%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU316+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 : Tue Sep 29 12:48:18 PM UTC 2026
% Result : Theorem 20.47s 4.23s
% Output : Refutation 24.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 73
% Syntax : Number of formulae : 483 ( 66 unt; 55 def)
% Number of atoms : 1860 ( 162 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 2437 (1060 ~;1170 |; 110 &)
% ( 70 <=>; 25 =>; 0 <=; 2 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 65 ( 63 usr; 55 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 3 con; 0-3 aty)
% Number of variables : 370 ( 0 sgn 336 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0,X1] :
( ( X0 != empty_set
=> ( X1 = set_meet(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X3,X0)
=> in(X2,X3) ) ) ) )
& ( X0 = empty_set
=> ( X1 = set_meet(X0)
<=> X1 = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_setfam_1) ).
fof(f18,axiom,
! [X0] :
( one_sorted_str(X0)
=> cast_as_carrier_subset(X0) = the_carrier(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_pre_topc) ).
fof(f22,axiom,
! [X0] :
( one_sorted_str(X0)
=> element(cast_as_carrier_subset(X0),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_pre_topc) ).
fof(f23,axiom,
! [X0,X1] :
( ( top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(f25,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f31,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f33,axiom,
! [X0] :
( ( topological_space(X0)
& top_str(X0) )
=> closed_subset(cast_as_carrier_subset(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_pre_topc) ).
fof(f37,axiom,
! [X0] :
? [X1] :
( element(X1,powerset(X0))
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f39,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> meet_of_subsets(X0,X1) = set_meet(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
fof(f41,axiom,
! [X0,X1] :
( ( topological_space(X0)
& top_str(X0)
& element(X1,powerset(the_carrier(X0))) )
=> ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
fof(f43,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f45,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f46,axiom,
! [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)))
=> ( ( closed_subset(X3,X0)
& subset(X1,X3) )
=> in(X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_pre_topc) ).
fof(f47,conjecture,
! [X0] :
( ( topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ( closed_subset(X3,X0)
& subset(X1,X3) ) ) )
& topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_pre_topc) ).
fof(f48,negated_conjecture,
~ ! [X0] :
( ( topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ( closed_subset(X3,X0)
& subset(X1,X3) ) ) )
& topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f49,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f50,axiom,
! [X0,X1,X2] :
~ ( in(X0,X1)
& element(X1,powerset(X2))
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f51,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f52,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f81,plain,
! [X0,X1] :
( ( ( X1 = set_meet(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) )
| empty_set = X0 )
& ( ( X1 = set_meet(X0)
<=> X1 = empty_set )
| empty_set != X0 ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f82,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f83,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f84,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f23]) ).
fof(f85,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f84]) ).
fof(f87,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f88,plain,
! [X0] :
( closed_subset(cast_as_carrier_subset(X0),X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f89,plain,
! [X0] :
( closed_subset(cast_as_carrier_subset(X0),X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f88]) ).
fof(f93,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f39]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( ( in(X3,X2)
<=> ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) )
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f41]) ).
fof(f95,plain,
! [X0,X1] :
( ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( ( in(X3,X2)
<=> ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) ) )
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f94]) ).
fof(f97,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f98,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f97]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( in(X2,X3)
| ~ closed_subset(X3,X0)
| ~ subset(X1,X3)
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ in(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( in(X2,X3)
| ~ closed_subset(X3,X0)
| ~ subset(X1,X3)
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ in(X2,the_carrier(X0)) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
? [X0] :
( ? [X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( in(X3,X2)
<~> ( closed_subset(X3,X0)
& subset(X1,X3) ) )
& element(X3,powerset(the_carrier(X0))) )
| topstr_closure(X0,X1) != meet_of_subsets(the_carrier(X0),X2) )
& element(X1,powerset(the_carrier(X0))) )
& topological_space(X0)
& top_str(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f103,plain,
? [X0] :
( ? [X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( in(X3,X2)
<~> ( closed_subset(X3,X0)
& subset(X1,X3) ) )
& element(X3,powerset(the_carrier(X0))) )
| topstr_closure(X0,X1) != meet_of_subsets(the_carrier(X0),X2) )
& element(X1,powerset(the_carrier(X0))) )
& topological_space(X0)
& top_str(X0) ),
inference(flattening,[],[f102]) ).
fof(f104,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f49]) ).
fof(f105,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f104]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(ennf_transformation,[],[f50]) ).
fof(f107,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f108,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f52]) ).
fof(f110,plain,
! [X0,X1] :
( ( ( ( X1 = set_meet(X0)
| ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) ) )
& ( ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) ) )
| set_meet(X0) != X1 ) )
| empty_set = X0 )
& ( ( ( X1 = set_meet(X0)
| empty_set != X1 )
& ( X1 = empty_set
| set_meet(X0) != X1 ) )
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f111,plain,
! [X0,X1] :
( ( ( ( X1 = set_meet(X0)
| ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X4] :
( in(X2,X4)
| ~ in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ? [X6] :
( ~ in(X5,X6)
& in(X6,X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| set_meet(X0) != X1 ) )
| empty_set = X0 )
& ( ( ( X1 = set_meet(X0)
| empty_set != X1 )
& ( X1 = empty_set
| set_meet(X0) != X1 ) )
| empty_set != X0 ) ),
inference(rectify,[],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( ( ( ( X1 = set_meet(X0)
| ( ( ( ~ in(sK0(X0,X1),sK1(X0,X1))
& in(sK1(X0,X1),X0) )
| ~ in(sK0(X0,X1),X1) )
& ( ! [X4] :
( in(sK0(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ( ~ in(X5,sK2(X0,X5))
& in(sK2(X0,X5),X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| set_meet(X0) != X1 ) )
| empty_set = X0 )
& ( ( ( X1 = set_meet(X0)
| empty_set != X1 )
& ( X1 = empty_set
| set_meet(X0) != X1 ) )
| empty_set != X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1)),skolemize(X6,sK2(X0,X5))],[f111]) ).
fof(f115,plain,
! [X0] : element(sK5(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f31]) ).
fof(f118,plain,
! [X0] :
( element(sK8(X0),powerset(X0))
& empty(sK8(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X1,sK8(X0))],[f37]) ).
fof(f120,plain,
! [X0,X1] :
( ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( ( ( in(X3,X2)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) ) )
& ( ? [X4] :
( element(X4,powerset(the_carrier(X0)))
& X4 = X3
& closed_subset(X4,X0)
& subset(X1,X3) )
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(nnf_transformation,[],[f95]) ).
fof(f121,plain,
! [X0,X1] :
( ? [X2] :
( element(X2,powerset(powerset(the_carrier(X0))))
& ! [X3] :
( ( ( in(X3,X2)
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) ) )
& ( ? [X5] :
( element(X5,powerset(the_carrier(X0)))
& X3 = X5
& closed_subset(X5,X0)
& subset(X1,X3) )
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ( element(sK10(X0,X1),powerset(powerset(the_carrier(X0))))
& ! [X3] :
( ( ( in(X3,sK10(X0,X1))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3) ) )
& ( ( element(sK11(X0,X1,X3),powerset(the_carrier(X0)))
& sK11(X0,X1,X3) = X3
& closed_subset(sK11(X0,X1,X3),X0)
& subset(X1,X3) )
| ~ in(X3,sK10(X0,X1)) ) )
| ~ element(X3,powerset(the_carrier(X0))) ) )
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X2,sK10(X0,X1)),skolemize(X5,sK11(X0,X1,X3))],[f121]) ).
fof(f125,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,topstr_closure(X0,X1))
| ? [X3] :
( ~ in(X2,X3)
& closed_subset(X3,X0)
& subset(X1,X3)
& element(X3,powerset(the_carrier(X0))) ) )
& ( ! [X3] :
( in(X2,X3)
| ~ closed_subset(X3,X0)
| ~ subset(X1,X3)
| ~ 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,[],[f101]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,topstr_closure(X0,X1))
| ? [X3] :
( ~ in(X2,X3)
& closed_subset(X3,X0)
& subset(X1,X3)
& element(X3,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( in(X2,X4)
| ~ closed_subset(X4,X0)
| ~ subset(X1,X4)
| ~ 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,[],[f126]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( in(X2,topstr_closure(X0,X1))
| ( ~ in(X2,sK13(X0,X1,X2))
& closed_subset(sK13(X0,X1,X2),X0)
& subset(X1,sK13(X0,X1,X2))
& element(sK13(X0,X1,X2),powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( in(X2,X4)
| ~ closed_subset(X4,X0)
| ~ subset(X1,X4)
| ~ 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(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X3,sK13(X0,X1,X2))],[f127]) ).
fof(f129,plain,
? [X0] :
( ? [X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( ~ closed_subset(X3,X0)
| ~ subset(X1,X3)
| ~ in(X3,X2) )
& ( ( closed_subset(X3,X0)
& subset(X1,X3) )
| in(X3,X2) )
& element(X3,powerset(the_carrier(X0))) )
| topstr_closure(X0,X1) != meet_of_subsets(the_carrier(X0),X2) )
& element(X1,powerset(the_carrier(X0))) )
& topological_space(X0)
& top_str(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f130,plain,
? [X0] :
( ? [X1] :
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(X0))))
| ? [X3] :
( ( ~ closed_subset(X3,X0)
| ~ subset(X1,X3)
| ~ in(X3,X2) )
& ( ( closed_subset(X3,X0)
& subset(X1,X3) )
| in(X3,X2) )
& element(X3,powerset(the_carrier(X0))) )
| topstr_closure(X0,X1) != meet_of_subsets(the_carrier(X0),X2) )
& element(X1,powerset(the_carrier(X0))) )
& topological_space(X0)
& top_str(X0) ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
( ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK14))))
| ( ( ~ closed_subset(sK16(X2),sK14)
| ~ subset(sK15,sK16(X2))
| ~ in(sK16(X2),X2) )
& ( ( closed_subset(sK16(X2),sK14)
& subset(sK15,sK16(X2)) )
| in(sK16(X2),X2) )
& element(sK16(X2),powerset(the_carrier(sK14))) )
| topstr_closure(sK14,sK15) != meet_of_subsets(the_carrier(sK14),X2) )
& element(sK15,powerset(the_carrier(sK14)))
& topological_space(sK14)
& top_str(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X0,sK14),skolemize(X1,sK15),skolemize(X3,sK16(X2))],[f130]) ).
fof(f162,plain,
! [X0,X1,X4] :
( set_meet(X0) = X1
| in(sK0(X0,X1),X4)
| ~ in(X4,X0)
| in(sK0(X0,X1),X1)
| empty_set = X0 ),
inference(cnf_transformation,[],[f112]) ).
fof(f163,plain,
! [X0,X1] :
( set_meet(X0) = X1
| in(sK1(X0,X1),X0)
| ~ in(sK0(X0,X1),X1)
| empty_set = X0 ),
inference(cnf_transformation,[],[f112]) ).
fof(f164,plain,
! [X0,X1] :
( set_meet(X0) = X1
| ~ in(sK0(X0,X1),sK1(X0,X1))
| ~ in(sK0(X0,X1),X1)
| empty_set = X0 ),
inference(cnf_transformation,[],[f112]) ).
fof(f165,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f166,plain,
! [X0] :
( element(cast_as_carrier_subset(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f167,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f85]) ).
fof(f169,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f172,plain,
! [X0] : element(sK5(X0),X0),
inference(cnf_transformation,[],[f115]) ).
fof(f174,plain,
! [X0] :
( closed_subset(cast_as_carrier_subset(X0),X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f189,plain,
! [X0] : empty(sK8(X0)),
inference(cnf_transformation,[],[f118]) ).
fof(f193,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f93]) ).
fof(f195,plain,
! [X3,X0,X1] :
( subset(X1,X3)
| ~ in(X3,sK10(X0,X1))
| ~ element(X3,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f122]) ).
fof(f196,plain,
! [X3,X0,X1] :
( closed_subset(sK11(X0,X1,X3),X0)
| ~ in(X3,sK10(X0,X1))
| ~ element(X3,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f122]) ).
fof(f197,plain,
! [X3,X0,X1] :
( sK11(X0,X1,X3) = X3
| ~ in(X3,sK10(X0,X1))
| ~ element(X3,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f122]) ).
fof(f199,plain,
! [X3,X0,X1,X4] :
( in(X3,sK10(X0,X1))
| ~ element(X4,powerset(the_carrier(X0)))
| X3 != X4
| ~ closed_subset(X4,X0)
| ~ subset(X1,X3)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f122]) ).
fof(f200,plain,
! [X0,X1] :
( element(sK10(X0,X1),powerset(powerset(the_carrier(X0))))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f122]) ).
fof(f202,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f205,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f207,plain,
! [X2,X0,X1,X4] :
( in(X2,X4)
| ~ closed_subset(X4,X0)
| ~ subset(X1,X4)
| ~ 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(cnf_transformation,[],[f128]) ).
fof(f208,plain,
! [X2,X0,X1] :
( in(X2,topstr_closure(X0,X1))
| element(sK13(X0,X1,X2),powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f209,plain,
! [X2,X0,X1] :
( in(X2,topstr_closure(X0,X1))
| subset(X1,sK13(X0,X1,X2))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f210,plain,
! [X2,X0,X1] :
( in(X2,topstr_closure(X0,X1))
| closed_subset(sK13(X0,X1,X2),X0)
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f211,plain,
! [X2,X0,X1] :
( in(X2,topstr_closure(X0,X1))
| ~ in(X2,sK13(X0,X1,X2))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f212,plain,
top_str(sK14),
inference(cnf_transformation,[],[f131]) ).
fof(f213,plain,
topological_space(sK14),
inference(cnf_transformation,[],[f131]) ).
fof(f214,plain,
element(sK15,powerset(the_carrier(sK14))),
inference(cnf_transformation,[],[f131]) ).
fof(f215,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK14))))
| element(sK16(X2),powerset(the_carrier(sK14)))
| topstr_closure(sK14,sK15) != meet_of_subsets(the_carrier(sK14),X2) ),
inference(cnf_transformation,[],[f131]) ).
fof(f216,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK14))))
| subset(sK15,sK16(X2))
| in(sK16(X2),X2)
| topstr_closure(sK14,sK15) != meet_of_subsets(the_carrier(sK14),X2) ),
inference(cnf_transformation,[],[f131]) ).
fof(f217,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK14))))
| closed_subset(sK16(X2),sK14)
| in(sK16(X2),X2)
| topstr_closure(sK14,sK15) != meet_of_subsets(the_carrier(sK14),X2) ),
inference(cnf_transformation,[],[f131]) ).
fof(f218,plain,
! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK14))))
| ~ closed_subset(sK16(X2),sK14)
| ~ subset(sK15,sK16(X2))
| ~ in(sK16(X2),X2)
| topstr_closure(sK14,sK15) != meet_of_subsets(the_carrier(sK14),X2) ),
inference(cnf_transformation,[],[f131]) ).
fof(f219,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f220,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(cnf_transformation,[],[f106]) ).
fof(f221,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f222,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f108]) ).
fof(f231,plain,
! [X0,X1,X4] :
( in(X4,sK10(X0,X1))
| ~ element(X4,powerset(the_carrier(X0)))
| ~ closed_subset(X4,X0)
| ~ subset(X1,X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(equality_resolution,[],[f199]) ).
fof(f232,plain,
! [X2,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| sP17(X1) ),
inference(cnf_transformation,[],[f232_D]) ).
fof(f232_D,definition,
! [X1] :
( ! [X2] :
( ~ element(X1,powerset(X2))
| ~ empty(X2) )
<=> ~ sP17(X1) ),
introduced(definition,[new_symbols(definition,[sP17])],[general_splitting_component_introduction]) ).
fof(f233,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ sP17(X1) ),
inference(general_splitting,[],[f220,f232_D]) ).
fof(f234,plain,
! [X0,X1,X4] :
( in(X4,sK10(X0,X1))
| ~ element(X4,powerset(the_carrier(X0)))
| ~ closed_subset(X4,X0)
| ~ subset(X1,X4)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(duplicate_literal_removal,[],[f231]) ).
fof(f236,definition,
( spl18_1
<=> top_str(sK14) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
fof(f238,plain,
( top_str(sK14)
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f239,plain,
spl18_1,
inference(avatar_split_clause,[],[f212,f236]) ).
fof(f241,definition,
( spl18_2
<=> topological_space(sK14) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
fof(f243,plain,
( topological_space(sK14)
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f244,plain,
spl18_2,
inference(avatar_split_clause,[],[f213,f241]) ).
fof(f245,plain,
( closed_subset(cast_as_carrier_subset(sK14),sK14)
| ~ top_str(sK14)
| ~ spl18_2 ),
inference(resolution,[],[f243,f174]) ).
fof(f262,plain,
( closed_subset(cast_as_carrier_subset(sK14),sK14)
| ~ spl18_1
| ~ spl18_2 ),
inference(forward_subsumption_resolution,[],[f245,f238]) ).
fof(f264,plain,
( one_sorted_str(sK14)
| ~ spl18_1 ),
inference(resolution,[],[f238,f169]) ).
fof(f280,definition,
( spl18_3
<=> element(sK15,powerset(the_carrier(sK14))) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
fof(f282,plain,
( element(sK15,powerset(the_carrier(sK14)))
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f280]) ).
fof(f283,plain,
spl18_3,
inference(avatar_split_clause,[],[f214,f280]) ).
fof(f284,plain,
( element(topstr_closure(sK14,sK15),powerset(the_carrier(sK14)))
| ~ top_str(sK14)
| ~ spl18_3 ),
inference(resolution,[],[f282,f167]) ).
fof(f285,plain,
( ! [X0] :
( subset(sK15,X0)
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ topological_space(sK14)
| ~ top_str(sK14) )
| ~ spl18_3 ),
inference(resolution,[],[f282,f195]) ).
fof(f289,plain,
( ! [X0] :
( sK11(sK14,sK15,X0) = X0
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ topological_space(sK14)
| ~ top_str(sK14) )
| ~ spl18_3 ),
inference(resolution,[],[f282,f197]) ).
fof(f293,plain,
( element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ topological_space(sK14)
| ~ top_str(sK14)
| ~ spl18_3 ),
inference(resolution,[],[f282,f200]) ).
fof(f296,plain,
( ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| element(sK13(sK14,sK15,X0),powerset(the_carrier(sK14)))
| ~ in(X0,the_carrier(sK14))
| ~ top_str(sK14) )
| ~ spl18_3 ),
inference(resolution,[],[f282,f208]) ).
fof(f297,plain,
( ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| subset(sK15,sK13(sK14,sK15,X0))
| ~ in(X0,the_carrier(sK14))
| ~ top_str(sK14) )
| ~ spl18_3 ),
inference(resolution,[],[f282,f209]) ).
fof(f298,plain,
( ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| closed_subset(sK13(sK14,sK15,X0),sK14)
| ~ in(X0,the_carrier(sK14))
| ~ top_str(sK14) )
| ~ spl18_3 ),
inference(resolution,[],[f282,f210]) ).
fof(f299,plain,
( ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| ~ in(X0,sK13(sK14,sK15,X0))
| ~ in(X0,the_carrier(sK14))
| ~ top_str(sK14) )
| ~ spl18_3 ),
inference(resolution,[],[f282,f211]) ).
fof(f300,plain,
( ! [X0] :
( in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ closed_subset(X0,sK14)
| ~ subset(sK15,X0)
| ~ topological_space(sK14)
| ~ top_str(sK14) )
| ~ spl18_3 ),
inference(resolution,[],[f282,f234]) ).
fof(f317,plain,
( subset(sK15,the_carrier(sK14))
| ~ spl18_3 ),
inference(resolution,[],[f282,f205]) ).
fof(f319,plain,
( ~ empty(the_carrier(sK14))
| sP17(sK15)
| ~ spl18_3 ),
inference(resolution,[],[f282,f232]) ).
fof(f323,plain,
( ! [X0] :
( in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ closed_subset(X0,sK14)
| ~ subset(sK15,X0)
| ~ top_str(sK14) )
| ~ spl18_2
| ~ spl18_3 ),
inference(forward_subsumption_resolution,[],[f300,f243]) ).
fof(f324,plain,
( ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| ~ in(X0,sK13(sK14,sK15,X0))
| ~ in(X0,the_carrier(sK14)) )
| ~ spl18_1
| ~ spl18_3 ),
inference(forward_subsumption_resolution,[],[f299,f238]) ).
fof(f325,plain,
( ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| closed_subset(sK13(sK14,sK15,X0),sK14)
| ~ in(X0,the_carrier(sK14)) )
| ~ spl18_1
| ~ spl18_3 ),
inference(forward_subsumption_resolution,[],[f298,f238]) ).
fof(f326,plain,
( ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| subset(sK15,sK13(sK14,sK15,X0))
| ~ in(X0,the_carrier(sK14)) )
| ~ spl18_1
| ~ spl18_3 ),
inference(forward_subsumption_resolution,[],[f297,f238]) ).
fof(f327,plain,
( ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| element(sK13(sK14,sK15,X0),powerset(the_carrier(sK14)))
| ~ in(X0,the_carrier(sK14)) )
| ~ spl18_1
| ~ spl18_3 ),
inference(forward_subsumption_resolution,[],[f296,f238]) ).
fof(f330,plain,
( element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ top_str(sK14)
| ~ spl18_2
| ~ spl18_3 ),
inference(forward_subsumption_resolution,[],[f293,f243]) ).
fof(f334,plain,
( ! [X0] :
( sK11(sK14,sK15,X0) = X0
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ top_str(sK14) )
| ~ spl18_2
| ~ spl18_3 ),
inference(forward_subsumption_resolution,[],[f289,f243]) ).
fof(f338,plain,
( ! [X0] :
( subset(sK15,X0)
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ top_str(sK14) )
| ~ spl18_2
| ~ spl18_3 ),
inference(forward_subsumption_resolution,[],[f285,f243]) ).
fof(f339,plain,
( element(topstr_closure(sK14,sK15),powerset(the_carrier(sK14)))
| ~ spl18_1
| ~ spl18_3 ),
inference(forward_subsumption_resolution,[],[f284,f238]) ).
fof(f341,plain,
( ! [X0] :
( in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ closed_subset(X0,sK14)
| ~ subset(sK15,X0) )
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3 ),
inference(forward_subsumption_resolution,[],[f323,f238]) ).
fof(f342,plain,
( element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3 ),
inference(forward_subsumption_resolution,[],[f330,f238]) ).
fof(f346,plain,
( ! [X0] :
( sK11(sK14,sK15,X0) = X0
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14))) )
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3 ),
inference(forward_subsumption_resolution,[],[f334,f238]) ).
fof(f350,plain,
( ! [X0] :
( subset(sK15,X0)
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14))) )
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3 ),
inference(forward_subsumption_resolution,[],[f338,f238]) ).
fof(f352,definition,
( spl18_4
<=> ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK14))))
| ~ closed_subset(sK16(X2),sK14)
| ~ subset(sK15,sK16(X2))
| ~ in(sK16(X2),X2)
| topstr_closure(sK14,sK15) != meet_of_subsets(the_carrier(sK14),X2) ) ),
introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).
fof(f353,plain,
( ! [X2] :
( topstr_closure(sK14,sK15) != meet_of_subsets(the_carrier(sK14),X2)
| ~ closed_subset(sK16(X2),sK14)
| ~ subset(sK15,sK16(X2))
| ~ in(sK16(X2),X2)
| ~ element(X2,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f354,plain,
spl18_4,
inference(avatar_split_clause,[],[f218,f352]) ).
fof(f355,plain,
( ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| ~ closed_subset(sK16(X0),sK14)
| ~ subset(sK15,sK16(X0))
| ~ in(sK16(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK14))))
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_4 ),
inference(superposition,[],[f353,f193]) ).
fof(f356,plain,
( ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| ~ closed_subset(sK16(X0),sK14)
| ~ subset(sK15,sK16(X0))
| ~ in(sK16(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_4 ),
inference(duplicate_literal_removal,[],[f355]) ).
fof(f358,definition,
( spl18_5
<=> ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK14))))
| closed_subset(sK16(X2),sK14)
| in(sK16(X2),X2)
| topstr_closure(sK14,sK15) != meet_of_subsets(the_carrier(sK14),X2) ) ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
fof(f359,plain,
( ! [X2] :
( topstr_closure(sK14,sK15) != meet_of_subsets(the_carrier(sK14),X2)
| closed_subset(sK16(X2),sK14)
| in(sK16(X2),X2)
| ~ element(X2,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f360,plain,
spl18_5,
inference(avatar_split_clause,[],[f217,f358]) ).
fof(f361,plain,
( ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| closed_subset(sK16(X0),sK14)
| in(sK16(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK14))))
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_5 ),
inference(superposition,[],[f359,f193]) ).
fof(f362,plain,
( ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| closed_subset(sK16(X0),sK14)
| in(sK16(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_5 ),
inference(duplicate_literal_removal,[],[f361]) ).
fof(f364,definition,
( spl18_6
<=> closed_subset(cast_as_carrier_subset(sK14),sK14) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
fof(f366,plain,
( closed_subset(cast_as_carrier_subset(sK14),sK14)
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f367,plain,
( spl18_6
| ~ spl18_1
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f262,f241,f236,f364]) ).
fof(f376,definition,
( spl18_7
<=> ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK14))))
| subset(sK15,sK16(X2))
| in(sK16(X2),X2)
| topstr_closure(sK14,sK15) != meet_of_subsets(the_carrier(sK14),X2) ) ),
introduced(definition,[new_symbols(definition,[spl18_7])],[avatar_definition]) ).
fof(f377,plain,
( ! [X2] :
( topstr_closure(sK14,sK15) != meet_of_subsets(the_carrier(sK14),X2)
| subset(sK15,sK16(X2))
| in(sK16(X2),X2)
| ~ element(X2,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_7 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f378,plain,
spl18_7,
inference(avatar_split_clause,[],[f216,f376]) ).
fof(f379,plain,
( ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| subset(sK15,sK16(X0))
| in(sK16(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK14))))
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_7 ),
inference(superposition,[],[f377,f193]) ).
fof(f380,plain,
( ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| subset(sK15,sK16(X0))
| in(sK16(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_7 ),
inference(duplicate_literal_removal,[],[f379]) ).
fof(f382,definition,
( spl18_8
<=> element(topstr_closure(sK14,sK15),powerset(the_carrier(sK14))) ),
introduced(definition,[new_symbols(definition,[spl18_8])],[avatar_definition]) ).
fof(f384,plain,
( element(topstr_closure(sK14,sK15),powerset(the_carrier(sK14)))
| ~ spl18_8 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f385,plain,
( spl18_8
| ~ spl18_1
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f339,f280,f236,f382]) ).
fof(f387,definition,
( spl18_9
<=> ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| ~ closed_subset(sK16(X0),sK14)
| ~ subset(sK15,sK16(X0))
| ~ in(sK16(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) ) ),
introduced(definition,[new_symbols(definition,[spl18_9])],[avatar_definition]) ).
fof(f388,plain,
( ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| ~ closed_subset(sK16(X0),sK14)
| ~ subset(sK15,sK16(X0))
| ~ in(sK16(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_9 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f389,plain,
( spl18_9
| ~ spl18_4 ),
inference(avatar_split_clause,[],[f356,f352,f387]) ).
fof(f427,plain,
( ! [X0] :
( element(X0,the_carrier(sK14))
| ~ in(X0,topstr_closure(sK14,sK15)) )
| ~ spl18_8 ),
inference(resolution,[],[f384,f219]) ).
fof(f428,plain,
( ~ empty(the_carrier(sK14))
| sP17(topstr_closure(sK14,sK15))
| ~ spl18_8 ),
inference(resolution,[],[f384,f232]) ).
fof(f466,definition,
( spl18_11
<=> element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14)))) ),
introduced(definition,[new_symbols(definition,[spl18_11])],[avatar_definition]) ).
fof(f468,plain,
( element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_11 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f469,plain,
( spl18_11
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f342,f280,f241,f236,f466]) ).
fof(f488,plain,
( ! [X0] :
( element(X0,powerset(the_carrier(sK14)))
| ~ in(X0,sK10(sK14,sK15)) )
| ~ spl18_11 ),
inference(resolution,[],[f468,f219]) ).
fof(f508,definition,
( spl18_13
<=> subset(sK15,the_carrier(sK14)) ),
introduced(definition,[new_symbols(definition,[spl18_13])],[avatar_definition]) ).
fof(f510,plain,
( subset(sK15,the_carrier(sK14))
| ~ spl18_13 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f511,plain,
( spl18_13
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f317,f280,f508]) ).
fof(f518,definition,
( spl18_15
<=> one_sorted_str(sK14) ),
introduced(definition,[new_symbols(definition,[spl18_15])],[avatar_definition]) ).
fof(f520,plain,
( one_sorted_str(sK14)
| ~ spl18_15 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f521,plain,
( spl18_15
| ~ spl18_1 ),
inference(avatar_split_clause,[],[f264,f236,f518]) ).
fof(f523,plain,
( the_carrier(sK14) = cast_as_carrier_subset(sK14)
| ~ spl18_15 ),
inference(resolution,[],[f520,f165]) ).
fof(f527,definition,
( spl18_16
<=> ! [X0] :
( subset(sK15,X0)
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14))) ) ),
introduced(definition,[new_symbols(definition,[spl18_16])],[avatar_definition]) ).
fof(f528,plain,
( ! [X0] :
( subset(sK15,X0)
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14))) )
| ~ spl18_16 ),
inference(avatar_component_clause,[],[f527]) ).
fof(f529,plain,
( spl18_16
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f350,f280,f241,f236,f527]) ).
fof(f530,plain,
( ! [X0] :
( subset(sK15,X0)
| ~ in(X0,sK10(sK14,sK15)) )
| ~ spl18_11
| ~ spl18_16 ),
inference(forward_subsumption_resolution,[],[f528,f488]) ).
fof(f532,definition,
( spl18_17
<=> ! [X2] :
( ~ element(X2,powerset(powerset(the_carrier(sK14))))
| element(sK16(X2),powerset(the_carrier(sK14)))
| topstr_closure(sK14,sK15) != meet_of_subsets(the_carrier(sK14),X2) ) ),
introduced(definition,[new_symbols(definition,[spl18_17])],[avatar_definition]) ).
fof(f533,plain,
( ! [X2] :
( topstr_closure(sK14,sK15) != meet_of_subsets(the_carrier(sK14),X2)
| element(sK16(X2),powerset(the_carrier(sK14)))
| ~ element(X2,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_17 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f534,plain,
spl18_17,
inference(avatar_split_clause,[],[f215,f532]) ).
fof(f536,plain,
( ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| element(sK16(X0),powerset(the_carrier(sK14)))
| ~ element(X0,powerset(powerset(the_carrier(sK14))))
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_17 ),
inference(superposition,[],[f533,f193]) ).
fof(f537,plain,
( ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| element(sK16(X0),powerset(the_carrier(sK14)))
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_17 ),
inference(duplicate_literal_removal,[],[f536]) ).
fof(f539,definition,
( spl18_18
<=> ! [X0] :
( subset(sK15,X0)
| ~ in(X0,sK10(sK14,sK15)) ) ),
introduced(definition,[new_symbols(definition,[spl18_18])],[avatar_definition]) ).
fof(f540,plain,
( ! [X0] :
( ~ in(X0,sK10(sK14,sK15))
| subset(sK15,X0) )
| ~ spl18_18 ),
inference(avatar_component_clause,[],[f539]) ).
fof(f541,plain,
( spl18_18
| ~ spl18_11
| ~ spl18_16 ),
inference(avatar_split_clause,[],[f530,f527,f466,f539]) ).
fof(f548,plain,
( ! [X0] :
( subset(sK15,sK1(sK10(sK14,sK15),X0))
| set_meet(sK10(sK14,sK15)) = X0
| ~ in(sK0(sK10(sK14,sK15),X0),X0)
| empty_set = sK10(sK14,sK15) )
| ~ spl18_18 ),
inference(resolution,[],[f540,f163]) ).
fof(f553,definition,
( spl18_19
<=> the_carrier(sK14) = cast_as_carrier_subset(sK14) ),
introduced(definition,[new_symbols(definition,[spl18_19])],[avatar_definition]) ).
fof(f555,plain,
( the_carrier(sK14) = cast_as_carrier_subset(sK14)
| ~ spl18_19 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f556,plain,
( spl18_19
| ~ spl18_15 ),
inference(avatar_split_clause,[],[f523,f518,f553]) ).
fof(f558,definition,
( spl18_20
<=> ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| subset(sK15,sK16(X0))
| in(sK16(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) ) ),
introduced(definition,[new_symbols(definition,[spl18_20])],[avatar_definition]) ).
fof(f559,plain,
( ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| subset(sK15,sK16(X0))
| in(sK16(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_20 ),
inference(avatar_component_clause,[],[f558]) ).
fof(f560,plain,
( spl18_20
| ~ spl18_7 ),
inference(avatar_split_clause,[],[f380,f376,f558]) ).
fof(f565,definition,
( spl18_21
<=> ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| subset(sK15,sK13(sK14,sK15,X0))
| ~ in(X0,the_carrier(sK14)) ) ),
introduced(definition,[new_symbols(definition,[spl18_21])],[avatar_definition]) ).
fof(f566,plain,
( ! [X0] :
( subset(sK15,sK13(sK14,sK15,X0))
| in(X0,topstr_closure(sK14,sK15))
| ~ in(X0,the_carrier(sK14)) )
| ~ spl18_21 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f567,plain,
( spl18_21
| ~ spl18_1
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f326,f280,f236,f565]) ).
fof(f572,definition,
( spl18_22
<=> ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| closed_subset(sK16(X0),sK14)
| in(sK16(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) ) ),
introduced(definition,[new_symbols(definition,[spl18_22])],[avatar_definition]) ).
fof(f573,plain,
( ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| closed_subset(sK16(X0),sK14)
| in(sK16(X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_22 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f574,plain,
( spl18_22
| ~ spl18_5 ),
inference(avatar_split_clause,[],[f362,f358,f572]) ).
fof(f606,definition,
( spl18_24
<=> ! [X0] :
( sK11(sK14,sK15,X0) = X0
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14))) ) ),
introduced(definition,[new_symbols(definition,[spl18_24])],[avatar_definition]) ).
fof(f607,plain,
( ! [X0] :
( sK11(sK14,sK15,X0) = X0
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14))) )
| ~ spl18_24 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f608,plain,
( spl18_24
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f346,f280,f241,f236,f606]) ).
fof(f609,plain,
( ! [X0] :
( sK11(sK14,sK15,X0) = X0
| ~ in(X0,sK10(sK14,sK15)) )
| ~ spl18_11
| ~ spl18_24 ),
inference(forward_subsumption_resolution,[],[f607,f488]) ).
fof(f611,definition,
( spl18_25
<=> ! [X0] :
( sK11(sK14,sK15,X0) = X0
| ~ in(X0,sK10(sK14,sK15)) ) ),
introduced(definition,[new_symbols(definition,[spl18_25])],[avatar_definition]) ).
fof(f612,plain,
( ! [X0] :
( sK11(sK14,sK15,X0) = X0
| ~ in(X0,sK10(sK14,sK15)) )
| ~ spl18_25 ),
inference(avatar_component_clause,[],[f611]) ).
fof(f613,plain,
( spl18_25
| ~ spl18_11
| ~ spl18_24 ),
inference(avatar_split_clause,[],[f609,f606,f466,f611]) ).
fof(f614,plain,
( ! [X0] :
( closed_subset(X0,sK14)
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ topological_space(sK14)
| ~ top_str(sK14)
| ~ element(sK15,powerset(the_carrier(sK14)))
| ~ in(X0,sK10(sK14,sK15)) )
| ~ spl18_25 ),
inference(superposition,[],[f196,f612]) ).
fof(f617,plain,
( ! [X0] :
( closed_subset(X0,sK14)
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ topological_space(sK14)
| ~ top_str(sK14)
| ~ element(sK15,powerset(the_carrier(sK14))) )
| ~ spl18_25 ),
inference(duplicate_literal_removal,[],[f614]) ).
fof(f618,plain,
( ! [X0] :
( closed_subset(X0,sK14)
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ top_str(sK14)
| ~ element(sK15,powerset(the_carrier(sK14))) )
| ~ spl18_2
| ~ spl18_25 ),
inference(forward_subsumption_resolution,[],[f617,f243]) ).
fof(f619,plain,
( ! [X0] :
( closed_subset(X0,sK14)
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ element(sK15,powerset(the_carrier(sK14))) )
| ~ spl18_1
| ~ spl18_2
| ~ spl18_25 ),
inference(forward_subsumption_resolution,[],[f618,f238]) ).
fof(f620,plain,
( ! [X0] :
( closed_subset(X0,sK14)
| ~ in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14))) )
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_25 ),
inference(forward_subsumption_resolution,[],[f619,f282]) ).
fof(f621,plain,
( ! [X0] :
( closed_subset(X0,sK14)
| ~ in(X0,sK10(sK14,sK15)) )
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_11
| ~ spl18_25 ),
inference(forward_subsumption_resolution,[],[f620,f488]) ).
fof(f634,definition,
( spl18_27
<=> ! [X0] :
( closed_subset(X0,sK14)
| ~ in(X0,sK10(sK14,sK15)) ) ),
introduced(definition,[new_symbols(definition,[spl18_27])],[avatar_definition]) ).
fof(f635,plain,
( ! [X0] :
( ~ in(X0,sK10(sK14,sK15))
| closed_subset(X0,sK14) )
| ~ spl18_27 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f636,plain,
( spl18_27
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_11
| ~ spl18_25 ),
inference(avatar_split_clause,[],[f621,f611,f466,f280,f241,f236,f634]) ).
fof(f643,plain,
( ! [X0] :
( closed_subset(sK1(sK10(sK14,sK15),X0),sK14)
| set_meet(sK10(sK14,sK15)) = X0
| ~ in(sK0(sK10(sK14,sK15),X0),X0)
| empty_set = sK10(sK14,sK15) )
| ~ spl18_27 ),
inference(resolution,[],[f635,f163]) ).
fof(f651,definition,
( spl18_28
<=> ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| ~ in(X0,sK13(sK14,sK15,X0))
| ~ in(X0,the_carrier(sK14)) ) ),
introduced(definition,[new_symbols(definition,[spl18_28])],[avatar_definition]) ).
fof(f652,plain,
( ! [X0] :
( ~ in(X0,sK13(sK14,sK15,X0))
| in(X0,topstr_closure(sK14,sK15))
| ~ in(X0,the_carrier(sK14)) )
| ~ spl18_28 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f653,plain,
( spl18_28
| ~ spl18_1
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f324,f280,f236,f651]) ).
fof(f662,definition,
( spl18_29
<=> ! [X0] :
( in(X0,sK10(sK14,sK15))
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ closed_subset(X0,sK14)
| ~ subset(sK15,X0) ) ),
introduced(definition,[new_symbols(definition,[spl18_29])],[avatar_definition]) ).
fof(f663,plain,
( ! [X0] :
( ~ element(X0,powerset(the_carrier(sK14)))
| in(X0,sK10(sK14,sK15))
| ~ closed_subset(X0,sK14)
| ~ subset(sK15,X0) )
| ~ spl18_29 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f664,plain,
( spl18_29
| ~ spl18_1
| ~ spl18_2
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f341,f280,f241,f236,f662]) ).
fof(f667,plain,
( in(cast_as_carrier_subset(sK14),sK10(sK14,sK15))
| ~ closed_subset(cast_as_carrier_subset(sK14),sK14)
| ~ subset(sK15,cast_as_carrier_subset(sK14))
| ~ one_sorted_str(sK14)
| ~ spl18_29 ),
inference(resolution,[],[f663,f166]) ).
fof(f683,plain,
( in(cast_as_carrier_subset(sK14),sK10(sK14,sK15))
| ~ subset(sK15,cast_as_carrier_subset(sK14))
| ~ one_sorted_str(sK14)
| ~ spl18_6
| ~ spl18_29 ),
inference(forward_subsumption_resolution,[],[f667,f366]) ).
fof(f688,plain,
( in(cast_as_carrier_subset(sK14),sK10(sK14,sK15))
| ~ subset(sK15,cast_as_carrier_subset(sK14))
| ~ spl18_6
| ~ spl18_15
| ~ spl18_29 ),
inference(forward_subsumption_resolution,[],[f683,f520]) ).
fof(f691,plain,
( in(the_carrier(sK14),sK10(sK14,sK15))
| ~ subset(sK15,cast_as_carrier_subset(sK14))
| ~ spl18_6
| ~ spl18_15
| ~ spl18_19
| ~ spl18_29 ),
inference(forward_demodulation,[],[f688,f555]) ).
fof(f692,plain,
( ~ subset(sK15,the_carrier(sK14))
| in(the_carrier(sK14),sK10(sK14,sK15))
| ~ spl18_6
| ~ spl18_15
| ~ spl18_19
| ~ spl18_29 ),
inference(forward_demodulation,[],[f691,f555]) ).
fof(f693,plain,
( in(the_carrier(sK14),sK10(sK14,sK15))
| ~ spl18_6
| ~ spl18_13
| ~ spl18_15
| ~ spl18_19
| ~ spl18_29 ),
inference(forward_subsumption_resolution,[],[f692,f510]) ).
fof(f695,definition,
( spl18_30
<=> in(the_carrier(sK14),sK10(sK14,sK15)) ),
introduced(definition,[new_symbols(definition,[spl18_30])],[avatar_definition]) ).
fof(f697,plain,
( in(the_carrier(sK14),sK10(sK14,sK15))
| ~ spl18_30 ),
inference(avatar_component_clause,[],[f695]) ).
fof(f698,plain,
( spl18_30
| ~ spl18_6
| ~ spl18_13
| ~ spl18_15
| ~ spl18_19
| ~ spl18_29 ),
inference(avatar_split_clause,[],[f693,f662,f553,f518,f508,f364,f695]) ).
fof(f707,plain,
( ! [X0] :
( set_meet(sK10(sK14,sK15)) = X0
| in(sK0(sK10(sK14,sK15),X0),the_carrier(sK14))
| in(sK0(sK10(sK14,sK15),X0),X0)
| empty_set = sK10(sK14,sK15) )
| ~ spl18_30 ),
inference(resolution,[],[f697,f162]) ).
fof(f762,definition,
( spl18_36
<=> sP17(sK15) ),
introduced(definition,[new_symbols(definition,[spl18_36])],[avatar_definition]) ).
fof(f764,plain,
( sP17(sK15)
| ~ spl18_36 ),
inference(avatar_component_clause,[],[f762]) ).
fof(f766,definition,
( spl18_37
<=> empty(the_carrier(sK14)) ),
introduced(definition,[new_symbols(definition,[spl18_37])],[avatar_definition]) ).
fof(f767,plain,
( empty(the_carrier(sK14))
| ~ spl18_37 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f768,plain,
( ~ empty(the_carrier(sK14))
| spl18_37 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f769,plain,
( spl18_36
| ~ spl18_37
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f319,f280,f766,f762]) ).
fof(f860,definition,
( spl18_40
<=> ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| element(sK16(X0),powerset(the_carrier(sK14)))
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) ) ),
introduced(definition,[new_symbols(definition,[spl18_40])],[avatar_definition]) ).
fof(f861,plain,
( ! [X0] :
( set_meet(X0) != topstr_closure(sK14,sK15)
| element(sK16(X0),powerset(the_carrier(sK14)))
| ~ element(X0,powerset(powerset(the_carrier(sK14)))) )
| ~ spl18_40 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f862,plain,
( spl18_40
| ~ spl18_17 ),
inference(avatar_split_clause,[],[f537,f532,f860]) ).
fof(f867,definition,
( spl18_41
<=> ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| element(sK13(sK14,sK15,X0),powerset(the_carrier(sK14)))
| ~ in(X0,the_carrier(sK14)) ) ),
introduced(definition,[new_symbols(definition,[spl18_41])],[avatar_definition]) ).
fof(f868,plain,
( ! [X0] :
( element(sK13(sK14,sK15,X0),powerset(the_carrier(sK14)))
| in(X0,topstr_closure(sK14,sK15))
| ~ in(X0,the_carrier(sK14)) )
| ~ spl18_41 ),
inference(avatar_component_clause,[],[f867]) ).
fof(f869,plain,
( spl18_41
| ~ spl18_1
| ~ spl18_3 ),
inference(avatar_split_clause,[],[f327,f280,f236,f867]) ).
fof(f870,plain,
( ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| ~ in(X0,the_carrier(sK14))
| in(sK13(sK14,sK15,X0),sK10(sK14,sK15))
| ~ closed_subset(sK13(sK14,sK15,X0),sK14)
| ~ subset(sK15,sK13(sK14,sK15,X0)) )
| ~ spl18_29
| ~ spl18_41 ),
inference(resolution,[],[f868,f663]) ).
fof(f928,plain,
( ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| ~ in(X0,the_carrier(sK14))
| in(sK13(sK14,sK15,X0),sK10(sK14,sK15))
| ~ subset(sK15,sK13(sK14,sK15,X0)) )
| ~ spl18_1
| ~ spl18_3
| ~ spl18_29
| ~ spl18_41 ),
inference(forward_subsumption_resolution,[],[f870,f325]) ).
fof(f941,plain,
( ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| ~ in(X0,the_carrier(sK14))
| in(sK13(sK14,sK15,X0),sK10(sK14,sK15)) )
| ~ spl18_1
| ~ spl18_3
| ~ spl18_21
| ~ spl18_29
| ~ spl18_41 ),
inference(forward_subsumption_resolution,[],[f928,f566]) ).
fof(f1281,definition,
( spl18_57
<=> ! [X0] :
( in(X0,topstr_closure(sK14,sK15))
| ~ in(X0,the_carrier(sK14))
| in(sK13(sK14,sK15,X0),sK10(sK14,sK15)) ) ),
introduced(definition,[new_symbols(definition,[spl18_57])],[avatar_definition]) ).
fof(f1282,plain,
( ! [X0] :
( in(sK13(sK14,sK15,X0),sK10(sK14,sK15))
| ~ in(X0,the_carrier(sK14))
| in(X0,topstr_closure(sK14,sK15)) )
| ~ spl18_57 ),
inference(avatar_component_clause,[],[f1281]) ).
fof(f1283,plain,
( spl18_57
| ~ spl18_1
| ~ spl18_3
| ~ spl18_21
| ~ spl18_29
| ~ spl18_41 ),
inference(avatar_split_clause,[],[f941,f867,f662,f565,f280,f236,f1281]) ).
fof(f1292,plain,
( ! [X0,X1] :
( ~ in(X0,the_carrier(sK14))
| in(X0,topstr_closure(sK14,sK15))
| set_meet(sK10(sK14,sK15)) = X1
| in(sK0(sK10(sK14,sK15),X1),sK13(sK14,sK15,X0))
| in(sK0(sK10(sK14,sK15),X1),X1)
| empty_set = sK10(sK14,sK15) )
| ~ spl18_57 ),
inference(resolution,[],[f1282,f162]) ).
fof(f2547,definition,
( spl18_107
<=> ! [X0] :
( element(X0,the_carrier(sK14))
| ~ in(X0,topstr_closure(sK14,sK15)) ) ),
introduced(definition,[new_symbols(definition,[spl18_107])],[avatar_definition]) ).
fof(f2548,plain,
( ! [X0] :
( ~ in(X0,topstr_closure(sK14,sK15))
| element(X0,the_carrier(sK14)) )
| ~ spl18_107 ),
inference(avatar_component_clause,[],[f2547]) ).
fof(f2549,plain,
( spl18_107
| ~ spl18_8 ),
inference(avatar_split_clause,[],[f427,f382,f2547]) ).
fof(f3137,plain,
( ! [X0] : ~ in(X0,sK15)
| ~ spl18_36 ),
inference(resolution,[],[f764,f233]) ).
fof(f3295,definition,
( spl18_138
<=> ! [X0] : ~ in(X0,sK15) ),
introduced(definition,[new_symbols(definition,[spl18_138])],[avatar_definition]) ).
fof(f3296,plain,
( ! [X0] : ~ in(X0,sK15)
| ~ spl18_138 ),
inference(avatar_component_clause,[],[f3295]) ).
fof(f3297,plain,
( spl18_138
| ~ spl18_36 ),
inference(avatar_split_clause,[],[f3137,f762,f3295]) ).
fof(f3371,definition,
( spl18_145
<=> empty_set = sK10(sK14,sK15) ),
introduced(definition,[new_symbols(definition,[spl18_145])],[avatar_definition]) ).
fof(f3372,plain,
( empty_set != sK10(sK14,sK15)
| spl18_145 ),
inference(avatar_component_clause,[],[f3371]) ).
fof(f3373,plain,
( empty_set = sK10(sK14,sK15)
| ~ spl18_145 ),
inference(avatar_component_clause,[],[f3371]) ).
fof(f3382,plain,
( in(the_carrier(sK14),empty_set)
| ~ spl18_30
| ~ spl18_145 ),
inference(superposition,[],[f697,f3373]) ).
fof(f3559,plain,
( ! [X0] :
( subset(sK15,sK1(sK10(sK14,sK15),X0))
| set_meet(sK10(sK14,sK15)) = X0
| ~ in(sK0(sK10(sK14,sK15),X0),X0) )
| ~ spl18_18
| spl18_145 ),
inference(backward_subsumption_resolution,[],[f548,f3372]) ).
fof(f3858,definition,
( spl18_151
<=> ! [X0] :
( subset(sK15,sK1(sK10(sK14,sK15),X0))
| set_meet(sK10(sK14,sK15)) = X0
| ~ in(sK0(sK10(sK14,sK15),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl18_151])],[avatar_definition]) ).
fof(f3859,plain,
( ! [X0] :
( ~ in(sK0(sK10(sK14,sK15),X0),X0)
| set_meet(sK10(sK14,sK15)) = X0
| subset(sK15,sK1(sK10(sK14,sK15),X0)) )
| ~ spl18_151 ),
inference(avatar_component_clause,[],[f3858]) ).
fof(f3860,plain,
( spl18_151
| ~ spl18_18
| spl18_145 ),
inference(avatar_split_clause,[],[f3559,f3371,f539,f3858]) ).
fof(f3936,plain,
( ! [X0] :
( empty(sK15)
| ~ element(X0,sK15) )
| ~ spl18_138 ),
inference(resolution,[],[f3296,f202]) ).
fof(f4149,definition,
( spl18_161
<=> ! [X0] :
( element(X0,powerset(the_carrier(sK14)))
| ~ in(X0,sK10(sK14,sK15)) ) ),
introduced(definition,[new_symbols(definition,[spl18_161])],[avatar_definition]) ).
fof(f4150,plain,
( ! [X0] :
( ~ in(X0,sK10(sK14,sK15))
| element(X0,powerset(the_carrier(sK14))) )
| ~ spl18_161 ),
inference(avatar_component_clause,[],[f4149]) ).
fof(f4151,plain,
( spl18_161
| ~ spl18_11 ),
inference(avatar_split_clause,[],[f488,f466,f4149]) ).
fof(f4738,definition,
( spl18_199
<=> in(the_carrier(sK14),empty_set) ),
introduced(definition,[new_symbols(definition,[spl18_199])],[avatar_definition]) ).
fof(f4740,plain,
( in(the_carrier(sK14),empty_set)
| ~ spl18_199 ),
inference(avatar_component_clause,[],[f4738]) ).
fof(f4741,plain,
( spl18_199
| ~ spl18_30
| ~ spl18_145 ),
inference(avatar_split_clause,[],[f3382,f3371,f695,f4738]) ).
fof(f4778,plain,
( ! [X0] :
( set_meet(sK10(sK14,sK15)) = X0
| in(sK0(sK10(sK14,sK15),X0),the_carrier(sK14))
| in(sK0(sK10(sK14,sK15),X0),X0) )
| ~ spl18_30
| spl18_145 ),
inference(forward_subsumption_resolution,[],[f707,f3372]) ).
fof(f4796,plain,
( ! [X0] :
( element(sK1(sK10(sK14,sK15),X0),powerset(the_carrier(sK14)))
| set_meet(sK10(sK14,sK15)) = X0
| ~ in(sK0(sK10(sK14,sK15),X0),X0)
| empty_set = sK10(sK14,sK15) )
| ~ spl18_161 ),
inference(resolution,[],[f4150,f163]) ).
fof(f4881,definition,
( spl18_200
<=> ! [X0] :
( set_meet(sK10(sK14,sK15)) = X0
| in(sK0(sK10(sK14,sK15),X0),the_carrier(sK14))
| in(sK0(sK10(sK14,sK15),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl18_200])],[avatar_definition]) ).
fof(f4882,plain,
( ! [X0] :
( in(sK0(sK10(sK14,sK15),X0),the_carrier(sK14))
| set_meet(sK10(sK14,sK15)) = X0
| in(sK0(sK10(sK14,sK15),X0),X0) )
| ~ spl18_200 ),
inference(avatar_component_clause,[],[f4881]) ).
fof(f4883,plain,
( spl18_200
| ~ spl18_30
| spl18_145 ),
inference(avatar_split_clause,[],[f4778,f3371,f695,f4881]) ).
fof(f5142,plain,
( ! [X0] :
( in(the_carrier(sK14),X0)
| ~ empty(X0) )
| ~ spl18_199 ),
inference(superposition,[],[f4740,f221]) ).
fof(f5146,plain,
( ! [X0] : ~ empty(X0)
| ~ spl18_199 ),
inference(forward_subsumption_resolution,[],[f5142,f222]) ).
fof(f5158,plain,
( $false
| ~ spl18_199 ),
inference(backward_subsumption_resolution,[],[f189,f5146]) ).
fof(f5172,plain,
~ spl18_199,
inference(avatar_contradiction_clause,[],[f5158]) ).
fof(f5215,plain,
( ! [X0,X1] :
( ~ in(X0,the_carrier(sK14))
| in(X0,topstr_closure(sK14,sK15))
| set_meet(sK10(sK14,sK15)) = X1
| in(sK0(sK10(sK14,sK15),X1),sK13(sK14,sK15,X0))
| in(sK0(sK10(sK14,sK15),X1),X1) )
| ~ spl18_57
| spl18_145 ),
inference(forward_subsumption_resolution,[],[f1292,f3372]) ).
fof(f5220,plain,
( ! [X0] :
( closed_subset(sK1(sK10(sK14,sK15),X0),sK14)
| set_meet(sK10(sK14,sK15)) = X0
| ~ in(sK0(sK10(sK14,sK15),X0),X0) )
| ~ spl18_27
| spl18_145 ),
inference(forward_subsumption_resolution,[],[f643,f3372]) ).
fof(f5228,plain,
( ! [X0] :
( element(sK1(sK10(sK14,sK15),X0),powerset(the_carrier(sK14)))
| set_meet(sK10(sK14,sK15)) = X0
| ~ in(sK0(sK10(sK14,sK15),X0),X0) )
| spl18_145
| ~ spl18_161 ),
inference(forward_subsumption_resolution,[],[f4796,f3372]) ).
fof(f5242,definition,
( spl18_204
<=> ! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl18_204])],[avatar_definition]) ).
fof(f5243,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) )
| ~ spl18_204 ),
inference(avatar_component_clause,[],[f5242]) ).
fof(f5244,plain,
spl18_204,
inference(avatar_split_clause,[],[f202,f5242]) ).
fof(f5367,definition,
( spl18_205
<=> ! [X0] :
( closed_subset(sK1(sK10(sK14,sK15),X0),sK14)
| set_meet(sK10(sK14,sK15)) = X0
| ~ in(sK0(sK10(sK14,sK15),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl18_205])],[avatar_definition]) ).
fof(f5368,plain,
( ! [X0] :
( ~ in(sK0(sK10(sK14,sK15),X0),X0)
| set_meet(sK10(sK14,sK15)) = X0
| closed_subset(sK1(sK10(sK14,sK15),X0),sK14) )
| ~ spl18_205 ),
inference(avatar_component_clause,[],[f5367]) ).
fof(f5369,plain,
( spl18_205
| ~ spl18_27
| spl18_145 ),
inference(avatar_split_clause,[],[f5220,f3371,f634,f5367]) ).
fof(f5603,definition,
( spl18_217
<=> subset(sK15,sK16(sK10(sK14,sK15))) ),
introduced(definition,[new_symbols(definition,[spl18_217])],[avatar_definition]) ).
fof(f5605,plain,
( ~ subset(sK15,sK16(sK10(sK14,sK15)))
| spl18_217 ),
inference(avatar_component_clause,[],[f5603]) ).
fof(f5607,definition,
( spl18_218
<=> closed_subset(sK16(sK10(sK14,sK15)),sK14) ),
introduced(definition,[new_symbols(definition,[spl18_218])],[avatar_definition]) ).
fof(f5609,plain,
( ~ closed_subset(sK16(sK10(sK14,sK15)),sK14)
| spl18_218 ),
inference(avatar_component_clause,[],[f5607]) ).
fof(f5617,definition,
( spl18_220
<=> element(sK16(sK10(sK14,sK15)),powerset(the_carrier(sK14))) ),
introduced(definition,[new_symbols(definition,[spl18_220])],[avatar_definition]) ).
fof(f5618,plain,
( element(sK16(sK10(sK14,sK15)),powerset(the_carrier(sK14)))
| ~ spl18_220 ),
inference(avatar_component_clause,[],[f5617]) ).
fof(f5619,plain,
( ~ element(sK16(sK10(sK14,sK15)),powerset(the_carrier(sK14)))
| spl18_220 ),
inference(avatar_component_clause,[],[f5617]) ).
fof(f6276,definition,
( spl18_230
<=> in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),the_carrier(sK14)) ),
introduced(definition,[new_symbols(definition,[spl18_230])],[avatar_definition]) ).
fof(f6277,plain,
( in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),the_carrier(sK14))
| ~ spl18_230 ),
inference(avatar_component_clause,[],[f6276]) ).
fof(f6278,plain,
( ~ in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),the_carrier(sK14))
| spl18_230 ),
inference(avatar_component_clause,[],[f6276]) ).
fof(f6280,definition,
( spl18_231
<=> in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),topstr_closure(sK14,sK15)) ),
introduced(definition,[new_symbols(definition,[spl18_231])],[avatar_definition]) ).
fof(f6281,plain,
( ~ in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),topstr_closure(sK14,sK15))
| spl18_231 ),
inference(avatar_component_clause,[],[f6280]) ).
fof(f6282,plain,
( in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),topstr_closure(sK14,sK15))
| ~ spl18_231 ),
inference(avatar_component_clause,[],[f6280]) ).
fof(f7974,definition,
( spl18_316
<=> ! [X0,X1] :
( ~ in(X0,the_carrier(sK14))
| in(X0,topstr_closure(sK14,sK15))
| set_meet(sK10(sK14,sK15)) = X1
| in(sK0(sK10(sK14,sK15),X1),sK13(sK14,sK15,X0))
| in(sK0(sK10(sK14,sK15),X1),X1) ) ),
introduced(definition,[new_symbols(definition,[spl18_316])],[avatar_definition]) ).
fof(f7975,plain,
( ! [X0,X1] :
( in(sK0(sK10(sK14,sK15),X1),sK13(sK14,sK15,X0))
| in(X0,topstr_closure(sK14,sK15))
| set_meet(sK10(sK14,sK15)) = X1
| ~ in(X0,the_carrier(sK14))
| in(sK0(sK10(sK14,sK15),X1),X1) )
| ~ spl18_316 ),
inference(avatar_component_clause,[],[f7974]) ).
fof(f7976,plain,
( spl18_316
| ~ spl18_57
| spl18_145 ),
inference(avatar_split_clause,[],[f5215,f3371,f1281,f7974]) ).
fof(f7981,plain,
( ! [X0] :
( in(sK0(sK10(sK14,sK15),X0),topstr_closure(sK14,sK15))
| set_meet(sK10(sK14,sK15)) = X0
| ~ in(sK0(sK10(sK14,sK15),X0),the_carrier(sK14))
| in(sK0(sK10(sK14,sK15),X0),X0)
| in(sK0(sK10(sK14,sK15),X0),topstr_closure(sK14,sK15))
| ~ in(sK0(sK10(sK14,sK15),X0),the_carrier(sK14)) )
| ~ spl18_28
| ~ spl18_316 ),
inference(resolution,[],[f7975,f652]) ).
fof(f7995,plain,
( ! [X0] :
( in(sK0(sK10(sK14,sK15),X0),topstr_closure(sK14,sK15))
| set_meet(sK10(sK14,sK15)) = X0
| ~ in(sK0(sK10(sK14,sK15),X0),the_carrier(sK14))
| in(sK0(sK10(sK14,sK15),X0),X0) )
| ~ spl18_28
| ~ spl18_316 ),
inference(duplicate_literal_removal,[],[f7981]) ).
fof(f8002,plain,
( ! [X0] :
( in(sK0(sK10(sK14,sK15),X0),topstr_closure(sK14,sK15))
| set_meet(sK10(sK14,sK15)) = X0
| in(sK0(sK10(sK14,sK15),X0),X0) )
| ~ spl18_28
| ~ spl18_200
| ~ spl18_316 ),
inference(forward_subsumption_resolution,[],[f7995,f4882]) ).
fof(f8007,definition,
( spl18_317
<=> ! [X0] :
( in(sK0(sK10(sK14,sK15),X0),topstr_closure(sK14,sK15))
| set_meet(sK10(sK14,sK15)) = X0
| in(sK0(sK10(sK14,sK15),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl18_317])],[avatar_definition]) ).
fof(f8008,plain,
( ! [X0] :
( in(sK0(sK10(sK14,sK15),X0),topstr_closure(sK14,sK15))
| set_meet(sK10(sK14,sK15)) = X0
| in(sK0(sK10(sK14,sK15),X0),X0) )
| ~ spl18_317 ),
inference(avatar_component_clause,[],[f8007]) ).
fof(f8009,plain,
( spl18_317
| ~ spl18_28
| ~ spl18_200
| ~ spl18_316 ),
inference(avatar_split_clause,[],[f8002,f7974,f4881,f651,f8007]) ).
fof(f8025,plain,
( in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),topstr_closure(sK14,sK15))
| topstr_closure(sK14,sK15) = set_meet(sK10(sK14,sK15))
| ~ spl18_317 ),
inference(factoring,[],[f8008]) ).
fof(f9200,definition,
( spl18_371
<=> ! [X0] :
( element(sK1(sK10(sK14,sK15),X0),powerset(the_carrier(sK14)))
| set_meet(sK10(sK14,sK15)) = X0
| ~ in(sK0(sK10(sK14,sK15),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl18_371])],[avatar_definition]) ).
fof(f9201,plain,
( ! [X0] :
( element(sK1(sK10(sK14,sK15),X0),powerset(the_carrier(sK14)))
| set_meet(sK10(sK14,sK15)) = X0
| ~ in(sK0(sK10(sK14,sK15),X0),X0) )
| ~ spl18_371 ),
inference(avatar_component_clause,[],[f9200]) ).
fof(f9202,plain,
( spl18_371
| spl18_145
| ~ spl18_161 ),
inference(avatar_split_clause,[],[f5228,f4149,f3371,f9200]) ).
fof(f11307,definition,
( spl18_435
<=> empty(sK15) ),
introduced(definition,[new_symbols(definition,[spl18_435])],[avatar_definition]) ).
fof(f11308,plain,
( empty(sK15)
| ~ spl18_435 ),
inference(avatar_component_clause,[],[f11307]) ).
fof(f11309,plain,
( ~ empty(sK15)
| spl18_435 ),
inference(avatar_component_clause,[],[f11307]) ).
fof(f11312,definition,
( spl18_436
<=> ! [X0] : ~ element(X0,sK15) ),
introduced(definition,[new_symbols(definition,[spl18_436])],[avatar_definition]) ).
fof(f11313,plain,
( ! [X0] : ~ element(X0,sK15)
| ~ spl18_436 ),
inference(avatar_component_clause,[],[f11312]) ).
fof(f11315,plain,
( $false
| ~ spl18_436 ),
inference(resolution,[],[f11313,f172]) ).
fof(f11321,plain,
~ spl18_436,
inference(avatar_contradiction_clause,[],[f11315]) ).
fof(f11322,plain,
( ! [X0] : ~ element(X0,sK15)
| ~ spl18_138
| spl18_435 ),
inference(forward_subsumption_resolution,[],[f3936,f11309]) ).
fof(f11326,plain,
( spl18_436
| ~ spl18_138
| spl18_435 ),
inference(avatar_split_clause,[],[f11322,f11307,f3295,f11312]) ).
fof(f11332,plain,
( empty_set = sK15
| ~ spl18_435 ),
inference(resolution,[],[f11308,f221]) ).
fof(f11341,definition,
( spl18_437
<=> empty_set = sK15 ),
introduced(definition,[new_symbols(definition,[spl18_437])],[avatar_definition]) ).
fof(f11343,plain,
( empty_set = sK15
| ~ spl18_437 ),
inference(avatar_component_clause,[],[f11341]) ).
fof(f11344,plain,
( spl18_437
| ~ spl18_435 ),
inference(avatar_split_clause,[],[f11332,f11307,f11341]) ).
fof(f13395,plain,
( in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15))
| ~ closed_subset(sK16(sK10(sK14,sK15)),sK14)
| ~ subset(sK15,sK16(sK10(sK14,sK15)))
| ~ spl18_29
| ~ spl18_220 ),
inference(resolution,[],[f5618,f663]) ).
fof(f13473,definition,
( spl18_479
<=> in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15)) ),
introduced(definition,[new_symbols(definition,[spl18_479])],[avatar_definition]) ).
fof(f13474,plain,
( ~ in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15))
| spl18_479 ),
inference(avatar_component_clause,[],[f13473]) ).
fof(f13475,plain,
( in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15))
| ~ spl18_479 ),
inference(avatar_component_clause,[],[f13473]) ).
fof(f13476,plain,
( ~ spl18_217
| ~ spl18_218
| spl18_479
| ~ spl18_29
| ~ spl18_220 ),
inference(avatar_split_clause,[],[f13395,f5617,f662,f13473,f5607,f5603]) ).
fof(f13657,plain,
( element(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),the_carrier(sK14))
| ~ spl18_107
| ~ spl18_231 ),
inference(resolution,[],[f6282,f2548]) ).
fof(f13658,plain,
( ! [X0] :
( in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),X0)
| ~ closed_subset(X0,sK14)
| ~ subset(sK15,X0)
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),the_carrier(sK14))
| ~ element(sK15,powerset(the_carrier(sK14)))
| ~ top_str(sK14) )
| ~ spl18_231 ),
inference(resolution,[],[f6282,f207]) ).
fof(f13666,plain,
( ~ sP17(topstr_closure(sK14,sK15))
| ~ spl18_231 ),
inference(resolution,[],[f6282,f233]) ).
fof(f13722,definition,
( spl18_484
<=> element(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),the_carrier(sK14)) ),
introduced(definition,[new_symbols(definition,[spl18_484])],[avatar_definition]) ).
fof(f13724,plain,
( element(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),the_carrier(sK14))
| ~ spl18_484 ),
inference(avatar_component_clause,[],[f13722]) ).
fof(f13725,plain,
( spl18_484
| ~ spl18_107
| ~ spl18_231 ),
inference(avatar_split_clause,[],[f13657,f6280,f2547,f13722]) ).
fof(f13727,plain,
( in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),the_carrier(sK14))
| empty(the_carrier(sK14))
| ~ spl18_204
| ~ spl18_484 ),
inference(resolution,[],[f13724,f5243]) ).
fof(f13728,plain,
( empty(the_carrier(sK14))
| ~ spl18_204
| spl18_230
| ~ spl18_484 ),
inference(forward_subsumption_resolution,[],[f13727,f6278]) ).
fof(f13731,plain,
( $false
| spl18_37
| ~ spl18_204
| spl18_230
| ~ spl18_484 ),
inference(forward_subsumption_resolution,[],[f13728,f768]) ).
fof(f13732,plain,
( spl18_37
| ~ spl18_204
| spl18_230
| ~ spl18_484 ),
inference(avatar_contradiction_clause,[],[f13731]) ).
fof(f13734,plain,
( ! [X0] :
( in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),X0)
| ~ closed_subset(X0,sK14)
| ~ subset(sK15,X0)
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ element(sK15,powerset(the_carrier(sK14)))
| ~ top_str(sK14) )
| ~ spl18_230
| ~ spl18_231 ),
inference(forward_subsumption_resolution,[],[f13658,f6277]) ).
fof(f13738,plain,
( ! [X0] :
( in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),X0)
| ~ closed_subset(X0,sK14)
| ~ subset(sK15,X0)
| ~ element(X0,powerset(the_carrier(sK14)))
| ~ top_str(sK14) )
| ~ spl18_3
| ~ spl18_230
| ~ spl18_231 ),
inference(forward_subsumption_resolution,[],[f13734,f282]) ).
fof(f13740,plain,
( ! [X0] :
( in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),X0)
| ~ closed_subset(X0,sK14)
| ~ subset(sK15,X0)
| ~ element(X0,powerset(the_carrier(sK14))) )
| ~ spl18_1
| ~ spl18_3
| ~ spl18_230
| ~ spl18_231 ),
inference(forward_subsumption_resolution,[],[f13738,f238]) ).
fof(f13783,definition,
( spl18_485
<=> ! [X0] :
( in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),X0)
| ~ closed_subset(X0,sK14)
| ~ subset(sK15,X0)
| ~ element(X0,powerset(the_carrier(sK14))) ) ),
introduced(definition,[new_symbols(definition,[spl18_485])],[avatar_definition]) ).
fof(f13784,plain,
( ! [X0] :
( in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),X0)
| ~ closed_subset(X0,sK14)
| ~ subset(sK15,X0)
| ~ element(X0,powerset(the_carrier(sK14))) )
| ~ spl18_485 ),
inference(avatar_component_clause,[],[f13783]) ).
fof(f13785,plain,
( spl18_485
| ~ spl18_1
| ~ spl18_3
| ~ spl18_230
| ~ spl18_231 ),
inference(avatar_split_clause,[],[f13740,f6280,f6276,f280,f236,f13783]) ).
fof(f13812,plain,
( ~ closed_subset(sK1(sK10(sK14,sK15),topstr_closure(sK14,sK15)),sK14)
| ~ subset(sK15,sK1(sK10(sK14,sK15),topstr_closure(sK14,sK15)))
| ~ element(sK1(sK10(sK14,sK15),topstr_closure(sK14,sK15)),powerset(the_carrier(sK14)))
| topstr_closure(sK14,sK15) = set_meet(sK10(sK14,sK15))
| ~ in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),topstr_closure(sK14,sK15))
| empty_set = sK10(sK14,sK15)
| ~ spl18_485 ),
inference(resolution,[],[f13784,f164]) ).
fof(f13865,plain,
( ~ closed_subset(sK1(sK10(sK14,sK15),topstr_closure(sK14,sK15)),sK14)
| ~ element(sK1(sK10(sK14,sK15),topstr_closure(sK14,sK15)),powerset(the_carrier(sK14)))
| topstr_closure(sK14,sK15) = set_meet(sK10(sK14,sK15))
| ~ in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),topstr_closure(sK14,sK15))
| empty_set = sK10(sK14,sK15)
| ~ spl18_151
| ~ spl18_485 ),
inference(forward_subsumption_resolution,[],[f13812,f3859]) ).
fof(f13877,plain,
( ~ element(sK1(sK10(sK14,sK15),topstr_closure(sK14,sK15)),powerset(the_carrier(sK14)))
| topstr_closure(sK14,sK15) = set_meet(sK10(sK14,sK15))
| ~ in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),topstr_closure(sK14,sK15))
| empty_set = sK10(sK14,sK15)
| ~ spl18_151
| ~ spl18_205
| ~ spl18_485 ),
inference(forward_subsumption_resolution,[],[f13865,f5368]) ).
fof(f13888,plain,
( topstr_closure(sK14,sK15) = set_meet(sK10(sK14,sK15))
| ~ in(sK0(sK10(sK14,sK15),topstr_closure(sK14,sK15)),topstr_closure(sK14,sK15))
| empty_set = sK10(sK14,sK15)
| ~ spl18_151
| ~ spl18_205
| ~ spl18_371
| ~ spl18_485 ),
inference(forward_subsumption_resolution,[],[f13877,f9201]) ).
fof(f13895,plain,
( topstr_closure(sK14,sK15) = set_meet(sK10(sK14,sK15))
| empty_set = sK10(sK14,sK15)
| ~ spl18_151
| ~ spl18_205
| ~ spl18_231
| ~ spl18_371
| ~ spl18_485 ),
inference(forward_subsumption_resolution,[],[f13888,f6282]) ).
fof(f13901,plain,
( topstr_closure(sK14,sK15) = set_meet(sK10(sK14,sK15))
| spl18_145
| ~ spl18_151
| ~ spl18_205
| ~ spl18_231
| ~ spl18_371
| ~ spl18_485 ),
inference(forward_subsumption_resolution,[],[f13895,f3372]) ).
fof(f14351,plain,
( sP17(topstr_closure(sK14,sK15))
| ~ spl18_8
| ~ spl18_37 ),
inference(forward_subsumption_resolution,[],[f428,f767]) ).
fof(f15117,plain,
( ~ sP17(topstr_closure(sK14,empty_set))
| ~ spl18_231
| ~ spl18_437 ),
inference(forward_demodulation,[],[f13666,f11343]) ).
fof(f15120,plain,
( sP17(topstr_closure(sK14,empty_set))
| ~ spl18_8
| ~ spl18_37
| ~ spl18_437 ),
inference(forward_demodulation,[],[f14351,f11343]) ).
fof(f16354,plain,
( $false
| ~ spl18_8
| ~ spl18_37
| ~ spl18_231
| ~ spl18_437 ),
inference(forward_subsumption_resolution,[],[f15120,f15117]) ).
fof(f16355,plain,
( ~ spl18_8
| ~ spl18_37
| ~ spl18_231
| ~ spl18_437 ),
inference(avatar_contradiction_clause,[],[f16354]) ).
fof(f19231,definition,
( spl18_511
<=> topstr_closure(sK14,sK15) = set_meet(sK10(sK14,sK15)) ),
introduced(definition,[new_symbols(definition,[spl18_511])],[avatar_definition]) ).
fof(f19232,plain,
( topstr_closure(sK14,sK15) != set_meet(sK10(sK14,sK15))
| spl18_511 ),
inference(avatar_component_clause,[],[f19231]) ).
fof(f19233,plain,
( topstr_closure(sK14,sK15) = set_meet(sK10(sK14,sK15))
| ~ spl18_511 ),
inference(avatar_component_clause,[],[f19231]) ).
fof(f19234,plain,
( spl18_511
| spl18_145
| ~ spl18_151
| ~ spl18_205
| ~ spl18_231
| ~ spl18_371
| ~ spl18_485 ),
inference(avatar_split_clause,[],[f13901,f13783,f9200,f6280,f5367,f3858,f3371,f19231]) ).
fof(f19434,plain,
( topstr_closure(sK14,sK15) != topstr_closure(sK14,sK15)
| subset(sK15,sK16(sK10(sK14,sK15)))
| in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15))
| ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_20
| ~ spl18_511 ),
inference(superposition,[],[f559,f19233]) ).
fof(f19440,plain,
( subset(sK15,sK16(sK10(sK14,sK15)))
| in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15))
| ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_20
| ~ spl18_511 ),
inference(trivial_inequality_removal,[],[f19434]) ).
fof(f19444,plain,
( in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15))
| ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_20
| spl18_217
| ~ spl18_511 ),
inference(forward_subsumption_resolution,[],[f19440,f5605]) ).
fof(f19456,plain,
( ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_20
| spl18_217
| spl18_479
| ~ spl18_511 ),
inference(forward_subsumption_resolution,[],[f19444,f13474]) ).
fof(f19457,plain,
( $false
| ~ spl18_11
| ~ spl18_20
| spl18_217
| spl18_479
| ~ spl18_511 ),
inference(forward_subsumption_resolution,[],[f19456,f468]) ).
fof(f19458,plain,
( ~ spl18_11
| ~ spl18_20
| spl18_217
| spl18_479
| ~ spl18_511 ),
inference(avatar_contradiction_clause,[],[f19457]) ).
fof(f19520,plain,
( topstr_closure(sK14,sK15) = set_meet(sK10(sK14,sK15))
| spl18_231
| ~ spl18_317 ),
inference(forward_subsumption_resolution,[],[f8025,f6281]) ).
fof(f19570,plain,
( $false
| spl18_231
| ~ spl18_317
| spl18_511 ),
inference(forward_subsumption_resolution,[],[f19520,f19232]) ).
fof(f19571,plain,
( spl18_231
| ~ spl18_317
| spl18_511 ),
inference(avatar_contradiction_clause,[],[f19570]) ).
fof(f20341,plain,
( topstr_closure(sK14,sK15) != topstr_closure(sK14,sK15)
| ~ closed_subset(sK16(sK10(sK14,sK15)),sK14)
| ~ subset(sK15,sK16(sK10(sK14,sK15)))
| ~ in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15))
| ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_9
| ~ spl18_511 ),
inference(superposition,[],[f388,f19233]) ).
fof(f20343,plain,
( topstr_closure(sK14,sK15) != topstr_closure(sK14,sK15)
| closed_subset(sK16(sK10(sK14,sK15)),sK14)
| in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15))
| ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_22
| ~ spl18_511 ),
inference(superposition,[],[f573,f19233]) ).
fof(f20344,plain,
( topstr_closure(sK14,sK15) != topstr_closure(sK14,sK15)
| element(sK16(sK10(sK14,sK15)),powerset(the_carrier(sK14)))
| ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_40
| ~ spl18_511 ),
inference(superposition,[],[f861,f19233]) ).
fof(f20346,plain,
( element(sK16(sK10(sK14,sK15)),powerset(the_carrier(sK14)))
| ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_40
| ~ spl18_511 ),
inference(trivial_inequality_removal,[],[f20344]) ).
fof(f20347,plain,
( closed_subset(sK16(sK10(sK14,sK15)),sK14)
| in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15))
| ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_22
| ~ spl18_511 ),
inference(trivial_inequality_removal,[],[f20343]) ).
fof(f20349,plain,
( ~ closed_subset(sK16(sK10(sK14,sK15)),sK14)
| ~ subset(sK15,sK16(sK10(sK14,sK15)))
| ~ in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15))
| ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_9
| ~ spl18_511 ),
inference(trivial_inequality_removal,[],[f20341]) ).
fof(f20352,plain,
( ~ subset(sK15,sK16(sK10(sK14,sK15)))
| ~ in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15))
| ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_9
| ~ spl18_27
| ~ spl18_511 ),
inference(forward_subsumption_resolution,[],[f20349,f635]) ).
fof(f20363,plain,
( ~ in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15))
| ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_9
| ~ spl18_18
| ~ spl18_27
| ~ spl18_511 ),
inference(forward_subsumption_resolution,[],[f20352,f540]) ).
fof(f20364,plain,
( ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_9
| ~ spl18_18
| ~ spl18_27
| ~ spl18_479
| ~ spl18_511 ),
inference(forward_subsumption_resolution,[],[f20363,f13475]) ).
fof(f20365,plain,
( $false
| ~ spl18_9
| ~ spl18_11
| ~ spl18_18
| ~ spl18_27
| ~ spl18_479
| ~ spl18_511 ),
inference(forward_subsumption_resolution,[],[f20364,f468]) ).
fof(f20366,plain,
( ~ spl18_9
| ~ spl18_11
| ~ spl18_18
| ~ spl18_27
| ~ spl18_479
| ~ spl18_511 ),
inference(avatar_contradiction_clause,[],[f20365]) ).
fof(f20375,plain,
( in(sK16(sK10(sK14,sK15)),sK10(sK14,sK15))
| ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_22
| spl18_218
| ~ spl18_511 ),
inference(forward_subsumption_resolution,[],[f20347,f5609]) ).
fof(f20383,plain,
( ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_22
| spl18_218
| spl18_479
| ~ spl18_511 ),
inference(forward_subsumption_resolution,[],[f20375,f13474]) ).
fof(f20386,plain,
( $false
| ~ spl18_11
| ~ spl18_22
| spl18_218
| spl18_479
| ~ spl18_511 ),
inference(forward_subsumption_resolution,[],[f20383,f468]) ).
fof(f20387,plain,
( ~ spl18_11
| ~ spl18_22
| spl18_218
| spl18_479
| ~ spl18_511 ),
inference(avatar_contradiction_clause,[],[f20386]) ).
fof(f20392,plain,
( ~ element(sK10(sK14,sK15),powerset(powerset(the_carrier(sK14))))
| ~ spl18_40
| spl18_220
| ~ spl18_511 ),
inference(forward_subsumption_resolution,[],[f20346,f5619]) ).
fof(f20398,plain,
( $false
| ~ spl18_11
| ~ spl18_40
| spl18_220
| ~ spl18_511 ),
inference(forward_subsumption_resolution,[],[f20392,f468]) ).
fof(f20399,plain,
( ~ spl18_11
| ~ spl18_40
| spl18_220
| ~ spl18_511 ),
inference(avatar_contradiction_clause,[],[f20398]) ).
cnf(s1,plain,
spl18_1,
inference(sat_conversion,[],[f239]) ).
cnf(s2,plain,
spl18_2,
inference(sat_conversion,[],[f244]) ).
cnf(s3,plain,
spl18_3,
inference(sat_conversion,[],[f283]) ).
cnf(s4,plain,
spl18_4,
inference(sat_conversion,[],[f354]) ).
cnf(s5,plain,
spl18_5,
inference(sat_conversion,[],[f360]) ).
cnf(s6,plain,
( ~ spl18_1
| ~ spl18_2
| spl18_6 ),
inference(sat_conversion,[],[f367]) ).
cnf(s7,plain,
spl18_7,
inference(sat_conversion,[],[f378]) ).
cnf(s8,plain,
( ~ spl18_1
| ~ spl18_3
| spl18_8 ),
inference(sat_conversion,[],[f385]) ).
cnf(s9,plain,
( ~ spl18_4
| spl18_9 ),
inference(sat_conversion,[],[f389]) ).
cnf(s11,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| spl18_11 ),
inference(sat_conversion,[],[f469]) ).
cnf(s13,plain,
( ~ spl18_3
| spl18_13 ),
inference(sat_conversion,[],[f511]) ).
cnf(s15,plain,
( ~ spl18_1
| spl18_15 ),
inference(sat_conversion,[],[f521]) ).
cnf(s16,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| spl18_16 ),
inference(sat_conversion,[],[f529]) ).
cnf(s17,plain,
spl18_17,
inference(sat_conversion,[],[f534]) ).
cnf(s18,plain,
( ~ spl18_11
| ~ spl18_16
| spl18_18 ),
inference(sat_conversion,[],[f541]) ).
cnf(s19,plain,
( ~ spl18_15
| spl18_19 ),
inference(sat_conversion,[],[f556]) ).
cnf(s20,plain,
( ~ spl18_7
| spl18_20 ),
inference(sat_conversion,[],[f560]) ).
cnf(s21,plain,
( ~ spl18_1
| ~ spl18_3
| spl18_21 ),
inference(sat_conversion,[],[f567]) ).
cnf(s22,plain,
( ~ spl18_5
| spl18_22 ),
inference(sat_conversion,[],[f574]) ).
cnf(s24,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| spl18_24 ),
inference(sat_conversion,[],[f608]) ).
cnf(s25,plain,
( ~ spl18_11
| ~ spl18_24
| spl18_25 ),
inference(sat_conversion,[],[f613]) ).
cnf(s27,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| ~ spl18_11
| ~ spl18_25
| spl18_27 ),
inference(sat_conversion,[],[f636]) ).
cnf(s28,plain,
( ~ spl18_1
| ~ spl18_3
| spl18_28 ),
inference(sat_conversion,[],[f653]) ).
cnf(s29,plain,
( ~ spl18_1
| ~ spl18_2
| ~ spl18_3
| spl18_29 ),
inference(sat_conversion,[],[f664]) ).
cnf(s30,plain,
( ~ spl18_6
| ~ spl18_13
| ~ spl18_15
| ~ spl18_19
| ~ spl18_29
| spl18_30 ),
inference(sat_conversion,[],[f698]) ).
cnf(s35,plain,
( ~ spl18_3
| spl18_36
| ~ spl18_37 ),
inference(sat_conversion,[],[f769]) ).
cnf(s38,plain,
( ~ spl18_17
| spl18_40 ),
inference(sat_conversion,[],[f862]) ).
cnf(s39,plain,
( ~ spl18_1
| ~ spl18_3
| spl18_41 ),
inference(sat_conversion,[],[f869]) ).
cnf(s56,plain,
( ~ spl18_1
| ~ spl18_3
| ~ spl18_21
| ~ spl18_29
| ~ spl18_41
| spl18_57 ),
inference(sat_conversion,[],[f1283]) ).
cnf(s107,plain,
( ~ spl18_8
| spl18_107 ),
inference(sat_conversion,[],[f2549]) ).
cnf(s143,plain,
( ~ spl18_36
| spl18_138 ),
inference(sat_conversion,[],[f3297]) ).
cnf(s160,plain,
( ~ spl18_18
| spl18_145
| spl18_151 ),
inference(sat_conversion,[],[f3860]) ).
cnf(s172,plain,
( ~ spl18_11
| spl18_161 ),
inference(sat_conversion,[],[f4151]) ).
cnf(s210,plain,
( ~ spl18_30
| ~ spl18_145
| spl18_199 ),
inference(sat_conversion,[],[f4741]) ).
cnf(s211,plain,
( ~ spl18_30
| spl18_145
| spl18_200 ),
inference(sat_conversion,[],[f4883]) ).
cnf(s218,plain,
~ spl18_199,
inference(sat_conversion,[],[f5172]) ).
cnf(s219,plain,
spl18_204,
inference(sat_conversion,[],[f5244]) ).
cnf(s220,plain,
( ~ spl18_27
| spl18_145
| spl18_205 ),
inference(sat_conversion,[],[f5369]) ).
cnf(s330,plain,
( ~ spl18_57
| spl18_145
| spl18_316 ),
inference(sat_conversion,[],[f7976]) ).
cnf(s331,plain,
( ~ spl18_28
| ~ spl18_200
| ~ spl18_316
| spl18_317 ),
inference(sat_conversion,[],[f8009]) ).
cnf(s386,plain,
( spl18_145
| ~ spl18_161
| spl18_371 ),
inference(sat_conversion,[],[f9202]) ).
cnf(s452,plain,
~ spl18_436,
inference(sat_conversion,[],[f11321]) ).
cnf(s453,plain,
( ~ spl18_138
| spl18_435
| spl18_436 ),
inference(sat_conversion,[],[f11326]) ).
cnf(s454,plain,
( ~ spl18_435
| spl18_437 ),
inference(sat_conversion,[],[f11344]) ).
cnf(s505,plain,
( ~ spl18_29
| ~ spl18_217
| ~ spl18_218
| ~ spl18_220
| spl18_479 ),
inference(sat_conversion,[],[f13476]) ).
cnf(s520,plain,
( ~ spl18_107
| ~ spl18_231
| spl18_484 ),
inference(sat_conversion,[],[f13725]) ).
cnf(s522,plain,
( spl18_37
| ~ spl18_204
| spl18_230
| ~ spl18_484 ),
inference(sat_conversion,[],[f13732]) ).
cnf(s523,plain,
( ~ spl18_1
| ~ spl18_3
| ~ spl18_230
| ~ spl18_231
| spl18_485 ),
inference(sat_conversion,[],[f13785]) ).
cnf(s613,plain,
( ~ spl18_8
| ~ spl18_37
| ~ spl18_231
| ~ spl18_437 ),
inference(sat_conversion,[],[f16355]) ).
cnf(s739,plain,
( spl18_145
| ~ spl18_151
| ~ spl18_205
| ~ spl18_231
| ~ spl18_371
| ~ spl18_485
| spl18_511 ),
inference(sat_conversion,[],[f19234]) ).
cnf(s745,plain,
( ~ spl18_11
| ~ spl18_20
| spl18_217
| spl18_479
| ~ spl18_511 ),
inference(sat_conversion,[],[f19458]) ).
cnf(s749,plain,
( spl18_231
| ~ spl18_317
| spl18_511 ),
inference(sat_conversion,[],[f19571]) ).
cnf(s780,plain,
( ~ spl18_9
| ~ spl18_11
| ~ spl18_18
| ~ spl18_27
| ~ spl18_479
| ~ spl18_511 ),
inference(sat_conversion,[],[f20366]) ).
cnf(s782,plain,
( ~ spl18_11
| ~ spl18_22
| spl18_218
| spl18_479
| ~ spl18_511 ),
inference(sat_conversion,[],[f20387]) ).
cnf(s784,plain,
( ~ spl18_11
| ~ spl18_40
| spl18_220
| ~ spl18_511 ),
inference(sat_conversion,[],[f20399]) ).
cnf(s789,plain,
( ~ spl18_30
| ~ spl18_145 ),
inference(rat,[],[s210,s218]) ).
cnf(s790,plain,
spl18_40,
inference(rat,[],[s38,s17]) ).
cnf(s791,plain,
spl18_20,
inference(rat,[],[s20,s7]) ).
cnf(s792,plain,
spl18_22,
inference(rat,[],[s22,s5]) ).
cnf(s793,plain,
spl18_9,
inference(rat,[],[s9,s4]) ).
cnf(s796,plain,
spl18_13,
inference(rat,[],[s13,s3]) ).
cnf(s816,plain,
spl18_41,
inference(rat,[],[s39,s3,s1]) ).
cnf(s817,plain,
spl18_29,
inference(rat,[],[s29,s2,s3,s1]) ).
cnf(s818,plain,
spl18_28,
inference(rat,[],[s28,s3,s1]) ).
cnf(s820,plain,
spl18_24,
inference(rat,[],[s24,s2,s3,s1]) ).
cnf(s822,plain,
spl18_21,
inference(rat,[],[s21,s3,s1]) ).
cnf(s823,plain,
spl18_16,
inference(rat,[],[s16,s2,s3,s1]) ).
cnf(s824,plain,
spl18_15,
inference(rat,[],[s15,s1]) ).
cnf(s825,plain,
spl18_11,
inference(rat,[],[s11,s2,s3,s1]) ).
cnf(s826,plain,
spl18_8,
inference(rat,[],[s8,s3,s1]) ).
cnf(s827,plain,
spl18_6,
inference(rat,[],[s6,s2,s1]) ).
cnf(s856,plain,
spl18_57,
inference(rat,[],[s56,s817,s816,s1,s3,s822]) ).
cnf(s858,plain,
spl18_19,
inference(rat,[],[s19,s824]) ).
cnf(s859,plain,
spl18_161,
inference(rat,[],[s172,s825]) ).
cnf(s864,plain,
spl18_25,
inference(rat,[],[s25,s820,s825]) ).
cnf(s865,plain,
spl18_18,
inference(rat,[],[s18,s823,s825]) ).
cnf(s869,plain,
spl18_107,
inference(rat,[],[s107,s826]) ).
cnf(s873,plain,
spl18_30,
inference(rat,[],[s30,s824,s817,s858,s796,s827]) ).
cnf(s904,plain,
spl18_27,
inference(rat,[],[s27,s825,s1,s2,s3,s864]) ).
cnf(s914,plain,
~ spl18_145,
inference(rat,[],[s789,s873]) ).
cnf(s954,plain,
spl18_371,
inference(rat,[],[s386,s859,s914]) ).
cnf(s956,plain,
spl18_316,
inference(rat,[],[s330,s856,s914]) ).
cnf(s961,plain,
spl18_205,
inference(rat,[],[s220,s904,s914]) ).
cnf(s962,plain,
spl18_200,
inference(rat,[],[s211,s873,s914]) ).
cnf(s963,plain,
spl18_151,
inference(rat,[],[s160,s865,s914]) ).
cnf(s992,plain,
spl18_317,
inference(rat,[],[s331,s956,s818,s962]) ).
cnf(s1013,plain,
( spl18_511
| spl18_37 ),
inference(rat,[],[s522,s523,s520,s739,s749,s219,s3,s1,s869,s914,s961,s954,s963,s992]) ).
cnf(s1014,plain,
~ spl18_511,
inference(rat,[],[s505,s745,s782,s780,s784,s817,s791,s825,s792,s793,s865,s904,s790]) ).
cnf(s1015,plain,
spl18_231,
inference(rat,[],[s749,s992,s1014]) ).
cnf(s1017,plain,
spl18_37,
inference(rat,[],[s1013,s1014]) ).
cnf(s1020,plain,
~ spl18_437,
inference(rat,[],[s613,s1015,s826,s1017]) ).
cnf(s1031,plain,
spl18_36,
inference(rat,[],[s35,s3,s1017]) ).
cnf(s1033,plain,
~ spl18_435,
inference(rat,[],[s454,s1020]) ).
cnf(s1044,plain,
spl18_138,
inference(rat,[],[s143,s1031]) ).
cnf(s1045,plain,
$false,
inference(rat,[],[s453,s452,s1033,s1044]) ).
fof(f20405,plain,
$false,
inference(avatar_sat_refutation,[],[s1045]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU316+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 04:39:22 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.73/3.08 % (804768)Detected formulas, will run a generic FOF schedule.
% 15.73/3.08 % (804774)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1818037267:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 15.73/3.08 % (804775)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3196814989:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 15.73/3.08 % (804773)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2301715098:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 15.73/3.08 % (804776)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=810017104:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 15.73/3.08 % (804777)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3963375431:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 15.73/3.08 % (804779)dis-21_1_sil=8000:lcm=predicate:random_seed=1694588862:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 15.73/3.08 % (804778)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3642821136:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 15.73/3.08 % (804776)Refutation not found, incomplete strategy
% 15.73/3.08 % (804776)------------------------------
% 15.73/3.08 % (804776)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.73/3.08 % (804776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.73/3.08 % (804776)CaDiCaL version: 2.1.3
% 15.73/3.08 % (804776)Termination reason: Refutation not found, incomplete strategy
% 15.73/3.08 % (804776)Time elapsed: 0.015 s
% 15.73/3.08 % (804776)Peak memory usage: 88 MB
% 15.73/3.08 % (804776)Instructions burned: 23 (million)
% 15.73/3.08 % (804777)Instruction limit reached!
% 15.73/3.08 % (804777)------------------------------
% 15.73/3.08 % (804777)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.73/3.08 % (804777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.73/3.08 % (804777)CaDiCaL version: 2.1.3
% 15.73/3.08 % (804777)Termination reason: Instruction limit
% 15.73/3.08 % (804777)Termination phase: Saturation
% 15.73/3.08 % (804777)Time elapsed: 0.073 s
% 15.73/3.08 % (804777)Peak memory usage: 88 MB
% 15.73/3.08 % (804777)Instructions burned: 120 (million)
% 15.73/3.08 % (804779)Instruction limit reached!
% 15.73/3.08 % (804779)------------------------------
% 15.73/3.08 % (804779)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.73/3.08 % (804779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.73/3.08 % (804779)CaDiCaL version: 2.1.3
% 15.73/3.08 % (804779)Termination reason: Instruction limit
% 15.73/3.08 % (804779)Termination phase: Saturation
% 15.73/3.08 % (804779)Time elapsed: 0.074 s
% 15.73/3.08 % (804779)Peak memory usage: 89 MB
% 15.73/3.08 % (804779)Instructions burned: 130 (million)
% 15.73/3.08 % (804778)Instruction limit reached!
% 15.73/3.08 % (804778)------------------------------
% 15.73/3.08 % (804778)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.73/3.08 % (804778)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 15.73/3.08 % (804778)CaDiCaL version: 2.1.3
% 15.73/3.08 % (804778)Termination reason: Instruction limit
% 15.73/3.08 % (804778)Termination phase: Saturation
% 15.73/3.08 % (804778)Time elapsed: 0.097 s
% 15.73/3.08 % (804778)Peak memory usage: 90 MB
% 15.73/3.08 % (804778)Instructions burned: 139 (million)
% 15.73/3.08 % (804788)lrs+10_1_sil=32000:urr=on:br=off:random_seed=204479881:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 15.73/3.08 % (804787)lrs+10_1_sil=8000:sp=occurrence:random_seed=434514870:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 15.73/3.08 % (804789)lrs+1011_1_sil=32000:sp=occurrence:random_seed=376633082:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 15.73/3.08 % (804776)------------------------------
% 15.73/3.08 % (804776)------------------------------
% 15.73/3.08 % (804788)Instruction limit reached!
% 15.73/3.08 % (804788)------------------------------
% 15.73/3.08 % (804788)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 15.73/3.08 % (804788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.22/4.02 % (804788)CaDiCaL version: 2.1.3
% 21.22/4.02 % (804788)Termination reason: Instruction limit
% 21.22/4.02 % (804788)Termination phase: Saturation
% 21.22/4.02 % (804788)Time elapsed: 0.095 s
% 21.22/4.02 % (804788)Peak memory usage: 90 MB
% 21.22/4.02 % (804788)Instructions burned: 158 (million)
% 21.22/4.02 % (804787)Instruction limit reached!
% 21.22/4.02 % (804787)------------------------------
% 21.22/4.02 % (804787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.22/4.02 % (804787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.22/4.02 % (804787)CaDiCaL version: 2.1.3
% 21.22/4.02 % (804787)Termination reason: Instruction limit
% 21.22/4.02 % (804787)Termination phase: Saturation
% 21.22/4.02 % (804787)Time elapsed: 0.168 s
% 21.22/4.02 % (804787)Peak memory usage: 91 MB
% 21.22/4.02 % (804787)Instructions burned: 285 (million)
% 21.22/4.02 % (804793)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2641176797:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 21.22/4.02 % (804789)Instruction limit reached!
% 21.22/4.02 % (804789)------------------------------
% 21.22/4.02 % (804789)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.22/4.02 % (804789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.22/4.02 % (804789)CaDiCaL version: 2.1.3
% 21.22/4.02 % (804789)Termination reason: Instruction limit
% 21.22/4.02 % (804789)Termination phase: Saturation
% 21.22/4.02 % (804789)Time elapsed: 0.210 s
% 21.22/4.02 % (804789)Peak memory usage: 91 MB
% 21.22/4.02 % (804789)Instructions burned: 325 (million)
% 21.22/4.02 % (804794)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2396982693:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 21.22/4.02 % (804795)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=905853731:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 21.22/4.02 % (804793)Instruction limit reached!
% 21.22/4.02 % (804793)------------------------------
% 21.22/4.02 % (804793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.22/4.02 % (804793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.22/4.02 % (804793)CaDiCaL version: 2.1.3
% 21.22/4.02 % (804793)Termination reason: Instruction limit
% 21.22/4.02 % (804793)Termination phase: Saturation
% 21.22/4.02 % (804793)Time elapsed: 0.142 s
% 21.22/4.02 % (804793)Peak memory usage: 90 MB
% 21.22/4.02 % (804793)Instructions burned: 248 (million)
% 21.22/4.02 % (804797)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=4147532029:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 21.22/4.02 % (804794)Instruction limit reached!
% 21.22/4.02 % (804794)------------------------------
% 21.22/4.02 % (804794)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.22/4.02 % (804794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.22/4.02 % (804794)CaDiCaL version: 2.1.3
% 21.22/4.02 % (804794)Termination reason: Instruction limit
% 21.22/4.02 % (804794)Termination phase: Saturation
% 21.22/4.02 % (804794)Time elapsed: 0.167 s
% 21.22/4.02 % (804794)Peak memory usage: 89 MB
% 21.22/4.02 % (804794)Instructions burned: 296 (million)
% 21.22/4.02 % (804797)Instruction limit reached!
% 21.22/4.02 % (804797)------------------------------
% 21.22/4.02 % (804797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.22/4.02 % (804797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.22/4.02 % (804797)CaDiCaL version: 2.1.3
% 21.22/4.02 % (804797)Termination reason: Instruction limit
% 21.22/4.02 % (804797)Termination phase: Saturation
% 21.22/4.02 % (804797)Time elapsed: 0.079 s
% 21.22/4.02 % (804797)Peak memory usage: 90 MB
% 21.22/4.02 % (804797)Instructions burned: 114 (million)
% 21.22/4.02 % (804800)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=868498803:i=127:av=off:fsr=off:sup=off_2992 on theBenchmark for (2992ds/127Mi)
% 21.22/4.02 % (804800)Instruction limit reached!
% 21.22/4.02 % (804800)------------------------------
% 21.22/4.02 % (804800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 21.22/4.02 % (804800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 21.22/4.02 % (804800)CaDiCaL version: 2.1.3
% 21.22/4.02 % (804800)Termination reason: Instruction limit
% 21.22/4.02 % (804800)Termination phase: Saturation
% 21.22/4.02 % (804800)Time elapsed: 0.064 s
% 20.47/4.23 % (804800)Peak memory usage: 88 MB
% 20.47/4.23 % (804800)Instructions burned: 128 (million)
% 20.47/4.23 % (804802)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=58784476:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2991 on theBenchmark for (2991ds/114Mi)
% 20.47/4.23 % (804803)lrs+10_1_sil=8000:sp=occurrence:random_seed=102191232:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 20.47/4.23 % (804802)Instruction limit reached!
% 20.47/4.23 % (804802)------------------------------
% 20.47/4.23 % (804802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.47/4.23 % (804802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.47/4.23 % (804802)CaDiCaL version: 2.1.3
% 20.47/4.23 % (804802)Termination reason: Instruction limit
% 20.47/4.23 % (804802)Termination phase: Saturation
% 20.47/4.23 % (804802)Time elapsed: 0.071 s
% 20.47/4.23 % (804802)Peak memory usage: 89 MB
% 20.47/4.23 % (804802)Instructions burned: 114 (million)
% 20.47/4.23 % (804806)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2879933547:i=437:sd=1:aac=none:ss=included_2990 on theBenchmark for (2990ds/437Mi)
% 20.47/4.23 % (804808)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3918688439:i=5202:ss=axioms:sgt=16_2989 on theBenchmark for (2989ds/5202Mi)
% 20.47/4.23 % (804806)Instruction limit reached!
% 20.47/4.23 % (804806)------------------------------
% 20.47/4.23 % (804806)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.47/4.23 % (804806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.47/4.23 % (804806)CaDiCaL version: 2.1.3
% 20.47/4.23 % (804806)Termination reason: Instruction limit
% 20.47/4.23 % (804806)Termination phase: Saturation
% 20.47/4.23 % (804806)Time elapsed: 0.216 s
% 20.47/4.23 % (804806)Peak memory usage: 91 MB
% 20.47/4.23 % (804806)Instructions burned: 437 (million)
% 20.47/4.23 % (804811)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=4225845087:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2986 on theBenchmark for (2986ds/134Mi)
% 20.47/4.23 % (804803)Instruction limit reached!
% 20.47/4.23 % (804803)------------------------------
% 20.47/4.23 % (804803)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.47/4.23 % (804803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.47/4.23 % (804803)CaDiCaL version: 2.1.3
% 20.47/4.23 % (804803)Termination reason: Instruction limit
% 20.47/4.23 % (804803)Termination phase: Saturation
% 20.47/4.23 % (804803)Time elapsed: 0.518 s
% 20.47/4.23 % (804803)Peak memory usage: 97 MB
% 20.47/4.23 % (804803)Instructions burned: 908 (million)
% 20.47/4.23 % (804811)Instruction limit reached!
% 20.47/4.23 % (804811)------------------------------
% 20.47/4.23 % (804811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.47/4.23 % (804811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.47/4.23 % (804811)CaDiCaL version: 2.1.3
% 20.47/4.23 % (804811)Termination reason: Instruction limit
% 20.47/4.23 % (804811)Termination phase: Saturation
% 20.47/4.23 % (804811)Time elapsed: 0.079 s
% 20.47/4.23 % (804811)Peak memory usage: 90 MB
% 20.47/4.23 % (804811)Instructions burned: 135 (million)
% 20.47/4.23 % (804813)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3747440587:st=8:i=592:sd=3:ep=RST:ss=axioms_2984 on theBenchmark for (2984ds/592Mi)
% 20.47/4.23 % (804814)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=533455615:st=3:i=13193:sd=3:ss=axioms_2983 on theBenchmark for (2983ds/13193Mi)
% 20.47/4.23 % (804813)Instruction limit reached!
% 20.47/4.23 % (804813)------------------------------
% 20.47/4.23 % (804813)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.47/4.23 % (804813)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.47/4.23 % (804813)CaDiCaL version: 2.1.3
% 20.47/4.23 % (804813)Termination reason: Instruction limit
% 20.47/4.23 % (804813)Termination phase: Saturation
% 20.47/4.23 % (804813)Time elapsed: 0.276 s
% 20.47/4.23 % (804813)Peak memory usage: 90 MB
% 20.47/4.23 % (804813)Instructions burned: 593 (million)
% 20.47/4.23 % (804817)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=478091028:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2980 on theBenchmark for (2980ds/125Mi)
% 20.47/4.23 % (804817)Instruction limit reached!
% 20.47/4.23 % (804817)------------------------------
% 20.47/4.23 % (804817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.47/4.23 % (804817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.47/4.23 % (804817)CaDiCaL version: 2.1.3
% 20.47/4.23 % (804817)Termination reason: Instruction limit
% 20.47/4.23 % (804817)Termination phase: Saturation
% 20.47/4.23 % (804817)Time elapsed: 0.072 s
% 20.47/4.23 % (804817)Peak memory usage: 89 MB
% 20.47/4.23 % (804817)Instructions burned: 128 (million)
% 20.47/4.23 % (804795)Instruction limit reached!
% 20.47/4.23 % (804795)------------------------------
% 20.47/4.23 % (804795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.47/4.23 % (804795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.47/4.23 % (804795)CaDiCaL version: 2.1.3
% 20.47/4.23 % (804795)Termination reason: Instruction limit
% 20.47/4.23 % (804795)Termination phase: Saturation
% 20.47/4.23 % (804795)Time elapsed: 1.519 s
% 20.47/4.23 % (804795)Peak memory usage: 141 MB
% 20.47/4.23 % (804795)Instructions burned: 2350 (million)
% 20.47/4.23 % (804819)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=2173518479:i=134:gtgl=5:slsql=off:gtg=exists_sym_2977 on theBenchmark for (2977ds/134Mi)
% 20.47/4.23 % (804820)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=2333592382:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2977 on theBenchmark for (2977ds/141Mi)
% 20.47/4.23 % (804819)Instruction limit reached!
% 20.47/4.23 % (804819)------------------------------
% 20.47/4.23 % (804819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.47/4.23 % (804819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.47/4.23 % (804819)CaDiCaL version: 2.1.3
% 20.47/4.23 % (804819)Termination reason: Instruction limit
% 20.47/4.23 % (804819)Termination phase: Saturation
% 20.47/4.23 % (804819)Time elapsed: 0.086 s
% 20.47/4.23 % (804819)Peak memory usage: 90 MB
% 20.47/4.23 % (804819)Instructions burned: 134 (million)
% 20.47/4.23 % (804820)Instruction limit reached!
% 20.47/4.23 % (804820)------------------------------
% 20.47/4.23 % (804820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.47/4.23 % (804820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.47/4.23 % (804820)CaDiCaL version: 2.1.3
% 20.47/4.23 % (804820)Termination reason: Instruction limit
% 20.47/4.23 % (804820)Termination phase: Saturation
% 20.47/4.23 % (804820)Time elapsed: 0.083 s
% 20.47/4.23 % (804820)Peak memory usage: 90 MB
% 20.47/4.23 % (804820)Instructions burned: 142 (million)
% 20.47/4.23 % (804823)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=3307536982:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2975 on theBenchmark for (2975ds/431Mi)
% 20.47/4.23 % (804824)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=2178372612:i=6060:aac=none:ins=25_2974 on theBenchmark for (2974ds/6060Mi)
% 20.47/4.23 % (804823)Instruction limit reached!
% 20.47/4.23 % (804823)------------------------------
% 20.47/4.23 % (804823)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.47/4.23 % (804823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.47/4.23 % (804823)CaDiCaL version: 2.1.3
% 20.47/4.23 % (804823)Termination reason: Instruction limit
% 20.47/4.23 % (804823)Termination phase: Saturation
% 20.47/4.23 % (804823)Time elapsed: 0.260 s
% 20.47/4.23 % (804823)Peak memory usage: 92 MB
% 20.47/4.23 % (804823)Instructions burned: 431 (million)
% 20.47/4.23 % (804827)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=3630534791:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2971 on theBenchmark for (2971ds/150Mi)
% 20.47/4.23 % (804775)First to succeed.
% 20.47/4.23 % (804775)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-804768"
% 20.47/4.23 % (804827)Instruction limit reached!
% 20.47/4.23 % (804827)------------------------------
% 20.47/4.23 % (804827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.47/4.23 % (804827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.47/4.23 % (804827)CaDiCaL version: 2.1.3
% 20.47/4.23 % (804827)Termination reason: Instruction limit
% 20.47/4.23 % (804827)Termination phase: Saturation
% 20.47/4.23 % (804827)Time elapsed: 0.097 s
% 20.47/4.23 % (804827)Peak memory usage: 90 MB
% 20.47/4.23 % (804827)Instructions burned: 151 (million)
% 20.47/4.23 % (804829)lrs+1010_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=ground:npcc=on:sp=arity:urr=on:random_seed=2738036249:i=14155:bd=all_2968 on theBenchmark for (2968ds/14155Mi)
% 20.47/4.23 % (804775)Refutation found. Thanks to Tanya!
% 20.47/4.23 % SZS status Theorem for theBenchmark
% 20.47/4.23 % SZS output start Proof for theBenchmark
% See solution above
% 24.27/4.36 % (804775)------------------------------
% 24.27/4.36 % (804775)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 24.27/4.36 % (804775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 24.27/4.36 % (804775)CaDiCaL version: 2.1.3
% 24.27/4.36 % (804775)Termination reason: Refutation
% 24.27/4.36 % (804775)Time elapsed: 2.910 s
% 24.27/4.36 % (804775)Peak memory usage: 152 MB
% 24.27/4.36 % (804775)Instructions burned: 4237 (million)
% 24.27/4.36 % (804775)------------------------------
% 24.27/4.36 % (804775)------------------------------
% 24.27/4.36 % (804768)Success in time 3.362 s
% 24.27/4.36 % Vampire exiting
%------------------------------------------------------------------------------