%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU313+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 : n017.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 12:48:17 PM UTC 2026
% Result : Theorem 12.28s 2.86s
% Output : Refutation 14.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 38
% Syntax : Number of formulae : 348 ( 42 unt; 23 def)
% Number of atoms : 1268 ( 84 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 1612 ( 692 ~; 747 |; 106 &)
% ( 36 <=>; 29 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 19 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 373 ( 1 sgn 343 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( X2 = topstr_closure(X0,X1)
<=> ! [X3] :
( in(X3,the_carrier(X0))
=> ( in(X3,X2)
<=> ! [X4] :
( element(X4,powerset(the_carrier(X0)))
=> ~ ( open_subset(X4,X0)
& in(X3,X4)
& disjoint(X1,X4) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_pre_topc) ).
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(f19,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& ~ in(X3,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f20,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_pre_topc) ).
fof(f24,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f26,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(f28,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f42,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f46,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X0))
& element(X2,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f47,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f49,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(f51,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_pre_topc) ).
fof(f54,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f55,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,powerset(X0))
=> ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t43_subset_1) ).
fof(f56,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( in(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( closed_subset(X3,X0)
& subset(X1,X3) )
=> in(X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_pre_topc) ).
fof(f57,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( in(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( closed_subset(X3,X0)
& subset(X1,X3) )
=> in(X2,X3) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f56]) ).
fof(f64,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f47]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = topstr_closure(X0,X1)
<=> ! [X3] :
( ( in(X3,X2)
<=> ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) ) )
| ~ in(X3,the_carrier(X0)) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = topstr_closure(X0,X1)
<=> ! [X3] :
( ( in(X3,X2)
<=> ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) ) )
| ~ in(X3,the_carrier(X0)) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
! [X0] :
( cast_as_carrier_subset(X0) = the_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
<=> open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f96,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f97,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(ennf_transformation,[],[f26]) ).
fof(f98,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(flattening,[],[f97]) ).
fof(f101,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f107,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f42]) ).
fof(f109,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f46]) ).
fof(f110,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X1,powerset(X0))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f109]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f117,plain,
! [X0,X1] :
( ! [X2] :
( ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f55]) ).
fof(f118,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,[],[f57]) ).
fof(f119,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,[],[f118]) ).
fof(f126,definition,
! [X0,X1,X2] :
( sP0(X0,X1,X2)
<=> ! [X3] :
( ( in(X3,X2)
<=> ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) ) )
| ~ in(X3,the_carrier(X0)) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f127,definition,
! [X2,X1,X0] :
( ( X2 = topstr_closure(X0,X1)
<=> sP0(X0,X1,X2) )
| ~ sP1(X2,X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sP1(X2,X1,X0)
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(definition_folding,[],[f92,f127,f126]) ).
fof(f129,plain,
! [X2,X1,X0] :
( ( ( X2 = topstr_closure(X0,X1)
| ~ sP0(X0,X1,X2) )
& ( sP0(X0,X1,X2)
| topstr_closure(X0,X1) != X2 ) )
| ~ sP1(X2,X1,X0) ),
inference(nnf_transformation,[],[f127]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ( ( topstr_closure(X2,X1) = X0
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| topstr_closure(X2,X1) != X0 ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f129]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ? [X4] :
( open_subset(X4,X0)
& in(X3,X4)
& disjoint(X1,X4)
& element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| in(X3,X2) )
& in(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ? [X4] :
( open_subset(X4,X0)
& in(X3,X4)
& disjoint(X1,X4)
& element(X4,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ in(X3,the_carrier(X0)) )
| ~ sP0(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f126]) ).
fof(f132,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ? [X4] :
( open_subset(X4,X0)
& in(X3,X4)
& disjoint(X1,X4)
& element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| in(X3,X2) )
& in(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ? [X4] :
( open_subset(X4,X0)
& in(X3,X4)
& disjoint(X1,X4)
& element(X4,powerset(the_carrier(X0))) ) )
& ( ! [X4] :
( ~ open_subset(X4,X0)
| ~ in(X3,X4)
| ~ disjoint(X1,X4)
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ in(X3,the_carrier(X0)) )
| ~ sP0(X0,X1,X2) ) ),
inference(flattening,[],[f131]) ).
fof(f133,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ? [X4] :
( open_subset(X4,X0)
& in(X3,X4)
& disjoint(X1,X4)
& element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ! [X5] :
( ~ open_subset(X5,X0)
| ~ in(X3,X5)
| ~ disjoint(X1,X5)
| ~ element(X5,powerset(the_carrier(X0))) )
| in(X3,X2) )
& in(X3,the_carrier(X0)) ) )
& ( ! [X6] :
( ( ( in(X6,X2)
| ? [X7] :
( open_subset(X7,X0)
& in(X6,X7)
& disjoint(X1,X7)
& element(X7,powerset(the_carrier(X0))) ) )
& ( ! [X8] :
( ~ open_subset(X8,X0)
| ~ in(X6,X8)
| ~ disjoint(X1,X8)
| ~ element(X8,powerset(the_carrier(X0))) )
| ~ in(X6,X2) ) )
| ~ in(X6,the_carrier(X0)) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f132]) ).
fof(f134,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ( open_subset(sK3(X0,X1,X2),X0)
& in(sK2(X0,X1,X2),sK3(X0,X1,X2))
& disjoint(X1,sK3(X0,X1,X2))
& element(sK3(X0,X1,X2),powerset(the_carrier(X0))) )
| ~ in(sK2(X0,X1,X2),X2) )
& ( ! [X5] :
( ~ open_subset(X5,X0)
| ~ in(sK2(X0,X1,X2),X5)
| ~ disjoint(X1,X5)
| ~ element(X5,powerset(the_carrier(X0))) )
| in(sK2(X0,X1,X2),X2) )
& in(sK2(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X6] :
( ( ( in(X6,X2)
| ( open_subset(sK4(X0,X1,X6),X0)
& in(X6,sK4(X0,X1,X6))
& disjoint(X1,sK4(X0,X1,X6))
& element(sK4(X0,X1,X6),powerset(the_carrier(X0))) ) )
& ( ! [X8] :
( ~ open_subset(X8,X0)
| ~ in(X6,X8)
| ~ disjoint(X1,X8)
| ~ element(X8,powerset(the_carrier(X0))) )
| ~ in(X6,X2) ) )
| ~ in(X6,the_carrier(X0)) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,sK2(X0,X1,X2)),skolemize(X4,sK3(X0,X1,X2)),skolemize(X7,sK4(X0,X1,X6))],[f133]) ).
fof(f135,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f136,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| in(X3,X1) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(flattening,[],[f135]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& ~ in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(rectify,[],[f136]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ( X2 = set_difference(X0,X1)
| ( ( ~ in(sK5(X0,X1,X2),X0)
| in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( in(sK5(X0,X1,X2),X0)
& ~ in(sK5(X0,X1,X2),X1) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1) )
& ( ( in(X4,X0)
& ~ in(X4,X1) )
| ~ in(X4,X2) ) )
| set_difference(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f137]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subset(X1,X0)
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) )
& ( open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ closed_subset(X1,X0) ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f94]) ).
fof(f146,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f147,plain,
! [X0,X1] :
( ! [X2] :
( ( ( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2)) )
& ( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2) ) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(nnf_transformation,[],[f117]) ).
fof(f148,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& closed_subset(X3,X0)
& subset(X1,X3)
& element(X3,powerset(the_carrier(X0))) )
| ~ 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,topstr_closure(X0,X1)) )
& in(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f149,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& closed_subset(X3,X0)
& subset(X1,X3)
& element(X3,powerset(the_carrier(X0))) )
| ~ 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,topstr_closure(X0,X1)) )
& in(X2,the_carrier(X0)) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(flattening,[],[f148]) ).
fof(f150,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& closed_subset(X3,X0)
& subset(X1,X3)
& element(X3,powerset(the_carrier(X0))) )
| ~ in(X2,topstr_closure(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(rectify,[],[f149]) ).
fof(f151,plain,
( ( ( ~ in(sK14,sK15)
& closed_subset(sK15,sK12)
& subset(sK13,sK15)
& element(sK15,powerset(the_carrier(sK12))) )
| ~ in(sK14,topstr_closure(sK12,sK13)) )
& ( ! [X4] :
( in(sK14,X4)
| ~ closed_subset(X4,sK12)
| ~ subset(sK13,X4)
| ~ element(X4,powerset(the_carrier(sK12))) )
| in(sK14,topstr_closure(sK12,sK13)) )
& in(sK14,the_carrier(sK12))
& element(sK13,powerset(the_carrier(sK12)))
& top_str(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14),skolemize(X3,sK15)],[f150]) ).
fof(f177,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| topstr_closure(X2,X1) != X0
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f130]) ).
fof(f179,plain,
! [X2,X0,X1,X8,X6] :
( ~ element(X8,powerset(the_carrier(X0)))
| ~ in(X6,X8)
| ~ disjoint(X1,X8)
| ~ open_subset(X8,X0)
| ~ in(X6,X2)
| ~ in(X6,the_carrier(X0))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f134]) ).
fof(f180,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| element(sK4(X0,X1,X6),powerset(the_carrier(X0)))
| ~ in(X6,the_carrier(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f134]) ).
fof(f181,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| disjoint(X1,sK4(X0,X1,X6))
| ~ in(X6,the_carrier(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f134]) ).
fof(f182,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| in(X6,sK4(X0,X1,X6))
| ~ in(X6,the_carrier(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f134]) ).
fof(f183,plain,
! [X2,X0,X1,X6] :
( ~ sP0(X0,X1,X2)
| open_subset(sK4(X0,X1,X6),X0)
| ~ in(X6,the_carrier(X0))
| in(X6,X2) ),
inference(cnf_transformation,[],[f134]) ).
fof(f190,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(the_carrier(X0)))
| sP1(X2,X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f191,plain,
! [X0] :
( ~ one_sorted_str(X0)
| the_carrier(X0) = cast_as_carrier_subset(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f192,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f138]) ).
fof(f193,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f138]) ).
fof(f194,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| in(X4,X1)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f138]) ).
fof(f198,plain,
! [X0,X1] :
( open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f199,plain,
! [X0,X1] :
( ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f201,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f96]) ).
fof(f202,plain,
! [X0,X1] :
( element(topstr_closure(X0,X1),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(cnf_transformation,[],[f98]) ).
fof(f204,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f230,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f107]) ).
fof(f241,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0))
| subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
inference(cnf_transformation,[],[f110]) ).
fof(f242,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f64]) ).
fof(f244,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f246,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1)) = X1
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f249,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f146]) ).
fof(f250,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f146]) ).
fof(f251,plain,
! [X2,X0,X1] :
( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f147]) ).
fof(f252,plain,
! [X2,X0,X1] :
( ~ subset(X1,subset_complement(X0,X2))
| disjoint(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f147]) ).
fof(f253,plain,
top_str(sK12),
inference(cnf_transformation,[],[f151]) ).
fof(f254,plain,
element(sK13,powerset(the_carrier(sK12))),
inference(cnf_transformation,[],[f151]) ).
fof(f255,plain,
in(sK14,the_carrier(sK12)),
inference(cnf_transformation,[],[f151]) ).
fof(f256,plain,
! [X4] :
( in(sK14,X4)
| ~ closed_subset(X4,sK12)
| ~ subset(sK13,X4)
| ~ element(X4,powerset(the_carrier(sK12)))
| in(sK14,topstr_closure(sK12,sK13)) ),
inference(cnf_transformation,[],[f151]) ).
fof(f257,plain,
( element(sK15,powerset(the_carrier(sK12)))
| ~ in(sK14,topstr_closure(sK12,sK13)) ),
inference(cnf_transformation,[],[f151]) ).
fof(f258,plain,
( subset(sK13,sK15)
| ~ in(sK14,topstr_closure(sK12,sK13)) ),
inference(cnf_transformation,[],[f151]) ).
fof(f259,plain,
( closed_subset(sK15,sK12)
| ~ in(sK14,topstr_closure(sK12,sK13)) ),
inference(cnf_transformation,[],[f151]) ).
fof(f260,plain,
( ~ in(sK14,sK15)
| ~ in(sK14,topstr_closure(sK12,sK13)) ),
inference(cnf_transformation,[],[f151]) ).
fof(f267,plain,
! [X2,X1] :
( ~ sP1(topstr_closure(X2,X1),X1,X2)
| sP0(X2,X1,topstr_closure(X2,X1)) ),
inference(equality_resolution,[],[f177]) ).
fof(f268,plain,
! [X0,X1,X4] :
( in(X4,set_difference(X0,X1))
| ~ in(X4,X0)
| in(X4,X1) ),
inference(equality_resolution,[],[f194]) ).
fof(f269,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f193]) ).
fof(f270,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f192]) ).
fof(f271,definition,
sF16 = topstr_closure(sK12,sK13),
introduced(definition,[new_symbols(definition,[sF16])],[function_definition]) ).
fof(f272,plain,
topstr_closure(sK12,sK13) = sF16,
inference(reorient_equations,[],[f271]) ).
fof(f273,plain,
( ~ in(sK14,sK15)
| ~ in(sK14,sF16) ),
inference(definition_folding,[],[f260,f272]) ).
fof(f274,plain,
( closed_subset(sK15,sK12)
| ~ in(sK14,sF16) ),
inference(definition_folding,[],[f259,f272]) ).
fof(f275,plain,
( subset(sK13,sK15)
| ~ in(sK14,sF16) ),
inference(definition_folding,[],[f258,f272]) ).
fof(f276,definition,
sF17 = the_carrier(sK12),
introduced(definition,[new_symbols(definition,[sF17])],[function_definition]) ).
fof(f277,plain,
the_carrier(sK12) = sF17,
inference(reorient_equations,[],[f276]) ).
fof(f278,definition,
sF18 = powerset(sF17),
introduced(definition,[new_symbols(definition,[sF18])],[function_definition]) ).
fof(f279,plain,
powerset(sF17) = sF18,
inference(reorient_equations,[],[f278]) ).
fof(f280,plain,
( element(sK15,sF18)
| ~ in(sK14,sF16) ),
inference(definition_folding,[],[f257,f272,f279,f277]) ).
fof(f281,plain,
! [X4] :
( in(sK14,X4)
| ~ closed_subset(X4,sK12)
| ~ subset(sK13,X4)
| ~ element(X4,sF18)
| in(sK14,sF16) ),
inference(definition_folding,[],[f256,f272,f279,f277]) ).
fof(f282,plain,
in(sK14,sF17),
inference(definition_folding,[],[f255,f277]) ).
fof(f283,plain,
element(sK13,sF18),
inference(definition_folding,[],[f254,f279,f277]) ).
fof(f285,definition,
( spl19_1
<=> in(sK14,sF16) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f286,plain,
( ~ in(sK14,sF16)
| spl19_1 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f287,plain,
( in(sK14,sF16)
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f289,definition,
( spl19_2
<=> ! [X4] :
( in(sK14,X4)
| ~ element(X4,sF18)
| ~ subset(sK13,X4)
| ~ closed_subset(X4,sK12) ) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f290,plain,
( ! [X4] :
( ~ subset(sK13,X4)
| ~ element(X4,sF18)
| in(sK14,X4)
| ~ closed_subset(X4,sK12) )
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f291,plain,
( spl19_1
| spl19_2 ),
inference(avatar_split_clause,[],[f281,f289,f285]) ).
fof(f293,definition,
( spl19_3
<=> element(sK15,sF18) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
fof(f295,plain,
( element(sK15,sF18)
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f296,plain,
( ~ spl19_1
| spl19_3 ),
inference(avatar_split_clause,[],[f280,f293,f285]) ).
fof(f298,definition,
( spl19_4
<=> subset(sK13,sK15) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
fof(f300,plain,
( subset(sK13,sK15)
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f301,plain,
( ~ spl19_1
| spl19_4 ),
inference(avatar_split_clause,[],[f275,f298,f285]) ).
fof(f303,definition,
( spl19_5
<=> closed_subset(sK15,sK12) ),
introduced(definition,[new_symbols(definition,[spl19_5])],[avatar_definition]) ).
fof(f305,plain,
( closed_subset(sK15,sK12)
| ~ spl19_5 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f306,plain,
( ~ spl19_1
| spl19_5 ),
inference(avatar_split_clause,[],[f274,f303,f285]) ).
fof(f308,definition,
( spl19_6
<=> in(sK14,sK15) ),
introduced(definition,[new_symbols(definition,[spl19_6])],[avatar_definition]) ).
fof(f310,plain,
( ~ in(sK14,sK15)
| spl19_6 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f311,plain,
( ~ spl19_1
| ~ spl19_6 ),
inference(avatar_split_clause,[],[f273,f308,f285]) ).
fof(f312,plain,
( element(sF16,powerset(the_carrier(sK12)))
| ~ top_str(sK12)
| ~ element(sK13,powerset(the_carrier(sK12))) ),
inference(superposition,[],[f202,f272]) ).
fof(f313,plain,
! [X0] :
( element(topstr_closure(sK12,X0),powerset(sF17))
| ~ top_str(sK12)
| ~ element(X0,powerset(sF17)) ),
inference(superposition,[],[f202,f277]) ).
fof(f314,plain,
! [X0] :
( element(topstr_closure(sK12,X0),powerset(sF17))
| ~ element(X0,powerset(sF17)) ),
inference(forward_subsumption_resolution,[],[f313,f253]) ).
fof(f315,plain,
( element(sF16,powerset(the_carrier(sK12)))
| ~ element(sK13,powerset(the_carrier(sK12))) ),
inference(forward_subsumption_resolution,[],[f312,f253]) ).
fof(f316,plain,
! [X0] :
( element(topstr_closure(sK12,X0),sF18)
| ~ element(X0,powerset(sF17)) ),
inference(forward_demodulation,[],[f314,f279]) ).
fof(f317,plain,
( element(sF16,powerset(sF17))
| ~ element(sK13,powerset(the_carrier(sK12))) ),
inference(forward_demodulation,[],[f315,f277]) ).
fof(f318,plain,
! [X0] :
( element(topstr_closure(sK12,X0),sF18)
| ~ element(X0,sF18) ),
inference(forward_demodulation,[],[f316,f279]) ).
fof(f319,plain,
( element(sF16,sF18)
| ~ element(sK13,powerset(the_carrier(sK12))) ),
inference(forward_demodulation,[],[f317,f279]) ).
fof(f320,plain,
( ~ element(sK13,powerset(sF17))
| element(sF16,sF18) ),
inference(forward_demodulation,[],[f319,f277]) ).
fof(f321,plain,
( ~ element(sK13,sF18)
| element(sF16,sF18) ),
inference(forward_demodulation,[],[f320,f279]) ).
fof(f322,plain,
element(sF16,sF18),
inference(forward_subsumption_resolution,[],[f321,f283]) ).
fof(f323,plain,
! [X2,X0,X1] :
( sP1(topstr_closure(X0,X1),X2,X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(resolution,[],[f190,f202]) ).
fof(f324,plain,
! [X0,X1] :
( ~ element(X0,powerset(sF17))
| sP1(X0,X1,sK12)
| ~ element(X1,powerset(sF17))
| ~ top_str(sK12) ),
inference(superposition,[],[f190,f277]) ).
fof(f325,plain,
! [X2,X0,X1] :
( sP1(topstr_closure(X0,X1),X2,X0)
| ~ element(X2,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0))) ),
inference(duplicate_literal_removal,[],[f323]) ).
fof(f326,plain,
! [X0,X1] :
( ~ element(X0,powerset(sF17))
| sP1(X0,X1,sK12)
| ~ element(X1,powerset(sF17)) ),
inference(forward_subsumption_resolution,[],[f324,f253]) ).
fof(f327,plain,
! [X0,X1] :
( ~ element(X0,sF18)
| sP1(X0,X1,sK12)
| ~ element(X1,powerset(sF17)) ),
inference(forward_demodulation,[],[f326,f279]) ).
fof(f328,plain,
! [X0,X1] :
( sP1(X0,X1,sK12)
| ~ element(X0,sF18)
| ~ element(X1,sF18) ),
inference(forward_demodulation,[],[f327,f279]) ).
fof(f329,plain,
! [X0] :
( open_subset(subset_difference(sF17,cast_as_carrier_subset(sK12),X0),sK12)
| ~ closed_subset(X0,sK12)
| ~ element(X0,powerset(sF17))
| ~ top_str(sK12) ),
inference(superposition,[],[f198,f277]) ).
fof(f330,plain,
! [X0] :
( open_subset(subset_difference(sF17,cast_as_carrier_subset(sK12),X0),sK12)
| ~ closed_subset(X0,sK12)
| ~ element(X0,powerset(sF17)) ),
inference(forward_subsumption_resolution,[],[f329,f253]) ).
fof(f331,plain,
! [X0] :
( open_subset(subset_difference(sF17,cast_as_carrier_subset(sK12),X0),sK12)
| ~ element(X0,sF18)
| ~ closed_subset(X0,sK12) ),
inference(forward_demodulation,[],[f330,f279]) ).
fof(f333,plain,
! [X2,X3,X0,X1] :
( ~ element(X0,powerset(sF17))
| ~ in(X1,X0)
| ~ disjoint(X2,X0)
| ~ open_subset(X0,sK12)
| ~ in(X1,X3)
| ~ in(X1,sF17)
| ~ sP0(sK12,X2,X3) ),
inference(superposition,[],[f179,f277]) ).
fof(f334,plain,
! [X2,X3,X0,X1] :
( ~ sP0(sK12,X2,X3)
| ~ in(X1,X0)
| ~ disjoint(X2,X0)
| ~ open_subset(X0,sK12)
| ~ in(X1,X3)
| ~ in(X1,sF17)
| ~ element(X0,sF18) ),
inference(forward_demodulation,[],[f333,f279]) ).
fof(f336,plain,
! [X0,X1] :
( ~ element(X1,sF18)
| ~ element(X0,sF18)
| subset_difference(sF17,X1,X0) = set_difference(X1,X0) ),
inference(superposition,[],[f241,f279]) ).
fof(f341,plain,
one_sorted_str(sK12),
inference(resolution,[],[f204,f253]) ).
fof(f342,plain,
! [X0] :
( sP0(sK12,X0,topstr_closure(sK12,X0))
| ~ element(topstr_closure(sK12,X0),sF18)
| ~ element(X0,sF18) ),
inference(resolution,[],[f267,f328]) ).
fof(f345,definition,
( spl19_7
<=> sP0(sK12,sK13,sF16) ),
introduced(definition,[new_symbols(definition,[spl19_7])],[avatar_definition]) ).
fof(f347,plain,
( sP0(sK12,sK13,sF16)
| ~ spl19_7 ),
inference(avatar_component_clause,[],[f345]) ).
fof(f353,plain,
! [X0] :
( sP0(sK12,X0,topstr_closure(sK12,X0))
| ~ element(X0,sF18) ),
inference(forward_subsumption_resolution,[],[f342,f318]) ).
fof(f354,plain,
! [X0,X1] :
( ~ element(X0,sF18)
| disjoint(X0,sK4(sK12,X0,X1))
| ~ in(X1,the_carrier(sK12))
| in(X1,topstr_closure(sK12,X0)) ),
inference(resolution,[],[f353,f181]) ).
fof(f356,plain,
( sP0(sK12,sK13,sF16)
| ~ element(sK13,sF18) ),
inference(superposition,[],[f353,f272]) ).
fof(f357,plain,
sP0(sK12,sK13,sF16),
inference(forward_subsumption_resolution,[],[f356,f283]) ).
fof(f359,plain,
! [X0,X1] :
( disjoint(X0,sK4(sK12,X0,X1))
| ~ element(X0,sF18)
| ~ in(X1,sF17)
| in(X1,topstr_closure(sK12,X0)) ),
inference(forward_demodulation,[],[f354,f277]) ).
fof(f360,plain,
spl19_7,
inference(avatar_split_clause,[],[f357,f345]) ).
fof(f367,plain,
! [X0] :
( ~ element(X0,sF18)
| subset_complement(sF17,subset_complement(sF17,X0)) = X0 ),
inference(superposition,[],[f230,f279]) ).
fof(f398,plain,
the_carrier(sK12) = cast_as_carrier_subset(sK12),
inference(resolution,[],[f341,f191]) ).
fof(f399,plain,
sF17 = cast_as_carrier_subset(sK12),
inference(forward_demodulation,[],[f398,f277]) ).
fof(f400,plain,
! [X0] :
( open_subset(subset_difference(sF17,sF17,X0),sK12)
| ~ element(X0,sF18)
| ~ closed_subset(X0,sK12) ),
inference(superposition,[],[f331,f399]) ).
fof(f410,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(X1))
| ~ subset(X0,X1)
| subset_difference(X1,X2,X0) = set_difference(X2,X0) ),
inference(resolution,[],[f250,f241]) ).
fof(f412,plain,
! [X0] :
( ~ subset(X0,sF17)
| element(X0,sF18) ),
inference(superposition,[],[f250,f279]) ).
fof(f414,plain,
! [X0,X1] :
( open_subset(sK4(sK12,X0,X1),sK12)
| ~ in(X1,the_carrier(sK12))
| in(X1,topstr_closure(sK12,X0))
| ~ element(X0,sF18) ),
inference(resolution,[],[f183,f353]) ).
fof(f417,plain,
! [X0,X1] :
( open_subset(sK4(sK12,X0,X1),sK12)
| ~ in(X1,sF17)
| in(X1,topstr_closure(sK12,X0))
| ~ element(X0,sF18) ),
inference(forward_demodulation,[],[f414,f277]) ).
fof(f420,plain,
! [X0] :
( ~ element(X0,powerset(sF17))
| subset_difference(sF17,cast_as_carrier_subset(sK12),subset_difference(sF17,cast_as_carrier_subset(sK12),X0)) = X0
| ~ one_sorted_str(sK12) ),
inference(superposition,[],[f246,f277]) ).
fof(f421,plain,
! [X0] :
( ~ element(X0,powerset(sF17))
| subset_difference(sF17,cast_as_carrier_subset(sK12),subset_difference(sF17,cast_as_carrier_subset(sK12),X0)) = X0 ),
inference(forward_subsumption_resolution,[],[f420,f341]) ).
fof(f423,plain,
! [X0] :
( ~ element(X0,sF18)
| subset_difference(sF17,cast_as_carrier_subset(sK12),subset_difference(sF17,cast_as_carrier_subset(sK12),X0)) = X0 ),
inference(forward_demodulation,[],[f421,f279]) ).
fof(f424,plain,
! [X0] :
( ~ element(X0,sF18)
| subset_difference(sF17,sF17,subset_difference(sF17,sF17,X0)) = X0 ),
inference(forward_demodulation,[],[f423,f399]) ).
fof(f427,plain,
sF16 = subset_difference(sF17,sF17,subset_difference(sF17,sF17,sF16)),
inference(resolution,[],[f424,f322]) ).
fof(f442,plain,
( ! [X0,X1] :
( ~ closed_subset(subset_complement(X1,X0),sK12)
| ~ element(X0,powerset(X1))
| ~ element(sK13,powerset(X1))
| ~ element(subset_complement(X1,X0),sF18)
| in(sK14,subset_complement(X1,X0))
| ~ disjoint(sK13,X0) )
| ~ spl19_2 ),
inference(resolution,[],[f251,f290]) ).
fof(f447,plain,
! [X0] :
( ~ element(X0,powerset(sF17))
| subset_difference(sF17,cast_as_carrier_subset(sK12),X0) = subset_complement(sF17,X0)
| ~ one_sorted_str(sK12) ),
inference(superposition,[],[f244,f277]) ).
fof(f448,plain,
! [X0] :
( ~ element(X0,powerset(sF17))
| subset_difference(sF17,cast_as_carrier_subset(sK12),X0) = subset_complement(sF17,X0) ),
inference(forward_subsumption_resolution,[],[f447,f341]) ).
fof(f450,plain,
! [X0] :
( ~ element(X0,sF18)
| subset_difference(sF17,cast_as_carrier_subset(sK12),X0) = subset_complement(sF17,X0) ),
inference(forward_demodulation,[],[f448,f279]) ).
fof(f451,plain,
! [X0] :
( ~ element(X0,sF18)
| subset_complement(sF17,X0) = subset_difference(sF17,sF17,X0) ),
inference(forward_demodulation,[],[f450,f399]) ).
fof(f454,plain,
subset_difference(sF17,sF17,sF16) = subset_complement(sF17,sF16),
inference(resolution,[],[f451,f322]) ).
fof(f467,plain,
! [X0,X1] :
( element(sK4(sK12,X0,X1),powerset(the_carrier(sK12)))
| ~ in(X1,the_carrier(sK12))
| in(X1,topstr_closure(sK12,X0))
| ~ element(X0,sF18) ),
inference(resolution,[],[f180,f353]) ).
fof(f468,plain,
( ! [X0] :
( element(sK4(sK12,sK13,X0),powerset(the_carrier(sK12)))
| ~ in(X0,the_carrier(sK12))
| in(X0,sF16) )
| ~ spl19_7 ),
inference(resolution,[],[f180,f347]) ).
fof(f469,plain,
( ! [X0] :
( element(sK4(sK12,sK13,X0),powerset(sF17))
| ~ in(X0,the_carrier(sK12))
| in(X0,sF16) )
| ~ spl19_7 ),
inference(forward_demodulation,[],[f468,f277]) ).
fof(f470,plain,
! [X0,X1] :
( element(sK4(sK12,X0,X1),powerset(sF17))
| ~ in(X1,the_carrier(sK12))
| in(X1,topstr_closure(sK12,X0))
| ~ element(X0,sF18) ),
inference(forward_demodulation,[],[f467,f277]) ).
fof(f471,plain,
( ! [X0] :
( element(sK4(sK12,sK13,X0),sF18)
| ~ in(X0,the_carrier(sK12))
| in(X0,sF16) )
| ~ spl19_7 ),
inference(forward_demodulation,[],[f469,f279]) ).
fof(f472,plain,
! [X0,X1] :
( element(sK4(sK12,X0,X1),sF18)
| ~ in(X1,the_carrier(sK12))
| in(X1,topstr_closure(sK12,X0))
| ~ element(X0,sF18) ),
inference(forward_demodulation,[],[f470,f279]) ).
fof(f473,plain,
( ! [X0] :
( element(sK4(sK12,sK13,X0),sF18)
| ~ in(X0,sF17)
| in(X0,sF16) )
| ~ spl19_7 ),
inference(forward_demodulation,[],[f471,f277]) ).
fof(f474,plain,
! [X0,X1] :
( element(sK4(sK12,X0,X1),sF18)
| ~ in(X1,sF17)
| in(X1,topstr_closure(sK12,X0))
| ~ element(X0,sF18) ),
inference(forward_demodulation,[],[f472,f277]) ).
fof(f475,plain,
( ! [X0] :
( ~ in(X0,sF17)
| in(X0,sF16)
| subset_complement(sF17,sK4(sK12,sK13,X0)) = subset_difference(sF17,sF17,sK4(sK12,sK13,X0)) )
| ~ spl19_7 ),
inference(resolution,[],[f473,f451]) ).
fof(f476,plain,
( ! [X0] :
( ~ in(X0,sF17)
| in(X0,sF16)
| sK4(sK12,sK13,X0) = subset_difference(sF17,sF17,subset_difference(sF17,sF17,sK4(sK12,sK13,X0))) )
| ~ spl19_7 ),
inference(resolution,[],[f473,f424]) ).
fof(f487,plain,
! [X0] :
( ~ open_subset(subset_difference(sF17,cast_as_carrier_subset(sK12),X0),sK12)
| closed_subset(X0,sK12)
| ~ element(X0,powerset(sF17))
| ~ top_str(sK12) ),
inference(superposition,[],[f199,f277]) ).
fof(f491,plain,
! [X0] :
( ~ open_subset(subset_difference(sF17,cast_as_carrier_subset(sK12),X0),sK12)
| closed_subset(X0,sK12)
| ~ element(X0,powerset(sF17)) ),
inference(forward_subsumption_resolution,[],[f487,f253]) ).
fof(f493,plain,
! [X0] :
( ~ open_subset(subset_difference(sF17,sF17,X0),sK12)
| closed_subset(X0,sK12)
| ~ element(X0,powerset(sF17)) ),
inference(forward_demodulation,[],[f491,f399]) ).
fof(f495,plain,
! [X0] :
( ~ open_subset(subset_difference(sF17,sF17,X0),sK12)
| ~ element(X0,sF18)
| closed_subset(X0,sK12) ),
inference(forward_demodulation,[],[f493,f279]) ).
fof(f513,plain,
! [X0] :
( ~ element(X0,sF18)
| subset(X0,sF17) ),
inference(superposition,[],[f249,f279]) ).
fof(f517,plain,
subset(sF16,sF17),
inference(resolution,[],[f513,f322]) ).
fof(f530,plain,
( ! [X0,X1] :
( ~ disjoint(sK13,X1)
| ~ in(X0,X1)
| ~ open_subset(X1,sK12)
| ~ in(X0,sF16)
| ~ in(X0,sF17)
| ~ element(X1,sF18) )
| ~ spl19_7 ),
inference(resolution,[],[f334,f347]) ).
fof(f542,definition,
( spl19_21
<=> element(subset_complement(sF17,sF16),sF18) ),
introduced(definition,[new_symbols(definition,[spl19_21])],[avatar_definition]) ).
fof(f543,plain,
( element(subset_complement(sF17,sF16),sF18)
| ~ spl19_21 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f544,plain,
( ~ element(subset_complement(sF17,sF16),sF18)
| spl19_21 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f551,plain,
( in(sK14,sF16)
| subset_complement(sF17,sK4(sK12,sK13,sK14)) = subset_difference(sF17,sF17,sK4(sK12,sK13,sK14))
| ~ spl19_7 ),
inference(resolution,[],[f475,f282]) ).
fof(f552,plain,
( subset_complement(sF17,sK4(sK12,sK13,sK14)) = subset_difference(sF17,sF17,sK4(sK12,sK13,sK14))
| spl19_1
| ~ spl19_7 ),
inference(forward_subsumption_resolution,[],[f551,f286]) ).
fof(f560,definition,
( spl19_24
<=> element(sK4(sK12,sK13,sK14),sF18) ),
introduced(definition,[new_symbols(definition,[spl19_24])],[avatar_definition]) ).
fof(f561,plain,
( element(sK4(sK12,sK13,sK14),sF18)
| ~ spl19_24 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f562,plain,
( ~ element(sK4(sK12,sK13,sK14),sF18)
| spl19_24 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f593,plain,
! [X0] :
( element(subset_complement(sF17,X0),sF18)
| ~ element(X0,sF18) ),
inference(superposition,[],[f201,f279]) ).
fof(f640,plain,
sF16 = subset_difference(sF17,sF17,subset_complement(sF17,sF16)),
inference(superposition,[],[f427,f454]) ).
fof(f718,plain,
element(sF17,sF18),
inference(resolution,[],[f242,f412]) ).
fof(f832,plain,
( in(sK14,sF16)
| sK4(sK12,sK13,sK14) = subset_difference(sF17,sF17,subset_difference(sF17,sF17,sK4(sK12,sK13,sK14)))
| ~ spl19_7 ),
inference(resolution,[],[f476,f282]) ).
fof(f833,plain,
( sK4(sK12,sK13,sK14) = subset_difference(sF17,sF17,subset_difference(sF17,sF17,sK4(sK12,sK13,sK14)))
| spl19_1
| ~ spl19_7 ),
inference(forward_subsumption_resolution,[],[f832,f286]) ).
fof(f834,plain,
( sK4(sK12,sK13,sK14) = subset_difference(sF17,sF17,subset_complement(sF17,sK4(sK12,sK13,sK14)))
| spl19_1
| ~ spl19_7 ),
inference(forward_demodulation,[],[f833,f552]) ).
fof(f835,plain,
( ~ open_subset(sK4(sK12,sK13,sK14),sK12)
| ~ element(subset_complement(sF17,sK4(sK12,sK13,sK14)),sF18)
| closed_subset(subset_complement(sF17,sK4(sK12,sK13,sK14)),sK12)
| spl19_1
| ~ spl19_7 ),
inference(superposition,[],[f495,f834]) ).
fof(f842,definition,
( spl19_34
<=> closed_subset(subset_complement(sF17,sK4(sK12,sK13,sK14)),sK12) ),
introduced(definition,[new_symbols(definition,[spl19_34])],[avatar_definition]) ).
fof(f843,plain,
( closed_subset(subset_complement(sF17,sK4(sK12,sK13,sK14)),sK12)
| ~ spl19_34 ),
inference(avatar_component_clause,[],[f842]) ).
fof(f846,definition,
( spl19_35
<=> element(subset_complement(sF17,sK4(sK12,sK13,sK14)),sF18) ),
introduced(definition,[new_symbols(definition,[spl19_35])],[avatar_definition]) ).
fof(f847,plain,
( element(subset_complement(sF17,sK4(sK12,sK13,sK14)),sF18)
| ~ spl19_35 ),
inference(avatar_component_clause,[],[f846]) ).
fof(f848,plain,
( ~ element(subset_complement(sF17,sK4(sK12,sK13,sK14)),sF18)
| spl19_35 ),
inference(avatar_component_clause,[],[f846]) ).
fof(f850,definition,
( spl19_36
<=> open_subset(sK4(sK12,sK13,sK14),sK12) ),
introduced(definition,[new_symbols(definition,[spl19_36])],[avatar_definition]) ).
fof(f851,plain,
( ~ open_subset(sK4(sK12,sK13,sK14),sK12)
| spl19_36 ),
inference(avatar_component_clause,[],[f850]) ).
fof(f854,plain,
( spl19_34
| ~ spl19_35
| ~ spl19_36
| spl19_1
| ~ spl19_7 ),
inference(avatar_split_clause,[],[f835,f345,f285,f850,f846,f842]) ).
fof(f861,plain,
( ~ element(sK4(sK12,sK13,sK14),sF18)
| spl19_35 ),
inference(resolution,[],[f848,f593]) ).
fof(f889,plain,
! [X0] :
( ~ element(X0,sF18)
| subset_difference(sF17,sF17,X0) = set_difference(sF17,X0) ),
inference(resolution,[],[f718,f336]) ).
fof(f902,plain,
( ~ in(sK14,sF17)
| in(sK14,topstr_closure(sK12,sK13))
| ~ element(sK13,sF18)
| spl19_24 ),
inference(resolution,[],[f562,f474]) ).
fof(f903,plain,
( in(sK14,topstr_closure(sK12,sK13))
| ~ element(sK13,sF18)
| spl19_24 ),
inference(forward_subsumption_resolution,[],[f902,f282]) ).
fof(f905,plain,
( in(sK14,topstr_closure(sK12,sK13))
| spl19_24 ),
inference(forward_subsumption_resolution,[],[f903,f283]) ).
fof(f908,plain,
( in(sK14,sF16)
| spl19_24 ),
inference(forward_demodulation,[],[f905,f272]) ).
fof(f909,plain,
( $false
| spl19_1
| spl19_24 ),
inference(forward_subsumption_resolution,[],[f908,f286]) ).
fof(f910,plain,
( spl19_1
| spl19_24 ),
inference(avatar_contradiction_clause,[],[f909]) ).
fof(f915,plain,
( $false
| ~ spl19_24
| spl19_35 ),
inference(forward_subsumption_resolution,[],[f861,f561]) ).
fof(f916,plain,
( ~ spl19_24
| spl19_35 ),
inference(avatar_contradiction_clause,[],[f915]) ).
fof(f932,plain,
( ~ in(sK14,sF17)
| in(sK14,topstr_closure(sK12,sK13))
| ~ element(sK13,sF18)
| spl19_36 ),
inference(resolution,[],[f851,f417]) ).
fof(f933,plain,
( in(sK14,topstr_closure(sK12,sK13))
| ~ element(sK13,sF18)
| spl19_36 ),
inference(forward_subsumption_resolution,[],[f932,f282]) ).
fof(f935,plain,
( in(sK14,topstr_closure(sK12,sK13))
| spl19_36 ),
inference(forward_subsumption_resolution,[],[f933,f283]) ).
fof(f938,plain,
( in(sK14,sF16)
| spl19_36 ),
inference(forward_demodulation,[],[f935,f272]) ).
fof(f939,plain,
( $false
| spl19_1
| spl19_36 ),
inference(forward_subsumption_resolution,[],[f938,f286]) ).
fof(f940,plain,
( spl19_1
| spl19_36 ),
inference(avatar_contradiction_clause,[],[f939]) ).
fof(f941,plain,
( ~ element(sK4(sK12,sK13,sK14),powerset(sF17))
| ~ element(sK13,powerset(sF17))
| ~ element(subset_complement(sF17,sK4(sK12,sK13,sK14)),sF18)
| in(sK14,subset_complement(sF17,sK4(sK12,sK13,sK14)))
| ~ disjoint(sK13,sK4(sK12,sK13,sK14))
| ~ spl19_2
| ~ spl19_34 ),
inference(resolution,[],[f843,f442]) ).
fof(f942,plain,
( ~ element(sK4(sK12,sK13,sK14),powerset(sF17))
| ~ element(sK13,powerset(sF17))
| in(sK14,subset_complement(sF17,sK4(sK12,sK13,sK14)))
| ~ disjoint(sK13,sK4(sK12,sK13,sK14))
| ~ spl19_2
| ~ spl19_34
| ~ spl19_35 ),
inference(forward_subsumption_resolution,[],[f941,f847]) ).
fof(f943,plain,
( ~ element(sK4(sK12,sK13,sK14),sF18)
| ~ element(sK13,powerset(sF17))
| in(sK14,subset_complement(sF17,sK4(sK12,sK13,sK14)))
| ~ disjoint(sK13,sK4(sK12,sK13,sK14))
| ~ spl19_2
| ~ spl19_34
| ~ spl19_35 ),
inference(forward_demodulation,[],[f942,f279]) ).
fof(f944,plain,
( ~ element(sK13,powerset(sF17))
| in(sK14,subset_complement(sF17,sK4(sK12,sK13,sK14)))
| ~ disjoint(sK13,sK4(sK12,sK13,sK14))
| ~ spl19_2
| ~ spl19_24
| ~ spl19_34
| ~ spl19_35 ),
inference(forward_subsumption_resolution,[],[f943,f561]) ).
fof(f945,plain,
( ~ element(sK13,sF18)
| in(sK14,subset_complement(sF17,sK4(sK12,sK13,sK14)))
| ~ disjoint(sK13,sK4(sK12,sK13,sK14))
| ~ spl19_2
| ~ spl19_24
| ~ spl19_34
| ~ spl19_35 ),
inference(forward_demodulation,[],[f944,f279]) ).
fof(f946,plain,
( in(sK14,subset_complement(sF17,sK4(sK12,sK13,sK14)))
| ~ disjoint(sK13,sK4(sK12,sK13,sK14))
| ~ spl19_2
| ~ spl19_24
| ~ spl19_34
| ~ spl19_35 ),
inference(forward_subsumption_resolution,[],[f945,f283]) ).
fof(f948,definition,
( spl19_37
<=> disjoint(sK13,sK4(sK12,sK13,sK14)) ),
introduced(definition,[new_symbols(definition,[spl19_37])],[avatar_definition]) ).
fof(f950,plain,
( ~ disjoint(sK13,sK4(sK12,sK13,sK14))
| spl19_37 ),
inference(avatar_component_clause,[],[f948]) ).
fof(f952,definition,
( spl19_38
<=> in(sK14,subset_complement(sF17,sK4(sK12,sK13,sK14))) ),
introduced(definition,[new_symbols(definition,[spl19_38])],[avatar_definition]) ).
fof(f954,plain,
( in(sK14,subset_complement(sF17,sK4(sK12,sK13,sK14)))
| ~ spl19_38 ),
inference(avatar_component_clause,[],[f952]) ).
fof(f955,plain,
( ~ spl19_37
| spl19_38
| ~ spl19_2
| ~ spl19_24
| ~ spl19_34
| ~ spl19_35 ),
inference(avatar_split_clause,[],[f946,f846,f842,f560,f289,f952,f948]) ).
fof(f957,plain,
( ~ element(sK13,sF18)
| ~ in(sK14,sF17)
| in(sK14,topstr_closure(sK12,sK13))
| spl19_37 ),
inference(resolution,[],[f950,f359]) ).
fof(f958,plain,
( ~ in(sK14,sF17)
| in(sK14,topstr_closure(sK12,sK13))
| spl19_37 ),
inference(forward_subsumption_resolution,[],[f957,f283]) ).
fof(f960,plain,
( in(sK14,topstr_closure(sK12,sK13))
| spl19_37 ),
inference(forward_subsumption_resolution,[],[f958,f282]) ).
fof(f963,plain,
( in(sK14,sF16)
| spl19_37 ),
inference(forward_demodulation,[],[f960,f272]) ).
fof(f964,plain,
( $false
| spl19_1
| spl19_37 ),
inference(forward_subsumption_resolution,[],[f963,f286]) ).
fof(f965,plain,
( spl19_1
| spl19_37 ),
inference(avatar_contradiction_clause,[],[f964]) ).
fof(f974,plain,
( sK15 = subset_complement(sF17,subset_complement(sF17,sK15))
| ~ spl19_3 ),
inference(resolution,[],[f295,f367]) ).
fof(f1011,plain,
( ! [X0] :
( ~ subset(X0,sK15)
| disjoint(X0,subset_complement(sF17,sK15))
| ~ element(subset_complement(sF17,sK15),powerset(sF17))
| ~ element(X0,powerset(sF17)) )
| ~ spl19_3 ),
inference(superposition,[],[f252,f974]) ).
fof(f1012,plain,
( ! [X0] :
( ~ element(subset_complement(sF17,sK15),sF18)
| ~ subset(X0,sK15)
| disjoint(X0,subset_complement(sF17,sK15))
| ~ element(X0,powerset(sF17)) )
| ~ spl19_3 ),
inference(forward_demodulation,[],[f1011,f279]) ).
fof(f1015,plain,
( ! [X0] :
( ~ element(X0,sF18)
| ~ element(subset_complement(sF17,sK15),sF18)
| ~ subset(X0,sK15)
| disjoint(X0,subset_complement(sF17,sK15)) )
| ~ spl19_3 ),
inference(forward_demodulation,[],[f1012,f279]) ).
fof(f1018,definition,
( spl19_42
<=> element(subset_complement(sF17,sK15),sF18) ),
introduced(definition,[new_symbols(definition,[spl19_42])],[avatar_definition]) ).
fof(f1019,plain,
( element(subset_complement(sF17,sK15),sF18)
| ~ spl19_42 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f1020,plain,
( ~ element(subset_complement(sF17,sK15),sF18)
| spl19_42 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f1022,definition,
( spl19_43
<=> ! [X0] :
( ~ element(X0,sF18)
| disjoint(X0,subset_complement(sF17,sK15))
| ~ subset(X0,sK15) ) ),
introduced(definition,[new_symbols(definition,[spl19_43])],[avatar_definition]) ).
fof(f1023,plain,
( ! [X0] :
( disjoint(X0,subset_complement(sF17,sK15))
| ~ element(X0,sF18)
| ~ subset(X0,sK15) )
| ~ spl19_43 ),
inference(avatar_component_clause,[],[f1022]) ).
fof(f1024,plain,
( ~ spl19_42
| spl19_43
| ~ spl19_3 ),
inference(avatar_split_clause,[],[f1015,f293,f1022,f1018]) ).
fof(f1054,plain,
( ~ element(sK15,sF18)
| spl19_42 ),
inference(resolution,[],[f1020,f593]) ).
fof(f1055,plain,
( $false
| ~ spl19_3
| spl19_42 ),
inference(forward_subsumption_resolution,[],[f1054,f295]) ).
fof(f1056,plain,
( ~ spl19_3
| spl19_42 ),
inference(avatar_contradiction_clause,[],[f1055]) ).
fof(f1059,plain,
( subset_complement(sF17,sK4(sK12,sK13,sK14)) = subset_difference(sF17,sF17,sK4(sK12,sK13,sK14))
| spl19_1
| ~ spl19_7 ),
inference(forward_subsumption_resolution,[],[f551,f286]) ).
fof(f1130,plain,
( subset(sK4(sK12,sK13,sK14),sF17)
| ~ spl19_24 ),
inference(resolution,[],[f561,f513]) ).
fof(f1264,plain,
! [X2,X0,X1] :
( ~ subset(X2,X1)
| subset_difference(X1,X2,X0) = set_difference(X2,X0)
| ~ subset(X0,X1) ),
inference(resolution,[],[f410,f250]) ).
fof(f1269,plain,
! [X0,X1] :
( ~ subset(X1,sF17)
| ~ element(X0,sF18)
| set_difference(X0,X1) = subset_difference(sF17,X0,X1) ),
inference(superposition,[],[f410,f279]) ).
fof(f1275,plain,
! [X0] :
( ~ element(X0,sF18)
| set_difference(X0,sF16) = subset_difference(sF17,X0,sF16) ),
inference(resolution,[],[f1269,f517]) ).
fof(f1345,plain,
( ~ element(sF16,sF18)
| spl19_21 ),
inference(resolution,[],[f544,f593]) ).
fof(f1346,plain,
( $false
| spl19_21 ),
inference(forward_subsumption_resolution,[],[f1345,f322]) ).
fof(f1347,plain,
spl19_21,
inference(avatar_contradiction_clause,[],[f1346]) ).
fof(f1362,plain,
( subset(subset_complement(sF17,sF16),sF17)
| ~ spl19_21 ),
inference(resolution,[],[f543,f513]) ).
fof(f1832,plain,
subset_difference(sF17,sF17,sF16) = set_difference(sF17,sF16),
inference(resolution,[],[f1275,f718]) ).
fof(f1833,plain,
subset_complement(sF17,sF16) = set_difference(sF17,sF16),
inference(forward_demodulation,[],[f1832,f454]) ).
fof(f1837,plain,
sF16 = subset_difference(sF17,sF17,set_difference(sF17,sF16)),
inference(superposition,[],[f640,f1833]) ).
fof(f3152,plain,
! [X0,X1] :
( ~ element(X0,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1)))
| sP0(X1,X0,topstr_closure(X1,X0)) ),
inference(resolution,[],[f325,f267]) ).
fof(f3155,plain,
! [X0,X1] :
( sP0(X1,X0,topstr_closure(X1,X0))
| ~ top_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(duplicate_literal_removal,[],[f3152]) ).
fof(f3168,plain,
! [X2,X0,X1] :
( in(X2,sK4(X0,X1,X2))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ in(X2,the_carrier(X0))
| in(X2,topstr_closure(X0,X1)) ),
inference(resolution,[],[f3155,f182]) ).
fof(f3471,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| set_difference(X0,X1) = subset_difference(X0,X0,X1) ),
inference(resolution,[],[f1264,f242]) ).
fof(f3581,plain,
( subset_difference(sF17,sF17,subset_complement(sF17,sF16)) = set_difference(sF17,subset_complement(sF17,sF16))
| ~ spl19_21 ),
inference(resolution,[],[f3471,f1362]) ).
fof(f3584,plain,
( subset_difference(sF17,sF17,sK4(sK12,sK13,sK14)) = set_difference(sF17,sK4(sK12,sK13,sK14))
| ~ spl19_24 ),
inference(resolution,[],[f3471,f1130]) ).
fof(f3591,plain,
( subset_complement(sF17,sK4(sK12,sK13,sK14)) = set_difference(sF17,sK4(sK12,sK13,sK14))
| spl19_1
| ~ spl19_7
| ~ spl19_24 ),
inference(forward_demodulation,[],[f3584,f1059]) ).
fof(f3592,plain,
( subset_difference(sF17,sF17,set_difference(sF17,sF16)) = set_difference(sF17,set_difference(sF17,sF16))
| ~ spl19_21 ),
inference(forward_demodulation,[],[f3581,f1833]) ).
fof(f3599,plain,
( sF16 = set_difference(sF17,set_difference(sF17,sF16))
| ~ spl19_21 ),
inference(forward_demodulation,[],[f3592,f1837]) ).
fof(f3606,plain,
( ! [X0] :
( ~ in(X0,sF16)
| in(X0,sF17) )
| ~ spl19_21 ),
inference(superposition,[],[f269,f3599]) ).
fof(f3611,plain,
( in(sK14,set_difference(sF17,sK4(sK12,sK13,sK14)))
| spl19_1
| ~ spl19_7
| ~ spl19_24
| ~ spl19_38 ),
inference(superposition,[],[f954,f3591]) ).
fof(f3666,plain,
( ~ in(sK14,sK4(sK12,sK13,sK14))
| spl19_1
| ~ spl19_7
| ~ spl19_24
| ~ spl19_38 ),
inference(resolution,[],[f3611,f270]) ).
fof(f6572,plain,
( ~ element(sK13,powerset(the_carrier(sK12)))
| ~ top_str(sK12)
| ~ in(sK14,the_carrier(sK12))
| in(sK14,topstr_closure(sK12,sK13))
| spl19_1
| ~ spl19_7
| ~ spl19_24
| ~ spl19_38 ),
inference(resolution,[],[f3666,f3168]) ).
fof(f6574,plain,
( ~ element(sK13,powerset(the_carrier(sK12)))
| ~ in(sK14,the_carrier(sK12))
| in(sK14,topstr_closure(sK12,sK13))
| spl19_1
| ~ spl19_7
| ~ spl19_24
| ~ spl19_38 ),
inference(forward_subsumption_resolution,[],[f6572,f253]) ).
fof(f6578,plain,
( ~ element(sK13,powerset(sF17))
| ~ in(sK14,the_carrier(sK12))
| in(sK14,topstr_closure(sK12,sK13))
| spl19_1
| ~ spl19_7
| ~ spl19_24
| ~ spl19_38 ),
inference(forward_demodulation,[],[f6574,f277]) ).
fof(f6583,plain,
( ~ element(sK13,sF18)
| ~ in(sK14,the_carrier(sK12))
| in(sK14,topstr_closure(sK12,sK13))
| spl19_1
| ~ spl19_7
| ~ spl19_24
| ~ spl19_38 ),
inference(forward_demodulation,[],[f6578,f279]) ).
fof(f6586,plain,
( ~ in(sK14,the_carrier(sK12))
| in(sK14,topstr_closure(sK12,sK13))
| spl19_1
| ~ spl19_7
| ~ spl19_24
| ~ spl19_38 ),
inference(forward_subsumption_resolution,[],[f6583,f283]) ).
fof(f6590,plain,
( ~ in(sK14,sF17)
| in(sK14,topstr_closure(sK12,sK13))
| spl19_1
| ~ spl19_7
| ~ spl19_24
| ~ spl19_38 ),
inference(forward_demodulation,[],[f6586,f277]) ).
fof(f6592,plain,
( in(sK14,topstr_closure(sK12,sK13))
| spl19_1
| ~ spl19_7
| ~ spl19_24
| ~ spl19_38 ),
inference(forward_subsumption_resolution,[],[f6590,f282]) ).
fof(f6595,plain,
( in(sK14,sF16)
| spl19_1
| ~ spl19_7
| ~ spl19_24
| ~ spl19_38 ),
inference(forward_demodulation,[],[f6592,f272]) ).
fof(f6596,plain,
( $false
| spl19_1
| ~ spl19_7
| ~ spl19_24
| ~ spl19_38 ),
inference(forward_subsumption_resolution,[],[f6595,f286]) ).
fof(f6597,plain,
( spl19_1
| ~ spl19_7
| ~ spl19_24
| ~ spl19_38 ),
inference(avatar_contradiction_clause,[],[f6596]) ).
fof(f6849,plain,
( subset_complement(sF17,sK15) = subset_difference(sF17,sF17,sK15)
| ~ spl19_3 ),
inference(resolution,[],[f295,f451]) ).
fof(f6862,plain,
( subset_difference(sF17,sF17,sK15) = set_difference(sF17,sK15)
| ~ spl19_3 ),
inference(resolution,[],[f295,f889]) ).
fof(f6895,plain,
( subset_complement(sF17,sK15) = set_difference(sF17,sK15)
| ~ spl19_3 ),
inference(forward_demodulation,[],[f6849,f6862]) ).
fof(f6997,plain,
( ! [X0] :
( ~ element(sK13,sF18)
| ~ subset(sK13,sK15)
| ~ in(X0,subset_complement(sF17,sK15))
| ~ open_subset(subset_complement(sF17,sK15),sK12)
| ~ in(X0,sF16)
| ~ in(X0,sF17)
| ~ element(subset_complement(sF17,sK15),sF18) )
| ~ spl19_7
| ~ spl19_43 ),
inference(resolution,[],[f1023,f530]) ).
fof(f6998,plain,
( ! [X0] :
( ~ element(sK13,sF18)
| ~ subset(sK13,sK15)
| ~ in(X0,subset_complement(sF17,sK15))
| ~ open_subset(subset_complement(sF17,sK15),sK12)
| ~ in(X0,sF16)
| ~ element(subset_complement(sF17,sK15),sF18) )
| ~ spl19_7
| ~ spl19_21
| ~ spl19_43 ),
inference(forward_subsumption_resolution,[],[f6997,f3606]) ).
fof(f7001,plain,
( ! [X0] :
( ~ subset(sK13,sK15)
| ~ in(X0,subset_complement(sF17,sK15))
| ~ open_subset(subset_complement(sF17,sK15),sK12)
| ~ in(X0,sF16)
| ~ element(subset_complement(sF17,sK15),sF18) )
| ~ spl19_7
| ~ spl19_21
| ~ spl19_43 ),
inference(forward_subsumption_resolution,[],[f6998,f283]) ).
fof(f7003,plain,
( ! [X0] :
( ~ in(X0,subset_complement(sF17,sK15))
| ~ open_subset(subset_complement(sF17,sK15),sK12)
| ~ in(X0,sF16)
| ~ element(subset_complement(sF17,sK15),sF18) )
| ~ spl19_4
| ~ spl19_7
| ~ spl19_21
| ~ spl19_43 ),
inference(forward_subsumption_resolution,[],[f7001,f300]) ).
fof(f7005,plain,
( ! [X0] :
( ~ in(X0,subset_complement(sF17,sK15))
| ~ open_subset(subset_complement(sF17,sK15),sK12)
| ~ in(X0,sF16) )
| ~ spl19_4
| ~ spl19_7
| ~ spl19_21
| ~ spl19_42
| ~ spl19_43 ),
inference(forward_subsumption_resolution,[],[f7003,f1019]) ).
fof(f7007,plain,
( ! [X0] :
( ~ in(X0,set_difference(sF17,sK15))
| ~ open_subset(subset_complement(sF17,sK15),sK12)
| ~ in(X0,sF16) )
| ~ spl19_3
| ~ spl19_4
| ~ spl19_7
| ~ spl19_21
| ~ spl19_42
| ~ spl19_43 ),
inference(forward_demodulation,[],[f7005,f6895]) ).
fof(f7012,definition,
( spl19_146
<=> open_subset(set_difference(sF17,sK15),sK12) ),
introduced(definition,[new_symbols(definition,[spl19_146])],[avatar_definition]) ).
fof(f7014,plain,
( ~ open_subset(set_difference(sF17,sK15),sK12)
| spl19_146 ),
inference(avatar_component_clause,[],[f7012]) ).
fof(f7016,plain,
( ! [X0] :
( ~ open_subset(set_difference(sF17,sK15),sK12)
| ~ in(X0,set_difference(sF17,sK15))
| ~ in(X0,sF16) )
| ~ spl19_3
| ~ spl19_4
| ~ spl19_7
| ~ spl19_21
| ~ spl19_42
| ~ spl19_43 ),
inference(forward_demodulation,[],[f7007,f6895]) ).
fof(f7018,definition,
( spl19_147
<=> ! [X0] :
( ~ in(X0,set_difference(sF17,sK15))
| ~ in(X0,sF16) ) ),
introduced(definition,[new_symbols(definition,[spl19_147])],[avatar_definition]) ).
fof(f7019,plain,
( ! [X0] :
( ~ in(X0,set_difference(sF17,sK15))
| ~ in(X0,sF16) )
| ~ spl19_147 ),
inference(avatar_component_clause,[],[f7018]) ).
fof(f7020,plain,
( spl19_147
| ~ spl19_146
| ~ spl19_3
| ~ spl19_4
| ~ spl19_7
| ~ spl19_21
| ~ spl19_42
| ~ spl19_43 ),
inference(avatar_split_clause,[],[f7016,f1022,f1018,f542,f345,f298,f293,f7012,f7018]) ).
fof(f7633,plain,
( open_subset(set_difference(sF17,sK15),sK12)
| ~ element(sK15,sF18)
| ~ closed_subset(sK15,sK12)
| ~ spl19_3 ),
inference(superposition,[],[f400,f6862]) ).
fof(f7642,plain,
( ~ element(sK15,sF18)
| ~ closed_subset(sK15,sK12)
| ~ spl19_3
| spl19_146 ),
inference(forward_subsumption_resolution,[],[f7633,f7014]) ).
fof(f7643,plain,
( ~ closed_subset(sK15,sK12)
| ~ spl19_3
| spl19_146 ),
inference(forward_subsumption_resolution,[],[f7642,f295]) ).
fof(f7644,plain,
( $false
| ~ spl19_3
| ~ spl19_5
| spl19_146 ),
inference(forward_subsumption_resolution,[],[f7643,f305]) ).
fof(f7645,plain,
( ~ spl19_3
| ~ spl19_5
| spl19_146 ),
inference(avatar_contradiction_clause,[],[f7644]) ).
fof(f7653,plain,
( ! [X0] :
( ~ in(X0,sF16)
| ~ in(X0,sF17)
| in(X0,sK15) )
| ~ spl19_147 ),
inference(resolution,[],[f7019,f268]) ).
fof(f7656,plain,
( ! [X0] :
( ~ in(X0,sF16)
| in(X0,sK15) )
| ~ spl19_21
| ~ spl19_147 ),
inference(forward_subsumption_resolution,[],[f7653,f3606]) ).
fof(f7658,plain,
( in(sK14,sK15)
| ~ spl19_1
| ~ spl19_21
| ~ spl19_147 ),
inference(resolution,[],[f7656,f287]) ).
fof(f7659,plain,
( $false
| ~ spl19_1
| spl19_6
| ~ spl19_21
| ~ spl19_147 ),
inference(forward_subsumption_resolution,[],[f7658,f310]) ).
fof(f7660,plain,
( ~ spl19_1
| spl19_6
| ~ spl19_21
| ~ spl19_147 ),
inference(avatar_contradiction_clause,[],[f7659]) ).
cnf(s1,plain,
( spl19_1
| spl19_2 ),
inference(sat_conversion,[],[f291]) ).
cnf(s2,plain,
( ~ spl19_1
| spl19_3 ),
inference(sat_conversion,[],[f296]) ).
cnf(s3,plain,
( ~ spl19_1
| spl19_4 ),
inference(sat_conversion,[],[f301]) ).
cnf(s4,plain,
( ~ spl19_1
| spl19_5 ),
inference(sat_conversion,[],[f306]) ).
cnf(s5,plain,
( ~ spl19_1
| ~ spl19_6 ),
inference(sat_conversion,[],[f311]) ).
cnf(s7,plain,
spl19_7,
inference(sat_conversion,[],[f360]) ).
cnf(s28,plain,
( spl19_1
| ~ spl19_7
| spl19_34
| ~ spl19_35
| ~ spl19_36 ),
inference(sat_conversion,[],[f854]) ).
cnf(s32,plain,
( spl19_1
| spl19_24 ),
inference(sat_conversion,[],[f910]) ).
cnf(s33,plain,
( ~ spl19_24
| spl19_35 ),
inference(sat_conversion,[],[f916]) ).
cnf(s35,plain,
( spl19_1
| spl19_36 ),
inference(sat_conversion,[],[f940]) ).
cnf(s36,plain,
( ~ spl19_2
| ~ spl19_24
| ~ spl19_34
| ~ spl19_35
| ~ spl19_37
| spl19_38 ),
inference(sat_conversion,[],[f955]) ).
cnf(s38,plain,
( spl19_1
| spl19_37 ),
inference(sat_conversion,[],[f965]) ).
cnf(s41,plain,
( ~ spl19_3
| ~ spl19_42
| spl19_43 ),
inference(sat_conversion,[],[f1024]) ).
cnf(s43,plain,
( ~ spl19_3
| spl19_42 ),
inference(sat_conversion,[],[f1056]) ).
cnf(s48,plain,
spl19_21,
inference(sat_conversion,[],[f1347]) ).
cnf(s112,plain,
( spl19_1
| ~ spl19_7
| ~ spl19_24
| ~ spl19_38 ),
inference(sat_conversion,[],[f6597]) ).
cnf(s119,plain,
( ~ spl19_3
| ~ spl19_4
| ~ spl19_7
| ~ spl19_21
| ~ spl19_42
| ~ spl19_43
| ~ spl19_146
| spl19_147 ),
inference(sat_conversion,[],[f7020]) ).
cnf(s134,plain,
( ~ spl19_3
| ~ spl19_5
| spl19_146 ),
inference(sat_conversion,[],[f7645]) ).
cnf(s135,plain,
( ~ spl19_1
| spl19_6
| ~ spl19_21
| ~ spl19_147 ),
inference(sat_conversion,[],[f7660]) ).
cnf(s145,plain,
spl19_1,
inference(rat,[],[s28,s36,s112,s33,s1,s32,s35,s38,s7]) ).
cnf(s147,plain,
~ spl19_6,
inference(rat,[],[s5,s145]) ).
cnf(s148,plain,
spl19_5,
inference(rat,[],[s4,s145]) ).
cnf(s149,plain,
spl19_4,
inference(rat,[],[s3,s145]) ).
cnf(s150,plain,
spl19_3,
inference(rat,[],[s2,s145]) ).
cnf(s153,plain,
~ spl19_147,
inference(rat,[],[s135,s145,s48,s147]) ).
cnf(s155,plain,
spl19_146,
inference(rat,[],[s134,s148,s150]) ).
cnf(s157,plain,
spl19_42,
inference(rat,[],[s43,s150]) ).
cnf(s161,plain,
spl19_43,
inference(rat,[],[s41,s150,s157]) ).
cnf(s162,plain,
$false,
inference(rat,[],[s119,s153,s155,s150,s149,s48,s7,s161,s157]) ).
fof(f7662,plain,
$false,
inference(avatar_sat_refutation,[],[s162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU313+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 04:34:05 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 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
% 12.28/2.86 % (3205386)Detected formulas, will run a generic FOF schedule.
% 12.28/2.86 % (3205497)dis-21_1_sil=8000:lcm=predicate:random_seed=2658916861: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)
% 12.28/2.86 % (3205495)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=184757614:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.28/2.86 % (3205492)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=2149063677:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.28/2.86 % (3205493)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=666250922:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.28/2.86 % (3205496)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=76258540:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.28/2.86 % (3205491)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=830364712:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.28/2.86 % (3205497)Instruction limit reached!
% 12.28/2.86 % (3205497)------------------------------
% 12.28/2.86 % (3205497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.28/2.86 % (3205497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.28/2.86 % (3205497)CaDiCaL version: 2.1.3
% 12.28/2.86 % (3205497)Termination reason: Instruction limit
% 12.28/2.86 % (3205497)Termination phase: Saturation
% 12.28/2.86 % (3205497)Time elapsed: 0.043 s
% 12.28/2.86 % (3205497)Peak memory usage: 89 MB
% 12.28/2.86 % (3205497)Instructions burned: 132 (million)
% 12.28/2.86 % (3205494)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=257451983:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.28/2.86 % (3205494)Refutation not found, incomplete strategy
% 12.28/2.86 % (3205494)------------------------------
% 12.28/2.86 % (3205494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.28/2.86 % (3205494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.28/2.86 % (3205494)CaDiCaL version: 2.1.3
% 12.28/2.86 % (3205494)Termination reason: Refutation not found, incomplete strategy
% 12.28/2.86 % (3205494)Time elapsed: 0.004 s
% 12.28/2.86 % (3205494)Peak memory usage: 89 MB
% 12.28/2.86 % (3205494)Instructions burned: 3 (million)
% 12.28/2.86 % (3205495)Instruction limit reached!
% 12.28/2.86 % (3205495)------------------------------
% 12.28/2.86 % (3205495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.28/2.86 % (3205495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.28/2.86 % (3205495)CaDiCaL version: 2.1.3
% 12.28/2.86 % (3205495)Termination reason: Instruction limit
% 12.28/2.86 % (3205495)Termination phase: Saturation
% 12.28/2.86 % (3205495)Time elapsed: 0.079 s
% 12.28/2.86 % (3205495)Peak memory usage: 88 MB
% 12.28/2.86 % (3205495)Instructions burned: 120 (million)
% 12.28/2.86 % (3205496)Instruction limit reached!
% 12.28/2.86 % (3205496)------------------------------
% 12.28/2.86 % (3205496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.28/2.86 % (3205496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.28/2.86 % (3205496)CaDiCaL version: 2.1.3
% 12.28/2.86 % (3205496)Termination reason: Instruction limit
% 12.28/2.86 % (3205496)Termination phase: Saturation
% 12.28/2.86 % (3205496)Time elapsed: 0.108 s
% 12.28/2.86 % (3205496)Peak memory usage: 89 MB
% 12.28/2.86 % (3205496)Instructions burned: 140 (million)
% 12.28/2.86 % (3205504)lrs+10_1_sil=8000:sp=occurrence:random_seed=4251492185:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 12.28/2.86 % (3205504)Instruction limit reached!
% 12.28/2.86 % (3205504)------------------------------
% 12.28/2.86 % (3205504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.28/2.86 % (3205504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.28/2.86 % (3205504)CaDiCaL version: 2.1.3
% 12.28/2.86 % (3205504)Termination reason: Instruction limit
% 12.28/2.86 % (3205504)Termination phase: Saturation
% 12.28/2.86 % (3205504)Time elapsed: 0.158 s
% 12.28/2.86 % (3205504)Peak memory usage: 92 MB
% 12.28/2.86 % (3205504)Instructions burned: 285 (million)
% 12.28/2.86 % (3205518)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2174257037:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 12.28/2.86 % (3205494)------------------------------
% 12.28/2.86 % (3205494)------------------------------
% 12.28/2.86 % (3205528)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1590226553:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 12.28/2.86 % (3205518)Instruction limit reached!
% 12.28/2.86 % (3205518)------------------------------
% 12.28/2.86 % (3205518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.28/2.86 % (3205518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.28/2.86 % (3205518)CaDiCaL version: 2.1.3
% 12.28/2.86 % (3205518)Termination reason: Instruction limit
% 12.28/2.86 % (3205518)Termination phase: Saturation
% 12.28/2.86 % (3205518)Time elapsed: 0.159 s
% 12.28/2.86 % (3205518)Peak memory usage: 90 MB
% 12.28/2.86 % (3205518)Instructions burned: 157 (million)
% 12.28/2.86 % (3205544)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=2494863215:s2a=on:i=248:s2at=1.23:gtg=position_2994 on theBenchmark for (2994ds/248Mi)
% 12.28/2.86 % (3205544)Instruction limit reached!
% 12.28/2.86 % (3205544)------------------------------
% 12.28/2.86 % (3205544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.28/2.86 % (3205544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.28/2.86 % (3205544)CaDiCaL version: 2.1.3
% 12.28/2.86 % (3205544)Termination reason: Instruction limit
% 12.28/2.86 % (3205544)Termination phase: Saturation
% 12.28/2.86 % (3205544)Time elapsed: 0.120 s
% 12.28/2.86 % (3205544)Peak memory usage: 93 MB
% 12.28/2.86 % (3205544)Instructions burned: 248 (million)
% 12.28/2.86 % (3205547)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2696678743:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 12.28/2.86 % (3205528)Instruction limit reached!
% 12.28/2.86 % (3205528)------------------------------
% 12.28/2.86 % (3205528)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.28/2.86 % (3205528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.28/2.86 % (3205528)CaDiCaL version: 2.1.3
% 12.28/2.86 % (3205528)Termination reason: Instruction limit
% 12.28/2.86 % (3205528)Termination phase: Saturation
% 12.28/2.86 % (3205528)Time elapsed: 0.356 s
% 12.28/2.86 % (3205528)Peak memory usage: 91 MB
% 12.28/2.86 % (3205528)Instructions burned: 326 (million)
% 12.28/2.86 % (3205552)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3870117987:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 12.28/2.86 % (3205554)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1610121299:cts=off:i=113:fsr=off:ss=included:sgt=4_2991 on theBenchmark for (2991ds/113Mi)
% 12.28/2.86 % (3205547)Instruction limit reached!
% 12.28/2.86 % (3205547)------------------------------
% 12.28/2.86 % (3205547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.28/2.86 % (3205547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.28/2.86 % (3205547)CaDiCaL version: 2.1.3
% 12.28/2.86 % (3205547)Termination reason: Instruction limit
% 12.28/2.86 % (3205547)Termination phase: Saturation
% 12.28/2.86 % (3205547)Time elapsed: 0.270 s
% 12.28/2.86 % (3205547)Peak memory usage: 90 MB
% 12.28/2.86 % (3205547)Instructions burned: 294 (million)
% 12.28/2.86 % (3205556)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=762150751:i=127:av=off:fsr=off:sup=off_2990 on theBenchmark for (2990ds/127Mi)
% 12.28/2.86 % (3205554)Instruction limit reached!
% 12.28/2.86 % (3205554)------------------------------
% 12.28/2.86 % (3205554)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.28/2.86 % (3205554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.28/2.86 % (3205554)CaDiCaL version: 2.1.3
% 12.28/2.86 % (3205554)Termination reason: Instruction limit
% 12.28/2.86 % (3205554)Termination phase: Saturation
% 12.28/2.86 % (3205554)Time elapsed: 0.095 s
% 12.28/2.86 % (3205554)Peak memory usage: 89 MB
% 12.28/2.86 % (3205554)Instructions burned: 113 (million)
% 12.28/2.86 % (3205556)Instruction limit reached!
% 12.28/2.86 % (3205556)------------------------------
% 12.28/2.86 % (3205556)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.28/2.86 % (3205556)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.28/2.86 % (3205556)CaDiCaL version: 2.1.3
% 12.28/2.86 % (3205556)Termination reason: Instruction limit
% 12.28/2.86 % (3205556)Termination phase: Saturation
% 12.28/2.86 % (3205556)Time elapsed: 0.118 s
% 12.28/2.86 % (3205556)Peak memory usage: 88 MB
% 12.28/2.86 % (3205556)Instructions burned: 127 (million)
% 12.28/2.86 % (3205563)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3249443964:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2988 on theBenchmark for (2988ds/114Mi)
% 12.28/2.86 % (3205567)lrs+10_1_sil=8000:sp=occurrence:random_seed=2873915282:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2988 on theBenchmark for (2988ds/907Mi)
% 12.28/2.86 % (3205563)Instruction limit reached!
% 12.28/2.86 % (3205563)------------------------------
% 12.28/2.86 % (3205563)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.28/2.86 % (3205563)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.28/2.86 % (3205563)CaDiCaL version: 2.1.3
% 12.28/2.86 % (3205563)Termination reason: Instruction limit
% 12.28/2.86 % (3205563)Termination phase: Saturation
% 12.28/2.86 % (3205563)Time elapsed: 0.117 s
% 12.28/2.86 % (3205563)Peak memory usage: 89 MB
% 12.28/2.86 % (3205563)Instructions burned: 114 (million)
% 12.28/2.86 % (3205570)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2082536277:i=437:sd=1:aac=none:ss=included_2987 on theBenchmark for (2987ds/437Mi)
% 12.28/2.86 % (3205491)First to succeed.
% 12.28/2.86 % (3205491)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3205386"
% 12.28/2.86 % (3205573)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3068143236:i=5202:ss=axioms:sgt=16_2984 on theBenchmark for (2984ds/5202Mi)
% 12.28/2.86 % (3205491)Refutation found. Thanks to Tanya!
% 12.28/2.86 % SZS status Theorem for theBenchmark
% 12.28/2.86 % SZS output start Proof for theBenchmark
% See solution above
% 14.74/3.12 % (3205491)------------------------------
% 14.74/3.12 % (3205491)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 14.74/3.12 % (3205491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.74/3.12 % (3205491)CaDiCaL version: 2.1.3
% 14.74/3.12 % (3205491)Termination reason: Refutation
% 14.74/3.12 % (3205491)Time elapsed: 1.588 s
% 14.74/3.12 % (3205491)Peak memory usage: 140 MB
% 14.74/3.12 % (3205491)Instructions burned: 2182 (million)
% 14.74/3.12 % (3205491)------------------------------
% 14.74/3.12 % (3205491)------------------------------
% 14.74/3.12 % (3205386)Success in time 1.999 s
% 14.74/3.12 % Vampire exiting
%------------------------------------------------------------------------------