%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM476+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 : n011.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 02:25:09 PM UTC 2026
% Result : Theorem 15.19s 2.93s
% Output : CNFRefutation 15.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 124 ( 26 unt; 0 def)
% Number of atoms : 441 ( 177 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 531 ( 214 ~; 231 |; 62 &)
% ( 9 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 166 ( 0 sgn 152 !; 14 ?; 54 :)
% 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(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(f34,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
fof(f35,axiom,
( doDivides0(xl,sdtpldt0(xm,xn))
& doDivides0(xl,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324_04) ).
fof(f36,conjecture,
( ( xl != sz00
=> ? [X0] :
( ? [X1] :
( ? [X2] :
( xn = sdtasdt0(xl,X2)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& X2 = sdtmndt0(X1,X0) )
& sdtlseqdt0(X0,X1)
& X1 = sdtsldt0(sdtpldt0(xm,xn),xl) )
& X0 = sdtsldt0(xm,xl) ) )
=> doDivides0(xl,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f37,negated_conjecture,
~ ( ( xl != sz00
=> ? [X0] :
( ? [X1] :
( ? [X2] :
( xn = sdtasdt0(xl,X2)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& X2 = sdtmndt0(X1,X0) )
& sdtlseqdt0(X0,X1)
& X1 = sdtsldt0(sdtpldt0(xm,xn),xl) )
& X0 = sdtsldt0(xm,xl) ) )
=> doDivides0(xl,xn) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f41,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f42,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f44,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(flattening,[],[f43]) ).
fof(f49,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( X0 = sdtpldt0(sz00,X0)
& sdtpldt0(X0,sz00) = X0 ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f55,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| ( sz00 = sdtasdt0(sz00,X0)
& sdtasdt0(X0,sz00) = sz00 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| X1 = X2 ),
inference(ennf_transformation,[],[f14]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| X1 = X2 ),
inference(flattening,[],[f58]) ).
fof(f68,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f69,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( X2 = sdtmndt0(X1,X0)
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f68]) ).
fof(f85,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(ennf_transformation,[],[f30]) ).
fof(f86,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( doDivides0(X0,X1)
<=> ? [X2] :
( X1 = sdtasdt0(X0,X2)
& aNaturalNumber0(X2) ) ) ),
inference(flattening,[],[f85]) ).
fof(f87,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(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(flattening,[],[f87]) ).
fof(f93,plain,
( ( sz00 = xl
| ? [X0] :
( ? [X1] :
( ? [X2] :
( xn = sdtasdt0(xl,X2)
& sdtpldt0(sdtasdt0(xl,X0),sdtasdt0(xl,X2)) = sdtpldt0(sdtasdt0(xl,X0),xn)
& X2 = sdtmndt0(X1,X0) )
& sdtlseqdt0(X0,X1)
& X1 = sdtsldt0(sdtpldt0(xm,xn),xl) )
& X0 = sdtsldt0(xm,xl) ) )
& ~ doDivides0(xl,xn) ),
inference(ennf_transformation,[],[f37]) ).
fof(f97,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtmndt0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f98,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
& ( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| X2 = sdtmndt0(X1,X0) ) ) ),
inference(flattening,[],[f97]) ).
fof(f99,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,[],[f86]) ).
fof(f100,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,[],[f99]) ).
fof(f101,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))],[f100]) ).
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(nnf_transformation,[],[f88]) ).
fof(f103,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,[],[f102]) ).
fof(f104,plain,
( ( sz00 = xl
| ( xn = sdtasdt0(xl,sK4)
& sdtpldt0(sdtasdt0(xl,sK2),sdtasdt0(xl,sK4)) = sdtpldt0(sdtasdt0(xl,sK2),xn)
& sK4 = sdtmndt0(sK3,sK2)
& sdtlseqdt0(sK2,sK3)
& sdtsldt0(sdtpldt0(xm,xn),xl) = sK3
& sdtsldt0(xm,xl) = sK2 ) )
& ~ doDivides0(xl,xn) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f93]) ).
fof(f105,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f108,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f42]) ).
fof(f109,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f112,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 ),
inference(cnf_transformation,[],[f49]) ).
fof(f118,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f123,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f59]) ).
fof(f133,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| sdtmndt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f151,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sdtasdt0(X0,sK1(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f101]) ).
fof(f152,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| aNaturalNumber0(sK1(X0,X1)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| sdtsldt0(X1,X0) != X2
| aNaturalNumber0(X2) ),
inference(cnf_transformation,[],[f103]) ).
fof(f159,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f34]) ).
fof(f160,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f34]) ).
fof(f161,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f34]) ).
fof(f162,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f35]) ).
fof(f163,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f35]) ).
fof(f164,plain,
( sz00 = xl
| xn = sdtasdt0(xl,sK4) ),
inference(cnf_transformation,[],[f104]) ).
fof(f166,plain,
( sz00 = xl
| sK4 = sdtmndt0(sK3,sK2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f167,plain,
( sz00 = xl
| sdtlseqdt0(sK2,sK3) ),
inference(cnf_transformation,[],[f104]) ).
fof(f168,plain,
( sz00 = xl
| sdtsldt0(sdtpldt0(xm,xn),xl) = sK3 ),
inference(cnf_transformation,[],[f104]) ).
fof(f169,plain,
( sz00 = xl
| sdtsldt0(xm,xl) = sK2 ),
inference(cnf_transformation,[],[f104]) ).
fof(f170,plain,
~ doDivides0(xl,xn),
inference(cnf_transformation,[],[f104]) ).
fof(f173,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| aNaturalNumber0(sdtmndt0(X1,X0)) ),
inference(equality_resolution,[],[f133]) ).
fof(f177,plain,
! [X2,X0] :
( ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,sdtasdt0(X0,X2)) ),
inference(equality_resolution,[],[f153]) ).
fof(f179,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1)
| sz00 = X0
| aNaturalNumber0(sdtsldt0(X1,X0)) ),
inference(equality_resolution,[],[f155]) ).
tcf(c_49,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f105]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_57,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_63,plain,
! [X0: $i] :
( ( sdtasdt0(sz00,X0) = sz00 )
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sdtpldt0(X0,X2) ) ),
inference(cnf_transformation,[],[f123]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f173]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( doDivides0(X0,sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtasdt0(X0,X1)) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sK1(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(X0,sK1(X0,X1)) = X1 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ( X0 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_102,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f161]) ).
tcf(c_103,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f160]) ).
tcf(c_104,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f159]) ).
tcf(c_105,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f163]) ).
tcf(c_106,plain,
doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f162]) ).
tcf(c_107,negated_conjecture,
~ doDivides0(xl,xn),
inference(cnf_transformation,[],[f170]) ).
tcf(c_108,negated_conjecture,
( ( sz00 = xl )
| ( sdtsldt0(xm,xl) = sK2 ) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_109,negated_conjecture,
( ( sz00 = xl )
| ( sdtsldt0(sdtpldt0(xm,xn),xl) = sK3 ) ),
inference(cnf_transformation,[],[f168]) ).
tcf(c_110,negated_conjecture,
( sdtlseqdt0(sK2,sK3)
| ( sz00 = xl ) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_111,negated_conjecture,
( ( sz00 = xl )
| ( sdtmndt0(sK3,sK2) = sK4 ) ),
inference(cnf_transformation,[],[f166]) ).
tcf(c_113,negated_conjecture,
( ( sz00 = xl )
| ( sdtasdt0(xl,sK4) = xn ) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_147,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_1011,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1013,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1015,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sdtpldt0(X0,X2) = sdtpldt0(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1019,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1962,plain,
! [X0: $i,X1: $i] :
( doDivides0(xl,xn)
| ~ doDivides0(X0,X1)
| ( xn != X1 )
| ( xl != X0 ) ),
inference(instantiation,[status(thm)],[c_1019]) ).
tcf(c_1976,plain,
! [X0: $i,X1: $i,X2: $i] :
( doDivides0(xl,xn)
| ~ doDivides0(X0,sdtpldt0(X1,X2))
| ( xn != sdtpldt0(X1,X2) )
| ( xl != X0 ) ),
inference(instantiation,[status(thm)],[c_1962]) ).
tcf(c_2025,plain,
( doDivides0(xl,xn)
| ~ doDivides0(xl,sdtpldt0(xm,xn))
| ( xn != sdtpldt0(xm,xn) )
| ( xl != xl ) ),
inference(instantiation,[status(thm)],[c_1976]) ).
tcf(c_2047,plain,
( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_2051,plain,
! [X0: $i] :
( ( xn = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ( sdtpldt0(X0,xn) != sdtpldt0(X0,sdtpldt0(xm,xn)) ) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_2052,plain,
( ( xn = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ( sdtpldt0(sz00,xn) != sdtpldt0(sz00,sdtpldt0(xm,xn)) ) ),
inference(instantiation,[status(thm)],[c_2051]) ).
tcf(c_2435,plain,
xl = xl,
inference(instantiation,[status(thm)],[c_1011]) ).
tcf(c_2676,plain,
( ( sdtpldt0(sz00,sdtpldt0(xm,xn)) = sdtpldt0(xm,xn) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_2995,plain,
( doDivides0(xl,xn)
| ( sz00 = xl )
| ~ aNaturalNumber0(sK4)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_113,c_147]) ).
tcf(c_3281,plain,
( ~ aNaturalNumber0(sK4)
| ( sz00 = xl ) ),
inference(global_subsumption_just,[status(thm)],[c_2995,c_102,c_107,c_2995]) ).
tcf(c_3282,plain,
( ( sz00 = xl )
| ~ aNaturalNumber0(sK4) ),
inference(renaming,[status(thm)],[c_3281]) ).
tcf(c_3360,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sdtpldt0(X0,X2) = sdtpldt0(X0,sdtpldt0(xm,xn)) )
| ( sdtpldt0(X0,X2) != X1 )
| ( sdtpldt0(X0,sdtpldt0(xm,xn)) != X1 ) ),
inference(instantiation,[status(thm)],[c_1013]) ).
tcf(c_3846,plain,
! [X0: $i,X1: $i] :
( ( sdtpldt0(X0,X1) = sdtpldt0(xm,X1) )
| ( X1 != X1 )
| ( X0 != xm ) ),
inference(instantiation,[status(thm)],[c_1015]) ).
tcf(c_4060,plain,
xn = xn,
inference(instantiation,[status(thm)],[c_1011]) ).
tcf(c_4952,plain,
( aNaturalNumber0(sK4)
| ( sz00 = xl )
| ~ aNaturalNumber0(sK3)
| ~ aNaturalNumber0(sK2)
| ~ sdtlseqdt0(sK2,sK3) ),
inference(superposition,[status(thm)],[c_111,c_77]) ).
tcf(c_5302,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(sK2,sK3)
| sdtlseqdt0(X0,sz00)
| ~ sdtlseqdt0(X1,xl)
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_1017,c_110]) ).
tcf(c_7095,plain,
( sdtlseqdt0(sK2,sK3)
| sdtlseqdt0(sdtsldt0(xm,xl),sz00)
| ( sz00 = xl )
| ~ sdtlseqdt0(sK2,xl) ),
inference(resolution,[status(thm)],[c_5302,c_108]) ).
tcf(c_7409,plain,
( ( sdtasdt0(xl,sK1(xl,xm)) = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_105,c_96]) ).
tcf(c_7471,plain,
( aNaturalNumber0(sK2)
| ( sz00 = xl )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl)
| ~ doDivides0(xl,xm) ),
inference(superposition,[status(thm)],[c_108,c_98]) ).
tcf(c_7472,plain,
( aNaturalNumber0(sK3)
| ( sz00 = xl )
| ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ doDivides0(xl,sdtpldt0(xm,xn)) ),
inference(superposition,[status(thm)],[c_109,c_98]) ).
tcf(c_7674,plain,
sz00 = xl,
inference(global_subsumption_just,[status(thm)],[c_7095,c_104,c_103,c_102,c_105,c_106,c_110,c_2047,c_3282,c_4952,c_7471,c_7472]) ).
tcf(c_9188,plain,
! [X0: $i] :
( ( sdtpldt0(sz00,X0) = sdtpldt0(sz00,sdtpldt0(xm,xn)) )
| ( sdtpldt0(sz00,X0) != sdtpldt0(xm,xn) )
| ( sdtpldt0(sz00,sdtpldt0(xm,xn)) != sdtpldt0(xm,xn) ) ),
inference(instantiation,[status(thm)],[c_3360]) ).
tcf(c_9856,plain,
! [X0: $i] :
( ( sdtpldt0(X0,xn) = sdtpldt0(xm,xn) )
| ( xn != xn )
| ( X0 != xm ) ),
inference(instantiation,[status(thm)],[c_3846]) ).
tcf(c_9857,plain,
( ( sdtpldt0(sz00,xn) = sdtpldt0(xm,xn) )
| ( xn != xn )
| ( sz00 != xm ) ),
inference(instantiation,[status(thm)],[c_9856]) ).
tcf(c_10290,negated_conjecture,
sz00 = xl,
inference(global_subsumption_just,[status(thm)],[c_110,c_7674]) ).
tcf(c_10306,plain,
doDivides0(sz00,xm),
inference(superposition,[status(thm)],[c_10290,c_105]) ).
tcf(c_10582,plain,
! [X0: $i,X1: $i] :
( ( sdtasdt0(sz00,sK1(X0,X1)) = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,X1) ),
inference(superposition,[status(thm)],[c_95,c_63]) ).
tcf(c_10807,plain,
( ( sdtasdt0(xl,sK1(xl,xm)) = xm )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xl) ),
inference(superposition,[status(thm)],[c_105,c_96]) ).
tcf(c_10886,plain,
sdtasdt0(xl,sK1(xl,xm)) = xm,
inference(global_subsumption_just,[status(thm)],[c_10807,c_103,c_102,c_7409]) ).
tcf(c_10888,plain,
sdtasdt0(sz00,sK1(sz00,xm)) = xm,
inference(superposition,[status(thm)],[c_10290,c_10886]) ).
tcf(c_16625,plain,
( ( sdtpldt0(sz00,xn) = sdtpldt0(sz00,sdtpldt0(xm,xn)) )
| ( sdtpldt0(sz00,xn) != sdtpldt0(xm,xn) )
| ( sdtpldt0(sz00,sdtpldt0(xm,xn)) != sdtpldt0(xm,xn) ) ),
inference(instantiation,[status(thm)],[c_9188]) ).
tcf(c_17253,plain,
( ( sdtasdt0(sz00,sK1(sz00,xm)) = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00) ),
inference(superposition,[status(thm)],[c_10306,c_10582]) ).
tcf(c_18210,plain,
sdtasdt0(sz00,sK1(sz00,xm)) = sz00,
inference(global_subsumption_just,[status(thm)],[c_17253,c_103,c_49,c_17253]) ).
tcf(c_18217,plain,
sz00 = xm,
inference(superposition,[status(thm)],[c_18210,c_10888]) ).
tcf(c_18218,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_18217,c_16625,c_9857,c_4060,c_2676,c_2435,c_2052,c_2047,c_2025,c_106,c_107,c_49,c_103,c_104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM476+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.41 % Computer : n011.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Thu Sep 24 04:10:27 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/0.47 Running first-order theorem proving
% 0.16/0.47 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
% 0.16/0.48
% 0.16/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.48
% 0.16/0.48 % Detected problem language: tptp
% 0.22/0.50 % Proving...
% 15.19/2.93 % SZS status Started for theBenchmark.p
% 15.19/2.93 % SZS status Theorem for theBenchmark.p
% 15.19/2.93
% 15.19/2.93 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 15.19/2.93
% 15.19/2.93 % ------ iProver source info
% 15.19/2.93
% 15.19/2.93 % git: date: 2026-07-19 20:42:38 +0200
% 15.19/2.93 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 15.19/2.93 % git: non_committed_changes: false
% 15.19/2.93
% 15.19/2.93 % ------ Parsing...
% 15.19/2.93 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 15.19/2.93
% 15.19/2.93 % ------ 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 %
% 15.19/2.93
% 15.19/2.93 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 15.19/2.93
% 15.19/2.93 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 15.19/2.93 % ------ Proving...
% 15.19/2.93 % ------ Problem Properties
% 15.19/2.93
% 15.19/2.93 %
% 15.19/2.93 % clauses 60
% 15.19/2.93 % conjectures 7
% 15.19/2.93 % EPR 15
% 15.19/2.93 % Horn 41
% 15.19/2.93 % unary 9
% 15.19/2.93 % binary 13
% 15.19/2.93 % lits 206
% 15.19/2.93 % lits eq 60
% 15.19/2.93 % fd_pure 0
% 15.19/2.93 % fd_pseudo 0
% 15.19/2.93 % fd_cond 6
% 15.19/2.93 % fd_pseudo_cond 9
% 15.19/2.93 % AC symbols 0
% 15.19/2.93
% 15.19/2.93 % ------ Input Options Time Limit: Unbounded
% 15.19/2.93
% 15.19/2.93
% 15.19/2.93 % ------
% 15.19/2.93 % Current options:
% 15.19/2.93 % ------
% 15.19/2.93
% 15.19/2.93
% 15.19/2.93 %
% 15.19/2.93
% 15.19/2.93 % ------ Proving...
% 15.19/2.93 %
% 15.19/2.93
% 15.19/2.93 % SZS status Theorem for theBenchmark.p
% 15.19/2.93
% 15.19/2.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 15.19/2.94
% 15.19/2.94
%------------------------------------------------------------------------------