0,sK1(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f100]) ).
fof(f150,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| aNaturalNumber0(sK1(X0,X1)) ),
inference(cnf_transformation,[],[f100]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f102]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| doDivides0(X0,X2) ),
inference(cnf_transformation,[],[f91]) ).
fof(f156,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f33]) ).
fof(f157,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f33]) ).
fof(f158,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f33]) ).
fof(f159,plain,
doDivides0(xl,xn),
inference(cnf_transformation,[],[f34]) ).
fof(f160,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f34]) ).
fof(f161,plain,
( sz00 = xl
| sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f162,plain,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f40]) ).
fof(f163,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,sdtpldt0(X0,X2)) ),
inference(equality_resolution,[],[f129]) ).
fof(f169,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f151]) ).
fof(f171,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f153]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f103]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_62,plain,
! [X0: $i] :
( ( sdtasdt0(X0,sz00) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f117]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sK1(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,sK1(X0,X1)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_101,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f158]) ).
tcf(c_102,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f157]) ).
tcf(c_103,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f156]) ).
tcf(c_104,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f160]) ).
tcf(c_105,plain,
doDivides0(xl,xn),
inference(cnf_transformation,[],[f159]) ).
tcf(c_106,plain,
( ( sz00 = xl )
| ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = sdtpldt0(xm,xn) ) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_107,negated_conjecture,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f162]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_94,c_53,c_94]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X0,sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_52,c_73]) ).
tcf(c_1660,definition,
iPr_def_10 = sdtpldt0(xm,xn),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1661,negated_conjecture,
~ doDivides0(xl,iPr_def_10),
inference(demodulation,[status(thm)],[c_107,c_1660]) ).
tcf(c_2548,plain,
( ( sz00 = xl )
| ( sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_106,c_1660]) ).
tcf(c_2572,plain,
sdtpldt0(sz00,xn) = xn,
inference(superposition,[status(thm)],[c_103,c_57]) ).
tcf(c_2615,plain,
( aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_1660,c_52]) ).
tcf(c_2631,plain,
aNaturalNumber0(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2615,c_103,c_102]) ).
tcf(c_2657,plain,
sdtasdt0(iPr_def_10,sz00) = sz00,
inference(superposition,[status(thm)],[c_2631,c_62]) ).
tcf(c_2719,plain,
( doDivides0(xl,iPr_def_10)
| ( sz00 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
inference(superposition,[status(thm)],[c_2548,c_140]) ).
tcf(c_2746,plain,
( ( sz00 = xl )
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2719,c_1661,c_101]) ).
tcf(c_2759,plain,
( sdtlseqdt0(xm,iPr_def_10)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_1660,c_143]) ).
tcf(c_2778,plain,
sdtlseqdt0(xm,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2759,c_103,c_102]) ).
tcf(c_2807,plain,
( ( sz00 = xl )
| ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl)) ),
inference(superposition,[status(thm)],[c_52,c_2746]) ).
tcf(c_3274,plain,
( doDivides0(iPr_def_10,sz00)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_2657,c_140]) ).
tcf(c_3277,plain,
doDivides0(iPr_def_10,sz00),
inference(forward_subsumption_resolution,[status(thm)],[c_3274,c_2631,c_49]) ).
tcf(c_3847,plain,
( ( xm = iPr_def_10 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(iPr_def_10,xm) ),
inference(superposition,[status(thm)],[c_2778,c_80]) ).
tcf(c_3875,plain,
( ( xm = iPr_def_10 )
| ~ sdtlseqdt0(iPr_def_10,xm) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3847,c_2631,c_102]) ).
tcf(c_4020,plain,
( ( sz00 = xl )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xl)) ),
inference(superposition,[status(thm)],[c_98,c_2807]) ).
tcf(c_4021,plain,
( ( sz00 = xl )
| ~ aNaturalNumber0(sdtsldt0(xn,xl)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4020,c_102,c_101,c_104]) ).
tcf(c_4299,plain,
( ( sz00 = xl )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xn) ),
inference(superposition,[status(thm)],[c_98,c_4021]) ).
tcf(c_4300,plain,
sz00 = xl,
inference(forward_subsumption_resolution,[status(thm)],[c_4299,c_103,c_101,c_105]) ).
tcf(c_4314,plain,
doDivides0(sz00,xn),
inference(demodulation,[status(thm)],[c_105,c_4300]) ).
tcf(c_4315,plain,
doDivides0(sz00,xm),
inference(demodulation,[status(thm)],[c_104,c_4300]) ).
tcf(c_4317,plain,
~ doDivides0(sz00,iPr_def_10),
inference(demodulation,[status(thm)],[c_1661,c_4300]) ).
tcf(c_4455,plain,
! [X0: $i] :
( doDivides0(iPr_def_10,X0)
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(sz00,X0) ),
inference(superposition,[status(thm)],[c_3277,c_100]) ).
tcf(c_4472,plain,
! [X0: $i] :
( doDivides0(iPr_def_10,X0)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(sz00,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4455,c_2631,c_49]) ).
tcf(c_14526,plain,
( doDivides0(iPr_def_10,xm)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_4315,c_4472]) ).
tcf(c_14532,plain,
doDivides0(iPr_def_10,xm),
inference(forward_subsumption_resolution,[status(thm)],[c_14526,c_102]) ).
tcf(c_14561,plain,
( ( sdtasdt0(iPr_def_10,sK1(iPr_def_10,xm)) = xm )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xm) ),
inference(superposition,[status(thm)],[c_14532,c_96]) ).
tcf(c_14563,plain,
sdtasdt0(iPr_def_10,sK1(iPr_def_10,xm)) = xm,
inference(forward_subsumption_resolution,[status(thm)],[c_14561,c_2631,c_102]) ).
tcf(c_15007,plain,
( sdtlseqdt0(iPr_def_10,xm)
| ( sK1(iPr_def_10,xm) = sz00 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(sK1(iPr_def_10,xm)) ),
inference(superposition,[status(thm)],[c_14563,c_93]) ).
tcf(c_15014,plain,
( sdtlseqdt0(iPr_def_10,xm)
| ( sK1(iPr_def_10,xm) = sz00 )
| ~ aNaturalNumber0(sK1(iPr_def_10,xm)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15007,c_2631]) ).
tcf(c_48677,plain,
( sdtlseqdt0(iPr_def_10,xm)
| ( sK1(iPr_def_10,xm) = sz00 )
| ~ aNaturalNumber0(iPr_def_10)
| ~ aNaturalNumber0(xm)
| ~ doDivides0(iPr_def_10,xm) ),
inference(superposition,[status(thm)],[c_95,c_15014]) ).
tcf(c_48678,plain,
( sdtlseqdt0(iPr_def_10,xm)
| ( sK1(iPr_def_10,xm) = sz00 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_48677,c_2631,c_102,c_14532]) ).
tcf(c_48697,plain,
( ( xm = iPr_def_10 )
| ( sK1(iPr_def_10,xm) = sz00 ) ),
inference(superposition,[status(thm)],[c_48678,c_3875]) ).
tcf(c_48772,plain,
( ( xm = iPr_def_10 )
| ( sdtasdt0(iPr_def_10,sz00) = xm ) ),
inference(superposition,[status(thm)],[c_48697,c_14563]) ).
tcf(c_48773,plain,
( ( xm = iPr_def_10 )
| ( sz00 = xm ) ),
inference(light_normalisation,[status(thm)],[c_48772,c_2657]) ).
tcf(c_49235,plain,
( ( xm = iPr_def_10 )
| ( sdtpldt0(sz00,xn) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_48773,c_1660]) ).
tcf(c_49261,plain,
( ( xn = iPr_def_10 )
| ( xm = iPr_def_10 ) ),
inference(light_normalisation,[status(thm)],[c_49235,c_2572]) ).
tcf(c_49774,plain,
( doDivides0(sz00,iPr_def_10)
| ( xm = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_49261,c_4314]) ).
tcf(c_49791,plain,
xm = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_49774,c_4317]) ).
tcf(c_50012,plain,
doDivides0(sz00,iPr_def_10),
inference(demodulation,[status(thm)],[c_4315,c_49791]) ).
tcf(c_50256,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_50012,c_4317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM469+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 04:11:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 17.24/4.79 % SZS status Started for theBenchmark.p
% 17.24/4.79 % SZS status Theorem for theBenchmark.p
% 17.24/4.79
% 17.24/4.79 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 17.24/4.79
% 17.24/4.79 % ------ iProver source info
% 17.24/4.79
% 17.24/4.79 % git: date: 2026-07-19 20:42:38 +0200
% 17.24/4.79 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 17.24/4.79 % git: non_committed_changes: false
% 17.24/4.79
% 17.24/4.79 % ------ Parsing...
% 17.24/4.79 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 17.24/4.79
% 17.24/4.79 % ------ Preprocessing... sup_sim: 0 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 %
% 17.24/4.79
% 17.24/4.79 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 17.24/4.79
% 17.24/4.79 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 17.24/4.79 % ------ Proving...
% 17.24/4.79 % ------ Problem Properties
% 17.24/4.79
% 17.24/4.79 %
% 17.24/4.79 % clauses 55
% 17.24/4.79 % conjectures 1
% 17.24/4.79 % EPR 15
% 17.24/4.79 % Horn 41
% 17.24/4.79 % unary 10
% 17.24/4.79 % binary 8
% 17.24/4.79 % lits 191
% 17.24/4.79 % lits eq 52
% 17.24/4.79 % fd_pure 0
% 17.24/4.79 % fd_pseudo 0
% 17.24/4.79 % fd_cond 6
% 17.24/4.79 % fd_pseudo_cond 9
% 17.24/4.79 % AC symbols 0
% 17.24/4.79
% 17.24/4.79 % ------ Schedule dynamic 5 is on
% 17.24/4.79
% 17.24/4.79 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.24/4.79
% 17.24/4.79
% 17.24/4.79 % ------
% 17.24/4.79 % Current options:
% 17.24/4.79 % ------
% 17.24/4.79
% 17.24/4.79
% 17.24/4.79 %
% 17.24/4.79
% 17.24/4.79 % ------ Proving...
% 17.24/4.79 %
% 17.24/4.79
% 17.24/4.79 % SZS status Theorem for theBenchmark.p
% 17.24/4.79
% 17.24/4.79 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.24/4.79
% 17.24/4.79
%------------------------------------------------------------------------------