%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU376+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 02:20:20 PM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 24
% Syntax : Number of formulae : 120 ( 16 unt; 19 def)
% Number of atoms : 622 ( 0 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 828 ( 326 ~; 388 |; 71 &)
% ( 25 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 31 ( 30 usr; 20 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 187 ( 167 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( net_str(B,A)
& ~ empty_carrier(B) )
=> ! [C] :
( is_eventually_in(A,B,C)
<=> ? [D] :
( ! [E] :
( element(E,the_carrier(B))
=> ( related(B,D,E)
=> in(apply_netmap(A,B,E),C) ) )
& element(D,the_carrier(B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( net_str(B,A)
& ~ empty_carrier(B) )
=> ! [C] :
( is_often_in(A,B,C)
<=> ! [D] :
( element(D,the_carrier(B))
=> ? [E] :
( in(apply_netmap(A,B,E),C)
& related(B,D,E)
& element(E,the_carrier(B)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] :
( ( rel_str(A)
& ~ empty_carrier(A) )
=> ( directed_relstr(A)
<=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ? [D] :
( related(A,C,D)
& related(A,B,D)
& element(D,the_carrier(A)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> rel_str(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,conjecture,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( net_str(B,A)
& directed_relstr(B)
& transitive_relstr(B)
& ~ empty_carrier(B) )
=> ! [C] :
( is_eventually_in(A,B,C)
=> is_often_in(A,B,C) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
~ ! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( net_str(B,A)
& directed_relstr(B)
& transitive_relstr(B)
& ~ empty_carrier(B) )
=> ! [C] :
( is_eventually_in(A,B,C)
=> is_often_in(A,B,C) ) ) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
fof(f80,plain,
! [A] :
( ! [B] :
( ! [C] :
( is_eventually_in(A,B,C)
<=> ? [D] :
( ! [E] :
( in(apply_netmap(A,B,E),C)
| ~ related(B,D,E)
| ~ element(E,the_carrier(B)) )
& element(D,the_carrier(B)) ) )
| ~ net_str(B,A)
| empty_carrier(B) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f81,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ! [D] :
( ? [E] :
( ~ in(apply_netmap(A,B,E),C)
& related(B,D,E)
& element(E,the_carrier(B)) )
| ~ element(D,the_carrier(B)) )
| is_eventually_in(A,B,C) )
& ( ? [D] :
( ! [E] :
( in(apply_netmap(A,B,E),C)
| ~ related(B,D,E)
| ~ element(E,the_carrier(B)) )
& element(D,the_carrier(B)) )
| ~ is_eventually_in(A,B,C) ) )
| ~ net_str(B,A)
| empty_carrier(B) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f80]) ).
fof(f82,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( ! [D] :
( ? [E] :
( ~ in(apply_netmap(A,B,E),C)
& related(B,D,E)
& element(E,the_carrier(B)) )
| ~ element(D,the_carrier(B)) )
| is_eventually_in(A,B,C) )
& ! [C] :
( ? [D] :
( ! [E] :
( in(apply_netmap(A,B,E),C)
| ~ related(B,D,E)
| ~ element(E,the_carrier(B)) )
& element(D,the_carrier(B)) )
| ~ is_eventually_in(A,B,C) ) )
| ~ net_str(B,A)
| empty_carrier(B) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(miniscoping,[status(thm)],[f81]) ).
fof(f83,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( ! [D] :
( ( ~ in(apply_netmap(A,B,sK1_skl(D,C,B,A)),C)
& related(B,D,sK1_skl(D,C,B,A))
& element(sK1_skl(D,C,B,A),the_carrier(B)) )
| ~ element(D,the_carrier(B)) )
| is_eventually_in(A,B,C) )
& ! [C] :
( ( ! [E] :
( in(apply_netmap(A,B,E),C)
| ~ related(B,sK0_skl(C,B,A),E)
| ~ element(E,the_carrier(B)) )
& element(sK0_skl(C,B,A),the_carrier(B)) )
| ~ is_eventually_in(A,B,C) ) )
| ~ net_str(B,A)
| empty_carrier(B) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(D,sK0_skl(C,B,A)),skolemize(E,sK1_skl(D,C,B,A))],[f82]) ).
fof(f84,plain,
! [X0,X1,X2] :
( element(sK0_skl(X2,X1,X0),the_carrier(X1))
| ~ is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( in(apply_netmap(X0,X1,X3),X2)
| ~ related(X1,sK0_skl(X2,X1,X0),X3)
| ~ element(X3,the_carrier(X1))
| ~ is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f89,plain,
! [A] :
( ! [B] :
( ! [C] :
( is_often_in(A,B,C)
<=> ! [D] :
( ? [E] :
( in(apply_netmap(A,B,E),C)
& related(B,D,E)
& element(E,the_carrier(B)) )
| ~ element(D,the_carrier(B)) ) )
| ~ net_str(B,A)
| empty_carrier(B) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f90,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ? [D] :
( ! [E] :
( ~ in(apply_netmap(A,B,E),C)
| ~ related(B,D,E)
| ~ element(E,the_carrier(B)) )
& element(D,the_carrier(B)) )
| is_often_in(A,B,C) )
& ( ! [D] :
( ? [E] :
( in(apply_netmap(A,B,E),C)
& related(B,D,E)
& element(E,the_carrier(B)) )
| ~ element(D,the_carrier(B)) )
| ~ is_often_in(A,B,C) ) )
| ~ net_str(B,A)
| empty_carrier(B) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( ? [D] :
( ! [E] :
( ~ in(apply_netmap(A,B,E),C)
| ~ related(B,D,E)
| ~ element(E,the_carrier(B)) )
& element(D,the_carrier(B)) )
| is_often_in(A,B,C) )
& ! [C] :
( ! [D] :
( ? [E] :
( in(apply_netmap(A,B,E),C)
& related(B,D,E)
& element(E,the_carrier(B)) )
| ~ element(D,the_carrier(B)) )
| ~ is_often_in(A,B,C) ) )
| ~ net_str(B,A)
| empty_carrier(B) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(miniscoping,[status(thm)],[f90]) ).
fof(f92,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( ( ! [E] :
( ~ in(apply_netmap(A,B,E),C)
| ~ related(B,sK3_skl(C,B,A),E)
| ~ element(E,the_carrier(B)) )
& element(sK3_skl(C,B,A),the_carrier(B)) )
| is_often_in(A,B,C) )
& ! [C] :
( ! [D] :
( ( in(apply_netmap(A,B,sK2_skl(D,C,B,A)),C)
& related(B,D,sK2_skl(D,C,B,A))
& element(sK2_skl(D,C,B,A),the_carrier(B)) )
| ~ element(D,the_carrier(B)) )
| ~ is_often_in(A,B,C) ) )
| ~ net_str(B,A)
| empty_carrier(B) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(E,sK2_skl(D,C,B,A)),skolemize(D,sK3_skl(C,B,A))],[f91]) ).
fof(f96,plain,
! [X0,X1,X2] :
( element(sK3_skl(X2,X1,X0),the_carrier(X1))
| is_often_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f97,plain,
! [X0,X1,X2,X3] :
( ~ in(apply_netmap(X0,X1,X3),X2)
| ~ related(X1,sK3_skl(X2,X1,X0),X3)
| ~ element(X3,the_carrier(X1))
| is_often_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f98,plain,
! [A] :
( ( directed_relstr(A)
<=> ! [B] :
( ! [C] :
( ? [D] :
( related(A,C,D)
& related(A,B,D)
& element(D,the_carrier(A)) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) ) )
| ~ rel_str(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f99,plain,
! [A] :
( ( ( ? [B] :
( ? [C] :
( ! [D] :
( ~ related(A,C,D)
| ~ related(A,B,D)
| ~ element(D,the_carrier(A)) )
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
| directed_relstr(A) )
& ( ! [B] :
( ! [C] :
( ? [D] :
( related(A,C,D)
& related(A,B,D)
& element(D,the_carrier(A)) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ directed_relstr(A) ) )
| ~ rel_str(A)
| empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [A] :
( ( ( ( ! [D] :
( ~ related(A,sK6_skl(A),D)
| ~ related(A,sK5_skl(A),D)
| ~ element(D,the_carrier(A)) )
& element(sK6_skl(A),the_carrier(A))
& element(sK5_skl(A),the_carrier(A)) )
| directed_relstr(A) )
& ( ! [B] :
( ! [C] :
( ( related(A,C,sK4_skl(C,B,A))
& related(A,B,sK4_skl(C,B,A))
& element(sK4_skl(C,B,A),the_carrier(A)) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ directed_relstr(A) ) )
| ~ rel_str(A)
| empty_carrier(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl]),skolemize(D,sK4_skl(C,B,A)),skolemize(B,sK5_skl(A)),skolemize(C,sK6_skl(A))],[f99]) ).
fof(f101,plain,
! [X0,X1,X2] :
( element(sK4_skl(X2,X1,X0),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ directed_relstr(X0)
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( related(X0,X1,sK4_skl(X2,X1,X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ directed_relstr(X0)
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f103,plain,
! [X0,X1,X2] :
( related(X0,X2,sK4_skl(X2,X1,X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ directed_relstr(X0)
| ~ rel_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f115,plain,
! [A] :
( ! [B] :
( rel_str(B)
| ~ net_str(B,A) )
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f116,plain,
! [X0,X1] :
( rel_str(X1)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f203,plain,
? [A] :
( ? [B] :
( ? [C] :
( ~ is_often_in(A,B,C)
& is_eventually_in(A,B,C) )
& net_str(B,A)
& directed_relstr(B)
& transitive_relstr(B)
& ~ empty_carrier(B) )
& one_sorted_str(A)
& ~ empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f204,plain,
( ~ is_often_in(sK25_skl,sK26_skl,sK27_skl)
& is_eventually_in(sK25_skl,sK26_skl,sK27_skl)
& net_str(sK26_skl,sK25_skl)
& directed_relstr(sK26_skl)
& transitive_relstr(sK26_skl)
& ~ empty_carrier(sK26_skl)
& one_sorted_str(sK25_skl)
& ~ empty_carrier(sK25_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25_skl,sK26_skl,sK27_skl]),skolemize(A,sK25_skl),skolemize(B,sK26_skl),skolemize(C,sK27_skl)],[f203]) ).
fof(f205,plain,
~ empty_carrier(sK25_skl),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f206,plain,
one_sorted_str(sK25_skl),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f207,plain,
~ empty_carrier(sK26_skl),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f209,plain,
directed_relstr(sK26_skl),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f210,plain,
net_str(sK26_skl,sK25_skl),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f211,plain,
is_eventually_in(sK25_skl,sK26_skl,sK27_skl),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f212,plain,
~ is_often_in(sK25_skl,sK26_skl,sK27_skl),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f234,plain,
! [X0,X1] :
( related(sK26_skl,X0,sK4_skl(X1,X0,sK26_skl))
| ~ element(X1,the_carrier(sK26_skl))
| ~ element(X0,the_carrier(sK26_skl))
| ~ rel_str(sK26_skl)
| empty_carrier(sK26_skl) ),
inference(resolution,[status(thm)],[f102,f209]) ).
fof(f235,definition,
( sQ0_spl
<=> empty_carrier(sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f236,plain,
( ~ sQ0_spl
| empty_carrier(sK26_skl) ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,definition,
( sQ1_spl
<=> rel_str(sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( sQ1_spl
| ~ rel_str(sK26_skl) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,definition,
! [X0,X1] :
( sQ2_spl
<=> ( related(sK26_skl,X0,sK4_skl(X1,X0,sK26_skl))
| ~ element(X1,the_carrier(sK26_skl))
| ~ element(X0,the_carrier(sK26_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f242,plain,
! [X0,X1] :
( ~ sQ2_spl
| related(sK26_skl,X0,sK4_skl(X1,X0,sK26_skl))
| ~ element(X1,the_carrier(sK26_skl))
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,plain,
( sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f234,f235,f238,f241]) ).
fof(f245,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| in(apply_netmap(X1,sK26_skl,sK4_skl(X2,sK0_skl(X0,sK26_skl,X1),sK26_skl)),X0)
| ~ element(sK4_skl(X2,sK0_skl(X0,sK26_skl,X1),sK26_skl),the_carrier(sK26_skl))
| ~ is_eventually_in(X1,sK26_skl,X0)
| ~ net_str(sK26_skl,X1)
| empty_carrier(sK26_skl)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X2,the_carrier(sK26_skl))
| ~ element(sK0_skl(X0,sK26_skl,X1),the_carrier(sK26_skl)) ),
inference(resolution,[status(thm)],[f242,f85]) ).
fof(f246,definition,
! [X0,X1,X2] :
( sQ3_spl
<=> ( in(apply_netmap(X1,sK26_skl,sK4_skl(X2,sK0_skl(X0,sK26_skl,X1),sK26_skl)),X0)
| ~ element(sK4_skl(X2,sK0_skl(X0,sK26_skl,X1),sK26_skl),the_carrier(sK26_skl))
| ~ is_eventually_in(X1,sK26_skl,X0)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X2,the_carrier(sK26_skl))
| ~ element(sK0_skl(X0,sK26_skl,X1),the_carrier(sK26_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f247,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| in(apply_netmap(X1,sK26_skl,sK4_skl(X2,sK0_skl(X0,sK26_skl,X1),sK26_skl)),X0)
| ~ element(sK4_skl(X2,sK0_skl(X0,sK26_skl,X1),sK26_skl),the_carrier(sK26_skl))
| ~ is_eventually_in(X1,sK26_skl,X0)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X2,the_carrier(sK26_skl))
| ~ element(sK0_skl(X0,sK26_skl,X1),the_carrier(sK26_skl)) ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f249,plain,
( ~ sQ2_spl
| sQ0_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f245,f246,f235,f241]) ).
fof(f250,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f236,f207]) ).
fof(f251,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f250]) ).
fof(f252,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| empty_carrier(sK26_skl)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| in(apply_netmap(X1,sK26_skl,sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl)),X2)
| ~ element(sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl),the_carrier(sK26_skl))
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(resolution,[status(thm)],[f247,f84]) ).
fof(f253,definition,
! [X0,X1,X2] :
( sQ4_spl
<=> ( ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| in(apply_netmap(X1,sK26_skl,sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl)),X2)
| ~ element(sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl),the_carrier(sK26_skl))
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X0,the_carrier(sK26_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f254,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| in(apply_netmap(X1,sK26_skl,sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl)),X2)
| ~ element(sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl),the_carrier(sK26_skl))
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( ~ sQ3_spl
| sQ0_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f252,f253,f235,f246]) ).
fof(f257,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| in(apply_netmap(X1,sK26_skl,sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl)),X2)
| ~ element(sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl),the_carrier(sK26_skl))
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f254]) ).
fof(f258,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| ~ element(X0,the_carrier(sK26_skl))
| ~ element(sK0_skl(X2,sK26_skl,X1),the_carrier(sK26_skl))
| ~ directed_relstr(sK26_skl)
| ~ rel_str(sK26_skl)
| empty_carrier(sK26_skl)
| in(apply_netmap(X1,sK26_skl,sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl)),X2)
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(resolution,[status(thm)],[f257,f101]) ).
fof(f259,definition,
! [X0,X1,X2] :
( sQ5_spl
<=> ( ~ element(X0,the_carrier(sK26_skl))
| ~ element(sK0_skl(X2,sK26_skl,X1),the_carrier(sK26_skl))
| in(apply_netmap(X1,sK26_skl,sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl)),X2)
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X0,the_carrier(sK26_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f260,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| ~ element(X0,the_carrier(sK26_skl))
| ~ element(sK0_skl(X2,sK26_skl,X1),the_carrier(sK26_skl))
| in(apply_netmap(X1,sK26_skl,sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl)),X2)
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,definition,
( sQ6_spl
<=> directed_relstr(sK26_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( sQ6_spl
| ~ directed_relstr(sK26_skl) ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sQ0_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f258,f259,f235,f238,f262,f253]) ).
fof(f266,plain,
! [X0,X1] :
( related(sK26_skl,X1,sK4_skl(X1,X0,sK26_skl))
| ~ element(X1,the_carrier(sK26_skl))
| ~ element(X0,the_carrier(sK26_skl))
| ~ rel_str(sK26_skl)
| empty_carrier(sK26_skl) ),
inference(resolution,[status(thm)],[f103,f209]) ).
fof(f267,definition,
! [X0,X1] :
( sQ7_spl
<=> ( related(sK26_skl,X1,sK4_skl(X1,X0,sK26_skl))
| ~ element(X1,the_carrier(sK26_skl))
| ~ element(X0,the_carrier(sK26_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f268,plain,
! [X0,X1] :
( ~ sQ7_spl
| related(sK26_skl,X1,sK4_skl(X1,X0,sK26_skl))
| ~ element(X1,the_carrier(sK26_skl))
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,plain,
( sQ7_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f266,f235,f238,f267]) ).
fof(f272,definition,
( sQ8_spl
<=> empty_carrier(sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( ~ sQ8_spl
| empty_carrier(sK25_skl) ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f275,definition,
( sQ9_spl
<=> one_sorted_str(sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f277,plain,
( sQ9_spl
| ~ one_sorted_str(sK25_skl) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f282,plain,
! [X0] :
( sQ1_spl
| ~ net_str(sK26_skl,X0)
| ~ one_sorted_str(X0) ),
inference(resolution,[status(thm)],[f116,f240]) ).
fof(f283,plain,
( sQ1_spl
| ~ one_sorted_str(sK25_skl) ),
inference(resolution,[status(thm)],[f282,f210]) ).
fof(f284,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f206]) ).
fof(f285,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f284]) ).
fof(f286,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| ~ element(sK0_skl(X2,sK26_skl,X1),the_carrier(sK26_skl))
| in(apply_netmap(X1,sK26_skl,sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl)),X2)
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f260]) ).
fof(f309,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f209]) ).
fof(f310,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f344,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f277,f206]) ).
fof(f345,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f344]) ).
fof(f346,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f273,f205]) ).
fof(f347,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f346]) ).
fof(f352,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| empty_carrier(sK26_skl)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| in(apply_netmap(X1,sK26_skl,sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl)),X2)
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(resolution,[status(thm)],[f286,f84]) ).
fof(f353,definition,
! [X0,X1,X2] :
( sQ20_spl
<=> ( ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| in(apply_netmap(X1,sK26_skl,sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl)),X2)
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X0,the_carrier(sK26_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f354,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| in(apply_netmap(X1,sK26_skl,sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl)),X2)
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,plain,
( ~ sQ5_spl
| sQ0_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f352,f353,f235,f259]) ).
fof(f357,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| in(apply_netmap(X1,sK26_skl,sK4_skl(X0,sK0_skl(X2,sK26_skl,X1),sK26_skl)),X2)
| ~ is_eventually_in(X1,sK26_skl,X2)
| ~ net_str(sK26_skl,X1)
| ~ one_sorted_str(X1)
| empty_carrier(X1)
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f354]) ).
fof(f364,plain,
! [X0,X1] :
( ~ sQ20_spl
| in(apply_netmap(sK25_skl,sK26_skl,sK4_skl(X0,sK0_skl(X1,sK26_skl,sK25_skl),sK26_skl)),X1)
| ~ is_eventually_in(sK25_skl,sK26_skl,X1)
| ~ one_sorted_str(sK25_skl)
| empty_carrier(sK25_skl)
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(resolution,[status(thm)],[f357,f210]) ).
fof(f365,definition,
! [X0,X1] :
( sQ22_spl
<=> ( in(apply_netmap(sK25_skl,sK26_skl,sK4_skl(X0,sK0_skl(X1,sK26_skl,sK25_skl),sK26_skl)),X1)
| ~ is_eventually_in(sK25_skl,sK26_skl,X1)
| ~ element(X0,the_carrier(sK26_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f366,plain,
! [X0,X1] :
( ~ sQ22_spl
| in(apply_netmap(sK25_skl,sK26_skl,sK4_skl(X0,sK0_skl(X1,sK26_skl,sK25_skl),sK26_skl)),X1)
| ~ is_eventually_in(sK25_skl,sK26_skl,X1)
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( ~ sQ20_spl
| ~ sQ9_spl
| sQ8_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f364,f365,f272,f275,f353]) ).
fof(f369,plain,
! [X0] :
( ~ sQ22_spl
| in(apply_netmap(sK25_skl,sK26_skl,sK4_skl(X0,sK0_skl(sK27_skl,sK26_skl,sK25_skl),sK26_skl)),sK27_skl)
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(resolution,[status(thm)],[f366,f211]) ).
fof(f374,definition,
( sQ24_spl
<=> net_str(sK26_skl,sK25_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( sQ24_spl
| ~ net_str(sK26_skl,sK25_skl) ),
inference(component_clause,[status(thm)],[f374]) ).
fof(f378,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f376,f210]) ).
fof(f379,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f378]) ).
fof(f391,plain,
! [X0] :
( ~ sQ22_spl
| ~ related(sK26_skl,sK3_skl(sK27_skl,sK26_skl,sK25_skl),sK4_skl(X0,sK0_skl(sK27_skl,sK26_skl,sK25_skl),sK26_skl))
| ~ element(sK4_skl(X0,sK0_skl(sK27_skl,sK26_skl,sK25_skl),sK26_skl),the_carrier(sK26_skl))
| is_often_in(sK25_skl,sK26_skl,sK27_skl)
| ~ net_str(sK26_skl,sK25_skl)
| empty_carrier(sK26_skl)
| ~ one_sorted_str(sK25_skl)
| empty_carrier(sK25_skl)
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(resolution,[status(thm)],[f369,f97]) ).
fof(f393,definition,
! [X0] :
( sQ27_spl
<=> ( ~ related(sK26_skl,sK3_skl(sK27_skl,sK26_skl,sK25_skl),sK4_skl(X0,sK0_skl(sK27_skl,sK26_skl,sK25_skl),sK26_skl))
| ~ element(sK4_skl(X0,sK0_skl(sK27_skl,sK26_skl,sK25_skl),sK26_skl),the_carrier(sK26_skl))
| ~ element(X0,the_carrier(sK26_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f394,plain,
! [X0] :
( ~ sQ27_spl
| ~ related(sK26_skl,sK3_skl(sK27_skl,sK26_skl,sK25_skl),sK4_skl(X0,sK0_skl(sK27_skl,sK26_skl,sK25_skl),sK26_skl))
| ~ element(sK4_skl(X0,sK0_skl(sK27_skl,sK26_skl,sK25_skl),sK26_skl),the_carrier(sK26_skl))
| ~ element(X0,the_carrier(sK26_skl)) ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f396,definition,
( sQ28_spl
<=> is_often_in(sK25_skl,sK26_skl,sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f397,plain,
( ~ sQ28_spl
| is_often_in(sK25_skl,sK26_skl,sK27_skl) ),
inference(component_clause,[status(thm)],[f396]) ).
fof(f399,plain,
( ~ sQ22_spl
| sQ28_spl
| ~ sQ24_spl
| sQ0_spl
| ~ sQ9_spl
| sQ8_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f391,f393,f272,f275,f235,f374,f396,f365]) ).
fof(f400,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f397,f212]) ).
fof(f401,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f400]) ).
fof(f428,plain,
( ~ sQ7_spl
| ~ sQ27_spl
| ~ element(sK3_skl(sK27_skl,sK26_skl,sK25_skl),the_carrier(sK26_skl))
| ~ element(sK0_skl(sK27_skl,sK26_skl,sK25_skl),the_carrier(sK26_skl))
| ~ element(sK4_skl(sK3_skl(sK27_skl,sK26_skl,sK25_skl),sK0_skl(sK27_skl,sK26_skl,sK25_skl),sK26_skl),the_carrier(sK26_skl))
| ~ element(sK3_skl(sK27_skl,sK26_skl,sK25_skl),the_carrier(sK26_skl)) ),
inference(resolution,[status(thm)],[f394,f268]) ).
fof(f429,definition,
( sQ34_spl
<=> element(sK3_skl(sK27_skl,sK26_skl,sK25_skl),the_carrier(sK26_skl)) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( sQ34_spl
| ~ element(sK3_skl(sK27_skl,sK26_skl,sK25_skl),the_carrier(sK26_skl)) ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,definition,
( sQ35_spl
<=> element(sK4_skl(sK3_skl(sK27_skl,sK26_skl,sK25_skl),sK0_skl(sK27_skl,sK26_skl,sK25_skl),sK26_skl),the_carrier(sK26_skl)) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f434,plain,
( sQ35_spl
| ~ element(sK4_skl(sK3_skl(sK27_skl,sK26_skl,sK25_skl),sK0_skl(sK27_skl,sK26_skl,sK25_skl),sK26_skl),the_carrier(sK26_skl)) ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,definition,
( sQ36_spl
<=> element(sK0_skl(sK27_skl,sK26_skl,sK25_skl),the_carrier(sK26_skl)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( sQ36_spl
| ~ element(sK0_skl(sK27_skl,sK26_skl,sK25_skl),the_carrier(sK26_skl)) ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,plain,
( ~ sQ7_spl
| ~ sQ27_spl
| ~ sQ36_spl
| ~ sQ35_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f428,f429,f432,f435,f393,f267]) ).
fof(f439,plain,
( sQ36_spl
| ~ is_eventually_in(sK25_skl,sK26_skl,sK27_skl)
| ~ net_str(sK26_skl,sK25_skl)
| empty_carrier(sK26_skl)
| ~ one_sorted_str(sK25_skl)
| empty_carrier(sK25_skl) ),
inference(resolution,[status(thm)],[f437,f84]) ).
fof(f440,definition,
( sQ37_spl
<=> is_eventually_in(sK25_skl,sK26_skl,sK27_skl) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( sQ37_spl
| ~ is_eventually_in(sK25_skl,sK26_skl,sK27_skl) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( sQ36_spl
| ~ sQ37_spl
| ~ sQ24_spl
| sQ0_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f439,f272,f275,f235,f374,f440,f435]) ).
fof(f444,plain,
( sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f211]) ).
fof(f445,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f444]) ).
fof(f451,plain,
( sQ34_spl
| is_often_in(sK25_skl,sK26_skl,sK27_skl)
| ~ net_str(sK26_skl,sK25_skl)
| empty_carrier(sK26_skl)
| ~ one_sorted_str(sK25_skl)
| empty_carrier(sK25_skl) ),
inference(resolution,[status(thm)],[f431,f96]) ).
fof(f452,plain,
( sQ34_spl
| sQ28_spl
| ~ sQ24_spl
| sQ0_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f451,f272,f275,f235,f374,f396,f429]) ).
fof(f467,plain,
( sQ35_spl
| ~ element(sK3_skl(sK27_skl,sK26_skl,sK25_skl),the_carrier(sK26_skl))
| ~ element(sK0_skl(sK27_skl,sK26_skl,sK25_skl),the_carrier(sK26_skl))
| ~ directed_relstr(sK26_skl)
| ~ rel_str(sK26_skl)
| empty_carrier(sK26_skl) ),
inference(resolution,[status(thm)],[f434,f101]) ).
fof(f468,plain,
( sQ35_spl
| ~ sQ34_spl
| ~ sQ36_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f467,f235,f238,f262,f435,f429,f432]) ).
fof(f469,plain,
$false,
inference(sat_refutation,[status(thm)],[f244,f249,f251,f256,f265,f270,f285,f310,f345,f347,f356,f368,f379,f399,f401,f438,f443,f445,f452,f468]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU376+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 06:17:39 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.059509 seconds
% 0.12/0.43 % CPU time: 0.199335 seconds
% 0.12/0.43 % Total memory used: 78.284 MB
% 0.12/0.43 % Net memory used: 78.184 MB
%------------------------------------------------------------------------------