%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM516+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 : n001.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 22.62s 4.29s
% Output : CNFRefutation 22.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 74 ( 14 unt; 1 def)
% Number of atoms : 306 ( 107 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 372 ( 140 ~; 131 |; 89 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 70 ( 0 sgn 64 !; 6 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
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/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtpldt0(X0,X1) = sz00
=> ( X1 = sz00
& X0 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(f53,axiom,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& ? [X0] :
( sdtpldt0(sdtsldt0(xn,xr),X0) = xn
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& ~ ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> sdtsldt0(xn,xr) = xn ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2504) ).
fof(f54,axiom,
( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& ? [X0] :
( sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2529) ).
fof(f55,conjecture,
( ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X0] :
( sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(X0) ) ) )
& ~ ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f56,negated_conjecture,
~ ( ( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) )
=> ( sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X0] :
( sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0) = sdtpldt0(sdtpldt0(xn,xm),xp)
& aNaturalNumber0(X0) ) ) )
& ~ ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f65,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f66,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(flattening,[],[f65]) ).
fof(f82,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(f83,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,[],[f82]) ).
fof(f86,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f87,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| ( X1 = sz00
& X0 = sz00 ) ),
inference(flattening,[],[f86]) ).
fof(f99,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f100,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtlseqdt0(X1,X0)
& X1 != X0 )
| sdtlseqdt0(X0,X1) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ! [X2] :
( ~ aNaturalNumber0(X2)
| ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f102,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ! [X2] :
( ~ aNaturalNumber0(X2)
| ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X0,X2) != sdtpldt0(X1,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ),
inference(flattening,[],[f101]) ).
fof(f138,plain,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& ? [X0] :
( sdtpldt0(sdtsldt0(xn,xr),X0) = xn
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn != sdtsldt0(xn,xr) ),
inference(ennf_transformation,[],[f53]) ).
fof(f139,plain,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& ? [X0] :
( sdtpldt0(sdtsldt0(xn,xr),X0) = xn
& aNaturalNumber0(X0) )
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn != sdtsldt0(xn,xr) ),
inference(flattening,[],[f138]) ).
fof(f140,plain,
( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ! [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0)
| ~ aNaturalNumber0(X0) ) )
| ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f141,plain,
( ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ! [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0)
| ~ aNaturalNumber0(X0) ) )
| ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(flattening,[],[f140]) ).
fof(f182,plain,
( sdtlseqdt0(sdtsldt0(xn,xr),xn)
& xn = sdtpldt0(sdtsldt0(xn,xr),sK22)
& aNaturalNumber0(sK22)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn != sdtsldt0(xn,xr) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(X0,sK22)],[f139]) ).
fof(f183,plain,
( doDivides0(xp,sdtasdt0(sdtsldt0(xn,xr),xm))
& sdtasdt0(sdtsldt0(xn,xr),xm) = sdtasdt0(xp,sK23)
& aNaturalNumber0(sK23)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(X0,sK23)],[f54]) ).
fof(f188,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| aNaturalNumber0(sdtpldt0(X0,X1)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f202,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| X1 = X2 ),
inference(cnf_transformation,[],[f83]) ).
fof(f206,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sz00 != sdtpldt0(X0,X1)
| sz00 = X1 ),
inference(cnf_transformation,[],[f87]) ).
fof(f218,plain,
! [X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f220,plain,
! [X2,X0,X1] :
( ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2)) ),
inference(cnf_transformation,[],[f102]) ).
fof(f253,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f254,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f255,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f326,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[],[f182]) ).
fof(f333,plain,
xn != sdtsldt0(xn,xr),
inference(cnf_transformation,[],[f182]) ).
fof(f338,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f183]) ).
fof(f343,plain,
( sP3
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sdtpldt0(X2,X1) ) ),
inference(cnf_transformation,[],[f202]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( ( X1 = sz00 )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ( sdtpldt0(X0,X1) != sz00 ) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ( X0 = X1 )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f255]) ).
tcf(c_117,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f254]) ).
tcf(c_118,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f253]) ).
tcf(c_189,negated_conjecture,
sdtsldt0(xn,xr) != xn,
inference(cnf_transformation,[],[f333]) ).
tcf(c_196,plain,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(cnf_transformation,[],[f326]) ).
tcf(c_197,plain,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(cnf_transformation,[],[f338]) ).
tcf(c_208,negated_conjecture,
( sP3
| ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(cnf_transformation,[],[f343]) ).
tcf(c_7863,plain,
( aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_15740,plain,
( sP3
| ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(resolution,[status(thm)],[c_67,c_208]) ).
fof(f147,definition,
( ~ sP3
| ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ! [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0)
| ~ aNaturalNumber0(X0) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f148,plain,
( sP3
| ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp)
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr)) ) ),
inference(definition_folding,[],[f141,f147]) ).
fof(f184,plain,
( ~ sP3
| ( xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(sdtsldt0(xn,xr))
& ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ! [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),X0)
| ~ aNaturalNumber0(X0) ) ) ),
inference(nnf_transformation,[],[f147]) ).
fof(f341,plain,
( ~ sP3
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cnf_transformation,[],[f184]) ).
tcf(c_203,negated_conjecture,
( ~ sP3
| ~ sdtlseqdt0(sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
inference(cnf_transformation,[],[f341]) ).
tcf(c_11945,plain,
( ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) )
| ~ sP3
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm)) ),
inference(superposition,[status(thm)],[c_87,c_203]) ).
tcf(c_12968,plain,
( ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) )
| ~ sP3
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ sdtlseqdt0(sdtpldt0(sdtsldt0(xn,xr),xm),sdtpldt0(xn,xm)) ),
inference(global_subsumption_just,[status(thm)],[c_11945,c_118,c_117,c_116,c_7863,c_11945]) ).
tcf(c_12970,plain,
( sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(sdtsldt0(xn,xr),xm))
| ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) )
| ~ sP3
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(superposition,[status(thm)],[c_83,c_12968]) ).
tcf(c_12972,plain,
( ( sdtsldt0(xn,xr) = xn )
| ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) )
| ~ sP3
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr))
| ~ sdtlseqdt0(sdtsldt0(xn,xr),xn)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(superposition,[status(thm)],[c_87,c_12968]) ).
tcf(c_12973,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ~ sP3
| ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) ) ),
inference(global_subsumption_just,[status(thm)],[c_12970,c_117,c_116,c_197,c_196,c_189,c_12972]) ).
tcf(c_12974,plain,
( ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) )
| ~ sP3
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(renaming,[status(thm)],[c_12973]) ).
tcf(c_12975,plain,
( ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) )
| ~ sP3
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_52,c_12974]) ).
tcf(c_12976,plain,
( ~ sP3
| ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) ) ),
inference(global_subsumption_just,[status(thm)],[c_12972,c_117,c_197,c_12975]) ).
tcf(c_12977,plain,
( ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) )
| ~ sP3 ),
inference(renaming,[status(thm)],[c_12976]) ).
tcf(c_12978,plain,
( ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) )
| ( sdtpldt0(sdtpldt0(sdtsldt0(xn,xr),xm),xp) = sdtpldt0(sdtpldt0(xn,xm),xp) ) ),
inference(superposition,[status(thm)],[c_208,c_12977]) ).
tcf(c_13027,plain,
( ( sz00 = xp )
| ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ( sdtpldt0(sdtpldt0(xn,xm),xp) != sz00 ) ),
inference(superposition,[status(thm)],[c_12978,c_71]) ).
tcf(c_15888,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm))
| ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) ) ),
inference(global_subsumption_just,[status(thm)],[c_13027,c_118,c_117,c_116,c_7863,c_12977,c_15740]) ).
tcf(c_15889,plain,
( ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xn,xr),xm)) ),
inference(renaming,[status(thm)],[c_15888]) ).
tcf(c_15890,plain,
( ( sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(superposition,[status(thm)],[c_52,c_15889]) ).
tcf(c_16107,plain,
sdtpldt0(sdtsldt0(xn,xr),xm) = sdtpldt0(xn,xm),
inference(global_subsumption_just,[status(thm)],[c_15740,c_117,c_197,c_15890]) ).
tcf(c_16113,plain,
( ( sdtsldt0(xn,xr) = xn )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtsldt0(xn,xr)) ),
inference(resolution,[status(thm)],[c_16107,c_67]) ).
tcf(c_16114,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_16113,c_189,c_197,c_116,c_117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM516+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n001.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Thu Sep 24 04:29:06 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 22.62/4.29 % SZS status Started for theBenchmark.p
% 22.62/4.29 % SZS status Theorem for theBenchmark.p
% 22.62/4.29
% 22.62/4.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.62/4.29
% 22.62/4.29 % ------ iProver source info
% 22.62/4.29
% 22.62/4.29 % git: date: 2026-07-19 20:42:38 +0200
% 22.62/4.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.62/4.29 % git: non_committed_changes: false
% 22.62/4.29
% 22.62/4.29 % ------ Parsing...
% 22.62/4.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.62/4.29
% 22.62/4.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e %
% 22.62/4.29
% 22.62/4.29 % ------ Preprocessing...%
% 22.62/4.29
% 22.62/4.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 22.62/4.29 % ------ Proving...
% 22.62/4.29 % ------ Problem Properties
% 22.62/4.29
% 22.62/4.29 %
% 22.62/4.29 % clauses 144
% 22.62/4.29 % conjectures 21
% 22.62/4.29 % EPR 54
% 22.62/4.29 % Horn 101
% 22.62/4.29 % unary 57
% 22.62/4.29 % binary 20
% 22.62/4.29 % lits 424
% 22.62/4.29 % lits eq 131
% 22.62/4.29 % fd_pure 0
% 22.62/4.29 % fd_pseudo 0
% 22.62/4.29 % fd_cond 24
% 22.62/4.29 % fd_pseudo_cond 11
% 22.62/4.29 % AC symbols 0
% 22.62/4.29
% 22.62/4.29 % ------ Input Options Time Limit: Unbounded
% 22.62/4.29
% 22.62/4.29
% 22.62/4.29 % ------
% 22.62/4.29 % Current options:
% 22.62/4.29 % ------
% 22.62/4.29
% 22.62/4.29
% 22.62/4.29 %
% 22.62/4.29
% 22.62/4.29 % ------ Proving...
% 22.62/4.29 %
% 22.62/4.29
% 22.62/4.29 % SZS status Theorem for theBenchmark.p
% 22.62/4.29
% 22.62/4.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.62/4.29
% 22.62/4.29
%------------------------------------------------------------------------------