%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU109+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:19:14 PM UTC 2026
% Result : Theorem 121.76s 15.87s
% Output : CNFRefutation 121.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 70
% Syntax : Number of formulae : 336 ( 81 unt; 48 def)
% Number of atoms : 770 ( 34 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 788 ( 354 ~; 285 |; 87 &)
% ( 53 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 66 ( 64 usr; 49 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 281 ( 268 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( finite(B)
=> finite(set_intersection2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( finite(A)
=> finite(set_intersection2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
? [A] :
( preboolean(A)
& diff_closed(A)
& cap_closed(A)
& cup_closed(A)
& ~ empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A] :
( preboolean(A)
<=> ! [B,C] :
( ( in(C,A)
& in(B,A) )
=> ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A] :
( ( preboolean(A)
& ~ empty(A) )
=> in(empty_set,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,conjecture,
! [A] :
( ( preboolean(A)
& ~ empty(A) )
=> ! [B] :
( ( preboolean(B)
& ~ empty(B) )
=> ( preboolean(set_intersection2(A,B))
& ~ empty(set_intersection2(A,B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
~ ! [A] :
( ( preboolean(A)
& ~ empty(A) )
=> ! [B] :
( ( preboolean(B)
& ~ empty(B) )
=> ( preboolean(set_intersection2(A,B))
& ~ empty(set_intersection2(A,B)) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
fof(f37,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f60,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f61,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
( ! [A,B,C] :
( ( ( ( in(sK0_skl(C,B,A),B)
& in(sK0_skl(C,B,A),A) )
| in(sK0_skl(C,B,A),C) )
& ( ~ in(sK0_skl(C,B,A),B)
| ~ in(sK0_skl(C,B,A),A)
| ~ in(sK0_skl(C,B,A),C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f61]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f67,plain,
! [X0,X1,X2] :
( in(sK0_skl(X0,X1,X2),X0)
| set_intersection2(X2,X1) = X0
| in(sK0_skl(X0,X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f69,plain,
! [A] : element(sK1_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B,sK1_skl(A))],[f9]) ).
fof(f70,plain,
! [X0] : element(sK1_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [A,B] :
( finite(set_intersection2(A,B))
| ~ finite(B) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f72,plain,
! [B] :
( ! [A] : finite(set_intersection2(A,B))
| ~ finite(B) ),
inference(miniscoping,[status(thm)],[f71]) ).
fof(f73,plain,
! [X0,X1] :
( finite(set_intersection2(X1,X0))
| ~ finite(X0) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [A,B] :
( finite(set_intersection2(A,B))
| ~ finite(A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f75,plain,
! [A] :
( ! [B] : finite(set_intersection2(A,B))
| ~ finite(A) ),
inference(miniscoping,[status(thm)],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( finite(set_intersection2(X0,X1))
| ~ finite(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f80,plain,
( ! [A] : preboolean(powerset(A))
& ! [A] : diff_closed(powerset(A))
& ! [A] : cup_closed(powerset(A))
& ! [A] : ~ empty(powerset(A)) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f81,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f84,plain,
! [X0] : preboolean(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f86,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f97,plain,
! [A] : set_intersection2(A,A) = A,
inference(miniscoping,[status(thm)],[f20]) ).
fof(f98,plain,
! [X0] : X0 = set_intersection2(X0,X0),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
( finite(sK2_skl)
& ~ empty(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(A,sK2_skl)],[f21]) ).
fof(f101,plain,
finite(sK2_skl),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f102,plain,
( preboolean(sK3_skl)
& diff_closed(sK3_skl)
& cap_closed(sK3_skl)
& cup_closed(sK3_skl)
& ~ empty(sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f22]) ).
fof(f104,plain,
cup_closed(sK3_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f112,plain,
empty(sK5_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f24]) ).
fof(f113,plain,
empty(sK5_skl),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
! [A] :
( finite(sK6_skl(A))
& natural(sK6_skl(A))
& ordinal(sK6_skl(A))
& epsilon_connected(sK6_skl(A))
& epsilon_transitive(sK6_skl(A))
& one_to_one(sK6_skl(A))
& function(sK6_skl(A))
& relation(sK6_skl(A))
& empty(sK6_skl(A))
& element(sK6_skl(A),powerset(A)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(B,sK6_skl(A))],[f25]) ).
fof(f115,plain,
! [X0] : element(sK6_skl(X0),powerset(X0)),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
! [X0] : empty(sK6_skl(X0)),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f140,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f141,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f142,plain,
! [A] :
( preboolean(A)
<=> ! [B,C] :
( ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) )
| ~ in(C,A)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f143,plain,
! [A] :
( ( ? [B,C] :
( ( ~ in(set_difference(B,C),A)
| ~ in(set_union2(B,C),A) )
& in(C,A)
& in(B,A) )
| preboolean(A) )
& ( ! [B,C] :
( ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) )
| ~ in(C,A)
| ~ in(B,A) )
| ~ preboolean(A) ) ),
inference(NNF_transformation,[status(thm)],[f142]) ).
fof(f144,plain,
( ! [A] :
( ? [B,C] :
( ( ~ in(set_difference(B,C),A)
| ~ in(set_union2(B,C),A) )
& in(C,A)
& in(B,A) )
| preboolean(A) )
& ! [A] :
( ! [B,C] :
( ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) )
| ~ in(C,A)
| ~ in(B,A) )
| ~ preboolean(A) ) ),
inference(miniscoping,[status(thm)],[f143]) ).
fof(f145,plain,
( ! [A] :
( ( ( ~ in(set_difference(sK11_skl(A),sK12_skl(A)),A)
| ~ in(set_union2(sK11_skl(A),sK12_skl(A)),A) )
& in(sK12_skl(A),A)
& in(sK11_skl(A),A) )
| preboolean(A) )
& ! [A] :
( ! [B,C] :
( ( in(set_difference(B,C),A)
& in(set_union2(B,C),A) )
| ~ in(C,A)
| ~ in(B,A) )
| ~ preboolean(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl]),skolemize(B,sK11_skl(A)),skolemize(C,sK12_skl(A))],[f144]) ).
fof(f146,plain,
! [X0,X1,X2] :
( ~ preboolean(X2)
| ~ in(X0,X2)
| ~ in(X1,X2)
| in(set_union2(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
! [X0,X1,X2] :
( ~ preboolean(X1)
| ~ in(X2,X1)
| in(set_difference(X0,X2),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f148,plain,
! [X0] :
( in(sK11_skl(X0),X0)
| preboolean(X0) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f149,plain,
! [X0] :
( preboolean(X0)
| in(sK12_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f150,plain,
! [X0] :
( preboolean(X0)
| ~ in(set_difference(sK11_skl(X0),sK12_skl(X0)),X0)
| ~ in(set_union2(sK11_skl(X0),sK12_skl(X0)),X0) ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f151,plain,
! [A] :
( in(empty_set,A)
| ~ preboolean(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f152,plain,
! [X0] :
( ~ preboolean(X0)
| empty(X0)
| in(empty_set,X0) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
fof(f156,plain,
? [A] :
( ? [B] :
( ( ~ preboolean(set_intersection2(A,B))
| empty(set_intersection2(A,B)) )
& preboolean(B)
& ~ empty(B) )
& preboolean(A)
& ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f157,plain,
( ( ~ preboolean(set_intersection2(sK13_skl,sK14_skl))
| empty(set_intersection2(sK13_skl,sK14_skl)) )
& preboolean(sK14_skl)
& ~ empty(sK14_skl)
& preboolean(sK13_skl)
& ~ empty(sK13_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(A,sK13_skl),skolemize(B,sK14_skl)],[f156]) ).
fof(f158,plain,
~ empty(sK13_skl),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f159,plain,
preboolean(sK13_skl),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f160,plain,
~ empty(sK14_skl),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f161,plain,
preboolean(sK14_skl),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f162,plain,
( ~ preboolean(set_intersection2(sK13_skl,sK14_skl))
| empty(set_intersection2(sK13_skl,sK14_skl)) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f163,plain,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f164,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f165,plain,
! [X0,X1] :
( ~ element(X1,X0)
| in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f167,plain,
! [A,B] :
( ( ~ subset(A,B)
| element(A,powerset(B)) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(NNF_transformation,[status(thm)],[f40]) ).
fof(f168,plain,
( ! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) )
& ! [A,B] :
( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(miniscoping,[status(thm)],[f167]) ).
fof(f170,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f175,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f176,plain,
! [C] :
( ~ empty(C)
| ! [B] :
( ~ element(B,powerset(C))
| ! [A] : ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f175]) ).
fof(f177,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| ~ element(X1,powerset(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f180,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f181,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f180]) ).
fof(f182,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f181]) ).
fof(f183,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f184,plain,
! [B] :
( ~ empty(B)
| ! [A] :
( A = B
| ~ empty(A) ) ),
inference(miniscoping,[status(thm)],[f183]) ).
fof(f185,plain,
! [X0,X1] :
( X0 = X1
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f184]) ).
fof(f186,definition,
( sQ0_spl
<=> empty(set_intersection2(sK13_skl,sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ0_spl
| empty(set_intersection2(sK13_skl,sK14_skl)) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,definition,
( sQ1_spl
<=> preboolean(set_intersection2(sK13_skl,sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ1_spl
| ~ preboolean(set_intersection2(sK13_skl,sK14_skl)) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f162,f186,f189]) ).
fof(f193,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f63]) ).
fof(f194,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f64]) ).
fof(f195,plain,
! [X0,X1,X2] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f65]) ).
fof(f200,plain,
! [X0] :
( ~ sQ0_spl
| set_intersection2(sK13_skl,sK14_skl) = X0
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f185,f187]) ).
fof(f201,plain,
( ~ sQ0_spl
| set_intersection2(sK13_skl,sK14_skl) = empty_set ),
inference(resolution,[status(thm)],[f200,f86]) ).
fof(f225,plain,
! [X0] :
( sK5_skl = X0
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f113,f185]) ).
fof(f230,plain,
empty_set = sK5_skl,
inference(resolution,[status(thm)],[f225,f86]) ).
fof(f235,plain,
! [X0] : set_intersection2(X0,empty_set) = sK5_skl,
inference(backward_demodulation,[status(thm)],[f230,f163]) ).
fof(f237,plain,
! [X0] :
( ~ preboolean(X0)
| empty(X0)
| in(sK5_skl,X0) ),
inference(backward_demodulation,[status(thm)],[f230,f152]) ).
fof(f240,plain,
! [X0] : sK5_skl = set_intersection2(X0,sK5_skl),
inference(forward_demodulation,[status(thm)],[f230,f235]) ).
fof(f241,plain,
! [X0] : sK5_skl = sK6_skl(X0),
inference(resolution,[status(thm)],[f116,f225]) ).
fof(f250,plain,
! [X0] : element(sK5_skl,powerset(X0)),
inference(backward_demodulation,[status(thm)],[f241,f115]) ).
fof(f261,plain,
! [X0] : set_intersection2(sK5_skl,X0) = sK5_skl,
inference(paramodulation,[status(thm)],[f59,f240]) ).
fof(f271,definition,
! [X0] :
( sQ4_spl
<=> ~ finite(X0) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f272,plain,
! [X0] :
( ~ sQ4_spl
| ~ finite(X0) ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f301,plain,
! [X0] : finite(set_intersection2(sK2_skl,X0)),
inference(resolution,[status(thm)],[f76,f101]) ).
fof(f307,plain,
! [X0] : finite(set_intersection2(X0,sK2_skl)),
inference(paramodulation,[status(thm)],[f59,f301]) ).
fof(f309,plain,
! [X0,X1] : finite(set_intersection2(set_intersection2(X0,sK2_skl),X1)),
inference(resolution,[status(thm)],[f307,f76]) ).
fof(f314,plain,
! [X0] :
( in(sK5_skl,powerset(X0))
| empty(powerset(X0)) ),
inference(resolution,[status(thm)],[f237,f84]) ).
fof(f315,plain,
( in(sK5_skl,sK13_skl)
| empty(sK13_skl) ),
inference(resolution,[status(thm)],[f237,f159]) ).
fof(f316,plain,
( in(sK5_skl,sK14_skl)
| empty(sK14_skl) ),
inference(resolution,[status(thm)],[f237,f161]) ).
fof(f318,definition,
( sQ6_spl
<=> empty(sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f319,plain,
( ~ sQ6_spl
| empty(sK14_skl) ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,definition,
( sQ7_spl
<=> in(sK5_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( ~ sQ7_spl
| in(sK5_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f321]) ).
fof(f324,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f316,f318,f321]) ).
fof(f325,plain,
! [X0] : in(sK5_skl,powerset(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f314,f81]) ).
fof(f326,definition,
( sQ8_spl
<=> empty(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( ~ sQ8_spl
| empty(sK13_skl) ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f329,definition,
( sQ9_spl
<=> in(sK5_skl,sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( ~ sQ9_spl
| in(sK5_skl,sK13_skl) ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,plain,
( sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f315,f326,f329]) ).
fof(f340,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f158]) ).
fof(f341,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f340]) ).
fof(f344,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f319,f160]) ).
fof(f345,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f344]) ).
fof(f346,plain,
! [X0] :
( ~ sQ9_spl
| ~ in(sK5_skl,X0)
| in(sK5_skl,set_intersection2(sK13_skl,X0)) ),
inference(resolution,[status(thm)],[f330,f195]) ).
fof(f348,plain,
! [X0,X1] : finite(set_intersection2(X0,set_intersection2(X1,sK2_skl))),
inference(resolution,[status(thm)],[f73,f307]) ).
fof(f352,plain,
! [X0] :
( ~ sQ7_spl
| in(sK5_skl,set_intersection2(sK14_skl,X0))
| ~ in(sK5_skl,X0) ),
inference(resolution,[status(thm)],[f322,f195]) ).
fof(f355,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| in(sK5_skl,set_intersection2(sK13_skl,sK14_skl)) ),
inference(resolution,[status(thm)],[f346,f322]) ).
fof(f364,plain,
! [X0,X1] :
( ~ in(X1,sK13_skl)
| ~ in(X0,sK13_skl)
| in(set_union2(X0,X1),sK13_skl) ),
inference(resolution,[status(thm)],[f146,f159]) ).
fof(f365,plain,
! [X0,X1] :
( ~ in(X1,sK14_skl)
| ~ in(X0,sK14_skl)
| in(set_union2(X0,X1),sK14_skl) ),
inference(resolution,[status(thm)],[f146,f161]) ).
fof(f367,plain,
! [X0] : ~ in(X0,sK5_skl),
inference(resolution,[status(thm)],[f182,f113]) ).
fof(f399,plain,
! [X0,X1,X2] : finite(set_intersection2(set_intersection2(set_intersection2(X0,sK2_skl),X1),X2)),
inference(resolution,[status(thm)],[f309,f76]) ).
fof(f417,plain,
! [X0,X1,X2] : finite(set_intersection2(X0,set_intersection2(X1,set_intersection2(X2,sK2_skl)))),
inference(resolution,[status(thm)],[f348,f73]) ).
fof(f435,plain,
( sQ1_spl
| in(sK12_skl(set_intersection2(sK13_skl,sK14_skl)),set_intersection2(sK13_skl,sK14_skl)) ),
inference(resolution,[status(thm)],[f149,f191]) ).
fof(f448,definition,
! [X0] :
( sQ12_spl
<=> ~ empty(X0) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f449,plain,
! [X0] :
( ~ sQ12_spl
| ~ empty(X0) ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f461,plain,
( ~ sQ12_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f113,f449]) ).
fof(f468,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f461]) ).
fof(f472,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| in(sK5_skl,set_intersection2(sK14_skl,set_intersection2(sK13_skl,sK14_skl))) ),
inference(resolution,[status(thm)],[f352,f355]) ).
fof(f521,plain,
! [X0,X1] :
( in(set_difference(X1,X0),sK13_skl)
| ~ in(X1,sK13_skl)
| ~ in(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f147,f159]) ).
fof(f522,plain,
! [X0,X1] :
( ~ in(X1,sK14_skl)
| in(set_difference(X1,X0),sK14_skl)
| ~ in(X0,sK14_skl) ),
inference(resolution,[status(thm)],[f147,f161]) ).
fof(f590,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ0_spl
| in(sK5_skl,set_intersection2(sK14_skl,sK5_skl)) ),
inference(backward_demodulation,[status(thm)],[f592,f472]) ).
fof(f592,plain,
( ~ sQ0_spl
| set_intersection2(sK13_skl,sK14_skl) = sK5_skl ),
inference(forward_demodulation,[status(thm)],[f230,f201]) ).
fof(f593,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ0_spl
| in(sK5_skl,sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f240,f590]) ).
fof(f594,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f593,f367]) ).
fof(f595,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f594]) ).
fof(f693,definition,
( sQ18_spl
<=> preboolean(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f695,plain,
( sQ18_spl
| ~ preboolean(sK5_skl) ),
inference(component_clause,[status(thm)],[f693]) ).
fof(f709,plain,
( sQ1_spl
| in(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),set_intersection2(sK13_skl,sK14_skl)) ),
inference(resolution,[status(thm)],[f148,f191]) ).
fof(f779,definition,
! [X0] :
( sQ19_spl
<=> ~ element(X0,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f780,plain,
! [X0] :
( ~ sQ19_spl
| ~ element(X0,sK5_skl) ),
inference(component_clause,[status(thm)],[f779]) ).
fof(f911,plain,
! [X0,X1] :
( in(sK0_skl(X1,X0,sK5_skl),X1)
| set_intersection2(sK5_skl,X0) = X1 ),
inference(resolution,[status(thm)],[f67,f367]) ).
fof(f915,plain,
! [X0,X1] :
( in(sK0_skl(X0,X1,sK5_skl),X0)
| X0 = sK5_skl ),
inference(forward_demodulation,[status(thm)],[f261,f911]) ).
fof(f1008,definition,
( sQ29_spl
<=> in(sK5_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f1009,plain,
( ~ sQ29_spl
| in(sK5_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f1008]) ).
fof(f1066,plain,
! [X0,X1,X2,X3] : finite(set_intersection2(set_intersection2(set_intersection2(set_intersection2(X0,sK2_skl),X1),X2),X3)),
inference(resolution,[status(thm)],[f399,f76]) ).
fof(f1203,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ element(X0,powerset(sK5_skl)) ),
inference(resolution,[status(thm)],[f177,f113]) ).
fof(f1208,plain,
! [X0] : ~ in(X0,sK1_skl(powerset(sK5_skl))),
inference(resolution,[status(thm)],[f1203,f70]) ).
fof(f1234,plain,
sK5_skl = sK1_skl(powerset(sK5_skl)),
inference(resolution,[status(thm)],[f1208,f915]) ).
fof(f1261,definition,
( sQ37_spl
<=> in(sK5_skl,sK1_skl(powerset(sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f1262,plain,
( ~ sQ37_spl
| in(sK5_skl,sK1_skl(powerset(sK5_skl))) ),
inference(component_clause,[status(thm)],[f1261]) ).
fof(f1280,definition,
( sQ39_spl
<=> empty(powerset(sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f1281,plain,
( ~ sQ39_spl
| empty(powerset(sK5_skl)) ),
inference(component_clause,[status(thm)],[f1280]) ).
fof(f1292,plain,
( ~ sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1281,f81]) ).
fof(f1293,plain,
~ sQ39_spl,
inference(contradiction_clause,[status(thm)],[f1292]) ).
fof(f1332,definition,
( sQ46_spl
<=> preboolean(powerset(sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1334,plain,
( sQ46_spl
| ~ preboolean(powerset(sK5_skl)) ),
inference(component_clause,[status(thm)],[f1332]) ).
fof(f1352,definition,
! [X0] :
( sQ49_spl
<=> ~ element(X0,sK12_skl(powerset(sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1353,plain,
! [X0] :
( ~ sQ49_spl
| ~ element(X0,sK12_skl(powerset(sK5_skl))) ),
inference(component_clause,[status(thm)],[f1352]) ).
fof(f1420,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1009,f367]) ).
fof(f1421,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f1420]) ).
fof(f1621,plain,
( sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1334,f84]) ).
fof(f1622,plain,
sQ46_spl,
inference(contradiction_clause,[status(thm)],[f1621]) ).
fof(f1627,plain,
( ~ sQ37_spl
| in(sK5_skl,sK5_skl) ),
inference(forward_demodulation,[status(thm)],[f1234,f1262]) ).
fof(f1628,plain,
( ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1627,f367]) ).
fof(f1629,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f1628]) ).
fof(f1631,plain,
( sQ18_spl
| in(sK11_skl(sK5_skl),sK5_skl) ),
inference(resolution,[status(thm)],[f695,f148]) ).
fof(f1634,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1631,f367]) ).
fof(f1635,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f1634]) ).
fof(f1667,plain,
( ~ sQ19_spl
| $false ),
inference(resolution,[status(thm)],[f780,f70]) ).
fof(f1669,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f1667]) ).
fof(f1714,plain,
( sQ1_spl
| ~ in(set_difference(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),set_intersection2(sK13_skl,sK14_skl))
| ~ in(set_union2(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),set_intersection2(sK13_skl,sK14_skl)) ),
inference(resolution,[status(thm)],[f150,f191]) ).
fof(f1724,definition,
( sQ72_spl
<=> in(set_union2(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),set_intersection2(sK13_skl,sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1726,plain,
( sQ72_spl
| ~ in(set_union2(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),set_intersection2(sK13_skl,sK14_skl)) ),
inference(component_clause,[status(thm)],[f1724]) ).
fof(f1727,definition,
( sQ73_spl
<=> in(set_difference(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),set_intersection2(sK13_skl,sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1729,plain,
( sQ73_spl
| ~ in(set_difference(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),set_intersection2(sK13_skl,sK14_skl)) ),
inference(component_clause,[status(thm)],[f1727]) ).
fof(f1730,plain,
( sQ1_spl
| ~ sQ73_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f1714,f1724,f1727,f189]) ).
fof(f1770,definition,
! [X0] :
( sQ78_spl
<=> ~ element(X0,sK9_skl(sK5_skl)) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1771,plain,
! [X0] :
( ~ sQ78_spl
| ~ element(X0,sK9_skl(sK5_skl)) ),
inference(component_clause,[status(thm)],[f1770]) ).
fof(f1957,plain,
( sQ72_spl
| ~ in(set_union2(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),sK13_skl)
| ~ in(set_union2(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),sK14_skl) ),
inference(resolution,[status(thm)],[f1726,f195]) ).
fof(f1963,definition,
( sQ91_spl
<=> in(set_union2(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1965,plain,
( sQ91_spl
| ~ in(set_union2(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),sK14_skl) ),
inference(component_clause,[status(thm)],[f1963]) ).
fof(f1966,definition,
( sQ92_spl
<=> in(set_union2(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1968,plain,
( sQ92_spl
| ~ in(set_union2(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),sK13_skl) ),
inference(component_clause,[status(thm)],[f1966]) ).
fof(f1969,plain,
( sQ72_spl
| ~ sQ92_spl
| ~ sQ91_spl ),
inference(split_clause,[status(thm)],[f1957,f1963,f1966,f1724]) ).
fof(f1991,definition,
! [X0] :
( sQ95_spl
<=> ( ~ element(sK5_skl,powerset(X0))
| ~ finite(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1992,plain,
! [X0] :
( ~ sQ95_spl
| ~ element(sK5_skl,powerset(X0))
| ~ finite(X0) ),
inference(component_clause,[status(thm)],[f1991]) ).
fof(f2017,plain,
( ~ sQ78_spl
| $false ),
inference(resolution,[status(thm)],[f1771,f70]) ).
fof(f2019,plain,
~ sQ78_spl,
inference(contradiction_clause,[status(thm)],[f2017]) ).
fof(f2130,plain,
( ~ sQ49_spl
| $false ),
inference(resolution,[status(thm)],[f1353,f70]) ).
fof(f2133,plain,
~ sQ49_spl,
inference(contradiction_clause,[status(thm)],[f2130]) ).
fof(f2170,plain,
( ~ sQ4_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1066,f272]) ).
fof(f2192,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f2170]) ).
fof(f2214,plain,
( ~ sQ95_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f417,f2217]) ).
fof(f2217,plain,
! [X0] :
( ~ sQ95_spl
| ~ finite(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1992,f250]) ).
fof(f2236,plain,
~ sQ95_spl,
inference(contradiction_clause,[status(thm)],[f2214]) ).
fof(f2242,plain,
( sQ73_spl
| ~ in(set_difference(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),sK13_skl)
| ~ in(set_difference(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),sK14_skl) ),
inference(resolution,[status(thm)],[f1729,f195]) ).
fof(f2245,definition,
( sQ104_spl
<=> in(set_difference(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f2247,plain,
( sQ104_spl
| ~ in(set_difference(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),sK14_skl) ),
inference(component_clause,[status(thm)],[f2245]) ).
fof(f2248,definition,
( sQ105_spl
<=> in(set_difference(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f2250,plain,
( sQ105_spl
| ~ in(set_difference(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK12_skl(set_intersection2(sK13_skl,sK14_skl))),sK13_skl) ),
inference(component_clause,[status(thm)],[f2248]) ).
fof(f2251,plain,
( sQ73_spl
| ~ sQ105_spl
| ~ sQ104_spl ),
inference(split_clause,[status(thm)],[f2242,f2245,f2248,f1727]) ).
fof(f2426,definition,
! [X0] :
( sQ106_spl
<=> ( ~ preboolean(X0)
| empty(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f2427,plain,
! [X0] :
( ~ sQ106_spl
| ~ preboolean(X0)
| empty(X0) ),
inference(component_clause,[status(thm)],[f2426]) ).
fof(f2500,plain,
! [X0] :
( ~ sQ106_spl
| empty(powerset(X0)) ),
inference(resolution,[status(thm)],[f2427,f84]) ).
fof(f2509,plain,
( ~ sQ106_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2500,f81]) ).
fof(f2510,plain,
~ sQ106_spl,
inference(contradiction_clause,[status(thm)],[f2509]) ).
fof(f2734,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| in(X1,powerset(X0))
| empty(powerset(X0)) ),
inference(resolution,[status(thm)],[f165,f170]) ).
fof(f2738,plain,
! [X0,X1] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2734,f81]) ).
fof(f2758,plain,
! [X0] : in(X0,powerset(X0)),
inference(resolution,[status(thm)],[f2738,f141]) ).
fof(f2812,definition,
! [X2] :
( sQ118_spl
<=> ~ in(sK14_skl,X2) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f2813,plain,
! [X0] :
( ~ sQ118_spl
| ~ in(sK14_skl,X0) ),
inference(component_clause,[status(thm)],[f2812]) ).
fof(f2827,plain,
( ~ sQ118_spl
| $false ),
inference(resolution,[status(thm)],[f2813,f2758]) ).
fof(f2831,plain,
~ sQ118_spl,
inference(contradiction_clause,[status(thm)],[f2827]) ).
fof(f3014,definition,
! [X1] :
( sQ123_spl
<=> ~ in(sK13_skl,X1) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f3015,plain,
! [X0] :
( ~ sQ123_spl
| ~ in(sK13_skl,X0) ),
inference(component_clause,[status(thm)],[f3014]) ).
fof(f3020,plain,
( ~ sQ123_spl
| $false ),
inference(resolution,[status(thm)],[f3015,f2758]) ).
fof(f3025,plain,
~ sQ123_spl,
inference(contradiction_clause,[status(thm)],[f3020]) ).
fof(f3166,definition,
( sQ129_spl
<=> cup_closed(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f3168,plain,
( sQ129_spl
| ~ cup_closed(sK3_skl) ),
inference(component_clause,[status(thm)],[f3166]) ).
fof(f3174,plain,
( sQ129_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3168,f104]) ).
fof(f3175,plain,
sQ129_spl,
inference(contradiction_clause,[status(thm)],[f3174]) ).
fof(f4221,definition,
! [X0] :
( sQ171_spl
<=> ~ in(sK11_skl(sK14_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f4222,plain,
! [X0] :
( ~ sQ171_spl
| ~ in(sK11_skl(sK14_skl),X0) ),
inference(component_clause,[status(thm)],[f4221]) ).
fof(f4391,definition,
! [X0] :
( sQ176_spl
<=> ~ in(sK12_skl(sK14_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f4392,plain,
! [X0] :
( ~ sQ176_spl
| ~ in(sK12_skl(sK14_skl),X0) ),
inference(component_clause,[status(thm)],[f4391]) ).
fof(f4418,definition,
! [X0] :
( sQ177_spl
<=> ~ in(sK11_skl(sK13_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f4419,plain,
! [X0] :
( ~ sQ177_spl
| ~ in(sK11_skl(sK13_skl),X0) ),
inference(component_clause,[status(thm)],[f4418]) ).
fof(f4437,definition,
! [X0] :
( sQ178_spl
<=> ~ in(sK12_skl(sK13_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f4438,plain,
! [X0] :
( ~ sQ178_spl
| ~ in(sK12_skl(sK13_skl),X0) ),
inference(component_clause,[status(thm)],[f4437]) ).
fof(f4744,definition,
( sQ183_spl
<=> in(sK11_skl(sK9_skl(sK5_skl)),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f4745,plain,
( ~ sQ183_spl
| in(sK11_skl(sK9_skl(sK5_skl)),sK5_skl) ),
inference(component_clause,[status(thm)],[f4744]) ).
fof(f4750,definition,
( sQ184_spl
<=> in(sK12_skl(sK9_skl(sK5_skl)),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f4751,plain,
( ~ sQ184_spl
| in(sK12_skl(sK9_skl(sK5_skl)),sK5_skl) ),
inference(component_clause,[status(thm)],[f4750]) ).
fof(f4754,plain,
( ~ sQ183_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4745,f367]) ).
fof(f4755,plain,
~ sQ183_spl,
inference(contradiction_clause,[status(thm)],[f4754]) ).
fof(f4756,plain,
( ~ sQ184_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4751,f367]) ).
fof(f4757,plain,
~ sQ184_spl,
inference(contradiction_clause,[status(thm)],[f4756]) ).
fof(f5570,definition,
( sQ206_spl
<=> in(sK11_skl(sK10_skl(sK5_skl)),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f5571,plain,
( ~ sQ206_spl
| in(sK11_skl(sK10_skl(sK5_skl)),sK5_skl) ),
inference(component_clause,[status(thm)],[f5570]) ).
fof(f5578,definition,
( sQ207_spl
<=> in(sK12_skl(sK10_skl(sK5_skl)),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f5579,plain,
( ~ sQ207_spl
| in(sK12_skl(sK10_skl(sK5_skl)),sK5_skl) ),
inference(component_clause,[status(thm)],[f5578]) ).
fof(f5582,plain,
( ~ sQ206_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5571,f367]) ).
fof(f5583,plain,
~ sQ206_spl,
inference(contradiction_clause,[status(thm)],[f5582]) ).
fof(f5584,plain,
( ~ sQ207_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5579,f367]) ).
fof(f5585,plain,
~ sQ207_spl,
inference(contradiction_clause,[status(thm)],[f5584]) ).
fof(f5796,definition,
! [X0] :
( sQ215_spl
<=> ~ in(set_intersection2(sK13_skl,sK14_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f5797,plain,
! [X0] :
( ~ sQ215_spl
| ~ in(set_intersection2(sK13_skl,sK14_skl),X0) ),
inference(component_clause,[status(thm)],[f5796]) ).
fof(f5813,plain,
( ~ sQ171_spl
| $false ),
inference(resolution,[status(thm)],[f4222,f2758]) ).
fof(f5819,plain,
~ sQ171_spl,
inference(contradiction_clause,[status(thm)],[f5813]) ).
fof(f5858,plain,
( ~ sQ215_spl
| $false ),
inference(resolution,[status(thm)],[f5797,f2758]) ).
fof(f5862,plain,
~ sQ215_spl,
inference(contradiction_clause,[status(thm)],[f5858]) ).
fof(f6106,definition,
! [X1] :
( sQ225_spl
<=> in(sK0_skl(sK5_skl,X1,sK5_skl),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f6107,plain,
! [X0] :
( ~ sQ225_spl
| in(sK0_skl(sK5_skl,X0,sK5_skl),sK5_skl) ),
inference(component_clause,[status(thm)],[f6106]) ).
fof(f6111,plain,
( ~ sQ225_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6107,f367]) ).
fof(f6112,plain,
~ sQ225_spl,
inference(contradiction_clause,[status(thm)],[f6111]) ).
fof(f6197,definition,
! [X0] :
( sQ226_spl
<=> ~ in(powerset(sK14_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f6198,plain,
! [X0] :
( ~ sQ226_spl
| ~ in(powerset(sK14_skl),X0) ),
inference(component_clause,[status(thm)],[f6197]) ).
fof(f6224,plain,
( ~ sQ226_spl
| $false ),
inference(resolution,[status(thm)],[f6198,f2758]) ).
fof(f6228,plain,
~ sQ226_spl,
inference(contradiction_clause,[status(thm)],[f6224]) ).
fof(f6305,definition,
! [X0] :
( sQ234_spl
<=> ~ in(powerset(sK13_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f6306,plain,
! [X0] :
( ~ sQ234_spl
| ~ in(powerset(sK13_skl),X0) ),
inference(component_clause,[status(thm)],[f6305]) ).
fof(f6309,plain,
( ~ sQ234_spl
| $false ),
inference(resolution,[status(thm)],[f6306,f2758]) ).
fof(f6314,plain,
~ sQ234_spl,
inference(contradiction_clause,[status(thm)],[f6309]) ).
fof(f6355,plain,
( sQ105_spl
| ~ in(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK13_skl)
| ~ in(sK12_skl(set_intersection2(sK13_skl,sK14_skl)),sK13_skl) ),
inference(resolution,[status(thm)],[f2250,f521]) ).
fof(f6358,definition,
( sQ235_spl
<=> in(sK12_skl(set_intersection2(sK13_skl,sK14_skl)),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f6360,plain,
( sQ235_spl
| ~ in(sK12_skl(set_intersection2(sK13_skl,sK14_skl)),sK13_skl) ),
inference(component_clause,[status(thm)],[f6358]) ).
fof(f6361,definition,
( sQ236_spl
<=> in(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f6363,plain,
( sQ236_spl
| ~ in(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK13_skl) ),
inference(component_clause,[status(thm)],[f6361]) ).
fof(f6364,plain,
( sQ105_spl
| ~ sQ236_spl
| ~ sQ235_spl ),
inference(split_clause,[status(thm)],[f6355,f6358,f6361,f2248]) ).
fof(f6394,plain,
! [X0] :
( sQ236_spl
| ~ in(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),set_intersection2(sK13_skl,X0)) ),
inference(resolution,[status(thm)],[f6363,f193]) ).
fof(f6395,plain,
( sQ1_spl
| sQ236_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f709,f6394]) ).
fof(f6396,plain,
( sQ1_spl
| sQ236_spl ),
inference(contradiction_clause,[status(thm)],[f6395]) ).
fof(f6398,plain,
! [X0] :
( sQ235_spl
| ~ in(sK12_skl(set_intersection2(sK13_skl,sK14_skl)),set_intersection2(sK13_skl,X0)) ),
inference(resolution,[status(thm)],[f6360,f193]) ).
fof(f6399,plain,
( sQ1_spl
| sQ235_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f435,f6398]) ).
fof(f6400,plain,
( sQ1_spl
| sQ235_spl ),
inference(contradiction_clause,[status(thm)],[f6399]) ).
fof(f6480,definition,
! [X0] :
( sQ238_spl
<=> ~ in(powerset(sK2_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f6481,plain,
! [X0] :
( ~ sQ238_spl
| ~ in(powerset(sK2_skl),X0) ),
inference(component_clause,[status(thm)],[f6480]) ).
fof(f6487,plain,
( ~ sQ238_spl
| $false ),
inference(resolution,[status(thm)],[f6481,f2758]) ).
fof(f6492,plain,
~ sQ238_spl,
inference(contradiction_clause,[status(thm)],[f6487]) ).
fof(f6557,definition,
! [X2] :
( sQ242_spl
<=> ~ in(sK3_skl,X2) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f6558,plain,
! [X0] :
( ~ sQ242_spl
| ~ in(sK3_skl,X0) ),
inference(component_clause,[status(thm)],[f6557]) ).
fof(f6569,plain,
( ~ sQ242_spl
| $false ),
inference(resolution,[status(thm)],[f6558,f2758]) ).
fof(f6573,plain,
~ sQ242_spl,
inference(contradiction_clause,[status(thm)],[f6569]) ).
fof(f6630,definition,
! [X0] :
( sQ245_spl
<=> ~ in(powerset(sK3_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f6631,plain,
! [X0] :
( ~ sQ245_spl
| ~ in(powerset(sK3_skl),X0) ),
inference(component_clause,[status(thm)],[f6630]) ).
fof(f6708,plain,
( ~ sQ245_spl
| $false ),
inference(resolution,[status(thm)],[f6631,f2758]) ).
fof(f6712,plain,
~ sQ245_spl,
inference(contradiction_clause,[status(thm)],[f6708]) ).
fof(f6716,plain,
( ~ sQ176_spl
| $false ),
inference(resolution,[status(thm)],[f4392,f2758]) ).
fof(f6720,plain,
~ sQ176_spl,
inference(contradiction_clause,[status(thm)],[f6716]) ).
fof(f6777,plain,
( sQ92_spl
| ~ in(sK12_skl(set_intersection2(sK13_skl,sK14_skl)),sK13_skl)
| ~ in(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK13_skl) ),
inference(resolution,[status(thm)],[f1968,f364]) ).
fof(f6782,plain,
( sQ92_spl
| ~ sQ235_spl
| ~ sQ236_spl ),
inference(split_clause,[status(thm)],[f6777,f6361,f6358,f1966]) ).
fof(f6810,plain,
( ~ sQ177_spl
| $false ),
inference(resolution,[status(thm)],[f4419,f2758]) ).
fof(f6816,plain,
~ sQ177_spl,
inference(contradiction_clause,[status(thm)],[f6810]) ).
fof(f6886,plain,
( ~ sQ178_spl
| $false ),
inference(resolution,[status(thm)],[f4438,f2758]) ).
fof(f6891,plain,
~ sQ178_spl,
inference(contradiction_clause,[status(thm)],[f6886]) ).
fof(f6923,definition,
! [X0] :
( sQ249_spl
<=> ~ in(powerset(sK8_skl),X0) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f6924,plain,
! [X0] :
( ~ sQ249_spl
| ~ in(powerset(sK8_skl),X0) ),
inference(component_clause,[status(thm)],[f6923]) ).
fof(f6930,plain,
( ~ sQ249_spl
| $false ),
inference(resolution,[status(thm)],[f6924,f2758]) ).
fof(f6934,plain,
~ sQ249_spl,
inference(contradiction_clause,[status(thm)],[f6930]) ).
fof(f6935,plain,
( sQ104_spl
| ~ in(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK14_skl)
| ~ in(sK12_skl(set_intersection2(sK13_skl,sK14_skl)),sK14_skl) ),
inference(resolution,[status(thm)],[f2247,f522]) ).
fof(f6938,definition,
( sQ251_spl
<=> in(sK12_skl(set_intersection2(sK13_skl,sK14_skl)),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f6940,plain,
( sQ251_spl
| ~ in(sK12_skl(set_intersection2(sK13_skl,sK14_skl)),sK14_skl) ),
inference(component_clause,[status(thm)],[f6938]) ).
fof(f6941,definition,
( sQ252_spl
<=> in(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f6943,plain,
( sQ252_spl
| ~ in(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK14_skl) ),
inference(component_clause,[status(thm)],[f6941]) ).
fof(f6944,plain,
( sQ104_spl
| ~ sQ252_spl
| ~ sQ251_spl ),
inference(split_clause,[status(thm)],[f6935,f6938,f6941,f2245]) ).
fof(f6947,plain,
! [X0] :
( sQ251_spl
| ~ in(sK12_skl(set_intersection2(sK13_skl,sK14_skl)),set_intersection2(X0,sK14_skl)) ),
inference(resolution,[status(thm)],[f6940,f194]) ).
fof(f6949,plain,
( sQ1_spl
| sQ251_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f435,f6947]) ).
fof(f6950,plain,
( sQ1_spl
| sQ251_spl ),
inference(contradiction_clause,[status(thm)],[f6949]) ).
fof(f6951,plain,
! [X0] :
( sQ252_spl
| ~ in(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),set_intersection2(X0,sK14_skl)) ),
inference(resolution,[status(thm)],[f6943,f194]) ).
fof(f6953,plain,
( sQ1_spl
| sQ252_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f709,f6951]) ).
fof(f6954,plain,
( sQ1_spl
| sQ252_spl ),
inference(contradiction_clause,[status(thm)],[f6953]) ).
fof(f7472,definition,
! [X0] :
( sQ276_spl
<=> ~ in(sK5_skl,set_intersection2(powerset(sK5_skl),X0)) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f7473,plain,
! [X0] :
( ~ sQ276_spl
| ~ in(sK5_skl,set_intersection2(powerset(sK5_skl),X0)) ),
inference(component_clause,[status(thm)],[f7472]) ).
fof(f7525,plain,
( ~ sQ276_spl
| ~ in(sK5_skl,powerset(sK5_skl)) ),
inference(paramodulation,[status(thm)],[f98,f7473]) ).
fof(f7526,plain,
( ~ sQ276_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7525,f325]) ).
fof(f7527,plain,
~ sQ276_spl,
inference(contradiction_clause,[status(thm)],[f7526]) ).
fof(f7901,plain,
( sQ91_spl
| ~ in(sK12_skl(set_intersection2(sK13_skl,sK14_skl)),sK14_skl)
| ~ in(sK11_skl(set_intersection2(sK13_skl,sK14_skl)),sK14_skl) ),
inference(resolution,[status(thm)],[f1965,f365]) ).
fof(f7906,plain,
( sQ91_spl
| ~ sQ251_spl
| ~ sQ252_spl ),
inference(split_clause,[status(thm)],[f7901,f6941,f6938,f1963]) ).
fof(f7907,plain,
$false,
inference(sat_refutation,[status(thm)],[f192,f324,f332,f341,f345,f468,f595,f1293,f1421,f1622,f1629,f1635,f1669,f1730,f1969,f2019,f2133,f2192,f2236,f2251,f2510,f2831,f3025,f3175,f4755,f4757,f5583,f5585,f5819,f5862,f6112,f6228,f6314,f6364,f6396,f6400,f6492,f6573,f6712,f6720,f6782,f6816,f6891,f6934,f6944,f6950,f6954,f7527,f7906]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU109+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.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 05:50:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 121.76/15.87 % Refutation found
% 121.76/15.87 % SZS status Theorem for theBenchmark: Theorem is valid
% 121.76/15.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.90/17.16 % Elapsed time: 16.582400 seconds
% 13.90/17.16 % CPU time: 120.521074 seconds
% 13.90/17.16 % Total memory used: 421.268 MB
% 13.90/17.16 % Net memory used: 375.669 MB
%------------------------------------------------------------------------------