%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ITP023+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:50:21 PM UTC 2026
% Result : Theorem 23.01s 3.35s
% Output : CNFRefutation 23.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 16
% Syntax : Number of formulae : 58 ( 18 unt; 7 def)
% Number of atoms : 144 ( 14 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 141 ( 55 ~; 58 |; 14 &)
% ( 11 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 55 ( 53 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [V0_2E0,V1_2E0] :
( ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<=> p(s(tyop_2Emin_2Ebool,V1_2E0)) )
=> s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V0t_2E0] :
( s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,V0t_2E0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ! [V0t_2E0] :
( ~ ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
<=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [V0x_2E0,V1e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0))))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0)))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [V0s_2E0,V1t_2E0] :
( ( p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0))))
& p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0)))) )
=> p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [V0x_2E0,V1e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0)))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
! [V0x_2E0,V1e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0)))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ! [V0x_2E0,V1e_2E0] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0)))))))),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f58,plain,
! [V0_2E0,V1_2E0] :
( s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0)
| ( p(s(tyop_2Emin_2Ebool,V0_2E0))
<~> p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f59,plain,
! [V0_2E0,V1_2E0] :
( s(tyop_2Emin_2Ebool,V0_2E0) = s(tyop_2Emin_2Ebool,V1_2E0)
| ( ( ~ p(s(tyop_2Emin_2Ebool,V1_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V1_2E0))
| p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ) ),
inference(NNF_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,X1)
| p(s(tyop_2Emin_2Ebool,X1))
| p(s(tyop_2Emin_2Ebool,X0)) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,plain,
p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f63,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f64,plain,
! [X0] :
( s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| s(tyop_2Emin_2Ebool,X0) = s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f162,plain,
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ! [V0t_2E0] :
( ( ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
| p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,V0t_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f163,plain,
( ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) )
& ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) )
& ! [V0t_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,V0t_2E0))
| p(s(tyop_2Emin_2Ebool,V0t_2E0)) )
& ! [V0t_2E0] :
( p(s(tyop_2Emin_2Ebool,V0t_2E0))
| ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ),
inference(miniscoping,[status(thm)],[f162]) ).
fof(f167,plain,
( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f215,plain,
! [X0,X1] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1))))),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f216,plain,
! [V0s_2E0,V1t_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0)))) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f217,plain,
! [V0s_2E0] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0))))
| ! [V1t_2E0] :
( ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),V1t_2E0)))) ) ),
inference(miniscoping,[status(thm)],[f216]) ).
fof(f218,plain,
! [X0,X1] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Epred__set_2ESUBSET_2E2(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X1),s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),X0)))) ),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f303,plain,
? [V0x_2E0,V1e_2E0] : ~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,V0x_2E0),s(tyop_2Erealax_2Ereal,V1e_2E0)))))))),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f304,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,sK5_skl),s(tyop_2Erealax_2Ereal,sK6_skl)))))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(V0x_2E0,sK5_skl),skolemize(V1e_2E0,sK6_skl)],[f303]) ).
fof(f305,plain,
~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,sK5_skl),s(tyop_2Erealax_2Ereal,sK6_skl)))))))),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f418,definition,
( sQ0_spl
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f421,definition,
! [X0] :
( sQ1_spl
<=> ~ p(s(tyop_2Emin_2Ebool,X0)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f422,plain,
! [X0] :
( ~ sQ1_spl
| ~ p(s(tyop_2Emin_2Ebool,X0)) ),
inference(component_clause,[status(thm)],[f421]) ).
fof(f429,definition,
( sQ3_spl
<=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f432,definition,
! [X0] :
( sQ4_spl
<=> p(s(tyop_2Emin_2Ebool,X0)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f433,plain,
! [X0] :
( ~ sQ4_spl
| p(s(tyop_2Emin_2Ebool,X0)) ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f449,plain,
( ~ sQ0_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f167,f429,f418]) ).
fof(f513,plain,
! [X0,X1,X2] :
( p(s(tyop_2Emin_2Ebool,X0))
| p(s(tyop_2Emin_2Ebool,X2))
| s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,X1)
| p(s(tyop_2Emin_2Ebool,X1))
| p(s(tyop_2Emin_2Ebool,X0)) ),
inference(paramodulation,[status(thm)],[f60,f60]) ).
fof(f519,definition,
! [X0] :
( sQ13_spl
<=> ( p(s(tyop_2Emin_2Ebool,X0))
| p(s(tyop_2Emin_2Ebool,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f520,plain,
! [X0] :
( ~ sQ13_spl
| p(s(tyop_2Emin_2Ebool,X0))
| p(s(tyop_2Emin_2Ebool,X0)) ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f522,definition,
! [X1,X2] :
( sQ14_spl
<=> ( p(s(tyop_2Emin_2Ebool,X2))
| s(tyop_2Emin_2Ebool,X2) = s(tyop_2Emin_2Ebool,X1)
| p(s(tyop_2Emin_2Ebool,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f523,plain,
! [X0,X1] :
( ~ sQ14_spl
| p(s(tyop_2Emin_2Ebool,X1))
| s(tyop_2Emin_2Ebool,X1) = s(tyop_2Emin_2Ebool,X0)
| p(s(tyop_2Emin_2Ebool,X0)) ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f525,plain,
( sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f513,f519,f522]) ).
fof(f534,plain,
! [X0] :
( ~ sQ13_spl
| p(s(tyop_2Emin_2Ebool,X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f520]) ).
fof(f535,plain,
( ~ sQ13_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f305,f534]) ).
fof(f536,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f568,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f215,f422]) ).
fof(f570,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f568]) ).
fof(f595,plain,
! [X0] :
( ~ sQ14_spl
| p(s(tyop_2Emin_2Ebool,X0))
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0))
| p(s(tyop_2Emin_2Ebool,X0)) ),
inference(paramodulation,[status(thm)],[f523,f62]) ).
fof(f597,plain,
( ~ sQ14_spl
| sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f595,f519,f429,f522]) ).
fof(f641,plain,
( s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,sK5_skl),s(tyop_2Erealax_2Ereal,sK6_skl))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)
| ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ),
inference(paramodulation,[status(thm)],[f64,f305]) ).
fof(f680,definition,
( sQ25_spl
<=> s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,sK5_skl),s(tyop_2Erealax_2Ereal,sK6_skl))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f681,plain,
( ~ sQ25_spl
| s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,sK5_skl),s(tyop_2Erealax_2Ereal,sK6_skl))))))) = s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) ),
inference(component_clause,[status(thm)],[f680]) ).
fof(f683,plain,
( sQ25_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f641,f429,f680]) ).
fof(f1416,plain,
( ~ sQ4_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f63,f433]) ).
fof(f1423,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f1416]) ).
fof(f14194,plain,
! [X0,X1] :
( p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1))))))))
| ~ p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Ecball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))) ),
inference(resolution,[status(thm)],[f218,f215]) ).
fof(f18169,plain,
! [X0,X1] : p(s(tyop_2Emin_2Ebool,c_2Ereal__topology_2Ebounded__def_2E1(s(tyop_2Emin_2Efun(tyop_2Erealax_2Ereal,tyop_2Emin_2Ebool),c_2Ereal__topology_2Eball_2E1(s(tyop_2Epair_2Eprod(tyop_2Erealax_2Ereal,tyop_2Erealax_2Ereal),c_2Epair_2E_2C_2E2(s(tyop_2Erealax_2Ereal,X0),s(tyop_2Erealax_2Ereal,X1)))))))),
inference(forward_subsumption_resolution,[status(thm)],[f14194,f219]) ).
fof(f18199,plain,
( ~ sQ25_spl
| p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ),
inference(paramodulation,[status(thm)],[f681,f18169]) ).
fof(f18210,plain,
( ~ sQ25_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f18199,f418,f680]) ).
fof(f18212,plain,
$false,
inference(sat_refutation,[status(thm)],[f449,f525,f536,f570,f597,f683,f1423,f18210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP023+1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 21:54:28 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.38 % Drodi V4.1.1
% 23.01/3.35 % Refutation found
% 23.01/3.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 23.01/3.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.70/3.45 % Elapsed time: 3.088167 seconds
% 1.70/3.45 % CPU time: 23.770978 seconds
% 1.70/3.45 % Total memory used: 415.313 MB
% 1.70/3.45 % Net memory used: 399.430 MB
%------------------------------------------------------------------------------