TSTP Solution File: SEU315+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU315+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 17:05:44 EDT 2023
% Result : Theorem 3.81s 1.14s
% Output : CNFRefutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 12
% Syntax : Number of formulae : 123 ( 18 unt; 0 def)
% Number of atoms : 612 ( 66 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 793 ( 304 ~; 313 |; 150 &)
% ( 9 <=>; 15 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 255 ( 2 sgn; 115 !; 52 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [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/sandbox2/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
fof(f2,negated_conjecture,
~ ! [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)))) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f29,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f30,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
fof(f31,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f35,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f39,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f58,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,[],[f2]) ).
fof(f59,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,[],[f58]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) ) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) )
& ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) ) ),
inference(ennf_transformation,[],[f31]) ).
fof(f77,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f79,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f81,plain,
? [X0,X1] :
( ! [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ? [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,[],[f59]) ).
fof(f82,plain,
? [X0,X1] :
( ! [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ? [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(flattening,[],[f81]) ).
fof(f83,plain,
? [X0,X1] :
( ! [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ? [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,[],[f82]) ).
fof(f84,plain,
( ? [X0,X1] :
( ! [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X2) )
& ( ? [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) )
=> ( ! [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ subset(sK1,X3)
| ~ closed_subset(X4,sK0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(sK0))) )
| ~ in(X3,X2) )
& ( ? [X5] :
( subset(sK1,X3)
& closed_subset(X5,sK0)
& X3 = X5
& element(X5,powerset(the_carrier(sK0))) )
| in(X3,X2) )
& element(X3,powerset(the_carrier(sK0))) )
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) )
& element(sK1,powerset(the_carrier(sK0)))
& top_str(sK0)
& topological_space(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ subset(sK1,X3)
| ~ closed_subset(X4,sK0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(sK0))) )
| ~ in(X3,X2) )
& ( ? [X5] :
( subset(sK1,X3)
& closed_subset(X5,sK0)
& X3 = X5
& element(X5,powerset(the_carrier(sK0))) )
| in(X3,X2) )
& element(X3,powerset(the_carrier(sK0))) )
=> ( ( ! [X4] :
( ~ subset(sK1,sK2(X2))
| ~ closed_subset(X4,sK0)
| sK2(X2) != X4
| ~ element(X4,powerset(the_carrier(sK0))) )
| ~ in(sK2(X2),X2) )
& ( ? [X5] :
( subset(sK1,sK2(X2))
& closed_subset(X5,sK0)
& sK2(X2) = X5
& element(X5,powerset(the_carrier(sK0))) )
| in(sK2(X2),X2) )
& element(sK2(X2),powerset(the_carrier(sK0))) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X2] :
( ? [X5] :
( subset(sK1,sK2(X2))
& closed_subset(X5,sK0)
& sK2(X2) = X5
& element(X5,powerset(the_carrier(sK0))) )
=> ( subset(sK1,sK2(X2))
& closed_subset(sK3(X2),sK0)
& sK2(X2) = sK3(X2)
& element(sK3(X2),powerset(the_carrier(sK0))) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
( ! [X2] :
( ( ( ! [X4] :
( ~ subset(sK1,sK2(X2))
| ~ closed_subset(X4,sK0)
| sK2(X2) != X4
| ~ element(X4,powerset(the_carrier(sK0))) )
| ~ in(sK2(X2),X2) )
& ( ( subset(sK1,sK2(X2))
& closed_subset(sK3(X2),sK0)
& sK2(X2) = sK3(X2)
& element(sK3(X2),powerset(the_carrier(sK0))) )
| in(sK2(X2),X2) )
& element(sK2(X2),powerset(the_carrier(sK0))) )
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) )
& element(sK1,powerset(the_carrier(sK0)))
& top_str(sK0)
& topological_space(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f83,f86,f85,f84]) ).
fof(f96,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0))) )
& ( ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(nnf_transformation,[],[f75]) ).
fof(f97,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0))) )
& ( ( ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0))) )
& ( ( ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(rectify,[],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0))) )
& ( ( ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) )
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK8(X0,X1))
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0))) )
& ( ( ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) )
& in(X3,powerset(the_carrier(X0))) )
| ~ in(X3,sK8(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f100,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(sK9(X0,X1,X3),X0)
& sK9(X0,X1,X3) = X3
& element(sK9(X0,X1,X3),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK8(X0,X1))
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,powerset(the_carrier(X0))) )
& ( ( subset(X1,X3)
& closed_subset(sK9(X0,X1,X3),X0)
& sK9(X0,X1,X3) = X3
& element(sK9(X0,X1,X3),powerset(the_carrier(X0)))
& in(X3,powerset(the_carrier(X0))) )
| ~ in(X3,sK8(X0,X1)) ) )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f98,f100,f99]) ).
fof(f102,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) )
& ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f105,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK11(X0,X1),X1)
& in(sK11(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK11(X0,X1),X1)
& in(sK11(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f77,f105]) ).
fof(f111,plain,
topological_space(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f112,plain,
top_str(sK0),
inference(cnf_transformation,[],[f87]) ).
fof(f113,plain,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f87]) ).
fof(f114,plain,
! [X2] :
( element(sK2(X2),powerset(the_carrier(sK0)))
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f87]) ).
fof(f116,plain,
! [X2] :
( sK2(X2) = sK3(X2)
| in(sK2(X2),X2)
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f87]) ).
fof(f117,plain,
! [X2] :
( closed_subset(sK3(X2),sK0)
| in(sK2(X2),X2)
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f87]) ).
fof(f118,plain,
! [X2] :
( subset(sK1,sK2(X2))
| in(sK2(X2),X2)
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f87]) ).
fof(f119,plain,
! [X2,X4] :
( ~ subset(sK1,sK2(X2))
| ~ closed_subset(X4,sK0)
| sK2(X2) != X4
| ~ element(X4,powerset(the_carrier(sK0)))
| ~ in(sK2(X2),X2)
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(cnf_transformation,[],[f87]) ).
fof(f158,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f159,plain,
! [X3,X0,X1] :
( in(X3,powerset(the_carrier(X0)))
| ~ in(X3,sK8(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f161,plain,
! [X3,X0,X1] :
( sK9(X0,X1,X3) = X3
| ~ in(X3,sK8(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f162,plain,
! [X3,X0,X1] :
( closed_subset(sK9(X0,X1,X3),X0)
| ~ in(X3,sK8(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f163,plain,
! [X3,X0,X1] :
( subset(X1,X3)
| ~ in(X3,sK8(X0,X1))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f164,plain,
! [X3,X0,X1,X4] :
( in(X3,sK8(X0,X1))
| ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X3,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f165,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f166,plain,
! [X0,X1] :
( element(X1,X0)
| ~ in(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f171,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| in(sK11(X0,X1),X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f172,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(sK11(X0,X1),X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f176,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f178,plain,
! [X2] :
( ~ subset(sK1,sK2(X2))
| ~ closed_subset(sK2(X2),sK0)
| ~ element(sK2(X2),powerset(the_carrier(sK0)))
| ~ in(sK2(X2),X2)
| ~ element(X2,powerset(powerset(the_carrier(sK0)))) ),
inference(equality_resolution,[],[f119]) ).
fof(f179,plain,
! [X0,X1,X4] :
( in(X4,sK8(X0,X1))
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,powerset(the_carrier(X0)))
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(equality_resolution,[],[f164]) ).
cnf(c_49,negated_conjecture,
( ~ element(sK2(X0),powerset(the_carrier(sK0)))
| ~ element(X0,powerset(powerset(the_carrier(sK0))))
| ~ in(sK2(X0),X0)
| ~ subset(sK1,sK2(X0))
| ~ closed_subset(sK2(X0),sK0) ),
inference(cnf_transformation,[],[f178]) ).
cnf(c_50,negated_conjecture,
( ~ element(X0,powerset(powerset(the_carrier(sK0))))
| in(sK2(X0),X0)
| subset(sK1,sK2(X0)) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_51,negated_conjecture,
( ~ element(X0,powerset(powerset(the_carrier(sK0))))
| in(sK2(X0),X0)
| closed_subset(sK3(X0),sK0) ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_52,negated_conjecture,
( ~ element(X0,powerset(powerset(the_carrier(sK0))))
| sK2(X0) = sK3(X0)
| in(sK2(X0),X0) ),
inference(cnf_transformation,[],[f116]) ).
cnf(c_54,negated_conjecture,
( ~ element(X0,powerset(powerset(the_carrier(sK0))))
| element(sK2(X0),powerset(the_carrier(sK0))) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_55,negated_conjecture,
element(sK1,powerset(the_carrier(sK0))),
inference(cnf_transformation,[],[f113]) ).
cnf(c_56,negated_conjecture,
top_str(sK0),
inference(cnf_transformation,[],[f112]) ).
cnf(c_57,negated_conjecture,
topological_space(sK0),
inference(cnf_transformation,[],[f111]) ).
cnf(c_96,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[],[f158]) ).
cnf(c_97,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X2,powerset(the_carrier(X1)))
| ~ subset(X0,X2)
| ~ closed_subset(X2,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| in(X2,sK8(X1,X0)) ),
inference(cnf_transformation,[],[f179]) ).
cnf(c_98,plain,
( ~ in(X0,sK8(X1,X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| subset(X2,X0) ),
inference(cnf_transformation,[],[f163]) ).
cnf(c_99,plain,
( ~ in(X0,sK8(X1,X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| closed_subset(sK9(X1,X2,X0),X1) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_100,plain,
( ~ in(X0,sK8(X1,X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| sK9(X1,X2,X0) = X0 ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_102,plain,
( ~ in(X0,sK8(X1,X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| in(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_105,plain,
( ~ in(X0,X1)
| element(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f166]) ).
cnf(c_106,plain,
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_109,plain,
( ~ in(sK11(X0,X1),X1)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_110,plain,
( in(sK11(X0,X1),X0)
| element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_114,plain,
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f176]) ).
cnf(c_159,plain,
( element(X0,X1)
| ~ in(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_105,c_114,c_105]) ).
cnf(c_160,plain,
( ~ in(X0,X1)
| element(X0,X1) ),
inference(renaming,[status(thm)],[c_159]) ).
cnf(c_161,negated_conjecture,
( ~ element(X0,powerset(powerset(the_carrier(sK0))))
| ~ in(sK2(X0),X0)
| ~ subset(sK1,sK2(X0))
| ~ closed_subset(sK2(X0),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_54,c_49]) ).
cnf(c_254,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ in(X2,powerset(the_carrier(X1)))
| ~ subset(X0,X2)
| ~ closed_subset(X2,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| in(X2,sK8(X1,X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_97,c_160]) ).
cnf(c_802,plain,
( X0 != sK0
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,powerset(the_carrier(X0)))
| ~ subset(X1,X2)
| ~ closed_subset(X2,X0)
| ~ topological_space(X0)
| in(X2,sK8(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_56,c_254]) ).
cnf(c_803,plain,
( ~ element(X0,powerset(the_carrier(sK0)))
| ~ in(X1,powerset(the_carrier(sK0)))
| ~ subset(X0,X1)
| ~ closed_subset(X1,sK0)
| ~ topological_space(sK0)
| in(X1,sK8(sK0,X0)) ),
inference(unflattening,[status(thm)],[c_802]) ).
cnf(c_805,plain,
( ~ closed_subset(X1,sK0)
| ~ subset(X0,X1)
| ~ in(X1,powerset(the_carrier(sK0)))
| ~ element(X0,powerset(the_carrier(sK0)))
| in(X1,sK8(sK0,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_803,c_57,c_803]) ).
cnf(c_806,plain,
( ~ element(X0,powerset(the_carrier(sK0)))
| ~ in(X1,powerset(the_carrier(sK0)))
| ~ subset(X0,X1)
| ~ closed_subset(X1,sK0)
| in(X1,sK8(sK0,X0)) ),
inference(renaming,[status(thm)],[c_805]) ).
cnf(c_823,plain,
( X0 != sK0
| ~ in(X1,sK8(X0,X2))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| in(X1,powerset(the_carrier(X0))) ),
inference(resolution_lifted,[status(thm)],[c_56,c_102]) ).
cnf(c_824,plain,
( ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ topological_space(sK0)
| in(X0,powerset(the_carrier(sK0))) ),
inference(unflattening,[status(thm)],[c_823]) ).
cnf(c_826,plain,
( ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1))
| in(X0,powerset(the_carrier(sK0))) ),
inference(global_subsumption_just,[status(thm)],[c_824,c_57,c_824]) ).
cnf(c_827,plain,
( ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0)))
| in(X0,powerset(the_carrier(sK0))) ),
inference(renaming,[status(thm)],[c_826]) ).
cnf(c_853,plain,
( X0 != sK0
| ~ in(X1,sK8(X0,X2))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| sK9(X0,X2,X1) = X1 ),
inference(resolution_lifted,[status(thm)],[c_56,c_100]) ).
cnf(c_854,plain,
( ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ topological_space(sK0)
| sK9(sK0,X1,X0) = X0 ),
inference(unflattening,[status(thm)],[c_853]) ).
cnf(c_856,plain,
( ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1))
| sK9(sK0,X1,X0) = X0 ),
inference(global_subsumption_just,[status(thm)],[c_854,c_57,c_854]) ).
cnf(c_857,plain,
( ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0)))
| sK9(sK0,X1,X0) = X0 ),
inference(renaming,[status(thm)],[c_856]) ).
cnf(c_868,plain,
( X0 != sK0
| ~ in(X1,sK8(X0,X2))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| closed_subset(sK9(X0,X2,X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_56,c_99]) ).
cnf(c_869,plain,
( ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ topological_space(sK0)
| closed_subset(sK9(sK0,X1,X0),sK0) ),
inference(unflattening,[status(thm)],[c_868]) ).
cnf(c_871,plain,
( ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1))
| closed_subset(sK9(sK0,X1,X0),sK0) ),
inference(global_subsumption_just,[status(thm)],[c_869,c_57,c_869]) ).
cnf(c_872,plain,
( ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0)))
| closed_subset(sK9(sK0,X1,X0),sK0) ),
inference(renaming,[status(thm)],[c_871]) ).
cnf(c_883,plain,
( X0 != sK0
| ~ in(X1,sK8(X0,X2))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ topological_space(X0)
| subset(X2,X1) ),
inference(resolution_lifted,[status(thm)],[c_56,c_98]) ).
cnf(c_884,plain,
( ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0)))
| ~ topological_space(sK0)
| subset(X1,X0) ),
inference(unflattening,[status(thm)],[c_883]) ).
cnf(c_885,plain,
( ~ element(X1,powerset(the_carrier(sK0)))
| ~ in(X0,sK8(sK0,X1))
| subset(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_884,c_57,c_884]) ).
cnf(c_886,plain,
( ~ in(X0,sK8(sK0,X1))
| ~ element(X1,powerset(the_carrier(sK0)))
| subset(X1,X0) ),
inference(renaming,[status(thm)],[c_885]) ).
cnf(c_2313,plain,
( ~ in(X0,sK8(sK0,sK1))
| in(X0,powerset(the_carrier(sK0))) ),
inference(superposition,[status(thm)],[c_55,c_827]) ).
cnf(c_2355,plain,
( ~ in(X0,powerset(the_carrier(sK0)))
| ~ subset(sK1,X0)
| ~ closed_subset(X0,sK0)
| in(X0,sK8(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_55,c_806]) ).
cnf(c_2695,plain,
( ~ in(sK2(X0),sK8(sK0,sK1))
| ~ element(sK1,powerset(the_carrier(sK0)))
| subset(sK1,sK2(X0)) ),
inference(instantiation,[status(thm)],[c_886]) ).
cnf(c_2799,plain,
( in(sK11(sK8(sK0,sK1),X0),powerset(the_carrier(sK0)))
| element(sK8(sK0,sK1),powerset(X0)) ),
inference(superposition,[status(thm)],[c_110,c_2313]) ).
cnf(c_4020,plain,
( ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ element(sK1,powerset(the_carrier(sK0)))
| subset(sK1,sK2(sK8(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_2695]) ).
cnf(c_4418,plain,
element(sK8(sK0,sK1),powerset(powerset(the_carrier(sK0)))),
inference(superposition,[status(thm)],[c_2799,c_109]) ).
cnf(c_4582,plain,
( ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ subset(sK1,sK2(sK8(sK0,sK1)))
| ~ closed_subset(sK2(sK8(sK0,sK1)),sK0) ),
inference(superposition,[status(thm)],[c_4418,c_161]) ).
cnf(c_4584,plain,
( sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1))
| in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_4418,c_52]) ).
cnf(c_4585,plain,
( in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| closed_subset(sK3(sK8(sK0,sK1)),sK0) ),
inference(superposition,[status(thm)],[c_4418,c_51]) ).
cnf(c_4586,plain,
( in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| subset(sK1,sK2(sK8(sK0,sK1))) ),
inference(superposition,[status(thm)],[c_4418,c_50]) ).
cnf(c_4587,plain,
element(sK2(sK8(sK0,sK1)),powerset(the_carrier(sK0))),
inference(superposition,[status(thm)],[c_4418,c_54]) ).
cnf(c_4643,plain,
( in(sK2(sK8(sK0,sK1)),powerset(the_carrier(sK0)))
| empty(powerset(the_carrier(sK0))) ),
inference(superposition,[status(thm)],[c_4587,c_106]) ).
cnf(c_4648,plain,
in(sK2(sK8(sK0,sK1)),powerset(the_carrier(sK0))),
inference(forward_subsumption_resolution,[status(thm)],[c_4643,c_96]) ).
cnf(c_4670,plain,
( ~ subset(sK1,sK2(sK8(sK0,sK1)))
| ~ closed_subset(sK2(sK8(sK0,sK1)),sK0)
| in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_4648,c_2355]) ).
cnf(c_4779,plain,
( ~ element(sK1,powerset(the_carrier(sK0)))
| sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1))
| closed_subset(sK3(sK8(sK0,sK1)),sK0) ),
inference(superposition,[status(thm)],[c_4585,c_857]) ).
cnf(c_4790,plain,
( sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1))
| closed_subset(sK3(sK8(sK0,sK1)),sK0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4779,c_55]) ).
cnf(c_4798,plain,
subset(sK1,sK2(sK8(sK0,sK1))),
inference(global_subsumption_just,[status(thm)],[c_4586,c_55,c_4020,c_4586]) ).
cnf(c_4841,plain,
( ~ element(sK1,powerset(the_carrier(sK0)))
| sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1))
| sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_4584,c_857]) ).
cnf(c_4850,plain,
( sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1))
| sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4841,c_55]) ).
cnf(c_4887,plain,
~ closed_subset(sK2(sK8(sK0,sK1)),sK0),
inference(global_subsumption_just,[status(thm)],[c_4582,c_4582,c_4670,c_4798]) ).
cnf(c_4907,plain,
( ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ element(sK1,powerset(the_carrier(sK0)))
| sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1))
| closed_subset(sK2(sK8(sK0,sK1)),sK0) ),
inference(superposition,[status(thm)],[c_4850,c_872]) ).
cnf(c_4910,plain,
( ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4907,c_4887,c_55]) ).
cnf(c_4953,plain,
sK2(sK8(sK0,sK1)) = sK3(sK8(sK0,sK1)),
inference(global_subsumption_just,[status(thm)],[c_4910,c_4584,c_4910]) ).
cnf(c_4957,plain,
( sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1))
| closed_subset(sK2(sK8(sK0,sK1)),sK0) ),
inference(demodulation,[status(thm)],[c_4790,c_4953]) ).
cnf(c_4959,plain,
( in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| closed_subset(sK2(sK8(sK0,sK1)),sK0) ),
inference(demodulation,[status(thm)],[c_4585,c_4953]) ).
cnf(c_4960,plain,
in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_4959,c_4887]) ).
cnf(c_4961,plain,
sK9(sK0,sK1,sK2(sK8(sK0,sK1))) = sK2(sK8(sK0,sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_4957,c_4887]) ).
cnf(c_4982,plain,
( ~ in(sK2(sK8(sK0,sK1)),sK8(sK0,sK1))
| ~ element(sK1,powerset(the_carrier(sK0)))
| closed_subset(sK2(sK8(sK0,sK1)),sK0) ),
inference(superposition,[status(thm)],[c_4961,c_872]) ).
cnf(c_4985,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4982,c_4887,c_55,c_4960]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU315+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n025.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 14:58:51 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.46 Running first-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.81/1.14 % SZS status Started for theBenchmark.p
% 3.81/1.14 % SZS status Theorem for theBenchmark.p
% 3.81/1.14
% 3.81/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.81/1.14
% 3.81/1.14 ------ iProver source info
% 3.81/1.14
% 3.81/1.14 git: date: 2023-05-31 18:12:56 +0000
% 3.81/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.81/1.14 git: non_committed_changes: false
% 3.81/1.14 git: last_make_outside_of_git: false
% 3.81/1.14
% 3.81/1.14 ------ Parsing...
% 3.81/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.81/1.14
% 3.81/1.14 ------ Preprocessing... sup_sim: 0 sf_s rm: 35 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe_e
% 3.81/1.14
% 3.81/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.81/1.14
% 3.81/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.81/1.14 ------ Proving...
% 3.81/1.14 ------ Problem Properties
% 3.81/1.14
% 3.81/1.14
% 3.81/1.14 clauses 36
% 3.81/1.14 conjectures 7
% 3.81/1.14 EPR 13
% 3.81/1.14 Horn 29
% 3.81/1.14 unary 12
% 3.81/1.14 binary 9
% 3.81/1.14 lits 78
% 3.81/1.14 lits eq 4
% 3.81/1.14 fd_pure 0
% 3.81/1.14 fd_pseudo 0
% 3.81/1.14 fd_cond 1
% 3.81/1.14 fd_pseudo_cond 1
% 3.81/1.14 AC symbols 0
% 3.81/1.14
% 3.81/1.14 ------ Schedule dynamic 5 is on
% 3.81/1.14
% 3.81/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.81/1.14
% 3.81/1.14
% 3.81/1.14 ------
% 3.81/1.14 Current options:
% 3.81/1.14 ------
% 3.81/1.14
% 3.81/1.14
% 3.81/1.14
% 3.81/1.14
% 3.81/1.14 ------ Proving...
% 3.81/1.14
% 3.81/1.14
% 3.81/1.14 % SZS status Theorem for theBenchmark.p
% 3.81/1.14
% 3.81/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.87/1.14
% 3.87/1.16
%------------------------------------------------------------------------------