TSTP Solution File: SEU319+2 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU319+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n007.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 88.89s 12.89s
% Output : CNFRefutation 88.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 100 ( 11 unt; 0 def)
% Number of atoms : 402 ( 61 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 518 ( 216 ~; 219 |; 57 &)
% ( 7 <=>; 18 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-3 aty)
% Number of variables : 141 ( 0 sgn; 59 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f102,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(f167,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f279,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f356,axiom,
! [X0] :
( one_sorted_str(X0)
=> the_carrier(X0) = cast_as_carrier_subset(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_pre_topc) ).
fof(f380,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(f418,conjecture,
! [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(f419,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(negated_conjecture,[],[f418]) ).
fof(f459,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( in(X3,X2)
<=> ( subset(X1,X3)
& closed_subset(X3,X0) ) ) )
& element(X2,powerset(powerset(the_carrier(X0)))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_pre_topc) ).
fof(f673,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,[],[f102]) ).
fof(f722,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f167]) ).
fof(f815,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f279]) ).
fof(f906,plain,
! [X0] :
( the_carrier(X0) = cast_as_carrier_subset(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f356]) ).
fof(f940,plain,
! [X0] :
( ! [X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1)
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f380]) ).
fof(f992,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,[],[f419]) ).
fof(f1030,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( ( in(X3,X2)
<=> ( subset(X1,X3)
& closed_subset(X3,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,[],[f459]) ).
fof(f1031,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( ( in(X3,X2)
<=> ( subset(X1,X3)
& closed_subset(X3,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,[],[f1030]) ).
fof(f1403,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,[],[f673]) ).
fof(f1507,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK169(X0))
& element(sK169(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1508,plain,
! [X0] :
( ( ~ empty(sK169(X0))
& element(sK169(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK169])],[f815,f1507]) ).
fof(f1906,plain,
? [X0] :
( ? [X1] :
( ( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(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,[],[f992]) ).
fof(f1907,plain,
? [X0] :
( ? [X1] :
( ( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(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(flattening,[],[f1906]) ).
fof(f1908,plain,
( ? [X0] :
( ? [X1] :
( ( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0) )
& ( open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) )
=> ( ? [X1] :
( ( ~ open_subset(subset_complement(the_carrier(sK373),X1),sK373)
| ~ closed_subset(X1,sK373) )
& ( open_subset(subset_complement(the_carrier(sK373),X1),sK373)
| closed_subset(X1,sK373) )
& element(X1,powerset(the_carrier(sK373))) )
& top_str(sK373) ) ),
introduced(choice_axiom,[]) ).
fof(f1909,plain,
( ? [X1] :
( ( ~ open_subset(subset_complement(the_carrier(sK373),X1),sK373)
| ~ closed_subset(X1,sK373) )
& ( open_subset(subset_complement(the_carrier(sK373),X1),sK373)
| closed_subset(X1,sK373) )
& element(X1,powerset(the_carrier(sK373))) )
=> ( ( ~ open_subset(subset_complement(the_carrier(sK373),sK374),sK373)
| ~ closed_subset(sK374,sK373) )
& ( open_subset(subset_complement(the_carrier(sK373),sK374),sK373)
| closed_subset(sK374,sK373) )
& element(sK374,powerset(the_carrier(sK373))) ) ),
introduced(choice_axiom,[]) ).
fof(f1910,plain,
( ( ~ open_subset(subset_complement(the_carrier(sK373),sK374),sK373)
| ~ closed_subset(sK374,sK373) )
& ( open_subset(subset_complement(the_carrier(sK373),sK374),sK373)
| closed_subset(sK374,sK373) )
& element(sK374,powerset(the_carrier(sK373)))
& top_str(sK373) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK373,sK374])],[f1907,f1909,f1908]) ).
fof(f1948,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( ( ( in(X3,X2)
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0) )
& ( ( subset(X1,X3)
& closed_subset(X3,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,[],[f1031]) ).
fof(f1949,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( ( ( in(X3,X2)
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0) )
& ( ( subset(X1,X3)
& closed_subset(X3,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(flattening,[],[f1948]) ).
fof(f1950,plain,
! [X0,X1] :
( ? [X2] :
( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),X2)
& ! [X3] :
( ( ( in(X3,X2)
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0) )
& ( ( subset(X1,X3)
& closed_subset(X3,X0) )
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& element(X2,powerset(powerset(the_carrier(X0)))) )
=> ( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),sK384(X0,X1))
& ! [X3] :
( ( ( in(X3,sK384(X0,X1))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0) )
& ( ( subset(X1,X3)
& closed_subset(X3,X0) )
| ~ in(X3,sK384(X0,X1)) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& element(sK384(X0,X1),powerset(powerset(the_carrier(X0)))) ) ),
introduced(choice_axiom,[]) ).
fof(f1951,plain,
! [X0] :
( ! [X1] :
( ( topstr_closure(X0,X1) = meet_of_subsets(the_carrier(X0),sK384(X0,X1))
& ! [X3] :
( ( ( in(X3,sK384(X0,X1))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0) )
& ( ( subset(X1,X3)
& closed_subset(X3,X0) )
| ~ in(X3,sK384(X0,X1)) ) )
| ~ element(X3,powerset(the_carrier(X0))) )
& element(sK384(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,[sK384])],[f1949,f1950]) ).
fof(f2330,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,[],[f1403]) ).
fof(f2331,plain,
! [X0,X1] :
( closed_subset(X1,X0)
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1403]) ).
fof(f2416,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f722]) ).
fof(f2652,plain,
! [X0] :
( element(sK169(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f1508]) ).
fof(f3095,plain,
! [X0] :
( the_carrier(X0) = cast_as_carrier_subset(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f906]) ).
fof(f3131,plain,
! [X0,X1] :
( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f940]) ).
fof(f3187,plain,
top_str(sK373),
inference(cnf_transformation,[],[f1910]) ).
fof(f3188,plain,
element(sK374,powerset(the_carrier(sK373))),
inference(cnf_transformation,[],[f1910]) ).
fof(f3189,plain,
( open_subset(subset_complement(the_carrier(sK373),sK374),sK373)
| closed_subset(sK374,sK373) ),
inference(cnf_transformation,[],[f1910]) ).
fof(f3190,plain,
( ~ open_subset(subset_complement(the_carrier(sK373),sK374),sK373)
| ~ closed_subset(sK374,sK373) ),
inference(cnf_transformation,[],[f1910]) ).
fof(f3265,plain,
! [X3,X0,X1] :
( closed_subset(X3,X0)
| ~ in(X3,sK384(X0,X1))
| ~ element(X3,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f1951]) ).
fof(f3267,plain,
! [X3,X0,X1] :
( in(X3,sK384(X0,X1))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| ~ element(X3,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f1951]) ).
cnf(c_389,plain,
( ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| closed_subset(X1,X0) ),
inference(cnf_transformation,[],[f2331]) ).
cnf(c_390,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ closed_subset(X0,X1)
| ~ top_str(X1)
| open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X0),X1) ),
inference(cnf_transformation,[],[f2330]) ).
cnf(c_475,plain,
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f2416]) ).
cnf(c_712,plain,
( element(sK169(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f2652]) ).
cnf(c_1154,plain,
( ~ one_sorted_str(X0)
| the_carrier(X0) = cast_as_carrier_subset(X0) ),
inference(cnf_transformation,[],[f3095]) ).
cnf(c_1190,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ one_sorted_str(X1)
| subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X0) = subset_complement(the_carrier(X1),X0) ),
inference(cnf_transformation,[],[f3131]) ).
cnf(c_1246,negated_conjecture,
( ~ open_subset(subset_complement(the_carrier(sK373),sK374),sK373)
| ~ closed_subset(sK374,sK373) ),
inference(cnf_transformation,[],[f3190]) ).
cnf(c_1247,negated_conjecture,
( open_subset(subset_complement(the_carrier(sK373),sK374),sK373)
| closed_subset(sK374,sK373) ),
inference(cnf_transformation,[],[f3189]) ).
cnf(c_1248,negated_conjecture,
element(sK374,powerset(the_carrier(sK373))),
inference(cnf_transformation,[],[f3188]) ).
cnf(c_1249,negated_conjecture,
top_str(sK373),
inference(cnf_transformation,[],[f3187]) ).
cnf(c_1324,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ subset(X0,X2)
| ~ closed_subset(X2,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| in(X2,sK384(X1,X0)) ),
inference(cnf_transformation,[],[f3267]) ).
cnf(c_1326,plain,
( ~ in(X0,sK384(X1,X2))
| ~ element(X0,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| closed_subset(X0,X1) ),
inference(cnf_transformation,[],[f3265]) ).
cnf(c_2890,plain,
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_475]) ).
cnf(c_2932,plain,
( ~ one_sorted_str(X0)
| the_carrier(X0) = cast_as_carrier_subset(X0) ),
inference(prop_impl_just,[status(thm)],[c_1154]) ).
cnf(c_49131,plain,
( X0 != sK373
| ~ in(X1,sK384(X0,X2))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| closed_subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_1326,c_1249]) ).
cnf(c_49132,plain,
( ~ in(X0,sK384(sK373,X1))
| ~ element(X0,powerset(the_carrier(sK373)))
| ~ element(X1,powerset(the_carrier(sK373)))
| ~ topological_space(sK373)
| closed_subset(X0,sK373) ),
inference(unflattening,[status(thm)],[c_49131]) ).
cnf(c_49166,plain,
( X0 != sK373
| ~ element(X1,powerset(the_carrier(X0)))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ subset(X1,X2)
| ~ closed_subset(X2,X0)
| ~ topological_space(X0)
| in(X2,sK384(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_1324,c_1249]) ).
cnf(c_49167,plain,
( ~ element(X0,powerset(the_carrier(sK373)))
| ~ element(X1,powerset(the_carrier(sK373)))
| ~ subset(X0,X1)
| ~ closed_subset(X1,sK373)
| ~ topological_space(sK373)
| in(X1,sK384(sK373,X0)) ),
inference(unflattening,[status(thm)],[c_49166]) ).
cnf(c_49736,plain,
( X0 != sK373
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_390,c_1249]) ).
cnf(c_49737,plain,
( ~ element(X0,powerset(the_carrier(sK373)))
| ~ closed_subset(X0,sK373)
| open_subset(subset_difference(the_carrier(sK373),cast_as_carrier_subset(sK373),X0),sK373) ),
inference(unflattening,[status(thm)],[c_49736]) ).
cnf(c_50064,plain,
( X0 != sK373
| one_sorted_str(X0) ),
inference(resolution_lifted,[status(thm)],[c_2890,c_1249]) ).
cnf(c_50065,plain,
one_sorted_str(sK373),
inference(unflattening,[status(thm)],[c_50064]) ).
cnf(c_50069,plain,
( X0 != sK373
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| closed_subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_389,c_1249]) ).
cnf(c_50070,plain,
( ~ open_subset(subset_difference(the_carrier(sK373),cast_as_carrier_subset(sK373),X0),sK373)
| ~ element(X0,powerset(the_carrier(sK373)))
| closed_subset(X0,sK373) ),
inference(unflattening,[status(thm)],[c_50069]) ).
cnf(c_50801,plain,
( X0 != sK373
| ~ element(X1,powerset(the_carrier(X0)))
| subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) ),
inference(resolution_lifted,[status(thm)],[c_1190,c_50065]) ).
cnf(c_50802,plain,
( ~ element(X0,powerset(the_carrier(sK373)))
| subset_difference(the_carrier(sK373),cast_as_carrier_subset(sK373),X0) = subset_complement(the_carrier(sK373),X0) ),
inference(unflattening,[status(thm)],[c_50801]) ).
cnf(c_50984,plain,
( X0 != sK373
| the_carrier(X0) = cast_as_carrier_subset(X0) ),
inference(resolution_lifted,[status(thm)],[c_2932,c_50065]) ).
cnf(c_50985,plain,
the_carrier(sK373) = cast_as_carrier_subset(sK373),
inference(unflattening,[status(thm)],[c_50984]) ).
cnf(c_60406,plain,
( ~ element(X0,powerset(the_carrier(sK373)))
| subset_difference(the_carrier(sK373),cast_as_carrier_subset(sK373),X0) = subset_complement(the_carrier(sK373),X0) ),
inference(prop_impl_just,[status(thm)],[c_50802]) ).
cnf(c_73338,plain,
( ~ element(X0,powerset(the_carrier(sK373)))
| subset_difference(the_carrier(sK373),the_carrier(sK373),X0) = subset_complement(the_carrier(sK373),X0) ),
inference(light_normalisation,[status(thm)],[c_60406,c_50985]) ).
cnf(c_73356,plain,
( ~ open_subset(subset_difference(the_carrier(sK373),the_carrier(sK373),X0),sK373)
| ~ element(X0,powerset(the_carrier(sK373)))
| closed_subset(X0,sK373) ),
inference(light_normalisation,[status(thm)],[c_50070,c_50985]) ).
cnf(c_73378,plain,
( ~ element(X0,powerset(the_carrier(sK373)))
| ~ closed_subset(X0,sK373)
| open_subset(subset_difference(the_carrier(sK373),the_carrier(sK373),X0),sK373) ),
inference(light_normalisation,[status(thm)],[c_49737,c_50985]) ).
cnf(c_108574,plain,
( ~ element(X0,powerset(the_carrier(sK373)))
| subset_difference(the_carrier(sK373),the_carrier(sK373),X0) = subset_complement(the_carrier(sK373),X0) ),
inference(prop_impl_just,[status(thm)],[c_73338]) ).
cnf(c_155171,plain,
X0 = X0,
theory(equality) ).
cnf(c_155173,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_155205,plain,
( X0 != X1
| X2 != X3
| ~ open_subset(X1,X3)
| open_subset(X0,X2) ),
theory(equality) ).
cnf(c_180976,plain,
( ~ element(X0,powerset(the_carrier(sK373)))
| ~ subset(X0,sK374)
| ~ closed_subset(sK374,sK373)
| ~ topological_space(sK373)
| in(sK374,sK384(sK373,X0)) ),
inference(superposition,[status(thm)],[c_1248,c_49167]) ).
cnf(c_187130,plain,
( ~ subset(sK169(the_carrier(sK373)),sK374)
| ~ closed_subset(sK374,sK373)
| ~ topological_space(sK373)
| in(sK374,sK384(sK373,sK169(the_carrier(sK373))))
| empty(the_carrier(sK373)) ),
inference(superposition,[status(thm)],[c_712,c_180976]) ).
cnf(c_189398,plain,
( X0 != subset_complement(the_carrier(sK373),sK374)
| X1 != sK373
| ~ open_subset(subset_complement(the_carrier(sK373),sK374),sK373)
| open_subset(X0,X1) ),
inference(instantiation,[status(thm)],[c_155205]) ).
cnf(c_200411,plain,
( X0 != subset_complement(the_carrier(sK373),sK374)
| sK373 != sK373
| ~ open_subset(subset_complement(the_carrier(sK373),sK374),sK373)
| open_subset(X0,sK373) ),
inference(instantiation,[status(thm)],[c_189398]) ).
cnf(c_200412,plain,
sK373 = sK373,
inference(instantiation,[status(thm)],[c_155171]) ).
cnf(c_214605,plain,
( ~ element(sK374,powerset(the_carrier(sK373)))
| ~ closed_subset(sK374,sK373)
| open_subset(subset_difference(the_carrier(sK373),the_carrier(sK373),sK374),sK373) ),
inference(instantiation,[status(thm)],[c_73378]) ).
cnf(c_214620,plain,
( ~ element(X0,powerset(the_carrier(sK373)))
| ~ subset(X0,sK374)
| ~ closed_subset(sK374,sK373)
| ~ topological_space(sK373)
| in(sK374,sK384(sK373,X0)) ),
inference(superposition,[status(thm)],[c_1248,c_49167]) ).
cnf(c_228825,plain,
( ~ open_subset(subset_difference(the_carrier(sK373),the_carrier(sK373),sK374),sK373)
| ~ element(sK374,powerset(the_carrier(sK373)))
| closed_subset(sK374,sK373) ),
inference(instantiation,[status(thm)],[c_73356]) ).
cnf(c_245356,plain,
( ~ in(X0,sK384(sK373,sK169(the_carrier(sK373))))
| ~ element(X0,powerset(the_carrier(sK373)))
| ~ topological_space(sK373)
| closed_subset(X0,sK373)
| empty(the_carrier(sK373)) ),
inference(superposition,[status(thm)],[c_712,c_49132]) ).
cnf(c_245370,plain,
( ~ subset(sK169(the_carrier(sK373)),sK374)
| ~ closed_subset(sK374,sK373)
| ~ topological_space(sK373)
| in(sK374,sK384(sK373,sK169(the_carrier(sK373))))
| empty(the_carrier(sK373)) ),
inference(superposition,[status(thm)],[c_712,c_214620]) ).
cnf(c_246461,plain,
subset_complement(the_carrier(sK373),sK374) = subset_complement(the_carrier(sK373),sK374),
inference(instantiation,[status(thm)],[c_155171]) ).
cnf(c_246499,plain,
( ~ element(sK374,powerset(the_carrier(sK373)))
| subset_difference(the_carrier(sK373),the_carrier(sK373),sK374) = subset_complement(the_carrier(sK373),sK374) ),
inference(instantiation,[status(thm)],[c_108574]) ).
cnf(c_264926,plain,
( subset_difference(the_carrier(sK373),the_carrier(sK373),sK374) != subset_complement(the_carrier(sK373),sK374)
| sK373 != sK373
| ~ open_subset(subset_complement(the_carrier(sK373),sK374),sK373)
| open_subset(subset_difference(the_carrier(sK373),the_carrier(sK373),sK374),sK373) ),
inference(instantiation,[status(thm)],[c_200411]) ).
cnf(c_266729,plain,
( ~ subset(sK169(the_carrier(sK373)),sK374)
| ~ topological_space(sK373)
| in(sK374,sK384(sK373,sK169(the_carrier(sK373))))
| empty(the_carrier(sK373)) ),
inference(global_subsumption_just,[status(thm)],[c_245370,c_1248,c_1247,c_187130,c_200412,c_228825,c_246499,c_264926]) ).
cnf(c_266741,plain,
( ~ element(sK374,powerset(the_carrier(sK373)))
| ~ subset(sK169(the_carrier(sK373)),sK374)
| ~ topological_space(sK373)
| empty(the_carrier(sK373))
| closed_subset(sK374,sK373) ),
inference(superposition,[status(thm)],[c_266729,c_245356]) ).
cnf(c_266750,plain,
( ~ subset(sK169(the_carrier(sK373)),sK374)
| ~ topological_space(sK373)
| empty(the_carrier(sK373))
| closed_subset(sK374,sK373) ),
inference(forward_subsumption_resolution,[status(thm)],[c_266741,c_1248]) ).
cnf(c_266755,plain,
closed_subset(sK374,sK373),
inference(global_subsumption_just,[status(thm)],[c_266750,c_1248,c_1247,c_200412,c_228825,c_246499,c_264926]) ).
cnf(c_319347,plain,
( subset_difference(the_carrier(sK373),the_carrier(sK373),X0) != X1
| subset_complement(the_carrier(sK373),sK374) != X1
| subset_complement(the_carrier(sK373),sK374) = subset_difference(the_carrier(sK373),the_carrier(sK373),X0) ),
inference(instantiation,[status(thm)],[c_155173]) ).
cnf(c_320982,plain,
( subset_difference(the_carrier(sK373),the_carrier(sK373),X0) != subset_complement(the_carrier(sK373),sK374)
| subset_complement(the_carrier(sK373),sK374) != subset_complement(the_carrier(sK373),sK374)
| subset_complement(the_carrier(sK373),sK374) = subset_difference(the_carrier(sK373),the_carrier(sK373),X0) ),
inference(instantiation,[status(thm)],[c_319347]) ).
cnf(c_325422,plain,
( subset_difference(the_carrier(sK373),the_carrier(sK373),sK374) != subset_complement(the_carrier(sK373),sK374)
| subset_complement(the_carrier(sK373),sK374) != subset_complement(the_carrier(sK373),sK374)
| subset_complement(the_carrier(sK373),sK374) = subset_difference(the_carrier(sK373),the_carrier(sK373),sK374) ),
inference(instantiation,[status(thm)],[c_320982]) ).
cnf(c_367807,plain,
( subset_complement(the_carrier(sK373),sK374) != X0
| sK373 != X1
| ~ open_subset(X0,X1)
| open_subset(subset_complement(the_carrier(sK373),sK374),sK373) ),
inference(instantiation,[status(thm)],[c_155205]) ).
cnf(c_377416,plain,
( subset_complement(the_carrier(sK373),sK374) != X0
| sK373 != sK373
| ~ open_subset(X0,sK373)
| open_subset(subset_complement(the_carrier(sK373),sK374),sK373) ),
inference(instantiation,[status(thm)],[c_367807]) ).
cnf(c_391936,plain,
( subset_complement(the_carrier(sK373),sK374) != subset_difference(the_carrier(sK373),the_carrier(sK373),sK374)
| sK373 != sK373
| ~ open_subset(subset_difference(the_carrier(sK373),the_carrier(sK373),sK374),sK373)
| open_subset(subset_complement(the_carrier(sK373),sK374),sK373) ),
inference(instantiation,[status(thm)],[c_377416]) ).
cnf(c_391937,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_391936,c_325422,c_266755,c_246499,c_246461,c_214605,c_200412,c_1246,c_1248]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU319+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 19:56:24 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.49 Running first-order theorem proving
% 0.22/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 88.89/12.89 % SZS status Started for theBenchmark.p
% 88.89/12.89 % SZS status Theorem for theBenchmark.p
% 88.89/12.89
% 88.89/12.89 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 88.89/12.89
% 88.89/12.89 ------ iProver source info
% 88.89/12.89
% 88.89/12.89 git: date: 2023-05-31 18:12:56 +0000
% 88.89/12.89 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 88.89/12.89 git: non_committed_changes: false
% 88.89/12.89 git: last_make_outside_of_git: false
% 88.89/12.89
% 88.89/12.89 ------ Parsing...
% 88.89/12.89 ------ Clausification by vclausify_rel & Parsing by iProver...
% 88.89/12.89
% 88.89/12.89 ------ 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
% 88.89/12.89
% 88.89/12.89 ------ Preprocessing... gs_s sp: 15 0s gs_e snvd_s sp: 0 0s snvd_e
% 88.89/12.89
% 88.89/12.89 ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 88.89/12.89 ------ Proving...
% 88.89/12.89 ------ Problem Properties
% 88.89/12.89
% 88.89/12.89
% 88.89/12.89 clauses 1281
% 88.89/12.89 conjectures 3
% 88.89/12.89 EPR 173
% 88.89/12.89 Horn 955
% 88.89/12.89 unary 172
% 88.89/12.89 binary 382
% 88.89/12.89 lits 3884
% 88.89/12.89 lits eq 548
% 88.89/12.89 fd_pure 0
% 88.89/12.89 fd_pseudo 0
% 88.89/12.89 fd_cond 44
% 88.89/12.89 fd_pseudo_cond 117
% 88.89/12.89 AC symbols 0
% 88.89/12.89
% 88.89/12.89 ------ Schedule dynamic 5 is on
% 88.89/12.89
% 88.89/12.89 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 88.89/12.89
% 88.89/12.89
% 88.89/12.89 ------
% 88.89/12.89 Current options:
% 88.89/12.89 ------
% 88.89/12.89
% 88.89/12.89
% 88.89/12.89
% 88.89/12.89
% 88.89/12.89 ------ Proving...
% 88.89/12.89
% 88.89/12.89
% 88.89/12.89 % SZS status Theorem for theBenchmark.p
% 88.89/12.89
% 88.89/12.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 88.89/12.89
% 88.89/12.90
%------------------------------------------------------------------------------