%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP023+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Thu Sep 24 12:50:22 PM UTC 2026
% Result : Theorem 43.90s 21.25s
% Output : CNFRefutation 43.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 80 ( 20 unt; 8 def)
% Number of atoms : 219 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 243 ( 104 ~; 98 |; 10 &)
% ( 10 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 78 ( 76 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B,F] :
( mem(F,arr(A,B))
=> ! [X] :
( mem(X,A)
=> mem(ap(F,X),B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
mem(c_2Ebool_2ET,bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
p(c_2Ebool_2ET),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
ne(ty_2Erealax_2Ereal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
mem(c_2Ereal__topology_2Ecball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1e] :
( mem(V1e,ty_2Erealax_2Ereal)
=> p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [V0s] :
( mem(V0s,arr(ty_2Erealax_2Ereal,bool))
=> ! [V1t] :
( mem(V1t,arr(ty_2Erealax_2Ereal,bool))
=> ( ( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),V0s),V1t))
& p(ap(c_2Ereal__topology_2Ebounded__def,V1t)) )
=> p(ap(c_2Ereal__topology_2Ebounded__def,V0s)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1e] :
( mem(V1e,ty_2Erealax_2Ereal)
=> p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( p(V1B)
| p(V0A) )
=> $false )
<=> ( ( p(V0A)
=> $false )
=> ( ~ p(V1B)
=> $false ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,conjecture,
! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1e] :
( mem(V1e,ty_2Erealax_2Ereal)
=> p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
~ ! [V0x] :
( mem(V0x,ty_2Erealax_2Ereal)
=> ! [V1e] :
( mem(V1e,ty_2Erealax_2Ereal)
=> p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e)))) ) ),
inference(negated_conjecture,[status(cth)],[f59]) ).
fof(f65,plain,
! [A,B,F] :
( ! [X] :
( mem(ap(F,X),B)
| ~ mem(X,A) )
| ~ mem(F,arr(A,B)) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( mem(ap(X0,X3),X2)
| ~ mem(X3,X1)
| ~ mem(X0,arr(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f80,plain,
mem(c_2Ebool_2ET,bool),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f81,plain,
p(c_2Ebool_2ET),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f90,plain,
ne(ty_2Erealax_2Ereal),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f93,plain,
mem(c_2Ereal__topology_2Eball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f96,plain,
! [A_27a] :
( ! [A_27b] :
( mem(c_2Epair_2E_2C(A_27a,A_27b),arr(A_27a,arr(A_27b,ty_2Epair_2Eprod(A_27a,A_27b))))
| ~ ne(A_27b) )
| ~ ne(A_27a) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f97,plain,
! [X0,X1] :
( mem(c_2Epair_2E_2C(X0,X1),arr(X0,arr(X1,ty_2Epair_2Eprod(X0,X1))))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
mem(c_2Ereal__topology_2Ecball,arr(ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),arr(ty_2Erealax_2Ereal,bool))),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f212,plain,
! [V0x] :
( ! [V1e] :
( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e))))
| ~ mem(V1e,ty_2Erealax_2Ereal) )
| ~ mem(V0x,ty_2Erealax_2Ereal) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f213,plain,
! [X0,X1] :
( p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))),ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))
| ~ mem(X1,ty_2Erealax_2Ereal)
| ~ mem(X0,ty_2Erealax_2Ereal) ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f214,plain,
! [V0s] :
( ! [V1t] :
( p(ap(c_2Ereal__topology_2Ebounded__def,V0s))
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),V0s),V1t))
| ~ p(ap(c_2Ereal__topology_2Ebounded__def,V1t))
| ~ mem(V1t,arr(ty_2Erealax_2Ereal,bool)) )
| ~ mem(V0s,arr(ty_2Erealax_2Ereal,bool)) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f215,plain,
! [X0,X1] :
( p(ap(c_2Ereal__topology_2Ebounded__def,X0))
| ~ p(ap(ap(c_2Epred__set_2ESUBSET(ty_2Erealax_2Ereal),X0),X1))
| ~ p(ap(c_2Ereal__topology_2Ebounded__def,X1))
| ~ mem(X1,arr(ty_2Erealax_2Ereal,bool))
| ~ mem(X0,arr(ty_2Erealax_2Ereal,bool)) ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f216,plain,
! [V0x] :
( ! [V1e] :
( p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e))))
| ~ mem(V1e,ty_2Erealax_2Ereal) )
| ~ mem(V0x,ty_2Erealax_2Ereal) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f217,plain,
! [X0,X1] :
( p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))
| ~ mem(X1,ty_2Erealax_2Ereal)
| ~ mem(X0,ty_2Erealax_2Ereal) ),
inference(cnf_transformation,[status(thm)],[f216]) ).
fof(f225,plain,
! [V0A] :
( ! [V1B] :
( ( ( $false
| p(V1B)
| p(V0A) )
<=> ( $false
| p(V1B)
| ( $true
& p(V0A) ) ) )
| ~ mem(V1B,bool) )
| ~ mem(V0A,bool) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f226,definition,
! [V0A,V1B] :
( sP2_prd(V1B,V0A)
<=> ( p(V1B)
| p(V0A) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f298,plain,
? [V0x] :
( ? [V1e] :
( ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),V0x),V1e))))
& mem(V1e,ty_2Erealax_2Ereal) )
& mem(V0x,ty_2Erealax_2Ereal) ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f299,plain,
( ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK5_skl),sK6_skl))))
& mem(sK6_skl,ty_2Erealax_2Ereal)
& mem(sK5_skl,ty_2Erealax_2Ereal) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(V0x,sK5_skl),skolemize(V1e,sK6_skl)],[f298]) ).
fof(f300,plain,
mem(sK5_skl,ty_2Erealax_2Ereal),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f301,plain,
mem(sK6_skl,ty_2Erealax_2Ereal),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f302,plain,
~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK5_skl),sK6_skl)))),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f313,plain,
! [V0A,V1B] :
( ( ( ~ p(V1B)
& ~ p(V0A) )
| sP2_prd(V1B,V0A) )
& ( p(V1B)
| p(V0A)
| ~ sP2_prd(V1B,V0A) ) ),
inference(NNF_transformation,[status(thm)],[f226]) ).
fof(f314,plain,
( ! [V0A,V1B] :
( ( ~ p(V1B)
& ~ p(V0A) )
| sP2_prd(V1B,V0A) )
& ! [V0A,V1B] :
( p(V1B)
| p(V0A)
| ~ sP2_prd(V1B,V0A) ) ),
inference(miniscoping,[status(thm)],[f313]) ).
fof(f317,plain,
! [X0,X1] :
( ~ p(X0)
| sP2_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f465,plain,
! [X0] :
( mem(ap(c_2Ereal__topology_2Eball,X0),arr(ty_2Erealax_2Ereal,bool))
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(resolution,[status(thm)],[f66,f93]) ).
fof(f568,definition,
( sQ12_spl
<=> ne(ty_2Erealax_2Ereal) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( sQ12_spl
| ~ ne(ty_2Erealax_2Ereal) ),
inference(component_clause,[status(thm)],[f568]) ).
fof(f585,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f570,f90]) ).
fof(f586,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f585]) ).
fof(f615,plain,
! [X0,X1,X2] :
( mem(ap(c_2Epair_2E_2C(X0,X1),X2),arr(X1,ty_2Epair_2Eprod(X0,X1)))
| ~ mem(X2,X0)
| ~ ne(X1)
| ~ ne(X0) ),
inference(resolution,[status(thm)],[f97,f66]) ).
fof(f652,plain,
! [X0] :
( mem(ap(c_2Ereal__topology_2Ecball,X0),arr(ty_2Erealax_2Ereal,bool))
| ~ mem(X0,ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(resolution,[status(thm)],[f98,f66]) ).
fof(f1209,definition,
! [X1] :
( sQ61_spl
<=> ~ mem(X1,ty_2Erealax_2Ereal) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1210,plain,
! [X0] :
( ~ sQ61_spl
| ~ mem(X0,ty_2Erealax_2Ereal) ),
inference(component_clause,[status(thm)],[f1209]) ).
fof(f1245,plain,
( ~ sQ61_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f301,f1210]) ).
fof(f2387,plain,
! [X0,X1,X2,X3] :
( mem(ap(ap(c_2Epair_2E_2C(X0,X1),X2),X3),ty_2Epair_2Eprod(X0,X1))
| ~ mem(X3,X1)
| ~ mem(X2,X0)
| ~ ne(X1)
| ~ ne(X0) ),
inference(resolution,[status(thm)],[f615,f66]) ).
fof(f2894,plain,
! [X0,X1] :
( ~ mem(X1,ty_2Erealax_2Ereal)
| ~ mem(X0,ty_2Erealax_2Ereal)
| p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))
| ~ p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))
| ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)),arr(ty_2Erealax_2Ereal,bool))
| ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)),arr(ty_2Erealax_2Ereal,bool)) ),
inference(resolution,[status(thm)],[f215,f213]) ).
fof(f2897,plain,
! [X0,X1] :
( ~ mem(X1,ty_2Erealax_2Ereal)
| ~ mem(X0,ty_2Erealax_2Ereal)
| p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))
| ~ mem(ap(c_2Ereal__topology_2Ecball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)),arr(ty_2Erealax_2Ereal,bool))
| ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)),arr(ty_2Erealax_2Ereal,bool)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2894,f217]) ).
fof(f3035,plain,
! [X0,X1] :
( ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| ~ mem(X1,ty_2Erealax_2Ereal)
| ~ mem(X0,ty_2Erealax_2Ereal)
| p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1))))
| ~ mem(ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)),arr(ty_2Erealax_2Ereal,bool)) ),
inference(resolution,[status(thm)],[f2897,f652]) ).
fof(f3036,plain,
! [X0,X1] :
( ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| ~ mem(X1,ty_2Erealax_2Ereal)
| ~ mem(X0,ty_2Erealax_2Ereal)
| p(ap(c_2Ereal__topology_2Ebounded__def,ap(c_2Ereal__topology_2Eball,ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),X0),X1)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f3035,f465]) ).
fof(f3483,definition,
( sQ242_spl
<=> sP2_prd(c_2Ebool_2ET,c_2Ebool_2EF) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f3485,plain,
( sQ242_spl
| ~ sP2_prd(c_2Ebool_2ET,c_2Ebool_2EF) ),
inference(component_clause,[status(thm)],[f3483]) ).
fof(f3789,plain,
( ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK5_skl),sK6_skl),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal))
| ~ mem(sK6_skl,ty_2Erealax_2Ereal)
| ~ mem(sK5_skl,ty_2Erealax_2Ereal) ),
inference(resolution,[status(thm)],[f3036,f302]) ).
fof(f3791,definition,
( sQ268_spl
<=> mem(sK5_skl,ty_2Erealax_2Ereal) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f3793,plain,
( sQ268_spl
| ~ mem(sK5_skl,ty_2Erealax_2Ereal) ),
inference(component_clause,[status(thm)],[f3791]) ).
fof(f3794,definition,
( sQ269_spl
<=> mem(sK6_skl,ty_2Erealax_2Ereal) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f3796,plain,
( sQ269_spl
| ~ mem(sK6_skl,ty_2Erealax_2Ereal) ),
inference(component_clause,[status(thm)],[f3794]) ).
fof(f3797,definition,
( sQ270_spl
<=> mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK5_skl),sK6_skl),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f3799,plain,
( sQ270_spl
| ~ mem(ap(ap(c_2Epair_2E_2C(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal),sK5_skl),sK6_skl),ty_2Epair_2Eprod(ty_2Erealax_2Ereal,ty_2Erealax_2Ereal)) ),
inference(component_clause,[status(thm)],[f3797]) ).
fof(f3800,plain,
( ~ sQ270_spl
| ~ sQ269_spl
| ~ sQ268_spl ),
inference(split_clause,[status(thm)],[f3789,f3791,f3794,f3797]) ).
fof(f3801,plain,
( sQ269_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3796,f301]) ).
fof(f3802,plain,
sQ269_spl,
inference(contradiction_clause,[status(thm)],[f3801]) ).
fof(f3803,plain,
( sQ268_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3793,f300]) ).
fof(f3804,plain,
sQ268_spl,
inference(contradiction_clause,[status(thm)],[f3803]) ).
fof(f3805,plain,
( sQ242_spl
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f3485,f317]) ).
fof(f3807,plain,
( sQ242_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3805,f81]) ).
fof(f3808,plain,
sQ242_spl,
inference(contradiction_clause,[status(thm)],[f3807]) ).
fof(f6518,plain,
~ sQ61_spl,
inference(contradiction_clause,[status(thm)],[f1245]) ).
fof(f6853,definition,
! [X0] :
( sQ502_spl
<=> ( ~ p(X0)
| ~ mem(X0,bool)
| ~ mem(X0,bool)
| ~ p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ502_spl])],[split_symbol_definition]) ).
fof(f6854,plain,
! [X0] :
( ~ sQ502_spl
| ~ p(X0)
| ~ mem(X0,bool)
| ~ mem(X0,bool)
| ~ p(X0) ),
inference(component_clause,[status(thm)],[f6853]) ).
fof(f6871,plain,
! [X0] :
( ~ sQ502_spl
| ~ mem(X0,bool)
| ~ p(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f6854]) ).
fof(f7024,plain,
( ~ sQ502_spl
| ~ p(c_2Ebool_2ET) ),
inference(resolution,[status(thm)],[f6871,f80]) ).
fof(f7068,plain,
( ~ sQ502_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7024,f81]) ).
fof(f7069,plain,
~ sQ502_spl,
inference(contradiction_clause,[status(thm)],[f7068]) ).
fof(f8779,plain,
( sQ270_spl
| ~ mem(sK6_skl,ty_2Erealax_2Ereal)
| ~ mem(sK5_skl,ty_2Erealax_2Ereal)
| ~ ne(ty_2Erealax_2Ereal)
| ~ ne(ty_2Erealax_2Ereal) ),
inference(resolution,[status(thm)],[f3799,f2387]) ).
fof(f8780,plain,
( sQ270_spl
| ~ sQ269_spl
| ~ sQ268_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f8779,f568,f3791,f3794,f3797]) ).
fof(f8781,plain,
$false,
inference(sat_refutation,[status(thm)],[f586,f3800,f3802,f3804,f3808,f6518,f7069,f8780]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP023+2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.13/15.65 % CPULimit : 300
% 0.13/15.65 % WCLimit : 300
% 0.13/15.65 % DateTime : Sun Sep 20 21:55:34 UTC 2026
% 0.13/15.65 % CPUTime :
% 0.13/15.67 % Drodi V4.1.1
% 43.90/21.25 % Refutation found
% 43.90/21.25 % SZS status Theorem for theBenchmark: Theorem is valid
% 43.90/21.25 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.94/21.34 % Elapsed time: 5.675164 seconds
% 9.94/21.34 % CPU time: 44.452350 seconds
% 9.94/21.34 % Total memory used: 395.315 MB
% 9.94/21.34 % Net memory used: 375.919 MB
%------------------------------------------------------------------------------