TSTP Solution File: SEU314+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU314+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n020.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 : Wed Aug 31 18:33:10 EDT 2022
% Result : Theorem 1.80s 0.59s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 21
% Syntax : Number of formulae : 136 ( 5 unt; 0 def)
% Number of atoms : 844 ( 137 equ)
% Maximal formula atoms : 30 ( 6 avg)
% Number of connectives : 1057 ( 349 ~; 420 |; 254 &)
% ( 16 <=>; 16 =>; 0 <=; 2 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 10 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 235 ( 138 !; 97 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f967,plain,
$false,
inference(avatar_sat_refutation,[],[f644,f691,f720,f721,f781,f872,f912,f919,f930,f937,f956,f958,f961]) ).
fof(f961,plain,
( spl18_22
| spl18_21
| ~ spl18_20 ),
inference(avatar_split_clause,[],[f881,f614,f667,f671]) ).
fof(f671,plain,
( spl18_22
<=> closed_subset(sK16(sK7(sK15,sK14)),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_22])]) ).
fof(f667,plain,
( spl18_21
<=> in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_21])]) ).
fof(f614,plain,
( spl18_20
<=> sK16(sK7(sK15,sK14)) = sK17(sK7(sK15,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_20])]) ).
fof(f881,plain,
( in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| closed_subset(sK16(sK7(sK15,sK14)),sK14)
| ~ spl18_20 ),
inference(superposition,[],[f159,f616]) ).
fof(f616,plain,
( sK16(sK7(sK15,sK14)) = sK17(sK7(sK15,sK14))
| ~ spl18_20 ),
inference(avatar_component_clause,[],[f614]) ).
fof(f159,plain,
! [X2] :
( closed_subset(sK17(X2),sK14)
| in(sK16(X2),X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
( ! [X2] :
( ( ~ in(sK16(X2),X2)
| ~ in(sK16(X2),powerset(the_carrier(sK14)))
| ! [X4] :
( ~ subset(sK15,sK16(X2))
| ~ closed_subset(X4,sK14)
| sK16(X2) != X4
| ~ element(X4,powerset(the_carrier(sK14))) ) )
& ( in(sK16(X2),X2)
| ( in(sK16(X2),powerset(the_carrier(sK14)))
& subset(sK15,sK16(X2))
& closed_subset(sK17(X2),sK14)
& sK17(X2) = sK16(X2)
& element(sK17(X2),powerset(the_carrier(sK14))) ) ) )
& top_str(sK14)
& element(sK15,powerset(the_carrier(sK14)))
& topological_space(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17])],[f97,f100,f99,f98]) ).
fof(f98,plain,
( ? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) ) )
& ( in(X3,X2)
| ( in(X3,powerset(the_carrier(X0)))
& ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) ) ) ) )
& top_str(X0)
& element(X1,powerset(the_carrier(X0)))
& topological_space(X0) )
=> ( ! [X2] :
? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,powerset(the_carrier(sK14)))
| ! [X4] :
( ~ subset(sK15,X3)
| ~ closed_subset(X4,sK14)
| X3 != X4
| ~ element(X4,powerset(the_carrier(sK14))) ) )
& ( in(X3,X2)
| ( in(X3,powerset(the_carrier(sK14)))
& ? [X5] :
( subset(sK15,X3)
& closed_subset(X5,sK14)
& X3 = X5
& element(X5,powerset(the_carrier(sK14))) ) ) ) )
& top_str(sK14)
& element(sK15,powerset(the_carrier(sK14)))
& topological_space(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
! [X2] :
( ? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,powerset(the_carrier(sK14)))
| ! [X4] :
( ~ subset(sK15,X3)
| ~ closed_subset(X4,sK14)
| X3 != X4
| ~ element(X4,powerset(the_carrier(sK14))) ) )
& ( in(X3,X2)
| ( in(X3,powerset(the_carrier(sK14)))
& ? [X5] :
( subset(sK15,X3)
& closed_subset(X5,sK14)
& X3 = X5
& element(X5,powerset(the_carrier(sK14))) ) ) ) )
=> ( ( ~ in(sK16(X2),X2)
| ~ in(sK16(X2),powerset(the_carrier(sK14)))
| ! [X4] :
( ~ subset(sK15,sK16(X2))
| ~ closed_subset(X4,sK14)
| sK16(X2) != X4
| ~ element(X4,powerset(the_carrier(sK14))) ) )
& ( in(sK16(X2),X2)
| ( in(sK16(X2),powerset(the_carrier(sK14)))
& ? [X5] :
( subset(sK15,sK16(X2))
& closed_subset(X5,sK14)
& sK16(X2) = X5
& element(X5,powerset(the_carrier(sK14))) ) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
! [X2] :
( ? [X5] :
( subset(sK15,sK16(X2))
& closed_subset(X5,sK14)
& sK16(X2) = X5
& element(X5,powerset(the_carrier(sK14))) )
=> ( subset(sK15,sK16(X2))
& closed_subset(sK17(X2),sK14)
& sK17(X2) = sK16(X2)
& element(sK17(X2),powerset(the_carrier(sK14))) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) ) )
& ( in(X3,X2)
| ( in(X3,powerset(the_carrier(X0)))
& ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) ) ) ) )
& top_str(X0)
& element(X1,powerset(the_carrier(X0)))
& topological_space(X0) ),
inference(rectify,[],[f96]) ).
fof(f96,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) ) )
& ( in(X3,X2)
| ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) ) ) ) )
& top_str(X0)
& element(X1,powerset(the_carrier(X0)))
& topological_space(X0) ),
inference(flattening,[],[f95]) ).
fof(f95,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ~ in(X3,X2)
| ~ in(X3,powerset(the_carrier(X0)))
| ! [X4] :
( ~ subset(X1,X3)
| ~ closed_subset(X4,X0)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) ) )
& ( in(X3,X2)
| ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) ) ) ) )
& top_str(X0)
& element(X1,powerset(the_carrier(X0)))
& topological_space(X0) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) ) )
<~> in(X3,X2) )
& top_str(X0)
& element(X1,powerset(the_carrier(X0)))
& topological_space(X0) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) ) )
<~> in(X3,X2) )
& top_str(X0)
& element(X1,powerset(the_carrier(X0)))
& topological_space(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( top_str(X0)
& element(X1,powerset(the_carrier(X0)))
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) ) )
<=> in(X3,X2) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0,X1] :
( ( top_str(X0)
& element(X1,powerset(the_carrier(X0)))
& topological_space(X0) )
=> ? [X2] :
! [X3] :
( ( in(X3,powerset(the_carrier(X0)))
& ? [X4] :
( subset(X1,X3)
& closed_subset(X4,X0)
& X3 = X4
& element(X4,powerset(the_carrier(X0))) ) )
<=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
fof(f958,plain,
( ~ spl18_22
| ~ spl18_23
| ~ spl18_24
| spl18_18
| spl18_21
| ~ spl18_25 ),
inference(avatar_split_clause,[],[f957,f701,f667,f606,f697,f680,f671]) ).
fof(f680,plain,
( spl18_23
<=> element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_23])]) ).
fof(f697,plain,
( spl18_24
<=> in(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_24])]) ).
fof(f606,plain,
( spl18_18
<=> sP1(sK14,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_18])]) ).
fof(f701,plain,
( spl18_25
<=> subset(sK15,sK16(sK7(sK15,sK14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_25])]) ).
fof(f957,plain,
( ~ in(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ closed_subset(sK16(sK7(sK15,sK14)),sK14)
| spl18_18
| spl18_21
| ~ spl18_25 ),
inference(subsumption_resolution,[],[f942,f607]) ).
fof(f607,plain,
( ~ sP1(sK14,sK15)
| spl18_18 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f942,plain,
( ~ closed_subset(sK16(sK7(sK15,sK14)),sK14)
| ~ element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| sP1(sK14,sK15)
| ~ in(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| spl18_21
| ~ spl18_25 ),
inference(subsumption_resolution,[],[f941,f702]) ).
fof(f702,plain,
( subset(sK15,sK16(sK7(sK15,sK14)))
| ~ spl18_25 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f941,plain,
( ~ in(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ subset(sK15,sK16(sK7(sK15,sK14)))
| sP1(sK14,sK15)
| ~ closed_subset(sK16(sK7(sK15,sK14)),sK14)
| spl18_21 ),
inference(subsumption_resolution,[],[f940,f156]) ).
fof(f156,plain,
top_str(sK14),
inference(cnf_transformation,[],[f101]) ).
fof(f940,plain,
( ~ top_str(sK14)
| ~ closed_subset(sK16(sK7(sK15,sK14)),sK14)
| ~ subset(sK15,sK16(sK7(sK15,sK14)))
| sP1(sK14,sK15)
| ~ in(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| spl18_21 ),
inference(subsumption_resolution,[],[f939,f155]) ).
fof(f155,plain,
element(sK15,powerset(the_carrier(sK14))),
inference(cnf_transformation,[],[f101]) ).
fof(f939,plain,
( ~ element(sK15,powerset(the_carrier(sK14)))
| ~ in(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ subset(sK15,sK16(sK7(sK15,sK14)))
| ~ closed_subset(sK16(sK7(sK15,sK14)),sK14)
| ~ top_str(sK14)
| sP1(sK14,sK15)
| spl18_21 ),
inference(subsumption_resolution,[],[f690,f154]) ).
fof(f154,plain,
topological_space(sK14),
inference(cnf_transformation,[],[f101]) ).
fof(f690,plain,
( ~ topological_space(sK14)
| ~ element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| sP1(sK14,sK15)
| ~ subset(sK15,sK16(sK7(sK15,sK14)))
| ~ in(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ closed_subset(sK16(sK7(sK15,sK14)),sK14)
| ~ top_str(sK14)
| ~ element(sK15,powerset(the_carrier(sK14)))
| spl18_21 ),
inference(resolution,[],[f669,f170]) ).
fof(f170,plain,
! [X0,X1,X5] :
( in(X5,sK7(X0,X1))
| sP1(X1,X0)
| ~ in(X5,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ element(X0,powerset(the_carrier(X1)))
| ~ closed_subset(X5,X1)
| ~ top_str(X1)
| ~ element(X5,powerset(the_carrier(X1)))
| ~ subset(X0,X5) ),
inference(equality_resolution,[],[f169]) ).
fof(f169,plain,
! [X0,X1,X4,X5] :
( ~ topological_space(X1)
| ~ top_str(X1)
| in(X4,sK7(X0,X1))
| ~ in(X4,powerset(the_carrier(X1)))
| ~ closed_subset(X5,X1)
| ~ subset(X0,X4)
| ~ element(X5,powerset(the_carrier(X1)))
| X4 != X5
| sP1(X1,X0)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(equality_resolution,[],[f120]) ).
fof(f120,plain,
! [X3,X0,X1,X4,X5] :
( ~ topological_space(X1)
| ~ top_str(X1)
| in(X3,sK7(X0,X1))
| ~ in(X4,powerset(the_carrier(X1)))
| X3 != X4
| ~ closed_subset(X5,X1)
| ~ subset(X0,X3)
| ~ element(X5,powerset(the_carrier(X1)))
| X3 != X5
| sP1(X1,X0)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( ~ topological_space(X1)
| ~ top_str(X1)
| ! [X3] :
( ( in(X3,sK7(X0,X1))
| ! [X4] :
( ~ in(X4,powerset(the_carrier(X1)))
| X3 != X4
| ! [X5] :
( ~ closed_subset(X5,X1)
| ~ subset(X0,X3)
| ~ element(X5,powerset(the_carrier(X1)))
| X3 != X5 ) ) )
& ( ( in(sK8(X0,X1,X3),powerset(the_carrier(X1)))
& sK8(X0,X1,X3) = X3
& closed_subset(sK9(X0,X1,X3),X1)
& subset(X0,X3)
& element(sK9(X0,X1,X3),powerset(the_carrier(X1)))
& sK9(X0,X1,X3) = X3 )
| ~ in(X3,sK7(X0,X1)) ) )
| sP1(X1,X0)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f81,f84,f83,f82]) ).
fof(f82,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,powerset(the_carrier(X1)))
| X3 != X4
| ! [X5] :
( ~ closed_subset(X5,X1)
| ~ subset(X0,X3)
| ~ element(X5,powerset(the_carrier(X1)))
| X3 != X5 ) ) )
& ( ? [X6] :
( in(X6,powerset(the_carrier(X1)))
& X3 = X6
& ? [X7] :
( closed_subset(X7,X1)
& subset(X0,X3)
& element(X7,powerset(the_carrier(X1)))
& X3 = X7 ) )
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK7(X0,X1))
| ! [X4] :
( ~ in(X4,powerset(the_carrier(X1)))
| X3 != X4
| ! [X5] :
( ~ closed_subset(X5,X1)
| ~ subset(X0,X3)
| ~ element(X5,powerset(the_carrier(X1)))
| X3 != X5 ) ) )
& ( ? [X6] :
( in(X6,powerset(the_carrier(X1)))
& X3 = X6
& ? [X7] :
( closed_subset(X7,X1)
& subset(X0,X3)
& element(X7,powerset(the_carrier(X1)))
& X3 = X7 ) )
| ~ in(X3,sK7(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0,X1,X3] :
( ? [X6] :
( in(X6,powerset(the_carrier(X1)))
& X3 = X6
& ? [X7] :
( closed_subset(X7,X1)
& subset(X0,X3)
& element(X7,powerset(the_carrier(X1)))
& X3 = X7 ) )
=> ( in(sK8(X0,X1,X3),powerset(the_carrier(X1)))
& sK8(X0,X1,X3) = X3
& ? [X7] :
( closed_subset(X7,X1)
& subset(X0,X3)
& element(X7,powerset(the_carrier(X1)))
& X3 = X7 ) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X0,X1,X3] :
( ? [X7] :
( closed_subset(X7,X1)
& subset(X0,X3)
& element(X7,powerset(the_carrier(X1)))
& X3 = X7 )
=> ( closed_subset(sK9(X0,X1,X3),X1)
& subset(X0,X3)
& element(sK9(X0,X1,X3),powerset(the_carrier(X1)))
& sK9(X0,X1,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X1] :
( ~ topological_space(X1)
| ~ top_str(X1)
| ? [X2] :
! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,powerset(the_carrier(X1)))
| X3 != X4
| ! [X5] :
( ~ closed_subset(X5,X1)
| ~ subset(X0,X3)
| ~ element(X5,powerset(the_carrier(X1)))
| X3 != X5 ) ) )
& ( ? [X6] :
( in(X6,powerset(the_carrier(X1)))
& X3 = X6
& ? [X7] :
( closed_subset(X7,X1)
& subset(X0,X3)
& element(X7,powerset(the_carrier(X1)))
& X3 = X7 ) )
| ~ in(X3,X2) ) )
| sP1(X1,X0)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(rectify,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ~ topological_space(X1)
| ~ top_str(X1)
| ? [X7] :
! [X8] :
( ( in(X8,X7)
| ! [X9] :
( ~ in(X9,powerset(the_carrier(X1)))
| X8 != X9
| ! [X10] :
( ~ closed_subset(X10,X1)
| ~ subset(X0,X8)
| ~ element(X10,powerset(the_carrier(X1)))
| X8 != X10 ) ) )
& ( ? [X9] :
( in(X9,powerset(the_carrier(X1)))
& X8 = X9
& ? [X10] :
( closed_subset(X10,X1)
& subset(X0,X8)
& element(X10,powerset(the_carrier(X1)))
& X8 = X10 ) )
| ~ in(X8,X7) ) )
| sP1(X1,X0)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(nnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ~ topological_space(X1)
| ~ top_str(X1)
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(the_carrier(X1)))
& X8 = X9
& ? [X10] :
( closed_subset(X10,X1)
& subset(X0,X8)
& element(X10,powerset(the_carrier(X1)))
& X8 = X10 ) ) )
| sP1(X1,X0)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(definition_folding,[],[f62,f69,f68]) ).
fof(f68,plain,
! [X1,X2,X0] :
( ? [X6] :
( closed_subset(X6,X1)
& element(X6,powerset(the_carrier(X1)))
& subset(X0,X2)
& X2 = X6 )
| ~ sP0(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f69,plain,
! [X1,X0] :
( ? [X3,X2,X4] :
( X3 = X4
& X2 != X4
& ? [X5] :
( X4 = X5
& closed_subset(X5,X1)
& subset(X0,X4)
& element(X5,powerset(the_carrier(X1))) )
& X2 = X3
& sP0(X1,X2,X0) )
| ~ sP1(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f62,plain,
! [X0,X1] :
( ~ topological_space(X1)
| ~ top_str(X1)
| ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(the_carrier(X1)))
& X8 = X9
& ? [X10] :
( closed_subset(X10,X1)
& subset(X0,X8)
& element(X10,powerset(the_carrier(X1)))
& X8 = X10 ) ) )
| ? [X3,X2,X4] :
( X3 = X4
& X2 != X4
& ? [X5] :
( X4 = X5
& closed_subset(X5,X1)
& subset(X0,X4)
& element(X5,powerset(the_carrier(X1))) )
& X2 = X3
& ? [X6] :
( closed_subset(X6,X1)
& element(X6,powerset(the_carrier(X1)))
& subset(X0,X2)
& X2 = X6 ) )
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(the_carrier(X1)))
& X8 = X9
& ? [X10] :
( closed_subset(X10,X1)
& subset(X0,X8)
& element(X10,powerset(the_carrier(X1)))
& X8 = X10 ) ) )
| ? [X4,X3,X2] :
( X2 != X4
& ? [X5] :
( X4 = X5
& closed_subset(X5,X1)
& subset(X0,X4)
& element(X5,powerset(the_carrier(X1))) )
& X2 = X3
& ? [X6] :
( closed_subset(X6,X1)
& element(X6,powerset(the_carrier(X1)))
& subset(X0,X2)
& X2 = X6 )
& X3 = X4 )
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( top_str(X1)
& topological_space(X1)
& element(X0,powerset(the_carrier(X1))) )
=> ( ! [X4,X3,X2] :
( ( ? [X5] :
( X4 = X5
& closed_subset(X5,X1)
& subset(X0,X4)
& element(X5,powerset(the_carrier(X1))) )
& X2 = X3
& ? [X6] :
( closed_subset(X6,X1)
& element(X6,powerset(the_carrier(X1)))
& subset(X0,X2)
& X2 = X6 )
& X3 = X4 )
=> X2 = X4 )
=> ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( in(X9,powerset(the_carrier(X1)))
& X8 = X9
& ? [X10] :
( closed_subset(X10,X1)
& subset(X0,X8)
& element(X10,powerset(the_carrier(X1)))
& X8 = X10 ) ) ) ) ),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X1,X0] :
( ( top_str(X0)
& topological_space(X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( ! [X3,X2,X4] :
( ( X2 = X4
& X2 = X3
& ? [X6] :
( X4 = X6
& subset(X1,X4)
& closed_subset(X6,X0)
& element(X6,powerset(the_carrier(X0))) )
& ? [X5] :
( X3 = X5
& closed_subset(X5,X0)
& element(X5,powerset(the_carrier(X0)))
& subset(X1,X3) ) )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( X3 = X4
& in(X4,powerset(the_carrier(X0)))
& ? [X7] :
( closed_subset(X7,X0)
& subset(X1,X3)
& X3 = X7
& element(X7,powerset(the_carrier(X0))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e1_40__pre_topc__1) ).
fof(f669,plain,
( ~ in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| spl18_21 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f956,plain,
( spl18_22
| ~ spl18_21
| spl18_18
| ~ spl18_19 ),
inference(avatar_split_clause,[],[f955,f610,f606,f667,f671]) ).
fof(f610,plain,
( spl18_19
<=> sK16(sK7(sK15,sK14)) = sK9(sK15,sK14,sK16(sK7(sK15,sK14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_19])]) ).
fof(f955,plain,
( ~ in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| closed_subset(sK16(sK7(sK15,sK14)),sK14)
| spl18_18
| ~ spl18_19 ),
inference(subsumption_resolution,[],[f726,f607]) ).
fof(f726,plain,
( ~ in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| sP1(sK14,sK15)
| closed_subset(sK16(sK7(sK15,sK14)),sK14)
| ~ spl18_19 ),
inference(subsumption_resolution,[],[f663,f155]) ).
fof(f663,plain,
( ~ element(sK15,powerset(the_carrier(sK14)))
| closed_subset(sK16(sK7(sK15,sK14)),sK14)
| ~ in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| sP1(sK14,sK15)
| ~ spl18_19 ),
inference(subsumption_resolution,[],[f662,f154]) ).
fof(f662,plain,
( ~ topological_space(sK14)
| ~ element(sK15,powerset(the_carrier(sK14)))
| closed_subset(sK16(sK7(sK15,sK14)),sK14)
| ~ in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| sP1(sK14,sK15)
| ~ spl18_19 ),
inference(subsumption_resolution,[],[f646,f156]) ).
fof(f646,plain,
( ~ top_str(sK14)
| ~ topological_space(sK14)
| sP1(sK14,sK15)
| ~ element(sK15,powerset(the_carrier(sK14)))
| closed_subset(sK16(sK7(sK15,sK14)),sK14)
| ~ in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| ~ spl18_19 ),
inference(superposition,[],[f117,f612]) ).
fof(f612,plain,
( sK16(sK7(sK15,sK14)) = sK9(sK15,sK14,sK16(sK7(sK15,sK14)))
| ~ spl18_19 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f117,plain,
! [X3,X0,X1] :
( closed_subset(sK9(X0,X1,X3),X1)
| sP1(X1,X0)
| ~ element(X0,powerset(the_carrier(X1)))
| ~ in(X3,sK7(X0,X1))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f937,plain,
( ~ spl18_21
| spl18_23
| spl18_18
| ~ spl18_19 ),
inference(avatar_split_clause,[],[f936,f610,f606,f680,f667]) ).
fof(f936,plain,
( element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| spl18_18
| ~ spl18_19 ),
inference(subsumption_resolution,[],[f722,f156]) ).
fof(f722,plain,
( ~ top_str(sK14)
| element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| spl18_18
| ~ spl18_19 ),
inference(subsumption_resolution,[],[f676,f607]) ).
fof(f676,plain,
( sP1(sK14,sK15)
| ~ in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| ~ top_str(sK14)
| element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ spl18_19 ),
inference(subsumption_resolution,[],[f675,f155]) ).
fof(f675,plain,
( ~ element(sK15,powerset(the_carrier(sK14)))
| ~ in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ top_str(sK14)
| sP1(sK14,sK15)
| ~ spl18_19 ),
inference(subsumption_resolution,[],[f645,f154]) ).
fof(f645,plain,
( element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ topological_space(sK14)
| sP1(sK14,sK15)
| ~ top_str(sK14)
| ~ element(sK15,powerset(the_carrier(sK14)))
| ~ in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| ~ spl18_19 ),
inference(superposition,[],[f115,f612]) ).
fof(f115,plain,
! [X3,X0,X1] :
( element(sK9(X0,X1,X3),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1)
| ~ in(X3,sK7(X0,X1))
| sP1(X1,X0)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f85]) ).
fof(f930,plain,
( spl18_23
| ~ spl18_20
| spl18_21 ),
inference(avatar_split_clause,[],[f929,f667,f614,f680]) ).
fof(f929,plain,
( element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ spl18_20
| spl18_21 ),
inference(forward_demodulation,[],[f686,f616]) ).
fof(f686,plain,
( element(sK17(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| spl18_21 ),
inference(resolution,[],[f669,f157]) ).
fof(f157,plain,
! [X2] :
( element(sK17(X2),powerset(the_carrier(sK14)))
| in(sK16(X2),X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f919,plain,
( spl18_24
| spl18_21 ),
inference(avatar_split_clause,[],[f685,f667,f697]) ).
fof(f685,plain,
( in(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| spl18_21 ),
inference(resolution,[],[f669,f161]) ).
fof(f161,plain,
! [X2] :
( in(sK16(X2),powerset(the_carrier(sK14)))
| in(sK16(X2),X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f912,plain,
( spl18_18
| ~ spl18_21
| spl18_24
| ~ spl18_26 ),
inference(avatar_contradiction_clause,[],[f911]) ).
fof(f911,plain,
( $false
| spl18_18
| ~ spl18_21
| spl18_24
| ~ spl18_26 ),
inference(subsumption_resolution,[],[f910,f155]) ).
fof(f910,plain,
( ~ element(sK15,powerset(the_carrier(sK14)))
| spl18_18
| ~ spl18_21
| spl18_24
| ~ spl18_26 ),
inference(subsumption_resolution,[],[f909,f156]) ).
fof(f909,plain,
( ~ top_str(sK14)
| ~ element(sK15,powerset(the_carrier(sK14)))
| spl18_18
| ~ spl18_21
| spl18_24
| ~ spl18_26 ),
inference(subsumption_resolution,[],[f908,f154]) ).
fof(f908,plain,
( ~ topological_space(sK14)
| ~ top_str(sK14)
| ~ element(sK15,powerset(the_carrier(sK14)))
| spl18_18
| ~ spl18_21
| spl18_24
| ~ spl18_26 ),
inference(subsumption_resolution,[],[f907,f699]) ).
fof(f699,plain,
( ~ in(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| spl18_24 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f907,plain,
( in(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ top_str(sK14)
| ~ element(sK15,powerset(the_carrier(sK14)))
| ~ topological_space(sK14)
| spl18_18
| ~ spl18_21
| ~ spl18_26 ),
inference(subsumption_resolution,[],[f906,f668]) ).
fof(f668,plain,
( in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| ~ spl18_21 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f906,plain,
( ~ in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| ~ element(sK15,powerset(the_carrier(sK14)))
| in(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ topological_space(sK14)
| ~ top_str(sK14)
| spl18_18
| ~ spl18_26 ),
inference(subsumption_resolution,[],[f900,f607]) ).
fof(f900,plain,
( sP1(sK14,sK15)
| ~ top_str(sK14)
| ~ topological_space(sK14)
| ~ in(sK16(sK7(sK15,sK14)),sK7(sK15,sK14))
| ~ element(sK15,powerset(the_carrier(sK14)))
| in(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ spl18_26 ),
inference(superposition,[],[f119,f806]) ).
fof(f806,plain,
( sK16(sK7(sK15,sK14)) = sK8(sK15,sK14,sK16(sK7(sK15,sK14)))
| ~ spl18_26 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f804,plain,
( spl18_26
<=> sK16(sK7(sK15,sK14)) = sK8(sK15,sK14,sK16(sK7(sK15,sK14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_26])]) ).
fof(f119,plain,
! [X3,X0,X1] :
( in(sK8(X0,X1,X3),powerset(the_carrier(X1)))
| ~ topological_space(X1)
| ~ top_str(X1)
| sP1(X1,X0)
| ~ element(X0,powerset(the_carrier(X1)))
| ~ in(X3,sK7(X0,X1)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f872,plain,
( spl18_26
| spl18_18
| spl18_24 ),
inference(avatar_split_clause,[],[f871,f697,f606,f804]) ).
fof(f871,plain,
( sK16(sK7(sK15,sK14)) = sK8(sK15,sK14,sK16(sK7(sK15,sK14)))
| spl18_18
| spl18_24 ),
inference(subsumption_resolution,[],[f870,f156]) ).
fof(f870,plain,
( ~ top_str(sK14)
| sK16(sK7(sK15,sK14)) = sK8(sK15,sK14,sK16(sK7(sK15,sK14)))
| spl18_18
| spl18_24 ),
inference(subsumption_resolution,[],[f869,f607]) ).
fof(f869,plain,
( sP1(sK14,sK15)
| sK16(sK7(sK15,sK14)) = sK8(sK15,sK14,sK16(sK7(sK15,sK14)))
| ~ top_str(sK14)
| spl18_24 ),
inference(subsumption_resolution,[],[f868,f154]) ).
fof(f868,plain,
( sK16(sK7(sK15,sK14)) = sK8(sK15,sK14,sK16(sK7(sK15,sK14)))
| ~ topological_space(sK14)
| ~ top_str(sK14)
| sP1(sK14,sK15)
| spl18_24 ),
inference(subsumption_resolution,[],[f858,f155]) ).
fof(f858,plain,
( sK16(sK7(sK15,sK14)) = sK8(sK15,sK14,sK16(sK7(sK15,sK14)))
| ~ element(sK15,powerset(the_carrier(sK14)))
| ~ top_str(sK14)
| sP1(sK14,sK15)
| ~ topological_space(sK14)
| spl18_24 ),
inference(resolution,[],[f699,f396]) ).
fof(f396,plain,
! [X2,X3] :
( in(sK16(sK7(X2,X3)),powerset(the_carrier(sK14)))
| sK8(X2,X3,sK16(sK7(X2,X3))) = sK16(sK7(X2,X3))
| sP1(X3,X2)
| ~ element(X2,powerset(the_carrier(X3)))
| ~ topological_space(X3)
| ~ top_str(X3) ),
inference(resolution,[],[f118,f161]) ).
fof(f118,plain,
! [X3,X0,X1] :
( ~ in(X3,sK7(X0,X1))
| sK8(X0,X1,X3) = X3
| ~ topological_space(X1)
| ~ element(X0,powerset(the_carrier(X1)))
| sP1(X1,X0)
| ~ top_str(X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f781,plain,
( spl18_18
| spl18_25 ),
inference(avatar_contradiction_clause,[],[f780]) ).
fof(f780,plain,
( $false
| spl18_18
| spl18_25 ),
inference(subsumption_resolution,[],[f779,f156]) ).
fof(f779,plain,
( ~ top_str(sK14)
| spl18_18
| spl18_25 ),
inference(subsumption_resolution,[],[f778,f154]) ).
fof(f778,plain,
( ~ topological_space(sK14)
| ~ top_str(sK14)
| spl18_18
| spl18_25 ),
inference(subsumption_resolution,[],[f777,f607]) ).
fof(f777,plain,
( sP1(sK14,sK15)
| ~ top_str(sK14)
| ~ topological_space(sK14)
| spl18_25 ),
inference(subsumption_resolution,[],[f734,f155]) ).
fof(f734,plain,
( ~ element(sK15,powerset(the_carrier(sK14)))
| ~ top_str(sK14)
| ~ topological_space(sK14)
| sP1(sK14,sK15)
| spl18_25 ),
inference(resolution,[],[f703,f453]) ).
fof(f453,plain,
! [X0] :
( subset(sK15,sK16(sK7(sK15,X0)))
| ~ element(sK15,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| sP1(X0,sK15) ),
inference(factoring,[],[f382]) ).
fof(f382,plain,
! [X8,X9] :
( subset(sK15,sK16(sK7(X8,X9)))
| subset(X8,sK16(sK7(X8,X9)))
| ~ element(X8,powerset(the_carrier(X9)))
| ~ topological_space(X9)
| ~ top_str(X9)
| sP1(X9,X8) ),
inference(resolution,[],[f116,f160]) ).
fof(f160,plain,
! [X2] :
( in(sK16(X2),X2)
| subset(sK15,sK16(X2)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f116,plain,
! [X3,X0,X1] :
( ~ in(X3,sK7(X0,X1))
| ~ element(X0,powerset(the_carrier(X1)))
| ~ topological_space(X1)
| subset(X0,X3)
| ~ top_str(X1)
| sP1(X1,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f703,plain,
( ~ subset(sK15,sK16(sK7(sK15,sK14)))
| spl18_25 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f721,plain,
( ~ spl18_22
| ~ spl18_24
| ~ spl18_25
| ~ spl18_23
| ~ spl18_21 ),
inference(avatar_split_clause,[],[f706,f667,f680,f701,f697,f671]) ).
fof(f706,plain,
( ~ element(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ subset(sK15,sK16(sK7(sK15,sK14)))
| ~ in(sK16(sK7(sK15,sK14)),powerset(the_carrier(sK14)))
| ~ closed_subset(sK16(sK7(sK15,sK14)),sK14)
| ~ spl18_21 ),
inference(resolution,[],[f668,f171]) ).
fof(f171,plain,
! [X2] :
( ~ in(sK16(X2),powerset(the_carrier(sK14)))
| ~ in(sK16(X2),X2)
| ~ element(sK16(X2),powerset(the_carrier(sK14)))
| ~ subset(sK15,sK16(X2))
| ~ closed_subset(sK16(X2),sK14) ),
inference(equality_resolution,[],[f162]) ).
fof(f162,plain,
! [X2,X4] :
( ~ in(sK16(X2),X2)
| ~ in(sK16(X2),powerset(the_carrier(sK14)))
| ~ subset(sK15,sK16(X2))
| ~ closed_subset(X4,sK14)
| sK16(X2) != X4
| ~ element(X4,powerset(the_carrier(sK14))) ),
inference(cnf_transformation,[],[f101]) ).
fof(f720,plain,
( spl18_19
| spl18_18
| ~ spl18_21 ),
inference(avatar_split_clause,[],[f719,f667,f606,f610]) ).
fof(f719,plain,
( sK16(sK7(sK15,sK14)) = sK9(sK15,sK14,sK16(sK7(sK15,sK14)))
| spl18_18
| ~ spl18_21 ),
inference(subsumption_resolution,[],[f718,f155]) ).
fof(f718,plain,
( sK16(sK7(sK15,sK14)) = sK9(sK15,sK14,sK16(sK7(sK15,sK14)))
| ~ element(sK15,powerset(the_carrier(sK14)))
| spl18_18
| ~ spl18_21 ),
inference(subsumption_resolution,[],[f717,f156]) ).
fof(f717,plain,
( ~ top_str(sK14)
| ~ element(sK15,powerset(the_carrier(sK14)))
| sK16(sK7(sK15,sK14)) = sK9(sK15,sK14,sK16(sK7(sK15,sK14)))
| spl18_18
| ~ spl18_21 ),
inference(subsumption_resolution,[],[f716,f607]) ).
fof(f716,plain,
( sK16(sK7(sK15,sK14)) = sK9(sK15,sK14,sK16(sK7(sK15,sK14)))
| sP1(sK14,sK15)
| ~ element(sK15,powerset(the_carrier(sK14)))
| ~ top_str(sK14)
| ~ spl18_21 ),
inference(subsumption_resolution,[],[f708,f154]) ).
fof(f708,plain,
( ~ topological_space(sK14)
| ~ element(sK15,powerset(the_carrier(sK14)))
| ~ top_str(sK14)
| sP1(sK14,sK15)
| sK16(sK7(sK15,sK14)) = sK9(sK15,sK14,sK16(sK7(sK15,sK14)))
| ~ spl18_21 ),
inference(resolution,[],[f668,f114]) ).
fof(f114,plain,
! [X3,X0,X1] :
( ~ in(X3,sK7(X0,X1))
| sP1(X1,X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| sK9(X0,X1,X3) = X3
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f85]) ).
fof(f691,plain,
( spl18_20
| spl18_21 ),
inference(avatar_split_clause,[],[f687,f667,f614]) ).
fof(f687,plain,
( sK16(sK7(sK15,sK14)) = sK17(sK7(sK15,sK14))
| spl18_21 ),
inference(resolution,[],[f669,f158]) ).
fof(f158,plain,
! [X2] :
( in(sK16(X2),X2)
| sK17(X2) = sK16(X2) ),
inference(cnf_transformation,[],[f101]) ).
fof(f644,plain,
~ spl18_18,
inference(avatar_contradiction_clause,[],[f643]) ).
fof(f643,plain,
( $false
| ~ spl18_18 ),
inference(subsumption_resolution,[],[f642,f620]) ).
fof(f620,plain,
( sK3(sK14,sK15) != sK4(sK14,sK15)
| ~ spl18_18 ),
inference(resolution,[],[f608,f108]) ).
fof(f108,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sK4(X0,X1) != sK3(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ( sK4(X0,X1) = sK2(X0,X1)
& sK4(X0,X1) != sK3(X0,X1)
& sK4(X0,X1) = sK5(X0,X1)
& closed_subset(sK5(X0,X1),X0)
& subset(X1,sK4(X0,X1))
& element(sK5(X0,X1),powerset(the_carrier(X0)))
& sK2(X0,X1) = sK3(X0,X1)
& sP0(X0,sK3(X0,X1),X1) )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f72,f74,f73]) ).
fof(f73,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X2 = X4
& X3 != X4
& ? [X5] :
( X4 = X5
& closed_subset(X5,X0)
& subset(X1,X4)
& element(X5,powerset(the_carrier(X0))) )
& X2 = X3
& sP0(X0,X3,X1) )
=> ( sK4(X0,X1) = sK2(X0,X1)
& sK4(X0,X1) != sK3(X0,X1)
& ? [X5] :
( sK4(X0,X1) = X5
& closed_subset(X5,X0)
& subset(X1,sK4(X0,X1))
& element(X5,powerset(the_carrier(X0))) )
& sK2(X0,X1) = sK3(X0,X1)
& sP0(X0,sK3(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X5] :
( sK4(X0,X1) = X5
& closed_subset(X5,X0)
& subset(X1,sK4(X0,X1))
& element(X5,powerset(the_carrier(X0))) )
=> ( sK4(X0,X1) = sK5(X0,X1)
& closed_subset(sK5(X0,X1),X0)
& subset(X1,sK4(X0,X1))
& element(sK5(X0,X1),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X2 = X4
& X3 != X4
& ? [X5] :
( X4 = X5
& closed_subset(X5,X0)
& subset(X1,X4)
& element(X5,powerset(the_carrier(X0))) )
& X2 = X3
& sP0(X0,X3,X1) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f71]) ).
fof(f71,plain,
! [X1,X0] :
( ? [X3,X2,X4] :
( X3 = X4
& X2 != X4
& ? [X5] :
( X4 = X5
& closed_subset(X5,X1)
& subset(X0,X4)
& element(X5,powerset(the_carrier(X1))) )
& X2 = X3
& sP0(X1,X2,X0) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f69]) ).
fof(f608,plain,
( sP1(sK14,sK15)
| ~ spl18_18 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f642,plain,
( sK3(sK14,sK15) = sK4(sK14,sK15)
| ~ spl18_18 ),
inference(forward_demodulation,[],[f622,f619]) ).
fof(f619,plain,
( sK2(sK14,sK15) = sK4(sK14,sK15)
| ~ spl18_18 ),
inference(resolution,[],[f608,f109]) ).
fof(f109,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sK4(X0,X1) = sK2(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f622,plain,
( sK2(sK14,sK15) = sK3(sK14,sK15)
| ~ spl18_18 ),
inference(resolution,[],[f608,f103]) ).
fof(f103,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| sK2(X0,X1) = sK3(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU314+1 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 15:12:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.51 % (19532)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.51 % (19549)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.19/0.52 % (19524)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.52 % (19543)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.52 % (19534)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.52 % (19527)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.53 % (19535)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.53 % (19521)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.53 % (19527)Instruction limit reached!
% 0.19/0.53 % (19527)------------------------------
% 0.19/0.53 % (19527)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.53 % (19527)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.53 % (19527)Termination reason: Unknown
% 0.19/0.53 % (19520)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.53 % (19527)Termination phase: Saturation
% 0.19/0.53
% 0.19/0.53 % (19527)Memory used [KB]: 5500
% 0.19/0.53 % (19527)Time elapsed: 0.077 s
% 0.19/0.53 % (19527)Instructions burned: 7 (million)
% 0.19/0.53 % (19527)------------------------------
% 0.19/0.53 % (19527)------------------------------
% 0.19/0.54 % (19523)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.54 % (19520)Refutation not found, incomplete strategy% (19520)------------------------------
% 0.19/0.54 % (19520)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54 % (19520)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.54 % (19520)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.54
% 0.19/0.54 % (19520)Memory used [KB]: 5500
% 0.19/0.54 % (19520)Time elapsed: 0.133 s
% 0.19/0.54 % (19520)Instructions burned: 6 (million)
% 0.19/0.54 % (19520)------------------------------
% 0.19/0.54 % (19520)------------------------------
% 0.19/0.54 % (19538)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.54 % (19548)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.19/0.54 % (19530)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.54 % (19537)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.55 % (19546)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.55 % (19540)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.55 % (19529)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.55 % (19545)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.56 % (19519)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.56 TRYING [1]
% 0.19/0.56 TRYING [2]
% 0.19/0.56 TRYING [3]
% 1.59/0.57 % (19544)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.59/0.57 % (19522)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.59/0.57 % (19525)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.59/0.57 % (19536)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.59/0.58 % (19550)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.59/0.58 % (19541)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.59/0.58 TRYING [1]
% 1.59/0.58 TRYING [1]
% 1.59/0.58 TRYING [2]
% 1.59/0.58 % (19524)First to succeed.
% 1.59/0.58 TRYING [2]
% 1.59/0.58 % (19547)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.80/0.58 % (19528)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.80/0.59 % (19528)Instruction limit reached!
% 1.80/0.59 % (19528)------------------------------
% 1.80/0.59 % (19528)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.80/0.59 % (19528)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.80/0.59 % (19528)Termination reason: Unknown
% 1.80/0.59 % (19528)Termination phase: Clausification
% 1.80/0.59
% 1.80/0.59 % (19528)Memory used [KB]: 1023
% 1.80/0.59 % (19528)Time elapsed: 0.003 s
% 1.80/0.59 % (19528)Instructions burned: 3 (million)
% 1.80/0.59 % (19528)------------------------------
% 1.80/0.59 % (19528)------------------------------
% 1.80/0.59 TRYING [3]
% 1.80/0.59 % (19539)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.80/0.59 TRYING [3]
% 1.80/0.59 % (19542)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.80/0.59 % (19531)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.80/0.59 TRYING [4]
% 1.80/0.59 TRYING [4]
% 1.80/0.59 % (19524)Refutation found. Thanks to Tanya!
% 1.80/0.59 % SZS status Theorem for theBenchmark
% 1.80/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.80/0.59 % (19524)------------------------------
% 1.80/0.59 % (19524)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.80/0.59 % (19524)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.80/0.60 % (19524)Termination reason: Refutation
% 1.80/0.60
% 1.80/0.60 % (19524)Memory used [KB]: 6140
% 1.80/0.60 % (19524)Time elapsed: 0.167 s
% 1.80/0.60 % (19524)Instructions burned: 46 (million)
% 1.80/0.60 % (19524)------------------------------
% 1.80/0.60 % (19524)------------------------------
% 1.80/0.60 % (19515)Success in time 0.239 s
%------------------------------------------------------------------------------