%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET802+4 : TPTP v9.3.1. Released v3.2.0.
% 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 02:48:37 PM UTC 2026
% Result : Theorem 2.57s 6.30s
% Output : CNFRefutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 97 ( 2 unt; 0 def)
% Number of atoms : 411 ( 29 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 510 ( 210 ~; 219 |; 64 &)
% ( 9 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 224 ( 0 sgn 204 !; 20 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0,X1,X2] :
( lower_bound(X2,X0,X1)
<=> ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',lower_bound) ).
fof(f17,axiom,
! [X0,X1,X2] :
( least(X2,X0,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) )
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',least) ).
fof(f21,axiom,
! [X0,X1,X2,X3] :
( greatest_lower_bound(X0,X1,X2,X3)
<=> ( ! [X4] :
( ( lower_bound(X4,X2,X1)
& member(X4,X3) )
=> apply(X2,X4,X0) )
& lower_bound(X0,X2,X1)
& member(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',greatest_lower_bound) ).
fof(f22,conjecture,
! [X0,X1] :
( order(X0,X1)
=> ! [X2] :
( subset(X2,X1)
=> ! [X3] :
( least(X3,X0,X2)
<=> ( greatest_lower_bound(X3,X2,X0,X1)
& member(X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV14) ).
fof(f23,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2] :
( subset(X2,X1)
=> ! [X3] :
( least(X3,X0,X2)
<=> ( greatest_lower_bound(X3,X2,X0,X1)
& member(X3,X2) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f30,plain,
! [X0,X1,X2] :
( lower_bound(X2,X0,X1)
<=> ! [X3] :
( ~ member(X3,X1)
| apply(X0,X2,X3) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f31,plain,
! [X0,X1,X2] :
( least(X2,X0,X1)
<=> ( ! [X3] :
( ~ member(X3,X1)
| apply(X0,X2,X3) )
& member(X2,X1) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( greatest_lower_bound(X0,X1,X2,X3)
<=> ( ! [X4] :
( ~ lower_bound(X4,X2,X1)
| ~ member(X4,X3)
| apply(X2,X4,X0) )
& lower_bound(X0,X2,X1)
& member(X0,X1) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( greatest_lower_bound(X0,X1,X2,X3)
<=> ( ! [X4] :
( ~ lower_bound(X4,X2,X1)
| ~ member(X4,X3)
| apply(X2,X4,X0) )
& lower_bound(X0,X2,X1)
& member(X0,X1) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
? [X0,X1] :
( order(X0,X1)
& ? [X2] :
( subset(X2,X1)
& ? [X3] :
( least(X3,X0,X2)
<~> ( greatest_lower_bound(X3,X2,X0,X1)
& member(X3,X2) ) ) ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ( ~ lower_bound(X2,X0,X1)
| ! [X3] :
( ~ member(X3,X1)
| apply(X0,X2,X3) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ apply(X0,X2,X3) )
| lower_bound(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f30]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ( ~ lower_bound(X2,X0,X1)
| ! [X4] :
( ~ member(X4,X1)
| apply(X0,X2,X4) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ apply(X0,X2,X3) )
| lower_bound(X2,X0,X1) ) ),
inference(rectify,[],[f54]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ( ~ lower_bound(X2,X0,X1)
| ! [X4] :
( ~ member(X4,X1)
| apply(X0,X2,X4) ) )
& ( ( member(sK3(X0,X1,X2),X1)
& ~ apply(X0,X2,sK3(X0,X1,X2)) )
| lower_bound(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f55]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ( ~ least(X2,X0,X1)
| ( ! [X3] :
( ~ member(X3,X1)
| apply(X0,X2,X3) )
& member(X2,X1) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ apply(X0,X2,X3) )
| ~ member(X2,X1)
| least(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f31]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ( ~ least(X2,X0,X1)
| ( ! [X3] :
( ~ member(X3,X1)
| apply(X0,X2,X3) )
& member(X2,X1) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ apply(X0,X2,X3) )
| ~ member(X2,X1)
| least(X2,X0,X1) ) ),
inference(flattening,[],[f57]) ).
fof(f59,plain,
! [X0,X1,X2] :
( ( ~ least(X2,X0,X1)
| ( ! [X4] :
( ~ member(X4,X1)
| apply(X0,X2,X4) )
& member(X2,X1) ) )
& ( ? [X3] :
( member(X3,X1)
& ~ apply(X0,X2,X3) )
| ~ member(X2,X1)
| least(X2,X0,X1) ) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0,X1,X2] :
( ( ~ least(X2,X0,X1)
| ( ! [X4] :
( ~ member(X4,X1)
| apply(X0,X2,X4) )
& member(X2,X1) ) )
& ( ( member(sK4(X0,X1,X2),X1)
& ~ apply(X0,X2,sK4(X0,X1,X2)) )
| ~ member(X2,X1)
| least(X2,X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f59]) ).
fof(f61,plain,
! [X0,X1,X2,X3] :
( ( ~ greatest_lower_bound(X0,X1,X2,X3)
| ( ! [X4] :
( ~ lower_bound(X4,X2,X1)
| ~ member(X4,X3)
| apply(X2,X4,X0) )
& lower_bound(X0,X2,X1)
& member(X0,X1) ) )
& ( ? [X4] :
( lower_bound(X4,X2,X1)
& member(X4,X3)
& ~ apply(X2,X4,X0) )
| ~ lower_bound(X0,X2,X1)
| ~ member(X0,X1)
| greatest_lower_bound(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( ( ~ greatest_lower_bound(X0,X1,X2,X3)
| ( ! [X4] :
( ~ lower_bound(X4,X2,X1)
| ~ member(X4,X3)
| apply(X2,X4,X0) )
& lower_bound(X0,X2,X1)
& member(X0,X1) ) )
& ( ? [X4] :
( lower_bound(X4,X2,X1)
& member(X4,X3)
& ~ apply(X2,X4,X0) )
| ~ lower_bound(X0,X2,X1)
| ~ member(X0,X1)
| greatest_lower_bound(X0,X1,X2,X3) ) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( ( ~ greatest_lower_bound(X0,X1,X2,X3)
| ( ! [X5] :
( ~ lower_bound(X5,X2,X1)
| ~ member(X5,X3)
| apply(X2,X5,X0) )
& lower_bound(X0,X2,X1)
& member(X0,X1) ) )
& ( ? [X4] :
( lower_bound(X4,X2,X1)
& member(X4,X3)
& ~ apply(X2,X4,X0) )
| ~ lower_bound(X0,X2,X1)
| ~ member(X0,X1)
| greatest_lower_bound(X0,X1,X2,X3) ) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( ( ~ greatest_lower_bound(X0,X1,X2,X3)
| ( ! [X5] :
( ~ lower_bound(X5,X2,X1)
| ~ member(X5,X3)
| apply(X2,X5,X0) )
& lower_bound(X0,X2,X1)
& member(X0,X1) ) )
& ( ( lower_bound(sK5(X0,X1,X2,X3),X2,X1)
& member(sK5(X0,X1,X2,X3),X3)
& ~ apply(X2,sK5(X0,X1,X2,X3),X0) )
| ~ lower_bound(X0,X2,X1)
| ~ member(X0,X1)
| greatest_lower_bound(X0,X1,X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X4,sK5(X0,X1,X2,X3))],[f63]) ).
fof(f65,plain,
? [X0,X1] :
( order(X0,X1)
& ? [X2] :
( subset(X2,X1)
& ? [X3] :
( ( least(X3,X0,X2)
| ( greatest_lower_bound(X3,X2,X0,X1)
& member(X3,X2) ) )
& ( ~ least(X3,X0,X2)
| ~ greatest_lower_bound(X3,X2,X0,X1)
| ~ member(X3,X2) ) ) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f66,plain,
? [X0,X1] :
( order(X0,X1)
& ? [X2] :
( subset(X2,X1)
& ? [X3] :
( ( least(X3,X0,X2)
| ( greatest_lower_bound(X3,X2,X0,X1)
& member(X3,X2) ) )
& ( ~ least(X3,X0,X2)
| ~ greatest_lower_bound(X3,X2,X0,X1)
| ~ member(X3,X2) ) ) ) ),
inference(flattening,[],[f65]) ).
fof(f67,plain,
( order(sK6,sK7)
& subset(sK8,sK7)
& ( least(sK9,sK6,sK8)
| ( greatest_lower_bound(sK9,sK8,sK6,sK7)
& member(sK9,sK8) ) )
& ( ~ least(sK9,sK6,sK8)
| ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
| ~ member(sK9,sK8) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9)],[f66]) ).
fof(f97,plain,
! [X2,X0,X1,X4] :
( ~ lower_bound(X2,X0,X1)
| ~ member(X4,X1)
| apply(X0,X2,X4) ),
inference(cnf_transformation,[],[f56]) ).
fof(f98,plain,
! [X2,X0,X1] :
( member(sK3(X0,X1,X2),X1)
| lower_bound(X2,X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ apply(X0,X2,sK3(X0,X1,X2))
| lower_bound(X2,X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f100,plain,
! [X2,X0,X1,X4] :
( ~ least(X2,X0,X1)
| ~ member(X4,X1)
| apply(X0,X2,X4) ),
inference(cnf_transformation,[],[f60]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ least(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f102,plain,
! [X2,X0,X1] :
( member(sK4(X0,X1,X2),X1)
| ~ member(X2,X1)
| least(X2,X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f103,plain,
! [X2,X0,X1] :
( ~ apply(X0,X2,sK4(X0,X1,X2))
| ~ member(X2,X1)
| least(X2,X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f105,plain,
! [X2,X3,X0,X1] :
( ~ greatest_lower_bound(X0,X1,X2,X3)
| lower_bound(X0,X2,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f107,plain,
! [X2,X3,X0,X1] :
( lower_bound(sK5(X0,X1,X2,X3),X2,X1)
| ~ lower_bound(X0,X2,X1)
| ~ member(X0,X1)
| greatest_lower_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f64]) ).
fof(f109,plain,
! [X2,X3,X0,X1] :
( ~ apply(X2,sK5(X0,X1,X2,X3),X0)
| ~ lower_bound(X0,X2,X1)
| ~ member(X0,X1)
| greatest_lower_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f64]) ).
fof(f112,plain,
( least(sK9,sK6,sK8)
| greatest_lower_bound(sK9,sK8,sK6,sK7) ),
inference(cnf_transformation,[],[f67]) ).
fof(f113,plain,
( least(sK9,sK6,sK8)
| member(sK9,sK8) ),
inference(cnf_transformation,[],[f67]) ).
fof(f114,plain,
( ~ least(sK9,sK6,sK8)
| ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
| ~ member(sK9,sK8) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] :
( lower_bound(X1,X0,X2)
| ~ apply(X0,X1,sK3(X0,X2,X1)) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( lower_bound(X2,X0,X1)
| member(sK3(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X0,X3)
| ~ member(X3,X2)
| ~ lower_bound(X0,X1,X2) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( least(X1,X0,X2)
| ~ member(X1,X2)
| ~ apply(X0,X1,sK4(X0,X2,X1)) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( least(X0,X2,X1)
| member(sK4(X2,X1,X0),X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ least(X0,X1,X2) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X0,X3)
| ~ member(X3,X2)
| ~ least(X0,X1,X2) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greatest_lower_bound(X1,X2,X0,X3)
| ~ member(X1,X2)
| ~ lower_bound(X1,X0,X2)
| ~ apply(X0,sK5(X1,X2,X0,X3),X1) ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greatest_lower_bound(X0,X2,X1,X3)
| lower_bound(sK5(X0,X2,X1,X3),X1,X2)
| ~ member(X0,X2)
| ~ lower_bound(X0,X1,X2) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( lower_bound(X0,X2,X1)
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_91,negated_conjecture,
( ~ member(sK9,sK8)
| ~ least(sK9,sK6,sK8)
| ~ greatest_lower_bound(sK9,sK8,sK6,sK7) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_92,negated_conjecture,
( member(sK9,sK8)
| least(sK9,sK6,sK8) ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_93,negated_conjecture,
( least(sK9,sK6,sK8)
| greatest_lower_bound(sK9,sK8,sK6,sK7) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ least(X0,X1,X2)
| member(X0,X2) ),
inference(prop_impl_just,[status(thm)],[c_83]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ least(X0,X1,X2) ),
inference(renaming,[status(thm)],[c_155]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( lower_bound(X0,X2,X1)
| ~ greatest_lower_bound(X0,X1,X2,X3) ),
inference(prop_impl_just,[status(thm)],[c_89]) ).
tcf(c_189,plain,
( least(sK9,sK6,sK8)
| member(sK9,sK8) ),
inference(prop_impl_just,[status(thm)],[c_92]) ).
tcf(c_190,plain,
( member(sK9,sK8)
| least(sK9,sK6,sK8) ),
inference(renaming,[status(thm)],[c_189]) ).
tcf(c_191,plain,
( least(sK9,sK6,sK8)
| greatest_lower_bound(sK9,sK8,sK6,sK7) ),
inference(prop_impl_just,[status(thm)],[c_93]) ).
tcf(c_313,plain,
member(sK9,sK8),
inference(forward_subsumption_resolution,[status(thm)],[c_190,c_156]) ).
tcf(c_317,plain,
( ~ least(sK9,sK6,sK8)
| ~ greatest_lower_bound(sK9,sK8,sK6,sK7) ),
inference(backward_subsumption_resolution,[status(thm)],[c_91,c_313]) ).
tcf(c_923,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X1,X2)
| ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
| ~ apply(X0,X1,sK4(X0,X2,X1))
| ( X2 != sK8 )
| ( X1 != sK9 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_81,c_317]) ).
tcf(c_924,plain,
( ~ member(sK9,sK8)
| ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
| ~ apply(sK6,sK9,sK4(sK6,sK8,sK9)) ),
inference(unflattening,[status(thm)],[c_923]) ).
tcf(c_925,plain,
( ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
| ~ greatest_lower_bound(sK9,sK8,sK6,sK7) ),
inference(global_subsumption_just,[status(thm)],[c_924,c_313,c_924]) ).
tcf(c_926,plain,
( ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
| ~ apply(sK6,sK9,sK4(sK6,sK8,sK9)) ),
inference(renaming,[status(thm)],[c_925]) ).
tcf(c_950,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK4(X2,X1,X0),X1)
| ~ member(X0,X1)
| ~ greatest_lower_bound(sK9,sK8,sK6,sK7)
| ( X2 != sK6 )
| ( X1 != sK8 )
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_82,c_317]) ).
tcf(c_951,plain,
( member(sK4(sK6,sK8,sK9),sK8)
| ~ member(sK9,sK8)
| ~ greatest_lower_bound(sK9,sK8,sK6,sK7) ),
inference(unflattening,[status(thm)],[c_950]) ).
tcf(c_952,plain,
( member(sK4(sK6,sK8,sK9),sK8)
| ~ greatest_lower_bound(sK9,sK8,sK6,sK7) ),
inference(global_subsumption_just,[status(thm)],[c_951,c_313,c_951]) ).
tcf(c_960,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X0,X3)
| greatest_lower_bound(sK9,sK8,sK6,sK7)
| ~ member(X3,X2)
| ( X2 != sK8 )
| ( X1 != sK6 )
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_84,c_191]) ).
tcf(c_961,plain,
! [X0: $i] :
( apply(sK6,sK9,X0)
| greatest_lower_bound(sK9,sK8,sK6,sK7)
| ~ member(X0,sK8) ),
inference(unflattening,[status(thm)],[c_960]) ).
tcf(c_1017,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK4(sK6,sK8,sK9),sK8)
| ~ member(X1,X2)
| ~ lower_bound(X1,X0,X2)
| ~ apply(X0,sK5(X1,X2,X0,X3),X1)
| ( X3 != sK7 )
| ( X2 != sK8 )
| ( X1 != sK9 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_85,c_952]) ).
tcf(c_1018,plain,
( member(sK4(sK6,sK8,sK9),sK8)
| ~ member(sK9,sK8)
| ~ lower_bound(sK9,sK6,sK8)
| ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9) ),
inference(unflattening,[status(thm)],[c_1017]) ).
tcf(c_1019,plain,
( member(sK4(sK6,sK8,sK9),sK8)
| ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9)
| ~ lower_bound(sK9,sK6,sK8) ),
inference(global_subsumption_just,[status(thm)],[c_1018,c_313,c_1018]) ).
tcf(c_1020,plain,
( member(sK4(sK6,sK8,sK9),sK8)
| ~ lower_bound(sK9,sK6,sK8)
| ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9) ),
inference(renaming,[status(thm)],[c_1019]) ).
tcf(c_1030,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ member(X1,X2)
| ~ lower_bound(X1,X0,X2)
| ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
| ~ apply(X0,sK5(X1,X2,X0,X3),X1)
| ( X3 != sK7 )
| ( X2 != sK8 )
| ( X1 != sK9 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_85,c_926]) ).
tcf(c_1031,plain,
( ~ member(sK9,sK8)
| ~ lower_bound(sK9,sK6,sK8)
| ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
| ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9) ),
inference(unflattening,[status(thm)],[c_1030]) ).
tcf(c_1032,plain,
( ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9)
| ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
| ~ lower_bound(sK9,sK6,sK8) ),
inference(global_subsumption_just,[status(thm)],[c_1031,c_313,c_1031]) ).
tcf(c_1033,plain,
( ~ lower_bound(sK9,sK6,sK8)
| ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
| ~ apply(sK6,sK5(sK9,sK8,sK6,sK7),sK9) ),
inference(renaming,[status(thm)],[c_1032]) ).
tcf(c_1055,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( member(sK4(sK6,sK8,sK9),sK8)
| lower_bound(sK5(X0,X2,X1,X3),X1,X2)
| ~ member(X0,X2)
| ~ lower_bound(X0,X1,X2)
| ( X3 != sK7 )
| ( X2 != sK8 )
| ( X1 != sK6 )
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_87,c_952]) ).
tcf(c_1056,plain,
( member(sK4(sK6,sK8,sK9),sK8)
| lower_bound(sK5(sK9,sK8,sK6,sK7),sK6,sK8)
| ~ member(sK9,sK8)
| ~ lower_bound(sK9,sK6,sK8) ),
inference(unflattening,[status(thm)],[c_1055]) ).
tcf(c_1057,plain,
( member(sK4(sK6,sK8,sK9),sK8)
| lower_bound(sK5(sK9,sK8,sK6,sK7),sK6,sK8)
| ~ lower_bound(sK9,sK6,sK8) ),
inference(global_subsumption_just,[status(thm)],[c_1056,c_313,c_1056]) ).
tcf(c_1068,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( lower_bound(sK5(X0,X2,X1,X3),X1,X2)
| ~ member(X0,X2)
| ~ lower_bound(X0,X1,X2)
| ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
| ( X3 != sK7 )
| ( X2 != sK8 )
| ( X1 != sK6 )
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_87,c_926]) ).
tcf(c_1069,plain,
( lower_bound(sK5(sK9,sK8,sK6,sK7),sK6,sK8)
| ~ member(sK9,sK8)
| ~ lower_bound(sK9,sK6,sK8)
| ~ apply(sK6,sK9,sK4(sK6,sK8,sK9)) ),
inference(unflattening,[status(thm)],[c_1068]) ).
tcf(c_1070,plain,
( lower_bound(sK5(sK9,sK8,sK6,sK7),sK6,sK8)
| ~ apply(sK6,sK9,sK4(sK6,sK8,sK9))
| ~ lower_bound(sK9,sK6,sK8) ),
inference(global_subsumption_just,[status(thm)],[c_1069,c_313,c_1069]) ).
tcf(c_1071,plain,
( lower_bound(sK5(sK9,sK8,sK6,sK7),sK6,sK8)
| ~ lower_bound(sK9,sK6,sK8)
| ~ apply(sK6,sK9,sK4(sK6,sK8,sK9)) ),
inference(renaming,[status(thm)],[c_1070]) ).
tcf(c_1125,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(sK6,sK9,X4)
| lower_bound(X0,X2,X1)
| ~ member(X4,sK8)
| ( X3 != sK7 )
| ( X2 != sK6 )
| ( X1 != sK8 )
| ( X0 != sK9 ) ),
inference(resolution_lifted,[status(thm)],[c_187,c_961]) ).
tcf(c_1126,plain,
! [X0: $i] :
( lower_bound(sK9,sK6,sK8)
| apply(sK6,sK9,X0)
| ~ member(X0,sK8) ),
inference(unflattening,[status(thm)],[c_1125]) ).
tcf(c_1134,plain,
! [X0: $i] :
( apply(sK6,sK9,X0)
| ~ member(X0,sK8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1126,c_80]) ).
tcf(c_1228,plain,
! [X0: $i] :
( apply(sK6,sK9,X0)
| ~ member(X0,sK8) ),
inference(prop_impl_just,[status(thm)],[c_1134]) ).
tcf(c_1799,plain,
( lower_bound(iPr_def_11,sK6,sK8)
| ~ lower_bound(sK9,sK6,sK8)
| ~ apply(sK6,sK9,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_1071]) ).
tcf(c_1800,plain,
( member(iPr_def_10,sK8)
| lower_bound(iPr_def_11,sK6,sK8)
| ~ lower_bound(sK9,sK6,sK8) ),
inference(demodulation,[status(thm)],[c_1057]) ).
tcf(c_1801,plain,
( ~ lower_bound(sK9,sK6,sK8)
| ~ apply(sK6,iPr_def_11,sK9)
| ~ apply(sK6,sK9,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_1033]) ).
tcf(c_1802,plain,
( member(iPr_def_10,sK8)
| ~ lower_bound(sK9,sK6,sK8)
| ~ apply(sK6,iPr_def_11,sK9) ),
inference(demodulation,[status(thm)],[c_1020]) ).
tcf(c_3536,plain,
! [X0: $i] :
( lower_bound(sK9,sK6,X0)
| ~ member(sK3(sK6,X0,sK9),sK8) ),
inference(superposition,[status(thm)],[c_1228,c_78]) ).
tcf(c_3539,plain,
( lower_bound(sK9,sK6,sK8)
| ~ member(sK3(sK6,sK8,sK9),sK8) ),
inference(instantiation,[status(thm)],[c_3536]) ).
tcf(c_3700,plain,
( apply(sK6,sK9,iPr_def_10)
| ~ member(iPr_def_10,sK8) ),
inference(instantiation,[status(thm)],[c_1228]) ).
tcf(c_3971,plain,
( lower_bound(sK9,sK6,sK8)
| member(sK3(sK6,sK8,sK9),sK8) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_4059,plain,
! [X0: $i] :
( apply(sK6,iPr_def_11,sK9)
| ~ member(sK9,X0)
| ~ lower_bound(iPr_def_11,sK6,X0) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_4060,plain,
( apply(sK6,iPr_def_11,sK9)
| ~ member(sK9,sK8)
| ~ lower_bound(iPr_def_11,sK6,sK8) ),
inference(instantiation,[status(thm)],[c_4059]) ).
tcf(c_4220,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4060,c_3971,c_3700,c_3539,c_1802,c_1801,c_1800,c_1799,c_313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET802+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.60 % Computer : n013.cluster.edu
% 0.10/5.60 % Model : x86_64 x86_64
% 0.10/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.60 % Memory : 8046.5625MB
% 0.10/5.60 % OS : Linux 6.8.0-71-generic
% 0.10/5.60 % CPULimit : 300
% 0.10/5.60 % WCLimit : 300
% 0.10/5.60 % DateTime : Thu Sep 24 11:59:09 UTC 2026
% 0.10/5.60 % CPUTime :
% 0.10/5.60 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.64 Running first-order theorem proving
% 0.10/5.64 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
% 0.10/5.65
% 0.10/5.65 % ======== iProver multi-core TPTP/SMT =========
% 0.10/5.65
% 0.10/5.65 % Detected problem language: tptp
% 0.10/5.66 % Proving...
% 2.57/6.30 % SZS status Started for theBenchmark.p
% 2.57/6.30 % SZS status Theorem for theBenchmark.p
% 2.57/6.30
% 2.57/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.57/6.30
% 2.57/6.30 % ------ iProver source info
% 2.57/6.30
% 2.57/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.57/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.57/6.30 % git: non_committed_changes: false
% 2.57/6.30
% 2.57/6.30 % ------ Parsing...
% 2.57/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.57/6.30
% 2.57/6.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 2.57/6.30
% 2.57/6.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.57/6.30
% 2.57/6.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.57/6.30 % ------ Proving...
% 2.57/6.30 % ------ Problem Properties
% 2.57/6.30
% 2.57/6.30 %
% 2.57/6.30 % clauses 45
% 2.57/6.30 % conjectures 1
% 2.57/6.30 % EPR 15
% 2.57/6.30 % Horn 36
% 2.57/6.30 % unary 8
% 2.57/6.30 % binary 19
% 2.57/6.30 % lits 107
% 2.57/6.30 % lits eq 6
% 2.57/6.30 % fd_pure 0
% 2.57/6.30 % fd_pseudo 0
% 2.57/6.30 % fd_cond 0
% 2.57/6.30 % fd_pseudo_cond 3
% 2.57/6.30 % AC symbols 0
% 2.57/6.30
% 2.57/6.30 % ------ Schedule dynamic 5 is on
% 2.57/6.30
% 2.57/6.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.57/6.30
% 2.57/6.30
% 2.57/6.30 % ------
% 2.57/6.30 % Current options:
% 2.57/6.30 % ------
% 2.57/6.30
% 2.57/6.30
% 2.57/6.30 %
% 2.57/6.30
% 2.57/6.30 % ------ Proving...
% 2.57/6.30 %
% 2.57/6.30
% 2.57/6.30 % SZS status Theorem for theBenchmark.p
% 2.57/6.30
% 2.57/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.57/6.31
% 2.57/6.31
%------------------------------------------------------------------------------