TSTP Solution File: SEU320+2 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU320+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:05:46 EDT 2023
% Result : Theorem 195.55s 26.85s
% Output : CNFRefutation 195.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 22
% Syntax : Number of formulae : 135 ( 39 unt; 0 def)
% Number of atoms : 449 ( 93 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 528 ( 214 ~; 212 |; 73 &)
% ( 9 <=>; 19 =>; 0 <=; 1 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 215 ( 1 sgn; 107 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f35,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f89,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f98,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> set_difference(X0,X1) = subset_complement(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f138,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f145,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(f247,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(f342,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
( ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
fof(f418,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_1) ).
fof(f425,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tops_1) ).
fof(f426,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(negated_conjecture,[],[f425]) ).
fof(f436,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f438,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f444,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(f446,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f468,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f475,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( ( ( topstr_closure(X0,X1) = X1
& topological_space(X0) )
=> closed_subset(X1,X0) )
& ( closed_subset(X1,X0)
=> topstr_closure(X0,X1) = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_pre_topc) ).
fof(f672,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f98]) ).
fof(f705,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f145]) ).
fof(f794,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f247]) ).
fof(f892,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ( in(X3,X2)
<=> ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& element(X2,powerset(powerset(the_carrier(X0)))) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f342]) ).
fof(f893,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ( in(X3,X2)
<=> ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& element(X2,powerset(powerset(the_carrier(X0)))) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f892]) ).
fof(f993,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f418]) ).
fof(f999,plain,
? [X0] :
( ? [X1] :
( ( open_subset(X1,X0)
<~> closed_subset(subset_complement(the_carrier(X0),X1),X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(ennf_transformation,[],[f426]) ).
fof(f1054,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subset(X1,X0)
| topstr_closure(X0,X1) != X1
| ~ topological_space(X0) )
& ( topstr_closure(X0,X1) = X1
| ~ closed_subset(X1,X0) ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f475]) ).
fof(f1055,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subset(X1,X0)
| topstr_closure(X0,X1) != X1
| ~ topological_space(X0) )
& ( topstr_closure(X0,X1) = X1
| ~ closed_subset(X1,X0) ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(flattening,[],[f1054]) ).
fof(f1865,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ( ( in(X3,X2)
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) ) )
& ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& element(X2,powerset(powerset(the_carrier(X0)))) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(nnf_transformation,[],[f893]) ).
fof(f1866,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ( ( in(X3,X2)
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) ) )
& ( ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& element(X2,powerset(powerset(the_carrier(X0)))) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(rectify,[],[f1865]) ).
fof(f1867,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ( ( in(X3,X2)
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) ) )
& ( ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& element(X2,powerset(powerset(the_carrier(X0)))) )
=> ( ! [X3] :
( ( ( in(X3,sK359(X0,X1))
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) ) )
& ( ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) )
| ~ in(X3,sK359(X0,X1)) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& element(sK359(X0,X1),powerset(powerset(the_carrier(X0)))) ) ),
introduced(choice_axiom,[]) ).
fof(f1868,plain,
! [X0,X1,X3] :
( ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) )
=> ( subset(X1,X3)
& closed_subset(sK360(X0,X1,X3),X0)
& sK360(X0,X1,X3) = X3
& element(sK360(X0,X1,X3),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f1869,plain,
! [X0,X1] :
( ( ! [X3] :
( ( ( in(X3,sK359(X0,X1))
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) ) )
& ( ( subset(X1,X3)
& closed_subset(sK360(X0,X1,X3),X0)
& sK360(X0,X1,X3) = X3
& element(sK360(X0,X1,X3),powerset(the_carrier(X0))) )
| ~ in(X3,sK359(X0,X1)) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& element(sK359(X0,X1),powerset(powerset(the_carrier(X0)))) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK359,sK360])],[f1866,f1868,f1867]) ).
fof(f1908,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subset(X1,X0)
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0) )
& ( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0) ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f993]) ).
fof(f1912,plain,
? [X0] :
( ? [X1] :
( ( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ open_subset(X1,X0) )
& ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| open_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(nnf_transformation,[],[f999]) ).
fof(f1913,plain,
? [X0] :
( ? [X1] :
( ( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ open_subset(X1,X0) )
& ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| open_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(flattening,[],[f1912]) ).
fof(f1914,plain,
( ? [X0] :
( ? [X1] :
( ( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ open_subset(X1,X0) )
& ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| open_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) )
=> ( ? [X1] :
( ( ~ closed_subset(subset_complement(the_carrier(sK374),X1),sK374)
| ~ open_subset(X1,sK374) )
& ( closed_subset(subset_complement(the_carrier(sK374),X1),sK374)
| open_subset(X1,sK374) )
& element(X1,powerset(the_carrier(sK374))) )
& top_str(sK374) ) ),
introduced(choice_axiom,[]) ).
fof(f1915,plain,
( ? [X1] :
( ( ~ closed_subset(subset_complement(the_carrier(sK374),X1),sK374)
| ~ open_subset(X1,sK374) )
& ( closed_subset(subset_complement(the_carrier(sK374),X1),sK374)
| open_subset(X1,sK374) )
& element(X1,powerset(the_carrier(sK374))) )
=> ( ( ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
| ~ open_subset(sK375,sK374) )
& ( closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
| open_subset(sK375,sK374) )
& element(sK375,powerset(the_carrier(sK374))) ) ),
introduced(choice_axiom,[]) ).
fof(f1916,plain,
( ( ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
| ~ open_subset(sK375,sK374) )
& ( closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
| open_subset(sK375,sK374) )
& element(sK375,powerset(the_carrier(sK374)))
& top_str(sK374) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK374,sK375])],[f1913,f1915,f1914]) ).
fof(f1927,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f438]) ).
fof(f1933,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f446]) ).
fof(f2045,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f35]) ).
fof(f2278,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f89]) ).
fof(f2323,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f672]) ).
fof(f2402,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f138]) ).
fof(f2404,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f705]) ).
fof(f2577,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f794]) ).
fof(f3076,plain,
! [X3,X0,X1] :
( subset(X1,X3)
| ~ in(X3,sK359(X0,X1))
| ~ element(X3,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f1869]) ).
fof(f3190,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1908]) ).
fof(f3191,plain,
! [X0,X1] :
( closed_subset(X1,X0)
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1908]) ).
fof(f3200,plain,
top_str(sK374),
inference(cnf_transformation,[],[f1916]) ).
fof(f3201,plain,
element(sK375,powerset(the_carrier(sK374))),
inference(cnf_transformation,[],[f1916]) ).
fof(f3202,plain,
( closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
| open_subset(sK375,sK374) ),
inference(cnf_transformation,[],[f1916]) ).
fof(f3203,plain,
( ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
| ~ open_subset(sK375,sK374) ),
inference(cnf_transformation,[],[f1916]) ).
fof(f3221,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f436]) ).
fof(f3225,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1927]) ).
fof(f3236,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f444]) ).
fof(f3238,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f1933]) ).
fof(f3239,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f1933]) ).
fof(f3281,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f468]) ).
fof(f3289,plain,
! [X0,X1] :
( topstr_closure(X0,X1) = X1
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1055]) ).
fof(f3386,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f2045,f3281,f3281]) ).
cnf(c_103,plain,
set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(cnf_transformation,[],[f3386]) ).
cnf(c_335,plain,
cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f2278]) ).
cnf(c_380,plain,
( ~ element(X0,powerset(X1))
| set_difference(X1,X0) = subset_complement(X1,X0) ),
inference(cnf_transformation,[],[f2323]) ).
cnf(c_458,plain,
element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f2402]) ).
cnf(c_460,plain,
( ~ element(X0,powerset(X1))
| element(subset_complement(X1,X0),powerset(X1)) ),
inference(cnf_transformation,[],[f2404]) ).
cnf(c_633,plain,
( ~ element(X0,powerset(X1))
| subset_complement(X1,subset_complement(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f2577]) ).
cnf(c_1129,plain,
( ~ in(X0,sK359(X1,X2))
| ~ element(X0,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f3076]) ).
cnf(c_1246,plain,
( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| closed_subset(X1,X0) ),
inference(cnf_transformation,[],[f3191]) ).
cnf(c_1247,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ closed_subset(X0,X1)
| ~ top_str(X1)
| open_subset(subset_complement(the_carrier(X1),X0),X1) ),
inference(cnf_transformation,[],[f3190]) ).
cnf(c_1256,negated_conjecture,
( ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
| ~ open_subset(sK375,sK374) ),
inference(cnf_transformation,[],[f3203]) ).
cnf(c_1257,negated_conjecture,
( closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
| open_subset(sK375,sK374) ),
inference(cnf_transformation,[],[f3202]) ).
cnf(c_1258,negated_conjecture,
element(sK375,powerset(the_carrier(sK374))),
inference(cnf_transformation,[],[f3201]) ).
cnf(c_1259,negated_conjecture,
top_str(sK374),
inference(cnf_transformation,[],[f3200]) ).
cnf(c_1277,plain,
subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f3221]) ).
cnf(c_1280,plain,
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f3225]) ).
cnf(c_1292,plain,
set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f3236]) ).
cnf(c_1294,plain,
( ~ subset(X0,X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f3239]) ).
cnf(c_1295,plain,
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f3238]) ).
cnf(c_1345,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ closed_subset(X0,X1)
| ~ top_str(X1)
| topstr_closure(X1,X0) = X0 ),
inference(cnf_transformation,[],[f3289]) ).
cnf(c_2832,plain,
( ~ subset(X0,X1)
| set_difference(X1,X0) = subset_complement(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_1294,c_380]) ).
cnf(c_2834,plain,
( ~ subset(X0,X1)
| element(subset_complement(X1,X0),powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_1294,c_460]) ).
cnf(c_2836,plain,
( ~ subset(X0,X1)
| subset_complement(X1,subset_complement(X1,X0)) = X0 ),
inference(prop_impl_just,[status(thm)],[c_1294,c_633]) ).
cnf(c_13791,plain,
element(X0,powerset(X0)),
inference(demodulation,[status(thm)],[c_458,c_335]) ).
cnf(c_49436,plain,
( X0 != sK374
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| topstr_closure(X0,X1) = X1 ),
inference(resolution_lifted,[status(thm)],[c_1345,c_1259]) ).
cnf(c_49437,plain,
( ~ element(X0,powerset(the_carrier(sK374)))
| ~ closed_subset(X0,sK374)
| topstr_closure(sK374,X0) = X0 ),
inference(unflattening,[status(thm)],[c_49436]) ).
cnf(c_49666,plain,
( X0 != sK374
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_1247,c_1259]) ).
cnf(c_49667,plain,
( ~ element(X0,powerset(the_carrier(sK374)))
| ~ closed_subset(X0,sK374)
| open_subset(subset_complement(the_carrier(sK374),X0),sK374) ),
inference(unflattening,[status(thm)],[c_49666]) ).
cnf(c_49774,plain,
( X0 != sK374
| ~ in(X1,sK359(X0,X2))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| subset(X2,X1) ),
inference(resolution_lifted,[status(thm)],[c_1129,c_1259]) ).
cnf(c_49775,plain,
( ~ in(X0,sK359(sK374,X1))
| ~ element(X0,powerset(the_carrier(sK374)))
| ~ element(X1,powerset(the_carrier(sK374)))
| ~ topological_space(sK374)
| subset(X1,X0) ),
inference(unflattening,[status(thm)],[c_49774]) ).
cnf(c_50340,plain,
( X0 != sK374
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| closed_subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_1246,c_1259]) ).
cnf(c_50341,plain,
( ~ open_subset(subset_complement(the_carrier(sK374),X0),sK374)
| ~ element(X0,powerset(the_carrier(sK374)))
| closed_subset(X0,sK374) ),
inference(unflattening,[status(thm)],[c_50340]) ).
cnf(c_109478,plain,
( ~ subset(X0,X1)
| set_difference(X1,X0) = subset_complement(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_2832]) ).
cnf(c_109480,plain,
( ~ subset(X0,X1)
| element(subset_complement(X1,X0),powerset(X1)) ),
inference(prop_impl_just,[status(thm)],[c_2834]) ).
cnf(c_109482,plain,
( ~ subset(X0,X1)
| subset_complement(X1,subset_complement(X1,X0)) = X0 ),
inference(prop_impl_just,[status(thm)],[c_2836]) ).
cnf(c_157955,plain,
X0 = X0,
theory(equality) ).
cnf(c_157957,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_157989,plain,
( X0 != X1
| X2 != X3
| ~ open_subset(X1,X3)
| open_subset(X0,X2) ),
theory(equality) ).
cnf(c_191351,plain,
( ~ element(subset_complement(the_carrier(sK374),sK375),powerset(the_carrier(sK374)))
| ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
| open_subset(subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)),sK374) ),
inference(instantiation,[status(thm)],[c_49667]) ).
cnf(c_197545,plain,
subset(sK375,the_carrier(sK374)),
inference(superposition,[status(thm)],[c_1258,c_1295]) ).
cnf(c_203459,plain,
( ~ subset(sK375,the_carrier(sK374))
| element(subset_complement(the_carrier(sK374),sK375),powerset(the_carrier(sK374))) ),
inference(instantiation,[status(thm)],[c_109480]) ).
cnf(c_203641,plain,
sK374 = sK374,
inference(instantiation,[status(thm)],[c_157955]) ).
cnf(c_233383,plain,
( X0 != sK375
| X1 != sK374
| ~ open_subset(sK375,sK374)
| open_subset(X0,X1) ),
inference(instantiation,[status(thm)],[c_157989]) ).
cnf(c_247886,plain,
( X0 != subset_complement(the_carrier(sK374),X1)
| X2 != sK374
| ~ open_subset(subset_complement(the_carrier(sK374),X1),sK374)
| open_subset(X0,X2) ),
inference(instantiation,[status(thm)],[c_157989]) ).
cnf(c_253837,plain,
( set_difference(sK375,empty_set) != sK375
| X0 != sK374
| ~ open_subset(sK375,sK374)
| open_subset(set_difference(sK375,empty_set),X0) ),
inference(instantiation,[status(thm)],[c_233383]) ).
cnf(c_253838,plain,
set_difference(sK375,empty_set) = sK375,
inference(instantiation,[status(thm)],[c_1292]) ).
cnf(c_253857,plain,
sK375 = sK375,
inference(instantiation,[status(thm)],[c_157955]) ).
cnf(c_272890,plain,
( set_difference(sK375,empty_set) != sK375
| sK374 != sK374
| ~ open_subset(sK375,sK374)
| open_subset(set_difference(sK375,empty_set),sK374) ),
inference(instantiation,[status(thm)],[c_253837]) ).
cnf(c_277173,plain,
( sK374 != sK374
| sK375 != subset_complement(the_carrier(sK374),X0)
| ~ open_subset(subset_complement(the_carrier(sK374),X0),sK374)
| open_subset(sK375,sK374) ),
inference(instantiation,[status(thm)],[c_247886]) ).
cnf(c_278864,plain,
( sK374 != sK374
| sK375 != subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375))
| ~ open_subset(subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)),sK374)
| open_subset(sK375,sK374) ),
inference(instantiation,[status(thm)],[c_277173]) ).
cnf(c_349040,plain,
set_difference(X0,set_difference(X0,X1)) = subset_complement(X0,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_1277,c_109478]) ).
cnf(c_427611,plain,
( ~ open_subset(set_difference(the_carrier(sK374),set_difference(the_carrier(sK374),X0)),sK374)
| ~ element(set_difference(the_carrier(sK374),X0),powerset(the_carrier(sK374)))
| closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
inference(superposition,[status(thm)],[c_349040,c_50341]) ).
cnf(c_432466,plain,
( ~ open_subset(set_difference(X0,set_difference(X0,the_carrier(sK374))),sK374)
| ~ element(set_difference(the_carrier(sK374),X0),powerset(the_carrier(sK374)))
| closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
inference(superposition,[status(thm)],[c_103,c_427611]) ).
cnf(c_449955,plain,
( ~ open_subset(set_difference(X0,set_difference(X0,the_carrier(sK374))),sK374)
| ~ subset(set_difference(the_carrier(sK374),X0),the_carrier(sK374))
| closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
inference(superposition,[status(thm)],[c_1294,c_432466]) ).
cnf(c_449967,plain,
( ~ open_subset(set_difference(X0,set_difference(X0,the_carrier(sK374))),sK374)
| closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
inference(forward_subsumption_resolution,[status(thm)],[c_449955,c_1277]) ).
cnf(c_505999,plain,
( ~ in(X0,sK359(sK374,sK375))
| ~ element(X0,powerset(the_carrier(sK374)))
| ~ topological_space(sK374)
| subset(sK375,X0) ),
inference(superposition,[status(thm)],[c_1258,c_49775]) ).
cnf(c_507567,plain,
( ~ in(the_carrier(sK374),sK359(sK374,sK375))
| ~ topological_space(sK374)
| subset(sK375,the_carrier(sK374)) ),
inference(superposition,[status(thm)],[c_13791,c_505999]) ).
cnf(c_507701,plain,
subset(sK375,the_carrier(sK374)),
inference(global_subsumption_just,[status(thm)],[c_507567,c_197545]) ).
cnf(c_542562,plain,
( subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)) != X0
| sK375 != X0
| sK375 = subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)) ),
inference(instantiation,[status(thm)],[c_157957]) ).
cnf(c_556717,plain,
set_difference(sK375,the_carrier(sK374)) = empty_set,
inference(superposition,[status(thm)],[c_507701,c_1280]) ).
cnf(c_563396,plain,
( ~ closed_subset(subset_complement(the_carrier(sK374),X0),sK374)
| ~ subset(X0,the_carrier(sK374))
| topstr_closure(sK374,subset_complement(the_carrier(sK374),X0)) = subset_complement(the_carrier(sK374),X0) ),
inference(superposition,[status(thm)],[c_109480,c_49437]) ).
cnf(c_573016,plain,
( subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)) != sK375
| sK375 != sK375
| sK375 = subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)) ),
inference(instantiation,[status(thm)],[c_542562]) ).
cnf(c_573017,plain,
( ~ subset(sK375,the_carrier(sK374))
| subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)) = sK375 ),
inference(instantiation,[status(thm)],[c_109482]) ).
cnf(c_575682,negated_conjecture,
open_subset(sK375,sK374),
inference(global_subsumption_just,[status(thm)],[c_1257,c_1257,c_191351,c_197545,c_203459,c_203641,c_253857,c_278864,c_573016,c_573017]) ).
cnf(c_625833,plain,
( ~ subset(sK375,the_carrier(sK374))
| topstr_closure(sK374,subset_complement(the_carrier(sK374),sK375)) = subset_complement(the_carrier(sK374),sK375)
| open_subset(sK375,sK374) ),
inference(superposition,[status(thm)],[c_1257,c_563396]) ).
cnf(c_625834,plain,
( topstr_closure(sK374,subset_complement(the_carrier(sK374),sK375)) = subset_complement(the_carrier(sK374),sK375)
| open_subset(sK375,sK374) ),
inference(forward_subsumption_resolution,[status(thm)],[c_625833,c_507701]) ).
cnf(c_625837,plain,
open_subset(sK375,sK374),
inference(global_subsumption_just,[status(thm)],[c_625834,c_575682]) ).
cnf(c_625845,plain,
~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374),
inference(backward_subsumption_resolution,[status(thm)],[c_1256,c_625837]) ).
cnf(c_645723,plain,
set_difference(X0,set_difference(X0,X1)) = subset_complement(X0,set_difference(X0,X1)),
inference(superposition,[status(thm)],[c_1277,c_109478]) ).
cnf(c_645730,plain,
set_difference(the_carrier(sK374),sK375) = subset_complement(the_carrier(sK374),sK375),
inference(superposition,[status(thm)],[c_507701,c_109478]) ).
cnf(c_646535,plain,
~ closed_subset(set_difference(the_carrier(sK374),sK375),sK374),
inference(demodulation,[status(thm)],[c_625845,c_645730]) ).
cnf(c_756434,plain,
( ~ open_subset(set_difference(the_carrier(sK374),set_difference(the_carrier(sK374),X0)),sK374)
| ~ element(set_difference(the_carrier(sK374),X0),powerset(the_carrier(sK374)))
| closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
inference(superposition,[status(thm)],[c_645723,c_50341]) ).
cnf(c_757064,plain,
( ~ open_subset(set_difference(X0,set_difference(X0,the_carrier(sK374))),sK374)
| ~ element(set_difference(the_carrier(sK374),X0),powerset(the_carrier(sK374)))
| closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
inference(superposition,[status(thm)],[c_103,c_756434]) ).
cnf(c_769891,plain,
( ~ open_subset(set_difference(X0,set_difference(X0,the_carrier(sK374))),sK374)
| closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
inference(global_subsumption_just,[status(thm)],[c_757064,c_449967]) ).
cnf(c_769906,plain,
( ~ open_subset(set_difference(sK375,empty_set),sK374)
| closed_subset(set_difference(the_carrier(sK374),sK375),sK374) ),
inference(superposition,[status(thm)],[c_556717,c_769891]) ).
cnf(c_769909,plain,
~ open_subset(set_difference(sK375,empty_set),sK374),
inference(forward_subsumption_resolution,[status(thm)],[c_769906,c_646535]) ).
cnf(c_769921,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_769909,c_575682,c_272890,c_253838,c_203641]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU320+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 21:20:54 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.47 Running first-order theorem proving
% 0.19/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 195.55/26.85 % SZS status Started for theBenchmark.p
% 195.55/26.85 % SZS status Theorem for theBenchmark.p
% 195.55/26.85
% 195.55/26.85 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 195.55/26.85
% 195.55/26.85 ------ iProver source info
% 195.55/26.85
% 195.55/26.85 git: date: 2023-05-31 18:12:56 +0000
% 195.55/26.85 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 195.55/26.85 git: non_committed_changes: false
% 195.55/26.85 git: last_make_outside_of_git: false
% 195.55/26.85
% 195.55/26.85 ------ Parsing...
% 195.55/26.85 ------ Clausification by vclausify_rel & Parsing by iProver...
% 195.55/26.85
% 195.55/26.85 ------ Preprocessing... sup_sim: 95 sf_s rm: 96 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e sup_sim: 67 sf_s rm: 25 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 25 0s sf_e pe_s pe_e
% 195.55/26.85
% 195.55/26.85 ------ Preprocessing... gs_s sp: 15 0s gs_e snvd_s sp: 0 0s snvd_e
% 195.55/26.85
% 195.55/26.85 ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 195.55/26.85 ------ Proving...
% 195.55/26.85 ------ Problem Properties
% 195.55/26.85
% 195.55/26.85
% 195.55/26.85 clauses 1285
% 195.55/26.85 conjectures 3
% 195.55/26.85 EPR 173
% 195.55/26.85 Horn 959
% 195.55/26.85 unary 172
% 195.55/26.85 binary 382
% 195.55/26.85 lits 3896
% 195.55/26.85 lits eq 548
% 195.55/26.85 fd_pure 0
% 195.55/26.85 fd_pseudo 0
% 195.55/26.85 fd_cond 44
% 195.55/26.85 fd_pseudo_cond 117
% 195.55/26.85 AC symbols 0
% 195.55/26.85
% 195.55/26.85 ------ Schedule dynamic 5 is on
% 195.55/26.85
% 195.55/26.85 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 195.55/26.85
% 195.55/26.85
% 195.55/26.85 ------
% 195.55/26.85 Current options:
% 195.55/26.85 ------
% 195.55/26.85
% 195.55/26.85
% 195.55/26.85
% 195.55/26.85
% 195.55/26.85 ------ Proving...
% 195.55/26.85 Proof_search_loop: time out after: 12171 full_loop iterations
% 195.55/26.85
% 195.55/26.85 ------ Input Options"--res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 195.55/26.85
% 195.55/26.85
% 195.55/26.85 ------
% 195.55/26.85 Current options:
% 195.55/26.85 ------
% 195.55/26.85
% 195.55/26.85
% 195.55/26.85
% 195.55/26.85
% 195.55/26.85 ------ Proving...
% 195.55/26.85
% 195.55/26.85
% 195.55/26.85 % SZS status Theorem for theBenchmark.p
% 195.55/26.85
% 195.55/26.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 195.55/26.85
% 195.55/26.86
%------------------------------------------------------------------------------