%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU367+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 : n014.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 02:20:18 PM UTC 2026
% Result : Theorem 0.16s 0.56s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 34
% Syntax : Number of formulae : 185 ( 22 unt; 19 def)
% Number of atoms : 873 ( 5 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 1133 ( 445 ~; 567 |; 72 &)
% ( 24 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 19 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 346 ( 324 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( empty(A)
=> finite(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,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(f6,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(f16,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( net_str(B,A)
=> rel_str(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( net_str(B,A)
& ~ empty_carrier(B) )
=> ! [C,D] :
( subset(C,D)
=> ( ( is_often_in(A,B,C)
=> is_often_in(A,B,D) )
& ( is_eventually_in(A,B,C)
=> is_eventually_in(A,B,D) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ ! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( ( net_str(B,A)
& ~ empty_carrier(B) )
=> ! [C,D] :
( subset(C,D)
=> ( ( is_often_in(A,B,C)
=> is_often_in(A,B,D) )
& ( is_eventually_in(A,B,C)
=> is_eventually_in(A,B,D) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f57,plain,
! [A] :
( finite(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f58,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f62,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f63,plain,
! [X0,X1] :
( finite(X1)
| ~ element(X1,powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,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)],[f5]) ).
fof(f65,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)],[f64]) ).
fof(f66,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)],[f65]) ).
fof(f67,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))],[f66]) ).
fof(f68,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)],[f67]) ).
fof(f69,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)],[f67]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( element(sK1_skl(X3,X2,X1,X0),the_carrier(X1))
| ~ 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)],[f67]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( related(X1,X3,sK1_skl(X3,X2,X1,X0))
| ~ 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)],[f67]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( ~ in(apply_netmap(X0,X1,sK1_skl(X3,X2,X1,X0)),X2)
| ~ 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)],[f67]) ).
fof(f73,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)],[f6]) ).
fof(f74,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)],[f73]) ).
fof(f75,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)],[f74]) ).
fof(f76,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))],[f75]) ).
fof(f77,plain,
! [X0,X1,X2,X3] :
( element(sK2_skl(X3,X2,X1,X0),the_carrier(X1))
| ~ 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)],[f76]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( related(X1,X3,sK2_skl(X3,X2,X1,X0))
| ~ 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)],[f76]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( in(apply_netmap(X0,X1,sK2_skl(X3,X2,X1,X0)),X2)
| ~ 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)],[f76]) ).
fof(f80,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)],[f76]) ).
fof(f81,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)],[f76]) ).
fof(f90,plain,
! [A] :
( ! [B] :
( rel_str(B)
| ~ net_str(B,A) )
| ~ one_sorted_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f91,plain,
! [X0,X1] :
( rel_str(X1)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f107,plain,
! [A] : element(sK8_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(B,sK8_skl(A))],[f26]) ).
fof(f108,plain,
! [X0] : element(sK8_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f116,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f128,plain,
! [A] :
( empty(sK13_skl(A))
& element(sK13_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(B,sK13_skl(A))],[f36]) ).
fof(f129,plain,
! [X0] : element(sK13_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
! [X0] : empty(sK13_skl(X0)),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f160,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f161,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f162,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f163,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f162]) ).
fof(f165,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f166,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f167,plain,
! [A,C] :
( element(A,C)
| ! [B] :
( ~ element(B,powerset(C))
| ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f166]) ).
fof(f168,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f169,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f170,plain,
! [C] :
( ~ empty(C)
| ! [B] :
( ~ element(B,powerset(C))
| ! [A] : ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f169]) ).
fof(f171,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f172,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f173,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f174,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f175,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f174]) ).
fof(f176,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f180,plain,
? [A] :
( ? [B] :
( ? [C,D] :
( ( ( ~ is_often_in(A,B,D)
& is_often_in(A,B,C) )
| ( ~ is_eventually_in(A,B,D)
& is_eventually_in(A,B,C) ) )
& subset(C,D) )
& net_str(B,A)
& ~ empty_carrier(B) )
& one_sorted_str(A)
& ~ empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f181,definition,
! [A,B,C,D] :
( sP0_prd(D,C,B,A)
<=> ( ~ is_eventually_in(A,B,D)
& is_eventually_in(A,B,C) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f182,plain,
? [A] :
( ? [B] :
( ? [C,D] :
( ( ( ~ is_often_in(A,B,D)
& is_often_in(A,B,C) )
| sP0_prd(D,C,B,A) )
& subset(C,D) )
& net_str(B,A)
& ~ empty_carrier(B) )
& one_sorted_str(A)
& ~ empty_carrier(A) ),
inference(formula_renaming,[status(thm)],[f180,f181]) ).
fof(f183,plain,
( ( ( ~ is_often_in(sK19_skl,sK20_skl,sK22_skl)
& is_often_in(sK19_skl,sK20_skl,sK21_skl) )
| sP0_prd(sK22_skl,sK21_skl,sK20_skl,sK19_skl) )
& subset(sK21_skl,sK22_skl)
& net_str(sK20_skl,sK19_skl)
& ~ empty_carrier(sK20_skl)
& one_sorted_str(sK19_skl)
& ~ empty_carrier(sK19_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl,sK21_skl,sK22_skl]),skolemize(A,sK19_skl),skolemize(B,sK20_skl),skolemize(C,sK21_skl),skolemize(D,sK22_skl)],[f182]) ).
fof(f184,plain,
~ empty_carrier(sK19_skl),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f185,plain,
one_sorted_str(sK19_skl),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f186,plain,
~ empty_carrier(sK20_skl),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f187,plain,
net_str(sK20_skl,sK19_skl),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f188,plain,
subset(sK21_skl,sK22_skl),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f189,plain,
( is_often_in(sK19_skl,sK20_skl,sK21_skl)
| sP0_prd(sK22_skl,sK21_skl,sK20_skl,sK19_skl) ),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f190,plain,
( ~ is_often_in(sK19_skl,sK20_skl,sK22_skl)
| sP0_prd(sK22_skl,sK21_skl,sK20_skl,sK19_skl) ),
inference(cnf_transformation,[status(thm)],[f183]) ).
fof(f191,plain,
! [A,B,C,D] :
( ( is_eventually_in(A,B,D)
| ~ is_eventually_in(A,B,C)
| sP0_prd(D,C,B,A) )
& ( ( ~ is_eventually_in(A,B,D)
& is_eventually_in(A,B,C) )
| ~ sP0_prd(D,C,B,A) ) ),
inference(NNF_transformation,[status(thm)],[f181]) ).
fof(f192,plain,
( ! [A,B,C,D] :
( is_eventually_in(A,B,D)
| ~ is_eventually_in(A,B,C)
| sP0_prd(D,C,B,A) )
& ! [A,B,C,D] :
( ( ~ is_eventually_in(A,B,D)
& is_eventually_in(A,B,C) )
| ~ sP0_prd(D,C,B,A) ) ),
inference(miniscoping,[status(thm)],[f191]) ).
fof(f193,plain,
! [X0,X1,X2,X3] :
( is_eventually_in(X3,X2,X1)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f194,plain,
! [X0,X1,X2,X3] :
( ~ is_eventually_in(X3,X2,X0)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f196,definition,
( sQ0_spl
<=> sP0_prd(sK22_skl,sK21_skl,sK20_skl,sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( ~ sQ0_spl
| sP0_prd(sK22_skl,sK21_skl,sK20_skl,sK19_skl) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,definition,
( sQ1_spl
<=> is_often_in(sK19_skl,sK20_skl,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ1_spl
| is_often_in(sK19_skl,sK20_skl,sK21_skl) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f189,f196,f199]) ).
fof(f203,definition,
( sQ2_spl
<=> is_often_in(sK19_skl,sK20_skl,sK22_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f190,f196,f203]) ).
fof(f209,plain,
finite(empty_set),
inference(resolution,[status(thm)],[f58,f116]) ).
fof(f211,plain,
( ~ sQ0_spl
| is_eventually_in(sK19_skl,sK20_skl,sK21_skl) ),
inference(resolution,[status(thm)],[f193,f197]) ).
fof(f212,plain,
( ~ sQ0_spl
| ~ is_eventually_in(sK19_skl,sK20_skl,sK22_skl) ),
inference(resolution,[status(thm)],[f194,f197]) ).
fof(f226,plain,
! [X0,X1,X2,X3,X4] :
( in(apply_netmap(X4,X1,sK1_skl(sK0_skl(X3,X1,X4),X2,X1,X0)),X3)
| ~ element(sK1_skl(sK0_skl(X3,X1,X4),X2,X1,X0),the_carrier(X1))
| ~ is_eventually_in(X4,X1,X3)
| ~ net_str(X1,X4)
| empty_carrier(X1)
| ~ one_sorted_str(X4)
| empty_carrier(X4)
| ~ element(sK0_skl(X3,X1,X4),the_carrier(X1))
| is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f71,f69]) ).
fof(f227,plain,
! [X0,X1,X2,X3,X4] :
( in(apply_netmap(X4,X1,sK1_skl(sK0_skl(X3,X1,X4),X2,X1,X0)),X3)
| ~ element(sK1_skl(sK0_skl(X3,X1,X4),X2,X1,X0),the_carrier(X1))
| ~ is_eventually_in(X4,X1,X3)
| ~ net_str(X1,X4)
| ~ one_sorted_str(X4)
| empty_carrier(X4)
| ~ element(sK0_skl(X3,X1,X4),the_carrier(X1))
| is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f226]) ).
fof(f228,plain,
! [X0,X1,X2,X3,X4] :
( in(apply_netmap(X3,X1,sK1_skl(sK0_skl(X4,X1,X3),X2,X1,X0)),X4)
| ~ element(sK1_skl(sK0_skl(X4,X1,X3),X2,X1,X0),the_carrier(X1))
| ~ is_eventually_in(X3,X1,X4)
| ~ net_str(X1,X3)
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f227,f68]) ).
fof(f234,plain,
! [X0] : sK13_skl(X0) = empty_set,
inference(resolution,[status(thm)],[f173,f130]) ).
fof(f244,plain,
! [X0,X1,X2,X3] :
( ~ empty(X2)
| ~ 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(resolution,[status(thm)],[f79,f176]) ).
fof(f248,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(forward_demodulation,[status(thm)],[f234,f129]) ).
fof(f250,plain,
! [X0] :
( finite(empty_set)
| ~ finite(X0) ),
inference(resolution,[status(thm)],[f248,f63]) ).
fof(f252,definition,
! [X0] :
( sQ5_spl
<=> ~ finite(X0) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f253,plain,
! [X0] :
( ~ sQ5_spl
| ~ finite(X0) ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
( sQ6_spl
<=> finite(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f250,f252,f255]) ).
fof(f262,plain,
! [X0,X1,X2,X3,X4] :
( ~ element(sK3_skl(X2,X1,X0),the_carrier(X1))
| ~ is_often_in(X4,X1,X3)
| ~ net_str(X1,X4)
| empty_carrier(X1)
| ~ one_sorted_str(X4)
| empty_carrier(X4)
| ~ in(apply_netmap(X0,X1,sK2_skl(sK3_skl(X2,X1,X0),X3,X1,X4)),X2)
| ~ element(sK2_skl(sK3_skl(X2,X1,X0),X3,X1,X4),the_carrier(X1))
| is_often_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f81,f78]) ).
fof(f264,plain,
! [X0,X1,X2,X3,X4] :
( ~ element(sK3_skl(X2,X1,X0),the_carrier(X1))
| ~ is_often_in(X4,X1,X3)
| ~ net_str(X1,X4)
| ~ one_sorted_str(X4)
| empty_carrier(X4)
| ~ in(apply_netmap(X0,X1,sK2_skl(sK3_skl(X2,X1,X0),X3,X1,X4)),X2)
| ~ element(sK2_skl(sK3_skl(X2,X1,X0),X3,X1,X4),the_carrier(X1))
| is_often_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f262]) ).
fof(f265,plain,
! [X0,X1,X2,X3,X4] :
( ~ element(sK3_skl(X2,X1,X0),the_carrier(X1))
| ~ is_often_in(X4,X1,X3)
| ~ net_str(X1,X4)
| ~ one_sorted_str(X4)
| empty_carrier(X4)
| ~ in(apply_netmap(X0,X1,sK2_skl(sK3_skl(X2,X1,X0),X3,X1,X4)),X2)
| is_often_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f264,f77]) ).
fof(f269,plain,
( ~ sQ5_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f209,f253]) ).
fof(f271,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f269]) ).
fof(f278,plain,
( rel_str(sK20_skl)
| ~ one_sorted_str(sK19_skl) ),
inference(resolution,[status(thm)],[f91,f187]) ).
fof(f279,definition,
( sQ7_spl
<=> one_sorted_str(sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( sQ7_spl
| ~ one_sorted_str(sK19_skl) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,definition,
( sQ8_spl
<=> rel_str(sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f285,plain,
( sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f278,f279,f282]) ).
fof(f286,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f281,f185]) ).
fof(f287,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f286]) ).
fof(f332,plain,
! [X0] :
( in(sK8_skl(X0),X0)
| empty(X0) ),
inference(resolution,[status(thm)],[f161,f108]) ).
fof(f359,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| element(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f168,f165]) ).
fof(f376,plain,
! [X0] :
( element(X0,sK22_skl)
| ~ in(X0,sK21_skl) ),
inference(resolution,[status(thm)],[f359,f188]) ).
fof(f380,plain,
! [X0,X1,X2] :
( ~ element(X2,the_carrier(X1))
| ~ is_often_in(X0,X1,sK21_skl)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| element(apply_netmap(X0,X1,sK2_skl(X2,sK21_skl,X1,X0)),sK22_skl) ),
inference(resolution,[status(thm)],[f376,f79]) ).
fof(f394,definition,
( sQ9_spl
<=> empty(sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( sQ9_spl
| ~ empty(sK21_skl) ),
inference(component_clause,[status(thm)],[f394]) ).
fof(f424,plain,
! [X0,X1,X2] :
( ~ subset(X1,X2)
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(resolution,[status(thm)],[f171,f165]) ).
fof(f484,definition,
( sQ16_spl
<=> empty(sK22_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f495,plain,
! [X0] :
( ~ empty(sK22_skl)
| ~ in(X0,sK21_skl) ),
inference(resolution,[status(thm)],[f188,f424]) ).
fof(f496,plain,
! [X0] :
( element(X0,sK22_skl)
| ~ in(X0,sK21_skl) ),
inference(resolution,[status(thm)],[f188,f359]) ).
fof(f498,definition,
! [X0] :
( sQ17_spl
<=> ~ in(X0,sK21_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f499,plain,
! [X0] :
( ~ sQ17_spl
| ~ in(X0,sK21_skl) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,plain,
( ~ sQ16_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f495,f498,f484]) ).
fof(f503,plain,
( ~ sQ17_spl
| empty(sK21_skl) ),
inference(resolution,[status(thm)],[f499,f332]) ).
fof(f504,plain,
! [X0,X1,X2,X3] :
( ~ sQ17_spl
| ~ element(sK1_skl(sK0_skl(sK21_skl,X1,X3),X2,X1,X0),the_carrier(X1))
| ~ is_eventually_in(X3,X1,sK21_skl)
| ~ net_str(X1,X3)
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f499,f228]) ).
fof(f509,plain,
( ~ sQ17_spl
| sK21_skl = empty_set ),
inference(resolution,[status(thm)],[f503,f173]) ).
fof(f512,plain,
( ~ sQ0_spl
| ~ sQ17_spl
| is_eventually_in(sK19_skl,sK20_skl,empty_set) ),
inference(backward_demodulation,[status(thm)],[f509,f211]) ).
fof(f535,plain,
! [X0,X1,X2,X3,X4] :
( ~ is_often_in(X4,X1,X3)
| ~ net_str(X1,X4)
| ~ one_sorted_str(X4)
| empty_carrier(X4)
| ~ in(apply_netmap(X0,X1,sK2_skl(sK3_skl(X2,X1,X0),X3,X1,X4)),X2)
| is_often_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f265,f80]) ).
fof(f553,plain,
! [X0,X1,X2,X3] :
( ~ sQ17_spl
| ~ element(sK1_skl(sK0_skl(sK21_skl,X1,X3),X2,X1,X0),the_carrier(X1))
| ~ is_eventually_in(X3,X1,empty_set)
| ~ net_str(X1,X3)
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(forward_demodulation,[status(thm)],[f509,f504]) ).
fof(f554,plain,
! [X0,X1,X2,X3] :
( ~ sQ17_spl
| ~ element(sK1_skl(sK0_skl(empty_set,X1,X3),X2,X1,X0),the_carrier(X1))
| ~ is_eventually_in(X3,X1,empty_set)
| ~ net_str(X1,X3)
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(forward_demodulation,[status(thm)],[f509,f553]) ).
fof(f555,plain,
! [X0,X1,X2,X3] :
( ~ sQ17_spl
| ~ element(sK0_skl(empty_set,X1,X3),the_carrier(X1))
| is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ is_eventually_in(X3,X1,empty_set)
| ~ net_str(X1,X3)
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f554,f70]) ).
fof(f556,plain,
! [X0,X1,X2,X3] :
( ~ sQ17_spl
| ~ element(sK0_skl(empty_set,X1,X3),the_carrier(X1))
| ~ is_eventually_in(X3,X1,empty_set)
| ~ net_str(X1,X3)
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f555]) ).
fof(f557,plain,
! [X0,X1,X2,X3] :
( ~ sQ17_spl
| ~ is_eventually_in(X3,X1,empty_set)
| ~ net_str(X1,X3)
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f556,f68]) ).
fof(f622,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ17_spl
| ~ net_str(sK20_skl,sK19_skl)
| ~ one_sorted_str(sK19_skl)
| empty_carrier(sK19_skl)
| is_eventually_in(X0,sK20_skl,X1)
| ~ net_str(sK20_skl,X0)
| empty_carrier(sK20_skl)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f557,f512]) ).
fof(f623,definition,
! [X0,X1] :
( sQ19_spl
<=> ( is_eventually_in(X0,sK20_skl,X1)
| ~ net_str(sK20_skl,X0)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f624,plain,
! [X0,X1] :
( ~ sQ19_spl
| is_eventually_in(X0,sK20_skl,X1)
| ~ net_str(sK20_skl,X0)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(component_clause,[status(thm)],[f623]) ).
fof(f626,definition,
( sQ20_spl
<=> empty_carrier(sK20_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f627,plain,
( ~ sQ20_spl
| empty_carrier(sK20_skl) ),
inference(component_clause,[status(thm)],[f626]) ).
fof(f629,definition,
( sQ21_spl
<=> empty_carrier(sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f630,plain,
( ~ sQ21_spl
| empty_carrier(sK19_skl) ),
inference(component_clause,[status(thm)],[f629]) ).
fof(f632,definition,
( sQ22_spl
<=> net_str(sK20_skl,sK19_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f634,plain,
( sQ22_spl
| ~ net_str(sK20_skl,sK19_skl) ),
inference(component_clause,[status(thm)],[f632]) ).
fof(f635,plain,
( ~ sQ0_spl
| ~ sQ17_spl
| ~ sQ22_spl
| ~ sQ7_spl
| sQ21_spl
| sQ20_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f622,f623,f626,f629,f279,f632,f498,f196]) ).
fof(f636,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f634,f187]) ).
fof(f637,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f636]) ).
fof(f638,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f630,f184]) ).
fof(f639,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f638]) ).
fof(f640,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f627,f186]) ).
fof(f641,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f640]) ).
fof(f642,plain,
( ~ sQ0_spl
| ~ sQ19_spl
| ~ net_str(sK20_skl,sK19_skl)
| ~ one_sorted_str(sK19_skl)
| empty_carrier(sK19_skl) ),
inference(resolution,[status(thm)],[f624,f212]) ).
fof(f644,plain,
( ~ sQ0_spl
| ~ sQ19_spl
| ~ sQ22_spl
| ~ sQ7_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f642,f629,f279,f632,f623,f196]) ).
fof(f649,plain,
! [X0] :
( ~ sQ1_spl
| ~ empty(sK21_skl)
| ~ element(X0,the_carrier(sK20_skl))
| ~ net_str(sK20_skl,sK19_skl)
| empty_carrier(sK20_skl)
| ~ one_sorted_str(sK19_skl)
| empty_carrier(sK19_skl) ),
inference(resolution,[status(thm)],[f200,f244]) ).
fof(f650,definition,
! [X0] :
( sQ24_spl
<=> ~ element(X0,the_carrier(sK20_skl)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f651,plain,
! [X0] :
( ~ sQ24_spl
| ~ element(X0,the_carrier(sK20_skl)) ),
inference(component_clause,[status(thm)],[f650]) ).
fof(f653,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| sQ24_spl
| ~ sQ22_spl
| sQ20_spl
| ~ sQ7_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f649,f629,f279,f626,f632,f650,f394,f199]) ).
fof(f666,plain,
( ~ sQ24_spl
| $false ),
inference(resolution,[status(thm)],[f651,f108]) ).
fof(f685,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f666]) ).
fof(f705,plain,
! [X0,X1,X2,X3] :
( ~ element(sK1_skl(sK0_skl(sK21_skl,X1,X0),X2,X1,X3),the_carrier(X1))
| ~ is_eventually_in(X0,X1,sK21_skl)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| is_eventually_in(X3,X1,X2)
| ~ net_str(X1,X3)
| empty_carrier(X1)
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| element(apply_netmap(X0,X1,sK1_skl(sK0_skl(sK21_skl,X1,X0),X2,X1,X3)),sK22_skl) ),
inference(resolution,[status(thm)],[f496,f228]) ).
fof(f773,plain,
! [X0,X1,X2] :
( in(apply_netmap(X0,X1,sK2_skl(X2,sK21_skl,X1,X0)),sK22_skl)
| empty(sK22_skl)
| ~ element(X2,the_carrier(X1))
| ~ is_often_in(X0,X1,sK21_skl)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f380,f161]) ).
fof(f774,definition,
! [X0,X1,X2] :
( sQ34_spl
<=> ( in(apply_netmap(X0,X1,sK2_skl(X2,sK21_skl,X1,X0)),sK22_skl)
| ~ element(X2,the_carrier(X1))
| ~ is_often_in(X0,X1,sK21_skl)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f775,plain,
! [X0,X1,X2] :
( ~ sQ34_spl
| in(apply_netmap(X0,X1,sK2_skl(X2,sK21_skl,X1,X0)),sK22_skl)
| ~ element(X2,the_carrier(X1))
| ~ is_often_in(X0,X1,sK21_skl)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(component_clause,[status(thm)],[f774]) ).
fof(f777,plain,
( sQ16_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f773,f774,f484]) ).
fof(f824,plain,
! [X0,X1] :
( ~ sQ34_spl
| ~ is_often_in(X0,X1,sK21_skl)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| is_often_in(X0,X1,sK22_skl)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ element(sK3_skl(sK22_skl,X1,X0),the_carrier(X1))
| ~ is_often_in(X0,X1,sK21_skl)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f775,f535]) ).
fof(f828,plain,
! [X0,X1] :
( ~ sQ34_spl
| is_often_in(X0,X1,sK22_skl)
| ~ element(sK3_skl(sK22_skl,X1,X0),the_carrier(X1))
| ~ is_often_in(X0,X1,sK21_skl)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f824]) ).
fof(f829,plain,
! [X0,X1] :
( ~ sQ34_spl
| is_often_in(X0,X1,sK22_skl)
| ~ is_often_in(X0,X1,sK21_skl)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f828,f80]) ).
fof(f834,plain,
! [X0,X1,X2,X3] :
( in(apply_netmap(X3,X1,sK1_skl(sK0_skl(sK21_skl,X1,X3),X2,X1,X0)),sK22_skl)
| empty(sK22_skl)
| ~ element(sK1_skl(sK0_skl(sK21_skl,X1,X3),X2,X1,X0),the_carrier(X1))
| ~ is_eventually_in(X3,X1,sK21_skl)
| ~ net_str(X1,X3)
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f705,f161]) ).
fof(f835,definition,
! [X0,X1,X2,X3] :
( sQ38_spl
<=> ( in(apply_netmap(X3,X1,sK1_skl(sK0_skl(sK21_skl,X1,X3),X2,X1,X0)),sK22_skl)
| ~ element(sK1_skl(sK0_skl(sK21_skl,X1,X3),X2,X1,X0),the_carrier(X1))
| ~ is_eventually_in(X3,X1,sK21_skl)
| ~ net_str(X1,X3)
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f836,plain,
! [X0,X1,X2,X3] :
( ~ sQ38_spl
| in(apply_netmap(X3,X1,sK1_skl(sK0_skl(sK21_skl,X1,X3),X2,X1,X0)),sK22_skl)
| ~ element(sK1_skl(sK0_skl(sK21_skl,X1,X3),X2,X1,X0),the_carrier(X1))
| ~ is_eventually_in(X3,X1,sK21_skl)
| ~ net_str(X1,X3)
| ~ one_sorted_str(X3)
| empty_carrier(X3)
| is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(component_clause,[status(thm)],[f835]) ).
fof(f838,plain,
( sQ16_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f834,f835,f484]) ).
fof(f871,plain,
! [X0,X1] :
( ~ sQ38_spl
| ~ element(sK0_skl(sK21_skl,X1,X0),the_carrier(X1))
| is_eventually_in(X0,X1,sK22_skl)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ element(sK1_skl(sK0_skl(sK21_skl,X1,X0),sK22_skl,X1,X0),the_carrier(X1))
| ~ is_eventually_in(X0,X1,sK21_skl)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| empty_carrier(X0)
| is_eventually_in(X0,X1,sK22_skl)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f836,f72]) ).
fof(f875,plain,
! [X0,X1] :
( ~ sQ38_spl
| ~ element(sK0_skl(sK21_skl,X1,X0),the_carrier(X1))
| ~ element(sK1_skl(sK0_skl(sK21_skl,X1,X0),sK22_skl,X1,X0),the_carrier(X1))
| ~ is_eventually_in(X0,X1,sK21_skl)
| is_eventually_in(X0,X1,sK22_skl)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f871]) ).
fof(f876,plain,
! [X0,X1] :
( ~ sQ38_spl
| ~ element(sK0_skl(sK21_skl,X1,X0),the_carrier(X1))
| ~ is_eventually_in(X0,X1,sK21_skl)
| is_eventually_in(X0,X1,sK22_skl)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f875,f70]) ).
fof(f881,plain,
! [X0,X1] :
( ~ sQ38_spl
| ~ is_eventually_in(X0,X1,sK21_skl)
| is_eventually_in(X0,X1,sK22_skl)
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f876,f68]) ).
fof(f882,plain,
( ~ sQ0_spl
| ~ sQ38_spl
| is_eventually_in(sK19_skl,sK20_skl,sK22_skl)
| ~ net_str(sK20_skl,sK19_skl)
| empty_carrier(sK20_skl)
| ~ one_sorted_str(sK19_skl)
| empty_carrier(sK19_skl) ),
inference(resolution,[status(thm)],[f881,f211]) ).
fof(f883,definition,
( sQ41_spl
<=> is_eventually_in(sK19_skl,sK20_skl,sK22_skl) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f884,plain,
( ~ sQ41_spl
| is_eventually_in(sK19_skl,sK20_skl,sK22_skl) ),
inference(component_clause,[status(thm)],[f883]) ).
fof(f886,plain,
( ~ sQ0_spl
| ~ sQ38_spl
| sQ41_spl
| ~ sQ22_spl
| sQ20_spl
| ~ sQ7_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f882,f629,f279,f626,f632,f883,f835,f196]) ).
fof(f902,plain,
( sQ9_spl
| ~ sQ17_spl
| ~ empty(empty_set) ),
inference(backward_demodulation,[status(thm)],[f509,f396]) ).
fof(f904,plain,
( sQ9_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f902,f116]) ).
fof(f905,plain,
( sQ9_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f904]) ).
fof(f923,plain,
( ~ sQ41_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f884,f212]) ).
fof(f924,plain,
( ~ sQ41_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f923]) ).
fof(f1000,plain,
( ~ sQ1_spl
| ~ sQ34_spl
| is_often_in(sK19_skl,sK20_skl,sK22_skl)
| ~ net_str(sK20_skl,sK19_skl)
| empty_carrier(sK20_skl)
| ~ one_sorted_str(sK19_skl)
| empty_carrier(sK19_skl) ),
inference(resolution,[status(thm)],[f829,f200]) ).
fof(f1001,plain,
( ~ sQ1_spl
| ~ sQ34_spl
| sQ2_spl
| ~ sQ22_spl
| sQ20_spl
| ~ sQ7_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f1000,f629,f279,f626,f632,f203,f774,f199]) ).
fof(f1002,plain,
$false,
inference(sat_refutation,[status(thm)],[f202,f206,f258,f271,f285,f287,f501,f635,f637,f639,f641,f644,f653,f685,f777,f838,f886,f905,f924,f1001]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU367+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n014.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 06:16:19 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.56 % Refutation found
% 0.16/0.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.33/0.60 % Elapsed time: 0.151759 seconds
% 0.33/0.60 % CPU time: 0.806805 seconds
% 0.33/0.60 % Total memory used: 96.417 MB
% 0.33/0.60 % Net memory used: 95.704 MB
%------------------------------------------------------------------------------