TSTP Solution File: SEU313+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU313+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:57:51 EDT 2023
% Result : Theorem 50.62s 7.60s
% Output : Refutation 50.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 28
% Syntax : Number of formulae : 153 ( 9 unt; 0 def)
% Number of atoms : 783 ( 57 equ)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 1003 ( 373 ~; 398 |; 172 &)
% ( 20 <=>; 38 =>; 0 <=; 2 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 7 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 284 (; 232 !; 52 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f161665,plain,
$false,
inference(avatar_sat_refutation,[],[f291,f296,f301,f306,f310,f115247,f161664]) ).
fof(f161664,plain,
( ~ spl15_1
| spl15_2
| ~ spl15_3
| ~ spl15_4
| ~ spl15_5 ),
inference(avatar_contradiction_clause,[],[f161663]) ).
fof(f161663,plain,
( $false
| ~ spl15_1
| spl15_2
| ~ spl15_3
| ~ spl15_4
| ~ spl15_5 ),
inference(subsumption_resolution,[],[f161662,f295]) ).
fof(f295,plain,
( subset(sK1,sK3)
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f293,plain,
( spl15_3
<=> subset(sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).
fof(f161662,plain,
( ~ subset(sK1,sK3)
| ~ spl15_1
| spl15_2
| ~ spl15_4
| ~ spl15_5 ),
inference(forward_demodulation,[],[f161658,f116456]) ).
fof(f116456,plain,
( sK3 = subset_complement(the_carrier(sK0),set_difference(the_carrier(sK0),sK3))
| ~ spl15_5 ),
inference(backward_demodulation,[],[f115320,f116454]) ).
fof(f116454,plain,
( set_difference(the_carrier(sK0),sK3) = subset_complement(the_carrier(sK0),sK3)
| ~ spl15_5 ),
inference(forward_demodulation,[],[f116453,f115890]) ).
fof(f115890,plain,
( set_difference(the_carrier(sK0),sK3) = subset_difference(the_carrier(sK0),the_carrier(sK0),sK3)
| ~ spl15_5 ),
inference(unit_resulting_resolution,[],[f320,f305,f257]) ).
fof(f257,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f123]) ).
fof(f123,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',redefinition_k6_subset_1) ).
fof(f305,plain,
( element(sK3,powerset(the_carrier(sK0)))
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f303,plain,
( spl15_5
<=> element(sK3,powerset(the_carrier(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).
fof(f320,plain,
element(the_carrier(sK0),powerset(the_carrier(sK0))),
inference(forward_demodulation,[],[f318,f319]) ).
fof(f319,plain,
the_carrier(sK0) = cast_as_carrier_subset(sK0),
inference(unit_resulting_resolution,[],[f311,f181]) ).
fof(f181,plain,
! [X0] :
( the_carrier(X0) = cast_as_carrier_subset(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0] :
( the_carrier(X0) = cast_as_carrier_subset(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( one_sorted_str(X0)
=> the_carrier(X0) = cast_as_carrier_subset(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',d3_pre_topc) ).
fof(f311,plain,
one_sorted_str(sK0),
inference(unit_resulting_resolution,[],[f161,f180]) ).
fof(f180,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',dt_l1_pre_topc) ).
fof(f161,plain,
top_str(sK0),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
( ( ( ~ in(sK2,sK3)
& subset(sK1,sK3)
& closed_subset(sK3,sK0)
& element(sK3,powerset(the_carrier(sK0))) )
| ~ in(sK2,topstr_closure(sK0,sK1)) )
& ( ! [X4] :
( in(sK2,X4)
| ~ subset(sK1,X4)
| ~ closed_subset(X4,sK0)
| ~ element(X4,powerset(the_carrier(sK0))) )
| in(sK2,topstr_closure(sK0,sK1)) )
& in(sK2,the_carrier(sK0))
& element(sK1,powerset(the_carrier(sK0)))
& top_str(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f128,f132,f131,f130,f129]) ).
fof(f129,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& subset(X1,X3)
& closed_subset(X3,X0)
& element(X3,powerset(the_carrier(X0))) )
| ~ in(X2,topstr_closure(X0,X1)) )
& ( ! [X4] :
( in(X2,X4)
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0))) )
| in(X2,topstr_closure(X0,X1)) )
& in(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) )
=> ( ? [X1] :
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& subset(X1,X3)
& closed_subset(X3,sK0)
& element(X3,powerset(the_carrier(sK0))) )
| ~ in(X2,topstr_closure(sK0,X1)) )
& ( ! [X4] :
( in(X2,X4)
| ~ subset(X1,X4)
| ~ closed_subset(X4,sK0)
| ~ element(X4,powerset(the_carrier(sK0))) )
| in(X2,topstr_closure(sK0,X1)) )
& in(X2,the_carrier(sK0)) )
& element(X1,powerset(the_carrier(sK0))) )
& top_str(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f130,plain,
( ? [X1] :
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& subset(X1,X3)
& closed_subset(X3,sK0)
& element(X3,powerset(the_carrier(sK0))) )
| ~ in(X2,topstr_closure(sK0,X1)) )
& ( ! [X4] :
( in(X2,X4)
| ~ subset(X1,X4)
| ~ closed_subset(X4,sK0)
| ~ element(X4,powerset(the_carrier(sK0))) )
| in(X2,topstr_closure(sK0,X1)) )
& in(X2,the_carrier(sK0)) )
& element(X1,powerset(the_carrier(sK0))) )
=> ( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& subset(sK1,X3)
& closed_subset(X3,sK0)
& element(X3,powerset(the_carrier(sK0))) )
| ~ in(X2,topstr_closure(sK0,sK1)) )
& ( ! [X4] :
( in(X2,X4)
| ~ subset(sK1,X4)
| ~ closed_subset(X4,sK0)
| ~ element(X4,powerset(the_carrier(sK0))) )
| in(X2,topstr_closure(sK0,sK1)) )
& in(X2,the_carrier(sK0)) )
& element(sK1,powerset(the_carrier(sK0))) ) ),
introduced(choice_axiom,[]) ).
fof(f131,plain,
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& subset(sK1,X3)
& closed_subset(X3,sK0)
& element(X3,powerset(the_carrier(sK0))) )
| ~ in(X2,topstr_closure(sK0,sK1)) )
& ( ! [X4] :
( in(X2,X4)
| ~ subset(sK1,X4)
| ~ closed_subset(X4,sK0)
| ~ element(X4,powerset(the_carrier(sK0))) )
| in(X2,topstr_closure(sK0,sK1)) )
& in(X2,the_carrier(sK0)) )
=> ( ( ? [X3] :
( ~ in(sK2,X3)
& subset(sK1,X3)
& closed_subset(X3,sK0)
& element(X3,powerset(the_carrier(sK0))) )
| ~ in(sK2,topstr_closure(sK0,sK1)) )
& ( ! [X4] :
( in(sK2,X4)
| ~ subset(sK1,X4)
| ~ closed_subset(X4,sK0)
| ~ element(X4,powerset(the_carrier(sK0))) )
| in(sK2,topstr_closure(sK0,sK1)) )
& in(sK2,the_carrier(sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f132,plain,
( ? [X3] :
( ~ in(sK2,X3)
& subset(sK1,X3)
& closed_subset(X3,sK0)
& element(X3,powerset(the_carrier(sK0))) )
=> ( ~ in(sK2,sK3)
& subset(sK1,sK3)
& closed_subset(sK3,sK0)
& element(sK3,powerset(the_carrier(sK0))) ) ),
introduced(choice_axiom,[]) ).
fof(f128,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& subset(X1,X3)
& closed_subset(X3,X0)
& element(X3,powerset(the_carrier(X0))) )
| ~ in(X2,topstr_closure(X0,X1)) )
& ( ! [X4] :
( in(X2,X4)
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0))) )
| in(X2,topstr_closure(X0,X1)) )
& in(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(rectify,[],[f127]) ).
fof(f127,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& subset(X1,X3)
& closed_subset(X3,X0)
& element(X3,powerset(the_carrier(X0))) )
| ~ in(X2,topstr_closure(X0,X1)) )
& ( ! [X3] :
( in(X2,X3)
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| ~ element(X3,powerset(the_carrier(X0))) )
| in(X2,topstr_closure(X0,X1)) )
& in(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& subset(X1,X3)
& closed_subset(X3,X0)
& element(X3,powerset(the_carrier(X0))) )
| ~ in(X2,topstr_closure(X0,X1)) )
& ( ! [X3] :
( in(X2,X3)
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| ~ element(X3,powerset(the_carrier(X0))) )
| in(X2,topstr_closure(X0,X1)) )
& in(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,topstr_closure(X0,X1))
<~> ! [X3] :
( in(X2,X3)
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| ~ element(X3,powerset(the_carrier(X0))) ) )
& in(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( in(X2,topstr_closure(X0,X1))
<~> ! [X3] :
( in(X2,X3)
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| ~ element(X3,powerset(the_carrier(X0))) ) )
& in(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( in(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( subset(X1,X3)
& closed_subset(X3,X0) )
=> in(X2,X3) ) ) ) ) ) ),
inference(negated_conjecture,[],[f56]) ).
fof(f56,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( in(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( subset(X1,X3)
& closed_subset(X3,X0) )
=> in(X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',t45_pre_topc) ).
fof(f318,plain,
element(cast_as_carrier_subset(sK0),powerset(the_carrier(sK0))),
inference(unit_resulting_resolution,[],[f311,f182]) ).
fof(f182,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( one_sorted_str(X0)
=> element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',dt_k2_pre_topc) ).
fof(f116453,plain,
( subset_complement(the_carrier(sK0),sK3) = subset_difference(the_carrier(sK0),the_carrier(sK0),sK3)
| ~ spl15_5 ),
inference(forward_demodulation,[],[f115315,f319]) ).
fof(f115315,plain,
( subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK3) = subset_complement(the_carrier(sK0),sK3)
| ~ spl15_5 ),
inference(unit_resulting_resolution,[],[f311,f305,f183]) ).
fof(f183,plain,
! [X0,X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',t17_pre_topc) ).
fof(f115320,plain,
( sK3 = subset_complement(the_carrier(sK0),subset_complement(the_carrier(sK0),sK3))
| ~ spl15_5 ),
inference(unit_resulting_resolution,[],[f305,f247]) ).
fof(f247,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',involutiveness_k3_subset_1) ).
fof(f161658,plain,
( ~ subset(sK1,subset_complement(the_carrier(sK0),set_difference(the_carrier(sK0),sK3)))
| ~ spl15_1
| spl15_2
| ~ spl15_4
| ~ spl15_5 ),
inference(unit_resulting_resolution,[],[f162,f116266,f159425,f249]) ).
fof(f249,plain,
! [X2,X0,X1] :
( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0,X1] :
( ! [X2] :
( ( ( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2)) )
& ( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2) ) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(nnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( ! [X2] :
( ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,powerset(X0))
=> ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',t43_subset_1) ).
fof(f159425,plain,
( ~ disjoint(sK1,set_difference(the_carrier(sK0),sK3))
| ~ spl15_1
| spl15_2
| ~ spl15_4
| ~ spl15_5 ),
inference(unit_resulting_resolution,[],[f161,f163,f162,f285,f115249,f338,f116450,f116266,f277]) ).
fof(f277,plain,
! [X0,X1,X8,X6] :
( ~ disjoint(X1,X8)
| ~ in(X6,X8)
| ~ open_subset(X8,X0)
| ~ element(X8,powerset(the_carrier(X0)))
| ~ in(X6,topstr_closure(X0,X1))
| ~ in(X6,the_carrier(X0))
| ~ element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(equality_resolution,[],[f187]) ).
fof(f187,plain,
! [X2,X0,X1,X8,X6] :
( ~ disjoint(X1,X8)
| ~ in(X6,X8)
| ~ open_subset(X8,X0)
| ~ element(X8,powerset(the_carrier(X0)))
| ~ in(X6,X2)
| ~ in(X6,the_carrier(X0))
| topstr_closure(X0,X1) != X2
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( topstr_closure(X0,X1) = X2
| ( ( ( disjoint(X1,sK6(X0,X1,X2))
& in(sK5(X0,X1,X2),sK6(X0,X1,X2))
& open_subset(sK6(X0,X1,X2),X0)
& element(sK6(X0,X1,X2),powerset(the_carrier(X0))) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( ! [X5] :
( ~ disjoint(X1,X5)
| ~ in(sK5(X0,X1,X2),X5)
| ~ open_subset(X5,X0)
| ~ element(X5,powerset(the_carrier(X0))) )
| in(sK5(X0,X1,X2),X2) )
& in(sK5(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X6] :
( ( ( in(X6,X2)
| ( disjoint(X1,sK7(X0,X1,X6))
& in(X6,sK7(X0,X1,X6))
& open_subset(sK7(X0,X1,X6),X0)
& element(sK7(X0,X1,X6),powerset(the_carrier(X0))) ) )
& ( ! [X8] :
( ~ disjoint(X1,X8)
| ~ in(X6,X8)
| ~ open_subset(X8,X0)
| ~ element(X8,powerset(the_carrier(X0))) )
| ~ in(X6,X2) ) )
| ~ in(X6,the_carrier(X0)) )
| topstr_closure(X0,X1) != X2 ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f139,f142,f141,f140]) ).
fof(f140,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ? [X4] :
( disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0)
& element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ! [X5] :
( ~ disjoint(X1,X5)
| ~ in(X3,X5)
| ~ open_subset(X5,X0)
| ~ element(X5,powerset(the_carrier(X0))) )
| in(X3,X2) )
& in(X3,the_carrier(X0)) )
=> ( ( ? [X4] :
( disjoint(X1,X4)
& in(sK5(X0,X1,X2),X4)
& open_subset(X4,X0)
& element(X4,powerset(the_carrier(X0))) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( ! [X5] :
( ~ disjoint(X1,X5)
| ~ in(sK5(X0,X1,X2),X5)
| ~ open_subset(X5,X0)
| ~ element(X5,powerset(the_carrier(X0))) )
| in(sK5(X0,X1,X2),X2) )
& in(sK5(X0,X1,X2),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f141,plain,
! [X0,X1,X2] :
( ? [X4] :
( disjoint(X1,X4)
& in(sK5(X0,X1,X2),X4)
& open_subset(X4,X0)
& element(X4,powerset(the_carrier(X0))) )
=> ( disjoint(X1,sK6(X0,X1,X2))
& in(sK5(X0,X1,X2),sK6(X0,X1,X2))
& open_subset(sK6(X0,X1,X2),X0)
& element(sK6(X0,X1,X2),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f142,plain,
! [X0,X1,X6] :
( ? [X7] :
( disjoint(X1,X7)
& in(X6,X7)
& open_subset(X7,X0)
& element(X7,powerset(the_carrier(X0))) )
=> ( disjoint(X1,sK7(X0,X1,X6))
& in(X6,sK7(X0,X1,X6))
& open_subset(sK7(X0,X1,X6),X0)
& element(sK7(X0,X1,X6),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( topstr_closure(X0,X1) = X2
| ? [X3] :
( ( ? [X4] :
( disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0)
& element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ! [X5] :
( ~ disjoint(X1,X5)
| ~ in(X3,X5)
| ~ open_subset(X5,X0)
| ~ element(X5,powerset(the_carrier(X0))) )
| in(X3,X2) )
& in(X3,the_carrier(X0)) ) )
& ( ! [X6] :
( ( ( in(X6,X2)
| ? [X7] :
( disjoint(X1,X7)
& in(X6,X7)
& open_subset(X7,X0)
& element(X7,powerset(the_carrier(X0))) ) )
& ( ! [X8] :
( ~ disjoint(X1,X8)
| ~ in(X6,X8)
| ~ open_subset(X8,X0)
| ~ element(X8,powerset(the_carrier(X0))) )
| ~ in(X6,X2) ) )
| ~ in(X6,the_carrier(X0)) )
| topstr_closure(X0,X1) != X2 ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(rectify,[],[f138]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( topstr_closure(X0,X1) = X2
| ? [X3] :
( ( ? [X4] :
( disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0)
& element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ! [X4] :
( ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0))) )
| in(X3,X2) )
& in(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ? [X4] :
( disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0)
& element(X4,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ in(X3,the_carrier(X0)) )
| topstr_closure(X0,X1) != X2 ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(flattening,[],[f137]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( topstr_closure(X0,X1) = X2
| ? [X3] :
( ( ? [X4] :
( disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0)
& element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ! [X4] :
( ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0))) )
| in(X3,X2) )
& in(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ? [X4] :
( disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0)
& element(X4,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ in(X3,the_carrier(X0)) )
| topstr_closure(X0,X1) != X2 ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( topstr_closure(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X2)
<=> ! [X4] :
( ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0))) ) )
| ~ in(X3,the_carrier(X0)) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( topstr_closure(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X2)
<=> ! [X4] :
( ~ disjoint(X1,X4)
| ~ in(X3,X4)
| ~ open_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0))) ) )
| ~ in(X3,the_carrier(X0)) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( topstr_closure(X0,X1) = X2
<=> ! [X3] :
( in(X3,the_carrier(X0))
=> ( in(X3,X2)
<=> ! [X4] :
( element(X4,powerset(the_carrier(X0)))
=> ~ ( disjoint(X1,X4)
& in(X3,X4)
& open_subset(X4,X0) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',d13_pre_topc) ).
fof(f116450,plain,
( open_subset(set_difference(the_carrier(sK0),sK3),sK0)
| ~ spl15_4
| ~ spl15_5 ),
inference(forward_demodulation,[],[f116449,f115890]) ).
fof(f116449,plain,
( open_subset(subset_difference(the_carrier(sK0),the_carrier(sK0),sK3),sK0)
| ~ spl15_4
| ~ spl15_5 ),
inference(forward_demodulation,[],[f115317,f319]) ).
fof(f115317,plain,
( open_subset(subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK3),sK0)
| ~ spl15_4
| ~ spl15_5 ),
inference(unit_resulting_resolution,[],[f161,f300,f305,f185]) ).
fof(f185,plain,
! [X0,X1] :
( open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subset(X1,X0)
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) )
& ( open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ closed_subset(X1,X0) ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
<=> open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',d6_pre_topc) ).
fof(f300,plain,
( closed_subset(sK3,sK0)
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f298,plain,
( spl15_4
<=> closed_subset(sK3,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).
fof(f338,plain,
element(topstr_closure(sK0,sK1),powerset(the_carrier(sK0))),
inference(unit_resulting_resolution,[],[f161,f162,f250]) ).
fof(f250,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(flattening,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0) )
=> element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',dt_k6_pre_topc) ).
fof(f115249,plain,
( in(sK2,set_difference(the_carrier(sK0),sK3))
| spl15_2 ),
inference(unit_resulting_resolution,[],[f163,f290,f278]) ).
fof(f278,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| in(X4,X1)
| ~ in(X4,X0) ),
inference(equality_resolution,[],[f260]) ).
fof(f260,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ( ( in(sK10(X0,X1,X2),X1)
| ~ in(sK10(X0,X1,X2),X0)
| ~ in(sK10(X0,X1,X2),X2) )
& ( ( ~ in(sK10(X0,X1,X2),X1)
& in(sK10(X0,X1,X2),X0) )
| in(sK10(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f152,f153]) ).
fof(f153,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) )
=> ( ( in(sK10(X0,X1,X2),X1)
| ~ in(sK10(X0,X1,X2),X0)
| ~ in(sK10(X0,X1,X2),X2) )
& ( ( ~ in(sK10(X0,X1,X2),X1)
& in(sK10(X0,X1,X2),X0) )
| in(sK10(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f152,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X1)
| ~ in(X4,X0) )
& ( ( ~ in(X4,X1)
& in(X4,X0) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f151]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f150]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',d4_xboole_0) ).
fof(f290,plain,
( ~ in(sK2,sK3)
| spl15_2 ),
inference(avatar_component_clause,[],[f288]) ).
fof(f288,plain,
( spl15_2
<=> in(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f285,plain,
( in(sK2,topstr_closure(sK0,sK1))
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f284,plain,
( spl15_1
<=> in(sK2,topstr_closure(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f163,plain,
in(sK2,the_carrier(sK0)),
inference(cnf_transformation,[],[f133]) ).
fof(f116266,plain,
( element(set_difference(the_carrier(sK0),sK3),powerset(the_carrier(sK0)))
| ~ spl15_5 ),
inference(forward_demodulation,[],[f115514,f115890]) ).
fof(f115514,plain,
( element(subset_difference(the_carrier(sK0),the_carrier(sK0),sK3),powerset(the_carrier(sK0)))
| ~ spl15_5 ),
inference(unit_resulting_resolution,[],[f320,f305,f256]) ).
fof(f256,plain,
! [X2,X0,X1] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> element(subset_difference(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',dt_k6_subset_1) ).
fof(f162,plain,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f133]) ).
fof(f115247,plain,
( spl15_1
| ~ spl15_6 ),
inference(avatar_contradiction_clause,[],[f115246]) ).
fof(f115246,plain,
( $false
| spl15_1
| ~ spl15_6 ),
inference(subsumption_resolution,[],[f115245,f411]) ).
fof(f411,plain,
( open_subset(sK7(sK0,sK1,sK2),sK0)
| spl15_1 ),
inference(unit_resulting_resolution,[],[f161,f163,f286,f162,f338,f275]) ).
fof(f275,plain,
! [X0,X1,X6] :
( in(X6,topstr_closure(X0,X1))
| open_subset(sK7(X0,X1,X6),X0)
| ~ in(X6,the_carrier(X0))
| ~ element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(equality_resolution,[],[f189]) ).
fof(f189,plain,
! [X2,X0,X1,X6] :
( in(X6,X2)
| open_subset(sK7(X0,X1,X6),X0)
| ~ in(X6,the_carrier(X0))
| topstr_closure(X0,X1) != X2
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f286,plain,
( ~ in(sK2,topstr_closure(sK0,sK1))
| spl15_1 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f115245,plain,
( ~ open_subset(sK7(sK0,sK1,sK2),sK0)
| spl15_1
| ~ spl15_6 ),
inference(forward_demodulation,[],[f115244,f1731]) ).
fof(f1731,plain,
( sK7(sK0,sK1,sK2) = subset_difference(the_carrier(sK0),the_carrier(sK0),set_difference(the_carrier(sK0),sK7(sK0,sK1,sK2)))
| spl15_1 ),
inference(forward_demodulation,[],[f1730,f1683]) ).
fof(f1683,plain,
( subset_difference(the_carrier(sK0),the_carrier(sK0),sK7(sK0,sK1,sK2)) = set_difference(the_carrier(sK0),sK7(sK0,sK1,sK2))
| spl15_1 ),
inference(unit_resulting_resolution,[],[f320,f410,f257]) ).
fof(f410,plain,
( element(sK7(sK0,sK1,sK2),powerset(the_carrier(sK0)))
| spl15_1 ),
inference(unit_resulting_resolution,[],[f161,f163,f286,f162,f338,f276]) ).
fof(f276,plain,
! [X0,X1,X6] :
( in(X6,topstr_closure(X0,X1))
| element(sK7(X0,X1,X6),powerset(the_carrier(X0)))
| ~ in(X6,the_carrier(X0))
| ~ element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(equality_resolution,[],[f188]) ).
fof(f188,plain,
! [X2,X0,X1,X6] :
( in(X6,X2)
| element(sK7(X0,X1,X6),powerset(the_carrier(X0)))
| ~ in(X6,the_carrier(X0))
| topstr_closure(X0,X1) != X2
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f1730,plain,
( sK7(sK0,sK1,sK2) = subset_difference(the_carrier(sK0),the_carrier(sK0),subset_difference(the_carrier(sK0),the_carrier(sK0),sK7(sK0,sK1,sK2)))
| spl15_1 ),
inference(forward_demodulation,[],[f1630,f319]) ).
fof(f1630,plain,
( sK7(sK0,sK1,sK2) = subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK7(sK0,sK1,sK2)))
| spl15_1 ),
inference(unit_resulting_resolution,[],[f311,f410,f184]) ).
fof(f184,plain,
! [X0,X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1
| ~ element(X1,powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820',t22_pre_topc) ).
fof(f115244,plain,
( ~ open_subset(subset_difference(the_carrier(sK0),the_carrier(sK0),set_difference(the_carrier(sK0),sK7(sK0,sK1,sK2))),sK0)
| spl15_1
| ~ spl15_6 ),
inference(forward_demodulation,[],[f115241,f319]) ).
fof(f115241,plain,
( ~ open_subset(subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),set_difference(the_carrier(sK0),sK7(sK0,sK1,sK2))),sK0)
| spl15_1
| ~ spl15_6 ),
inference(unit_resulting_resolution,[],[f161,f1714,f112045,f186]) ).
fof(f186,plain,
! [X0,X1] :
( closed_subset(X1,X0)
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f112045,plain,
( ~ closed_subset(set_difference(the_carrier(sK0),sK7(sK0,sK1,sK2)),sK0)
| spl15_1
| ~ spl15_6 ),
inference(unit_resulting_resolution,[],[f1736,f1356,f1714,f309]) ).
fof(f309,plain,
( ! [X4] :
( ~ element(X4,powerset(the_carrier(sK0)))
| in(sK2,X4)
| ~ closed_subset(X4,sK0)
| ~ subset(sK1,X4) )
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f308,plain,
( spl15_6
<=> ! [X4] :
( in(sK2,X4)
| ~ element(X4,powerset(the_carrier(sK0)))
| ~ closed_subset(X4,sK0)
| ~ subset(sK1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_6])]) ).
fof(f1356,plain,
( ! [X0] : ~ in(sK2,set_difference(X0,sK7(sK0,sK1,sK2)))
| spl15_1 ),
inference(unit_resulting_resolution,[],[f412,f279]) ).
fof(f279,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f259]) ).
fof(f259,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f154]) ).
fof(f412,plain,
( in(sK2,sK7(sK0,sK1,sK2))
| spl15_1 ),
inference(unit_resulting_resolution,[],[f161,f163,f286,f162,f338,f274]) ).
fof(f274,plain,
! [X0,X1,X6] :
( in(X6,topstr_closure(X0,X1))
| in(X6,sK7(X0,X1,X6))
| ~ in(X6,the_carrier(X0))
| ~ element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(equality_resolution,[],[f190]) ).
fof(f190,plain,
! [X2,X0,X1,X6] :
( in(X6,X2)
| in(X6,sK7(X0,X1,X6))
| ~ in(X6,the_carrier(X0))
| topstr_closure(X0,X1) != X2
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f1736,plain,
( subset(sK1,set_difference(the_carrier(sK0),sK7(sK0,sK1,sK2)))
| spl15_1 ),
inference(backward_demodulation,[],[f1635,f1733]) ).
fof(f1733,plain,
( subset_complement(the_carrier(sK0),sK7(sK0,sK1,sK2)) = set_difference(the_carrier(sK0),sK7(sK0,sK1,sK2))
| spl15_1 ),
inference(forward_demodulation,[],[f1732,f1683]) ).
fof(f1732,plain,
( subset_complement(the_carrier(sK0),sK7(sK0,sK1,sK2)) = subset_difference(the_carrier(sK0),the_carrier(sK0),sK7(sK0,sK1,sK2))
| spl15_1 ),
inference(forward_demodulation,[],[f1629,f319]) ).
fof(f1629,plain,
( subset_difference(the_carrier(sK0),cast_as_carrier_subset(sK0),sK7(sK0,sK1,sK2)) = subset_complement(the_carrier(sK0),sK7(sK0,sK1,sK2))
| spl15_1 ),
inference(unit_resulting_resolution,[],[f311,f410,f183]) ).
fof(f1635,plain,
( subset(sK1,subset_complement(the_carrier(sK0),sK7(sK0,sK1,sK2)))
| spl15_1 ),
inference(unit_resulting_resolution,[],[f162,f413,f410,f248]) ).
fof(f248,plain,
! [X2,X0,X1] :
( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f148]) ).
fof(f413,plain,
( disjoint(sK1,sK7(sK0,sK1,sK2))
| spl15_1 ),
inference(unit_resulting_resolution,[],[f161,f163,f286,f162,f338,f273]) ).
fof(f273,plain,
! [X0,X1,X6] :
( in(X6,topstr_closure(X0,X1))
| disjoint(X1,sK7(X0,X1,X6))
| ~ in(X6,the_carrier(X0))
| ~ element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(equality_resolution,[],[f191]) ).
fof(f191,plain,
! [X2,X0,X1,X6] :
( in(X6,X2)
| disjoint(X1,sK7(X0,X1,X6))
| ~ in(X6,the_carrier(X0))
| topstr_closure(X0,X1) != X2
| ~ element(X2,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f1714,plain,
( element(set_difference(the_carrier(sK0),sK7(sK0,sK1,sK2)),powerset(the_carrier(sK0)))
| spl15_1 ),
inference(forward_demodulation,[],[f1653,f1683]) ).
fof(f1653,plain,
( element(subset_difference(the_carrier(sK0),the_carrier(sK0),sK7(sK0,sK1,sK2)),powerset(the_carrier(sK0)))
| spl15_1 ),
inference(unit_resulting_resolution,[],[f320,f410,f256]) ).
fof(f310,plain,
( spl15_1
| spl15_6 ),
inference(avatar_split_clause,[],[f164,f308,f284]) ).
fof(f164,plain,
! [X4] :
( in(sK2,X4)
| ~ subset(sK1,X4)
| ~ closed_subset(X4,sK0)
| ~ element(X4,powerset(the_carrier(sK0)))
| in(sK2,topstr_closure(sK0,sK1)) ),
inference(cnf_transformation,[],[f133]) ).
fof(f306,plain,
( ~ spl15_1
| spl15_5 ),
inference(avatar_split_clause,[],[f165,f303,f284]) ).
fof(f165,plain,
( element(sK3,powerset(the_carrier(sK0)))
| ~ in(sK2,topstr_closure(sK0,sK1)) ),
inference(cnf_transformation,[],[f133]) ).
fof(f301,plain,
( ~ spl15_1
| spl15_4 ),
inference(avatar_split_clause,[],[f166,f298,f284]) ).
fof(f166,plain,
( closed_subset(sK3,sK0)
| ~ in(sK2,topstr_closure(sK0,sK1)) ),
inference(cnf_transformation,[],[f133]) ).
fof(f296,plain,
( ~ spl15_1
| spl15_3 ),
inference(avatar_split_clause,[],[f167,f293,f284]) ).
fof(f167,plain,
( subset(sK1,sK3)
| ~ in(sK2,topstr_closure(sK0,sK1)) ),
inference(cnf_transformation,[],[f133]) ).
fof(f291,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f168,f288,f284]) ).
fof(f168,plain,
( ~ in(sK2,sK3)
| ~ in(sK2,topstr_closure(sK0,sK1)) ),
inference(cnf_transformation,[],[f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU313+1 : TPTP v8.1.2. Released v3.3.0.
% 0.16/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.37 % Computer : n002.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Wed Aug 23 19:50:46 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.p1dPWeh9L0/Vampire---4.8_3820
% 0.16/0.37 % (4007)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44 % (4008)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.23/0.44 % (4013)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.23/0.44 % (4009)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.23/0.44 % (4011)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.23/0.44 % (4012)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.44 % (4014)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.23/0.44 % (4010)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 50.51/7.58 % (4011)First to succeed.
% 50.62/7.60 % (4011)Refutation found. Thanks to Tanya!
% 50.62/7.60 % SZS status Theorem for Vampire---4
% 50.62/7.60 % SZS output start Proof for Vampire---4
% See solution above
% 50.62/7.61 % (4011)------------------------------
% 50.62/7.61 % (4011)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 50.62/7.61 % (4011)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 50.62/7.61 % (4011)Termination reason: Refutation
% 50.62/7.61
% 50.62/7.61 % (4011)Memory used [KB]: 155434
% 50.62/7.61 % (4011)Time elapsed: 7.153 s
% 50.62/7.61 % (4011)------------------------------
% 50.62/7.61 % (4011)------------------------------
% 50.62/7.61 % (4007)Success in time 7.194 s
% 50.77/7.61 % Vampire---4.8 exiting
%------------------------------------------------------------------------------