TSTP Solution File: SEU314+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU314+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.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 : Tue Apr 30 15:28:16 EDT 2024
% Result : Theorem 0.11s 0.29s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 44
% Syntax : Number of formulae : 341 ( 19 unt; 0 def)
% Number of atoms : 1442 ( 180 equ)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 1708 ( 607 ~; 727 |; 324 &)
% ( 21 <=>; 27 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 34 ( 32 usr; 14 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 3 con; 0-3 aty)
% Number of variables : 560 ( 458 !; 102 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f548,plain,
$false,
inference(avatar_sat_refutation,[],[f213,f259,f327,f362,f375,f385,f409,f439,f442,f445,f477,f499,f543,f547]) ).
fof(f547,plain,
( spl23_8
| ~ spl23_10 ),
inference(avatar_contradiction_clause,[],[f546]) ).
fof(f546,plain,
( $false
| spl23_8
| ~ spl23_10 ),
inference(global_subsumption,[],[f115,f116,f182,f187,f124,f156,f157,f117,f131,f132,f138,f191,f192,f126,f155,f158,f121,f122,f193,f194,f120,f195,f125,f171,f176,f180,f118,f198,f199,f119,f196,f197,f200,f139,f202,f201,f154,f204,f203,f215,f162,f216,f164,f217,f153,f161,f163,f165,f167,f169,f170,f174,f175,f178,f179,f218,f221,f159,f160,f166,f168,f173,f177,f228,f230,f231,f232,f233,f235,f236,f237,f181,f248,f250,f260,f246,f225,f264,f265,f226,f268,f188,f277,f278,f279,f280,f219,f220,f222,f288,f286,f223,f297,f300,f299,f294,f242,f224,f302,f303,f190,f305,f306,f307,f308,f309,f310,f311,f312,f313,f314,f281,f262,f263,f266,f267,f292,f261,f329,f330,f240,f304,f284,f335,f285,f339,f295,f343,f341,f296,f347,f345,f342,f346,f234,f301,f349,f350,f351,f352,f353,f243,f432,f244,f455,f245,f478,f369,f516,f515,f519,f520,f514,f356]) ).
fof(f356,plain,
( sK9(sK14(sK7,sK8)) != sK19(sK9(sK14(sK7,sK8)),sK8,sK7)
| spl23_8 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f355,plain,
( spl23_8
<=> sK9(sK14(sK7,sK8)) = sK19(sK9(sK14(sK7,sK8)),sK8,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_8])]) ).
fof(f514,plain,
( sK9(sK14(sK7,sK8)) = sK19(sK9(sK14(sK7,sK8)),sK8,sK7)
| ~ spl23_10 ),
inference(resolution,[],[f369,f169]) ).
fof(f520,plain,
( in(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| ~ spl23_10 ),
inference(subsumption_resolution,[],[f518,f369]) ).
fof(f518,plain,
( in(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| ~ sP4(sK9(sK14(sK7,sK8)),sK8,sK7)
| ~ spl23_10 ),
inference(superposition,[],[f166,f515]) ).
fof(f519,plain,
( ~ in(powerset(the_carrier(sK7)),sK9(sK14(sK7,sK8)))
| ~ spl23_10 ),
inference(subsumption_resolution,[],[f517,f369]) ).
fof(f517,plain,
( ~ in(powerset(the_carrier(sK7)),sK9(sK14(sK7,sK8)))
| ~ sP4(sK9(sK14(sK7,sK8)),sK8,sK7)
| ~ spl23_10 ),
inference(superposition,[],[f230,f515]) ).
fof(f515,plain,
( sK9(sK14(sK7,sK8)) = sK18(sK9(sK14(sK7,sK8)),sK8,sK7)
| ~ spl23_10 ),
inference(resolution,[],[f369,f167]) ).
fof(f516,plain,
( subset(sK8,sK9(sK14(sK7,sK8)))
| ~ spl23_10 ),
inference(resolution,[],[f369,f171]) ).
fof(f369,plain,
( sP4(sK9(sK14(sK7,sK8)),sK8,sK7)
| ~ spl23_10 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f368,plain,
( spl23_10
<=> sP4(sK9(sK14(sK7,sK8)),sK8,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_10])]) ).
fof(f478,plain,
! [X2,X0,X1] :
( sP5(X0,sK21(X1,X2,X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ sP2(X1,X2,X0)
| sK9(sK14(X0,sK21(X1,X2,X0))) = sK10(sK14(X0,sK21(X1,X2,X0)))
| sK9(sK14(X0,sK21(X1,X2,X0))) = sK19(sK9(sK14(X0,sK21(X1,X2,X0))),sK21(X1,X2,X0),X0) ),
inference(resolution,[],[f245,f301]) ).
fof(f245,plain,
! [X2,X0,X1] :
( sP6(X0,sK21(X1,X2,X0))
| sP5(X0,sK21(X1,X2,X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ sP2(X1,X2,X0) ),
inference(resolution,[],[f181,f177]) ).
fof(f455,plain,
! [X2,X0,X1] :
( sP5(X0,sK20(X1,X2,X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ sP3(X1,X2,X0)
| sK9(sK14(X0,sK20(X1,X2,X0))) = sK10(sK14(X0,sK20(X1,X2,X0)))
| sK9(sK14(X0,sK20(X1,X2,X0))) = sK19(sK9(sK14(X0,sK20(X1,X2,X0))),sK20(X1,X2,X0),X0) ),
inference(resolution,[],[f244,f301]) ).
fof(f244,plain,
! [X2,X0,X1] :
( sP6(X0,sK20(X1,X2,X0))
| sP5(X0,sK20(X1,X2,X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ sP3(X1,X2,X0) ),
inference(resolution,[],[f181,f173]) ).
fof(f432,plain,
! [X2,X0,X1] :
( sP5(X0,sK19(X1,X2,X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ sP4(X1,X2,X0)
| sK9(sK14(X0,sK19(X1,X2,X0))) = sK10(sK14(X0,sK19(X1,X2,X0)))
| sK9(sK14(X0,sK19(X1,X2,X0))) = sK19(sK9(sK14(X0,sK19(X1,X2,X0))),sK19(X1,X2,X0),X0) ),
inference(resolution,[],[f243,f301]) ).
fof(f243,plain,
! [X2,X0,X1] :
( sP6(X0,sK19(X1,X2,X0))
| sP5(X0,sK19(X1,X2,X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ sP4(X1,X2,X0) ),
inference(resolution,[],[f181,f168]) ).
fof(f353,plain,
! [X0] :
( sK9(sK14(X0,sK11(the_carrier(X0)))) = sK10(sK14(X0,sK11(the_carrier(X0))))
| sK9(sK14(X0,sK11(the_carrier(X0)))) = sK19(sK9(sK14(X0,sK11(the_carrier(X0)))),sK11(the_carrier(X0)),X0)
| sP5(X0,sK11(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty(the_carrier(X0)) ),
inference(resolution,[],[f301,f240]) ).
fof(f352,plain,
! [X0] :
( sK9(sK14(X0,sK13(the_carrier(X0)))) = sK10(sK14(X0,sK13(the_carrier(X0))))
| sK9(sK14(X0,sK13(the_carrier(X0)))) = sK19(sK9(sK14(X0,sK13(the_carrier(X0)))),sK13(the_carrier(X0)),X0)
| sP5(X0,sK13(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f301,f242]) ).
fof(f351,plain,
! [X0] :
( sK9(sK14(X0,sK12(X0))) = sK10(sK14(X0,sK12(X0)))
| sK9(sK14(X0,sK12(X0))) = sK19(sK9(sK14(X0,sK12(X0))),sK12(X0),X0)
| sP5(X0,sK12(X0))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f301,f246]) ).
fof(f350,plain,
! [X0,X1] :
( sK9(sK14(sK7,sK10(sK14(X0,X1)))) = sK10(sK14(sK7,sK10(sK14(X0,X1))))
| sK9(sK14(sK7,sK10(sK14(X0,X1)))) = sK19(sK9(sK14(sK7,sK10(sK14(X0,X1)))),sK10(sK14(X0,X1)),sK7)
| subset(X1,sK9(sK14(X0,X1)))
| sP5(sK7,sK10(sK14(X0,X1)))
| ~ sP6(X0,X1) ),
inference(resolution,[],[f301,f292]) ).
fof(f349,plain,
! [X0] :
( sK9(sK14(sK7,sK10(X0))) = sK10(sK14(sK7,sK10(X0)))
| sK9(sK14(sK7,sK10(X0))) = sK19(sK9(sK14(sK7,sK10(X0))),sK10(X0),sK7)
| in(sK9(X0),X0)
| sP5(sK7,sK10(X0)) ),
inference(resolution,[],[f301,f250]) ).
fof(f301,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK10(sK14(X0,X1))
| sK9(sK14(X0,X1)) = sK19(sK9(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f224,f169]) ).
fof(f234,plain,
! [X2,X3,X0,X1] :
( ~ sP4(sK14(X2,X3),X1,X0)
| ~ sP6(X0,X1)
| ~ sP4(sK14(X0,X1),X3,X2)
| ~ sP6(X2,X3) ),
inference(resolution,[],[f228,f160]) ).
fof(f346,plain,
! [X0,X1] :
( ~ in(powerset(the_carrier(sK7)),sK9(sK14(X0,X1)))
| sK9(sK14(X0,X1)) = sK18(sK9(sK14(X0,X1)),X1,X0)
| ~ sP6(X0,X1) ),
inference(resolution,[],[f296,f158]) ).
fof(f342,plain,
! [X0,X1] :
( ~ in(powerset(the_carrier(sK7)),sK9(sK14(X0,X1)))
| sK9(sK14(X0,X1)) = sK19(sK9(sK14(X0,X1)),X1,X0)
| ~ sP6(X0,X1) ),
inference(resolution,[],[f295,f158]) ).
fof(f345,plain,
! [X2,X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK18(sK9(sK14(X0,X1)),X1,X0)
| ~ subset(X2,sK9(sK14(X0,X1)))
| ~ closed_subset(sK9(sK14(X0,X1)),sK7)
| ~ element(sK9(sK14(X0,X1)),powerset(the_carrier(sK7)))
| sP4(sK9(sK14(X0,X1)),X2,sK7) ),
inference(resolution,[],[f296,f190]) ).
fof(f347,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK18(sK9(sK14(X0,X1)),X1,X0)
| ~ closed_subset(sK9(sK14(X0,X1)),sK7)
| ~ element(sK9(sK14(X0,X1)),powerset(the_carrier(sK7)))
| ~ in(sK9(sK14(X0,X1)),sK14(X0,X1)) ),
inference(subsumption_resolution,[],[f344,f263]) ).
fof(f344,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK18(sK9(sK14(X0,X1)),X1,X0)
| ~ closed_subset(sK9(sK14(X0,X1)),sK7)
| ~ element(sK9(sK14(X0,X1)),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(sK14(X0,X1)))
| ~ in(sK9(sK14(X0,X1)),sK14(X0,X1)) ),
inference(resolution,[],[f296,f188]) ).
fof(f296,plain,
! [X0,X1] :
( in(sK9(sK14(X0,X1)),powerset(the_carrier(sK7)))
| ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK18(sK9(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f223,f167]) ).
fof(f341,plain,
! [X2,X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK19(sK9(sK14(X0,X1)),X1,X0)
| ~ subset(X2,sK9(sK14(X0,X1)))
| ~ closed_subset(sK9(sK14(X0,X1)),sK7)
| ~ element(sK9(sK14(X0,X1)),powerset(the_carrier(sK7)))
| sP4(sK9(sK14(X0,X1)),X2,sK7) ),
inference(resolution,[],[f295,f190]) ).
fof(f343,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK19(sK9(sK14(X0,X1)),X1,X0)
| ~ closed_subset(sK9(sK14(X0,X1)),sK7)
| ~ element(sK9(sK14(X0,X1)),powerset(the_carrier(sK7)))
| ~ in(sK9(sK14(X0,X1)),sK14(X0,X1)) ),
inference(subsumption_resolution,[],[f340,f262]) ).
fof(f340,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK19(sK9(sK14(X0,X1)),X1,X0)
| ~ closed_subset(sK9(sK14(X0,X1)),sK7)
| ~ element(sK9(sK14(X0,X1)),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(sK14(X0,X1)))
| ~ in(sK9(sK14(X0,X1)),sK14(X0,X1)) ),
inference(resolution,[],[f295,f188]) ).
fof(f295,plain,
! [X0,X1] :
( in(sK9(sK14(X0,X1)),powerset(the_carrier(sK7)))
| ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK19(sK9(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f223,f169]) ).
fof(f339,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK18(sK9(sK14(X0,X1)),X1,X0)
| sP5(sK7,sK10(sK14(X0,X1)))
| sP6(sK7,sK10(sK14(X0,X1))) ),
inference(subsumption_resolution,[],[f338,f115]) ).
fof(f338,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK18(sK9(sK14(X0,X1)),X1,X0)
| sP5(sK7,sK10(sK14(X0,X1)))
| sP6(sK7,sK10(sK14(X0,X1)))
| ~ topological_space(sK7) ),
inference(subsumption_resolution,[],[f336,f116]) ).
fof(f336,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK18(sK9(sK14(X0,X1)),X1,X0)
| sP5(sK7,sK10(sK14(X0,X1)))
| sP6(sK7,sK10(sK14(X0,X1)))
| ~ top_str(sK7)
| ~ topological_space(sK7) ),
inference(resolution,[],[f285,f181]) ).
fof(f285,plain,
! [X0,X1] :
( element(sK10(sK14(X0,X1)),powerset(the_carrier(sK7)))
| ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK18(sK9(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f222,f167]) ).
fof(f335,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK19(sK9(sK14(X0,X1)),X1,X0)
| sP5(sK7,sK10(sK14(X0,X1)))
| sP6(sK7,sK10(sK14(X0,X1))) ),
inference(subsumption_resolution,[],[f334,f115]) ).
fof(f334,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK19(sK9(sK14(X0,X1)),X1,X0)
| sP5(sK7,sK10(sK14(X0,X1)))
| sP6(sK7,sK10(sK14(X0,X1)))
| ~ topological_space(sK7) ),
inference(subsumption_resolution,[],[f332,f116]) ).
fof(f332,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK19(sK9(sK14(X0,X1)),X1,X0)
| sP5(sK7,sK10(sK14(X0,X1)))
| sP6(sK7,sK10(sK14(X0,X1)))
| ~ top_str(sK7)
| ~ topological_space(sK7) ),
inference(resolution,[],[f284,f181]) ).
fof(f284,plain,
! [X0,X1] :
( element(sK10(sK14(X0,X1)),powerset(the_carrier(sK7)))
| ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK19(sK9(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f222,f169]) ).
fof(f304,plain,
! [X0,X1] :
( ~ element(sK9(X1),powerset(the_carrier(sK7)))
| ~ closed_subset(sK9(X1),sK7)
| ~ subset(X0,sK9(X1))
| sP4(sK9(X1),X0,sK7)
| in(sK9(X1),X1) ),
inference(resolution,[],[f190,f118]) ).
fof(f240,plain,
! [X0] :
( sP6(X0,sK11(the_carrier(X0)))
| sP5(X0,sK11(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0)
| empty(the_carrier(X0)) ),
inference(resolution,[],[f181,f125]) ).
fof(f330,plain,
! [X0,X1] :
( sP5(sK7,sK10(sK14(X0,X1)))
| sP6(sK7,sK10(sK14(X0,X1)))
| ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK18(sK9(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f261,f167]) ).
fof(f329,plain,
! [X0,X1] :
( sP5(sK7,sK10(sK14(X0,X1)))
| sP6(sK7,sK10(sK14(X0,X1)))
| ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK19(sK9(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f261,f169]) ).
fof(f261,plain,
! [X0,X1] :
( sP4(sK9(sK14(X0,X1)),X1,X0)
| sP5(sK7,sK10(sK14(X0,X1)))
| sP6(sK7,sK10(sK14(X0,X1)))
| ~ sP6(X0,X1) ),
inference(resolution,[],[f250,f159]) ).
fof(f292,plain,
! [X0,X1] :
( sP6(sK7,sK10(sK14(X1,X0)))
| subset(X0,sK9(sK14(X1,X0)))
| sP5(sK7,sK10(sK14(X1,X0)))
| ~ sP6(X1,X0) ),
inference(subsumption_resolution,[],[f291,f115]) ).
fof(f291,plain,
! [X0,X1] :
( subset(X0,sK9(sK14(X1,X0)))
| ~ sP6(X1,X0)
| sP5(sK7,sK10(sK14(X1,X0)))
| sP6(sK7,sK10(sK14(X1,X0)))
| ~ topological_space(sK7) ),
inference(subsumption_resolution,[],[f289,f116]) ).
fof(f289,plain,
! [X0,X1] :
( subset(X0,sK9(sK14(X1,X0)))
| ~ sP6(X1,X0)
| sP5(sK7,sK10(sK14(X1,X0)))
| sP6(sK7,sK10(sK14(X1,X0)))
| ~ top_str(sK7)
| ~ topological_space(sK7) ),
inference(resolution,[],[f286,f181]) ).
fof(f267,plain,
! [X0,X1] :
( closed_subset(sK10(sK14(X0,X1)),sK7)
| ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK18(sK9(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f226,f167]) ).
fof(f266,plain,
! [X0,X1] :
( closed_subset(sK10(sK14(X0,X1)),sK7)
| ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK19(sK9(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f226,f169]) ).
fof(f263,plain,
! [X0,X1] :
( subset(sK8,sK9(sK14(X0,X1)))
| ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK18(sK9(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f225,f167]) ).
fof(f262,plain,
! [X0,X1] :
( subset(sK8,sK9(sK14(X0,X1)))
| ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK19(sK9(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f225,f169]) ).
fof(f281,plain,
( ~ closed_subset(sK9(powerset(the_carrier(sK7))),sK7)
| ~ element(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(powerset(the_carrier(sK7)))) ),
inference(subsumption_resolution,[],[f276,f198]) ).
fof(f276,plain,
( ~ closed_subset(sK9(powerset(the_carrier(sK7))),sK7)
| ~ element(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(powerset(the_carrier(sK7))))
| ~ in(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7))) ),
inference(resolution,[],[f188,f198]) ).
fof(f314,plain,
! [X2,X3,X0,X1] :
( ~ subset(X0,sK18(X1,X2,X3))
| ~ closed_subset(sK18(X1,X2,X3),X3)
| ~ element(sK18(X1,X2,X3),powerset(the_carrier(X3)))
| sP4(sK18(X1,X2,X3),X0,X3)
| ~ sP4(X1,X2,X3) ),
inference(resolution,[],[f190,f166]) ).
fof(f313,plain,
! [X2,X0,X1] :
( ~ subset(X0,sK9(sK14(X1,X2)))
| ~ closed_subset(sK9(sK14(X1,X2)),sK7)
| ~ element(sK9(sK14(X1,X2)),powerset(the_carrier(sK7)))
| sP4(sK9(sK14(X1,X2)),X0,sK7)
| sP4(sK9(sK14(X1,X2)),X2,X1)
| ~ sP6(X1,X2) ),
inference(resolution,[],[f190,f223]) ).
fof(f312,plain,
! [X2,X0,X1] :
( ~ subset(X0,sK9(sK14(X1,X2)))
| ~ closed_subset(sK9(sK14(X1,X2)),sK7)
| ~ element(sK9(sK14(X1,X2)),powerset(the_carrier(sK7)))
| sP4(sK9(sK14(X1,X2)),X0,sK7)
| subset(X2,sK9(sK14(X1,X2)))
| ~ sP6(X1,X2) ),
inference(resolution,[],[f190,f297]) ).
fof(f311,plain,
! [X0] :
( ~ subset(X0,sK9(powerset(the_carrier(sK7))))
| ~ closed_subset(sK9(powerset(the_carrier(sK7))),sK7)
| ~ element(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| sP4(sK9(powerset(the_carrier(sK7))),X0,sK7) ),
inference(resolution,[],[f190,f198]) ).
fof(f310,plain,
! [X0,X1] :
( ~ subset(X0,sK9(powerset(the_carrier(X1))))
| ~ closed_subset(sK9(powerset(the_carrier(X1))),X1)
| ~ element(sK9(powerset(the_carrier(X1))),powerset(the_carrier(X1)))
| sP4(sK9(powerset(the_carrier(X1))),X0,X1)
| closed_subset(sK10(powerset(the_carrier(X1))),sK7) ),
inference(resolution,[],[f190,f121]) ).
fof(f309,plain,
! [X0,X1] :
( ~ subset(X0,sK9(powerset(the_carrier(X1))))
| ~ closed_subset(sK9(powerset(the_carrier(X1))),X1)
| ~ element(sK9(powerset(the_carrier(X1))),powerset(the_carrier(X1)))
| sP4(sK9(powerset(the_carrier(X1))),X0,X1)
| subset(sK8,sK9(powerset(the_carrier(X1)))) ),
inference(resolution,[],[f190,f122]) ).
fof(f308,plain,
! [X0,X1] :
( ~ subset(X0,sK9(powerset(the_carrier(X1))))
| ~ closed_subset(sK9(powerset(the_carrier(X1))),X1)
| ~ element(sK9(powerset(the_carrier(X1))),powerset(the_carrier(X1)))
| sP4(sK9(powerset(the_carrier(X1))),X0,X1)
| sK9(powerset(the_carrier(X1))) = sK10(powerset(the_carrier(X1))) ),
inference(resolution,[],[f190,f120]) ).
fof(f307,plain,
! [X0,X1] :
( ~ subset(X0,sK9(powerset(the_carrier(X1))))
| ~ closed_subset(sK9(powerset(the_carrier(X1))),X1)
| ~ element(sK9(powerset(the_carrier(X1))),powerset(the_carrier(X1)))
| sP4(sK9(powerset(the_carrier(X1))),X0,X1)
| in(sK9(powerset(the_carrier(X1))),powerset(the_carrier(sK7))) ),
inference(resolution,[],[f190,f118]) ).
fof(f306,plain,
! [X0,X1] :
( ~ subset(X0,sK9(powerset(the_carrier(X1))))
| ~ closed_subset(sK9(powerset(the_carrier(X1))),X1)
| ~ element(sK9(powerset(the_carrier(X1))),powerset(the_carrier(X1)))
| sP4(sK9(powerset(the_carrier(X1))),X0,X1)
| element(sK10(powerset(the_carrier(X1))),powerset(the_carrier(sK7))) ),
inference(resolution,[],[f190,f119]) ).
fof(f305,plain,
! [X0,X1] :
( ~ subset(X0,sK9(powerset(the_carrier(X1))))
| ~ closed_subset(sK9(powerset(the_carrier(X1))),X1)
| ~ element(sK9(powerset(the_carrier(X1))),powerset(the_carrier(X1)))
| sP4(sK9(powerset(the_carrier(X1))),X0,X1)
| sP6(sK7,sK10(powerset(the_carrier(X1))))
| sP5(sK7,sK10(powerset(the_carrier(X1)))) ),
inference(resolution,[],[f190,f250]) ).
fof(f190,plain,
! [X2,X1,X4] :
( ~ in(X4,powerset(the_carrier(X2)))
| ~ subset(X1,X4)
| ~ closed_subset(X4,X2)
| ~ element(X4,powerset(the_carrier(X2)))
| sP4(X4,X1,X2) ),
inference(equality_resolution,[],[f189]) ).
fof(f189,plain,
! [X2,X3,X1,X4] :
( sP4(X4,X1,X2)
| ~ subset(X1,X4)
| ~ closed_subset(X4,X2)
| ~ element(X4,powerset(the_carrier(X2)))
| X3 != X4
| ~ in(X3,powerset(the_carrier(X2))) ),
inference(equality_resolution,[],[f172]) ).
fof(f172,plain,
! [X2,X3,X0,X1,X4] :
( sP4(X0,X1,X2)
| ~ subset(X1,X0)
| ~ closed_subset(X4,X2)
| X0 != X4
| ~ element(X4,powerset(the_carrier(X2)))
| X0 != X3
| ~ in(X3,powerset(the_carrier(X2))) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| ! [X3] :
( ! [X4] :
( ~ subset(X1,X0)
| ~ closed_subset(X4,X2)
| X0 != X4
| ~ element(X4,powerset(the_carrier(X2))) )
| X0 != X3
| ~ in(X3,powerset(the_carrier(X2))) ) )
& ( ( subset(X1,X0)
& closed_subset(sK19(X0,X1,X2),X2)
& sK19(X0,X1,X2) = X0
& element(sK19(X0,X1,X2),powerset(the_carrier(X2)))
& sK18(X0,X1,X2) = X0
& in(sK18(X0,X1,X2),powerset(the_carrier(X2))) )
| ~ sP4(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f101,f103,f102]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ? [X5] :
( ? [X6] :
( subset(X1,X0)
& closed_subset(X6,X2)
& X0 = X6
& element(X6,powerset(the_carrier(X2))) )
& X0 = X5
& in(X5,powerset(the_carrier(X2))) )
=> ( ? [X6] :
( subset(X1,X0)
& closed_subset(X6,X2)
& X0 = X6
& element(X6,powerset(the_carrier(X2))) )
& sK18(X0,X1,X2) = X0
& in(sK18(X0,X1,X2),powerset(the_carrier(X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ? [X6] :
( subset(X1,X0)
& closed_subset(X6,X2)
& X0 = X6
& element(X6,powerset(the_carrier(X2))) )
=> ( subset(X1,X0)
& closed_subset(sK19(X0,X1,X2),X2)
& sK19(X0,X1,X2) = X0
& element(sK19(X0,X1,X2),powerset(the_carrier(X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| ! [X3] :
( ! [X4] :
( ~ subset(X1,X0)
| ~ closed_subset(X4,X2)
| X0 != X4
| ~ element(X4,powerset(the_carrier(X2))) )
| X0 != X3
| ~ in(X3,powerset(the_carrier(X2))) ) )
& ( ? [X5] :
( ? [X6] :
( subset(X1,X0)
& closed_subset(X6,X2)
& X0 = X6
& element(X6,powerset(the_carrier(X2))) )
& X0 = X5
& in(X5,powerset(the_carrier(X2))) )
| ~ sP4(X0,X1,X2) ) ),
inference(rectify,[],[f100]) ).
fof(f100,plain,
! [X8,X1,X0] :
( ( sP4(X8,X1,X0)
| ! [X9] :
( ! [X10] :
( ~ subset(X1,X8)
| ~ closed_subset(X10,X0)
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) )
| X8 != X9
| ~ in(X9,powerset(the_carrier(X0))) ) )
& ( ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) )
| ~ sP4(X8,X1,X0) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X8,X1,X0] :
( sP4(X8,X1,X0)
<=> ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f303,plain,
! [X0,X1] :
( subset(X1,sK9(sK14(X0,X1)))
| sK9(sK14(X0,X1)) = sK10(sK14(X0,X1))
| ~ sP6(X0,X1) ),
inference(resolution,[],[f224,f171]) ).
fof(f302,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK10(sK14(X0,X1))
| sK9(sK14(X0,X1)) = sK18(sK9(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f224,f167]) ).
fof(f224,plain,
! [X0,X1] :
( sP4(sK9(sK14(X0,X1)),X1,X0)
| ~ sP6(X0,X1)
| sK9(sK14(X0,X1)) = sK10(sK14(X0,X1)) ),
inference(resolution,[],[f159,f120]) ).
fof(f242,plain,
! [X0] :
( sP6(X0,sK13(the_carrier(X0)))
| sP5(X0,sK13(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f181,f155]) ).
fof(f294,plain,
! [X0,X1] :
( ~ in(powerset(the_carrier(sK7)),sK9(sK14(X0,X1)))
| ~ sP6(X0,X1)
| sP4(sK9(sK14(X0,X1)),X1,X0) ),
inference(resolution,[],[f223,f158]) ).
fof(f299,plain,
! [X0,X1] :
( ~ in(powerset(the_carrier(sK7)),sK9(sK14(X1,X0)))
| ~ sP6(X1,X0)
| subset(X0,sK9(sK14(X1,X0))) ),
inference(resolution,[],[f297,f158]) ).
fof(f300,plain,
! [X0,X1] :
( subset(X0,sK9(sK14(X1,X0)))
| ~ sP6(X1,X0)
| ~ closed_subset(sK9(sK14(X1,X0)),sK7)
| ~ element(sK9(sK14(X1,X0)),powerset(the_carrier(sK7)))
| ~ in(sK9(sK14(X1,X0)),sK14(X1,X0)) ),
inference(subsumption_resolution,[],[f298,f264]) ).
fof(f298,plain,
! [X0,X1] :
( subset(X0,sK9(sK14(X1,X0)))
| ~ sP6(X1,X0)
| ~ closed_subset(sK9(sK14(X1,X0)),sK7)
| ~ element(sK9(sK14(X1,X0)),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(sK14(X1,X0)))
| ~ in(sK9(sK14(X1,X0)),sK14(X1,X0)) ),
inference(resolution,[],[f297,f188]) ).
fof(f297,plain,
! [X0,X1] :
( in(sK9(sK14(X0,X1)),powerset(the_carrier(sK7)))
| subset(X1,sK9(sK14(X0,X1)))
| ~ sP6(X0,X1) ),
inference(resolution,[],[f223,f171]) ).
fof(f223,plain,
! [X0,X1] :
( in(sK9(sK14(X0,X1)),powerset(the_carrier(sK7)))
| sP4(sK9(sK14(X0,X1)),X1,X0)
| ~ sP6(X0,X1) ),
inference(resolution,[],[f159,f118]) ).
fof(f286,plain,
! [X0,X1] :
( element(sK10(sK14(X0,X1)),powerset(the_carrier(sK7)))
| subset(X1,sK9(sK14(X0,X1)))
| ~ sP6(X0,X1) ),
inference(resolution,[],[f222,f171]) ).
fof(f288,plain,
! [X0,X1] :
( sP4(sK9(sK14(X0,X1)),X1,X0)
| ~ sP6(X0,X1)
| sP5(sK7,sK10(sK14(X0,X1)))
| sP6(sK7,sK10(sK14(X0,X1))) ),
inference(subsumption_resolution,[],[f287,f115]) ).
fof(f287,plain,
! [X0,X1] :
( sP4(sK9(sK14(X0,X1)),X1,X0)
| ~ sP6(X0,X1)
| sP5(sK7,sK10(sK14(X0,X1)))
| sP6(sK7,sK10(sK14(X0,X1)))
| ~ topological_space(sK7) ),
inference(subsumption_resolution,[],[f282,f116]) ).
fof(f282,plain,
! [X0,X1] :
( sP4(sK9(sK14(X0,X1)),X1,X0)
| ~ sP6(X0,X1)
| sP5(sK7,sK10(sK14(X0,X1)))
| sP6(sK7,sK10(sK14(X0,X1)))
| ~ top_str(sK7)
| ~ topological_space(sK7) ),
inference(resolution,[],[f222,f181]) ).
fof(f222,plain,
! [X0,X1] :
( element(sK10(sK14(X0,X1)),powerset(the_carrier(sK7)))
| sP4(sK9(sK14(X0,X1)),X1,X0)
| ~ sP6(X0,X1) ),
inference(resolution,[],[f159,f119]) ).
fof(f220,plain,
! [X0,X1] :
( ~ sP5(X0,X1)
| sK16(X0,X1) = sK21(sK16(X0,X1),X1,X0) ),
inference(resolution,[],[f178,f162]) ).
fof(f219,plain,
! [X0,X1] :
( ~ sP5(X0,X1)
| sK17(X0,X1) = sK20(sK17(X0,X1),X1,X0) ),
inference(resolution,[],[f174,f164]) ).
fof(f280,plain,
( ~ closed_subset(sK9(powerset(the_carrier(sK7))),sK7)
| ~ element(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(powerset(the_carrier(sK7))))
| closed_subset(sK10(powerset(the_carrier(sK7))),sK7) ),
inference(subsumption_resolution,[],[f275,f198]) ).
fof(f275,plain,
( ~ closed_subset(sK9(powerset(the_carrier(sK7))),sK7)
| ~ element(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(powerset(the_carrier(sK7))))
| ~ in(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| closed_subset(sK10(powerset(the_carrier(sK7))),sK7) ),
inference(resolution,[],[f188,f121]) ).
fof(f279,plain,
( ~ closed_subset(sK9(powerset(the_carrier(sK7))),sK7)
| ~ element(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(powerset(the_carrier(sK7))))
| sK9(powerset(the_carrier(sK7))) = sK10(powerset(the_carrier(sK7))) ),
inference(subsumption_resolution,[],[f273,f198]) ).
fof(f273,plain,
( ~ closed_subset(sK9(powerset(the_carrier(sK7))),sK7)
| ~ element(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(powerset(the_carrier(sK7))))
| ~ in(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| sK9(powerset(the_carrier(sK7))) = sK10(powerset(the_carrier(sK7))) ),
inference(resolution,[],[f188,f120]) ).
fof(f278,plain,
( ~ closed_subset(sK9(powerset(the_carrier(sK7))),sK7)
| ~ element(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(powerset(the_carrier(sK7))))
| element(sK10(powerset(the_carrier(sK7))),powerset(the_carrier(sK7))) ),
inference(subsumption_resolution,[],[f271,f198]) ).
fof(f271,plain,
( ~ closed_subset(sK9(powerset(the_carrier(sK7))),sK7)
| ~ element(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(powerset(the_carrier(sK7))))
| ~ in(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| element(sK10(powerset(the_carrier(sK7))),powerset(the_carrier(sK7))) ),
inference(resolution,[],[f188,f119]) ).
fof(f277,plain,
( ~ closed_subset(sK9(powerset(the_carrier(sK7))),sK7)
| ~ element(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(powerset(the_carrier(sK7))))
| sP6(sK7,sK10(powerset(the_carrier(sK7))))
| sP5(sK7,sK10(powerset(the_carrier(sK7)))) ),
inference(subsumption_resolution,[],[f270,f198]) ).
fof(f270,plain,
( ~ closed_subset(sK9(powerset(the_carrier(sK7))),sK7)
| ~ element(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(powerset(the_carrier(sK7))))
| ~ in(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7)))
| sP6(sK7,sK10(powerset(the_carrier(sK7))))
| sP5(sK7,sK10(powerset(the_carrier(sK7)))) ),
inference(resolution,[],[f188,f250]) ).
fof(f188,plain,
! [X2] :
( ~ in(sK9(X2),powerset(the_carrier(sK7)))
| ~ closed_subset(sK9(X2),sK7)
| ~ element(sK9(X2),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(X2))
| ~ in(sK9(X2),X2) ),
inference(equality_resolution,[],[f123]) ).
fof(f123,plain,
! [X2,X4] :
( ~ subset(sK8,sK9(X2))
| ~ closed_subset(X4,sK7)
| sK9(X2) != X4
| ~ element(X4,powerset(the_carrier(sK7)))
| ~ in(sK9(X2),powerset(the_carrier(sK7)))
| ~ in(sK9(X2),X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
( ! [X2] :
( ( ! [X4] :
( ~ subset(sK8,sK9(X2))
| ~ closed_subset(X4,sK7)
| sK9(X2) != X4
| ~ element(X4,powerset(the_carrier(sK7))) )
| ~ in(sK9(X2),powerset(the_carrier(sK7)))
| ~ in(sK9(X2),X2) )
& ( ( subset(sK8,sK9(X2))
& closed_subset(sK10(X2),sK7)
& sK9(X2) = sK10(X2)
& element(sK10(X2),powerset(the_carrier(sK7)))
& in(sK9(X2),powerset(the_carrier(sK7))) )
| in(sK9(X2),X2) ) )
& element(sK8,powerset(the_carrier(sK7)))
& top_str(sK7)
& topological_space(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f79,f82,f81,f80]) ).
fof(f80,plain,
( ? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [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) )
& ( ( ? [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) )
=> ( ! [X2] :
? [X3] :
( ( ! [X4] :
( ~ subset(sK8,X3)
| ~ closed_subset(X4,sK7)
| X3 != X4
| ~ element(X4,powerset(the_carrier(sK7))) )
| ~ in(X3,powerset(the_carrier(sK7)))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( subset(sK8,X3)
& closed_subset(X5,sK7)
& X3 = X5
& element(X5,powerset(the_carrier(sK7))) )
& in(X3,powerset(the_carrier(sK7))) )
| in(X3,X2) ) )
& element(sK8,powerset(the_carrier(sK7)))
& top_str(sK7)
& topological_space(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X2] :
( ? [X3] :
( ( ! [X4] :
( ~ subset(sK8,X3)
| ~ closed_subset(X4,sK7)
| X3 != X4
| ~ element(X4,powerset(the_carrier(sK7))) )
| ~ in(X3,powerset(the_carrier(sK7)))
| ~ in(X3,X2) )
& ( ( ? [X5] :
( subset(sK8,X3)
& closed_subset(X5,sK7)
& X3 = X5
& element(X5,powerset(the_carrier(sK7))) )
& in(X3,powerset(the_carrier(sK7))) )
| in(X3,X2) ) )
=> ( ( ! [X4] :
( ~ subset(sK8,sK9(X2))
| ~ closed_subset(X4,sK7)
| sK9(X2) != X4
| ~ element(X4,powerset(the_carrier(sK7))) )
| ~ in(sK9(X2),powerset(the_carrier(sK7)))
| ~ in(sK9(X2),X2) )
& ( ( ? [X5] :
( subset(sK8,sK9(X2))
& closed_subset(X5,sK7)
& sK9(X2) = X5
& element(X5,powerset(the_carrier(sK7))) )
& in(sK9(X2),powerset(the_carrier(sK7))) )
| in(sK9(X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X2] :
( ? [X5] :
( subset(sK8,sK9(X2))
& closed_subset(X5,sK7)
& sK9(X2) = X5
& element(X5,powerset(the_carrier(sK7))) )
=> ( subset(sK8,sK9(X2))
& closed_subset(sK10(X2),sK7)
& sK9(X2) = sK10(X2)
& element(sK10(X2),powerset(the_carrier(sK7))) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [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) )
& ( ( ? [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,[],[f78]) ).
fof(f78,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [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) )
& ( ( ? [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,[],[f77]) ).
fof(f77,plain,
? [X0,X1] :
( ! [X2] :
? [X3] :
( ( ! [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) )
& ( ( ? [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,[],[f50]) ).
fof(f50,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,[],[f49]) ).
fof(f49,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,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [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))) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [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(f268,plain,
! [X0,X1] :
( subset(X1,sK9(sK14(X0,X1)))
| closed_subset(sK10(sK14(X0,X1)),sK7)
| ~ sP6(X0,X1) ),
inference(resolution,[],[f226,f171]) ).
fof(f226,plain,
! [X0,X1] :
( sP4(sK9(sK14(X0,X1)),X1,X0)
| ~ sP6(X0,X1)
| closed_subset(sK10(sK14(X0,X1)),sK7) ),
inference(resolution,[],[f159,f121]) ).
fof(f265,plain,
! [X0] :
( subset(sK8,sK9(sK14(X0,sK8)))
| ~ sP6(X0,sK8) ),
inference(factoring,[],[f264]) ).
fof(f264,plain,
! [X0,X1] :
( subset(sK8,sK9(sK14(X0,X1)))
| subset(X1,sK9(sK14(X0,X1)))
| ~ sP6(X0,X1) ),
inference(resolution,[],[f225,f171]) ).
fof(f225,plain,
! [X0,X1] :
( sP4(sK9(sK14(X0,X1)),X1,X0)
| ~ sP6(X0,X1)
| subset(sK8,sK9(sK14(X0,X1))) ),
inference(resolution,[],[f159,f122]) ).
fof(f246,plain,
! [X0] :
( sP6(X0,sK12(X0))
| sP5(X0,sK12(X0))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(duplicate_literal_removal,[],[f241]) ).
fof(f241,plain,
! [X0] :
( sP5(X0,sK12(X0))
| sP6(X0,sK12(X0))
| ~ top_str(X0)
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(resolution,[],[f181,f153]) ).
fof(f260,plain,
! [X0] :
( ~ in(X0,sK9(X0))
| sP5(sK7,sK10(X0))
| sP6(sK7,sK10(X0)) ),
inference(resolution,[],[f250,f158]) ).
fof(f250,plain,
! [X0] :
( sP6(sK7,sK10(X0))
| in(sK9(X0),X0)
| sP5(sK7,sK10(X0)) ),
inference(subsumption_resolution,[],[f249,f115]) ).
fof(f249,plain,
! [X0] :
( sP5(sK7,sK10(X0))
| sP6(sK7,sK10(X0))
| ~ topological_space(sK7)
| in(sK9(X0),X0) ),
inference(subsumption_resolution,[],[f239,f116]) ).
fof(f239,plain,
! [X0] :
( sP5(sK7,sK10(X0))
| sP6(sK7,sK10(X0))
| ~ top_str(sK7)
| ~ topological_space(sK7)
| in(sK9(X0),X0) ),
inference(resolution,[],[f181,f119]) ).
fof(f248,plain,
( sP5(sK7,sK8)
| sP6(sK7,sK8) ),
inference(subsumption_resolution,[],[f247,f115]) ).
fof(f247,plain,
( sP5(sK7,sK8)
| sP6(sK7,sK8)
| ~ topological_space(sK7) ),
inference(subsumption_resolution,[],[f238,f116]) ).
fof(f238,plain,
( sP5(sK7,sK8)
| sP6(sK7,sK8)
| ~ top_str(sK7)
| ~ topological_space(sK7) ),
inference(resolution,[],[f181,f117]) ).
fof(f181,plain,
! [X0,X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| sP5(X0,X1)
| sP6(X0,X1)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( sP6(X0,X1)
| sP5(X0,X1)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(definition_folding,[],[f66,f75,f74,f73,f72,f71]) ).
fof(f71,plain,
! [X3,X1,X0] :
( ? [X6] :
( subset(X1,X3)
& closed_subset(X6,X0)
& X3 = X6
& element(X6,powerset(the_carrier(X0))) )
| ~ sP2(X3,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f72,plain,
! [X4,X1,X0] :
( ? [X5] :
( subset(X1,X4)
& closed_subset(X5,X0)
& X4 = X5
& element(X5,powerset(the_carrier(X0))) )
| ~ sP3(X4,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& sP3(X4,X1,X0)
& X2 = X4
& sP2(X3,X1,X0)
& X2 = X3 )
| ~ sP5(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> sP4(X8,X1,X0) )
| ~ sP6(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f66,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( subset(X1,X4)
& closed_subset(X5,X0)
& X4 = X5
& element(X5,powerset(the_carrier(X0))) )
& X2 = X4
& ? [X6] :
( subset(X1,X3)
& closed_subset(X6,X0)
& X3 = X6
& element(X6,powerset(the_carrier(X0))) )
& X2 = X3 )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) ) )
| ? [X2,X3,X4] :
( X3 != X4
& ? [X5] :
( subset(X1,X4)
& closed_subset(X5,X0)
& X4 = X5
& element(X5,powerset(the_carrier(X0))) )
& X2 = X4
& ? [X6] :
( subset(X1,X3)
& closed_subset(X6,X0)
& X3 = X6
& element(X6,powerset(the_carrier(X0))) )
& X2 = X3 )
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X5] :
( subset(X1,X4)
& closed_subset(X5,X0)
& X4 = X5
& element(X5,powerset(the_carrier(X0))) )
& X2 = X4
& ? [X6] :
( subset(X1,X3)
& closed_subset(X6,X0)
& X3 = X6
& element(X6,powerset(the_carrier(X0))) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X7] :
! [X8] :
( in(X8,X7)
<=> ? [X9] :
( ? [X10] :
( subset(X1,X8)
& closed_subset(X10,X0)
& X8 = X10
& element(X10,powerset(the_carrier(X0))) )
& X8 = X9
& in(X9,powerset(the_carrier(X0))) ) ) ) ),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( ( element(X1,powerset(the_carrier(X0)))
& top_str(X0)
& topological_space(X0) )
=> ( ! [X2,X3,X4] :
( ( ? [X6] :
( subset(X1,X4)
& closed_subset(X6,X0)
& X4 = X6
& element(X6,powerset(the_carrier(X0))) )
& X2 = X4
& ? [X5] :
( subset(X1,X3)
& closed_subset(X5,X0)
& X3 = X5
& element(X5,powerset(the_carrier(X0))) )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X7] :
( subset(X1,X3)
& closed_subset(X7,X0)
& X3 = X7
& element(X7,powerset(the_carrier(X0))) )
& X3 = X4
& in(X4,powerset(the_carrier(X0))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e1_40__pre_topc__1) ).
fof(f237,plain,
! [X2,X0,X1] :
( v5_membered(sK21(X0,X1,X2))
| ~ v5_membered(the_carrier(X2))
| ~ sP2(X0,X1,X2) ),
inference(resolution,[],[f233,f138]) ).
fof(f236,plain,
! [X2,X0,X1] :
( v5_membered(sK20(X0,X1,X2))
| ~ v5_membered(the_carrier(X2))
| ~ sP3(X0,X1,X2) ),
inference(resolution,[],[f232,f138]) ).
fof(f235,plain,
! [X2,X0,X1] :
( v5_membered(sK19(X0,X1,X2))
| ~ v5_membered(the_carrier(X2))
| ~ sP4(X0,X1,X2) ),
inference(resolution,[],[f231,f138]) ).
fof(f233,plain,
! [X2,X0,X1] :
( sP1(sK21(X0,X1,X2))
| ~ sP2(X0,X1,X2)
| ~ v5_membered(the_carrier(X2)) ),
inference(resolution,[],[f177,f139]) ).
fof(f232,plain,
! [X2,X0,X1] :
( sP1(sK20(X0,X1,X2))
| ~ sP3(X0,X1,X2)
| ~ v5_membered(the_carrier(X2)) ),
inference(resolution,[],[f173,f139]) ).
fof(f231,plain,
! [X2,X0,X1] :
( sP1(sK19(X0,X1,X2))
| ~ sP4(X0,X1,X2)
| ~ v5_membered(the_carrier(X2)) ),
inference(resolution,[],[f168,f139]) ).
fof(f230,plain,
! [X2,X0,X1] :
( ~ in(powerset(the_carrier(X2)),sK18(X0,X1,X2))
| ~ sP4(X0,X1,X2) ),
inference(resolution,[],[f166,f158]) ).
fof(f228,plain,
! [X2,X0,X1] :
( ~ in(sK14(X2,X1),X0)
| ~ sP6(X2,X1)
| ~ sP4(X0,X1,X2) ),
inference(resolution,[],[f160,f158]) ).
fof(f177,plain,
! [X2,X0,X1] :
( element(sK21(X0,X1,X2),powerset(the_carrier(X2)))
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ( subset(X1,X0)
& closed_subset(sK21(X0,X1,X2),X2)
& sK21(X0,X1,X2) = X0
& element(sK21(X0,X1,X2),powerset(the_carrier(X2))) )
| ~ sP2(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f110,f111]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ? [X3] :
( subset(X1,X0)
& closed_subset(X3,X2)
& X0 = X3
& element(X3,powerset(the_carrier(X2))) )
=> ( subset(X1,X0)
& closed_subset(sK21(X0,X1,X2),X2)
& sK21(X0,X1,X2) = X0
& element(sK21(X0,X1,X2),powerset(the_carrier(X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
! [X0,X1,X2] :
( ? [X3] :
( subset(X1,X0)
& closed_subset(X3,X2)
& X0 = X3
& element(X3,powerset(the_carrier(X2))) )
| ~ sP2(X0,X1,X2) ),
inference(rectify,[],[f109]) ).
fof(f109,plain,
! [X3,X1,X0] :
( ? [X6] :
( subset(X1,X3)
& closed_subset(X6,X0)
& X3 = X6
& element(X6,powerset(the_carrier(X0))) )
| ~ sP2(X3,X1,X0) ),
inference(nnf_transformation,[],[f71]) ).
fof(f173,plain,
! [X2,X0,X1] :
( element(sK20(X0,X1,X2),powerset(the_carrier(X2)))
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1,X2] :
( ( subset(X1,X0)
& closed_subset(sK20(X0,X1,X2),X2)
& sK20(X0,X1,X2) = X0
& element(sK20(X0,X1,X2),powerset(the_carrier(X2))) )
| ~ sP3(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f106,f107]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ? [X3] :
( subset(X1,X0)
& closed_subset(X3,X2)
& X0 = X3
& element(X3,powerset(the_carrier(X2))) )
=> ( subset(X1,X0)
& closed_subset(sK20(X0,X1,X2),X2)
& sK20(X0,X1,X2) = X0
& element(sK20(X0,X1,X2),powerset(the_carrier(X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ? [X3] :
( subset(X1,X0)
& closed_subset(X3,X2)
& X0 = X3
& element(X3,powerset(the_carrier(X2))) )
| ~ sP3(X0,X1,X2) ),
inference(rectify,[],[f105]) ).
fof(f105,plain,
! [X4,X1,X0] :
( ? [X5] :
( subset(X1,X4)
& closed_subset(X5,X0)
& X4 = X5
& element(X5,powerset(the_carrier(X0))) )
| ~ sP3(X4,X1,X0) ),
inference(nnf_transformation,[],[f72]) ).
fof(f168,plain,
! [X2,X0,X1] :
( element(sK19(X0,X1,X2),powerset(the_carrier(X2)))
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f166,plain,
! [X2,X0,X1] :
( in(sK18(X0,X1,X2),powerset(the_carrier(X2)))
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f160,plain,
! [X3,X0,X1] :
( in(X3,sK14(X0,X1))
| ~ sP4(X3,X1,X0)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( ! [X3] :
( ( in(X3,sK14(X0,X1))
| ~ sP4(X3,X1,X0) )
& ( sP4(X3,X1,X0)
| ~ in(X3,sK14(X0,X1)) ) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f94,f95]) ).
fof(f95,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ sP4(X3,X1,X0) )
& ( sP4(X3,X1,X0)
| ~ in(X3,X2) ) )
=> ! [X3] :
( ( in(X3,sK14(X0,X1))
| ~ sP4(X3,X1,X0) )
& ( sP4(X3,X1,X0)
| ~ in(X3,sK14(X0,X1)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2] :
! [X3] :
( ( in(X3,X2)
| ~ sP4(X3,X1,X0) )
& ( sP4(X3,X1,X0)
| ~ in(X3,X2) ) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f93]) ).
fof(f93,plain,
! [X0,X1] :
( ? [X7] :
! [X8] :
( ( in(X8,X7)
| ~ sP4(X8,X1,X0) )
& ( sP4(X8,X1,X0)
| ~ in(X8,X7) ) )
| ~ sP6(X0,X1) ),
inference(nnf_transformation,[],[f75]) ).
fof(f159,plain,
! [X3,X0,X1] :
( ~ in(X3,sK14(X0,X1))
| sP4(X3,X1,X0)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f221,plain,
! [X0] :
( v5_membered(sK12(X0))
| ~ top_str(X0)
| ~ v5_membered(the_carrier(X0))
| ~ topological_space(X0) ),
inference(resolution,[],[f218,f138]) ).
fof(f218,plain,
! [X0] :
( sP1(sK12(X0))
| ~ topological_space(X0)
| ~ top_str(X0)
| ~ v5_membered(the_carrier(X0)) ),
inference(resolution,[],[f153,f139]) ).
fof(f179,plain,
! [X2,X0,X1] :
( closed_subset(sK21(X0,X1,X2),X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f112]) ).
fof(f178,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| sK21(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f112]) ).
fof(f175,plain,
! [X2,X0,X1] :
( closed_subset(sK20(X0,X1,X2),X2)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f108]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1,X2)
| sK20(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f108]) ).
fof(f170,plain,
! [X2,X0,X1] :
( closed_subset(sK19(X0,X1,X2),X2)
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f169,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| sK19(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f104]) ).
fof(f167,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| sK18(X0,X1,X2) = X0 ),
inference(cnf_transformation,[],[f104]) ).
fof(f165,plain,
! [X0,X1] :
( sK16(X0,X1) != sK17(X0,X1)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ( sK16(X0,X1) != sK17(X0,X1)
& sP3(sK17(X0,X1),X1,X0)
& sK15(X0,X1) = sK17(X0,X1)
& sP2(sK16(X0,X1),X1,X0)
& sK15(X0,X1) = sK16(X0,X1) )
| ~ sP5(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f97,f98]) ).
fof(f98,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& sP3(X4,X1,X0)
& X2 = X4
& sP2(X3,X1,X0)
& X2 = X3 )
=> ( sK16(X0,X1) != sK17(X0,X1)
& sP3(sK17(X0,X1),X1,X0)
& sK15(X0,X1) = sK17(X0,X1)
& sP2(sK16(X0,X1),X1,X0)
& sK15(X0,X1) = sK16(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& sP3(X4,X1,X0)
& X2 = X4
& sP2(X3,X1,X0)
& X2 = X3 )
| ~ sP5(X0,X1) ),
inference(nnf_transformation,[],[f74]) ).
fof(f163,plain,
! [X0,X1] :
( ~ sP5(X0,X1)
| sK15(X0,X1) = sK17(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f161,plain,
! [X0,X1] :
( ~ sP5(X0,X1)
| sK15(X0,X1) = sK16(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f153,plain,
! [X0] :
( element(sK12(X0),powerset(the_carrier(X0)))
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( closed_subset(sK12(X0),X0)
& element(sK12(X0),powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f63,f89]) ).
fof(f89,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
=> ( closed_subset(sK12(X0),X0)
& element(sK12(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0) )
=> ? [X1] :
( closed_subset(X1,X0)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc6_pre_topc) ).
fof(f217,plain,
! [X0,X1] :
( subset(X1,sK17(X0,X1))
| ~ sP5(X0,X1) ),
inference(resolution,[],[f164,f176]) ).
fof(f164,plain,
! [X0,X1] :
( sP3(sK17(X0,X1),X1,X0)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f216,plain,
! [X0,X1] :
( subset(X1,sK16(X0,X1))
| ~ sP5(X0,X1) ),
inference(resolution,[],[f162,f180]) ).
fof(f162,plain,
! [X0,X1] :
( sP2(sK16(X0,X1),X1,X0)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f215,plain,
! [X0] :
( v5_membered(sK11(X0))
| empty(X0)
| ~ v5_membered(X0) ),
inference(resolution,[],[f203,f138]) ).
fof(f203,plain,
! [X0] :
( sP1(sK11(X0))
| ~ v5_membered(X0)
| empty(X0) ),
inference(resolution,[],[f139,f125]) ).
fof(f204,plain,
! [X0] :
( sP1(sK13(X0))
| ~ v5_membered(X0) ),
inference(resolution,[],[f139,f155]) ).
fof(f154,plain,
! [X0] :
( closed_subset(sK12(X0),X0)
| ~ top_str(X0)
| ~ topological_space(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f201,plain,
( sP1(sK8)
| ~ v5_membered(the_carrier(sK7)) ),
inference(resolution,[],[f139,f117]) ).
fof(f202,plain,
! [X0] :
( sP1(sK10(X0))
| ~ v5_membered(the_carrier(sK7))
| in(sK9(X0),X0) ),
inference(resolution,[],[f139,f119]) ).
fof(f139,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| sP1(X1)
| ~ v5_membered(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( sP1(X1)
| ~ element(X1,powerset(X0)) )
| ~ v5_membered(X0) ),
inference(definition_folding,[],[f54,f69]) ).
fof(f69,plain,
! [X1] :
( ( v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) )
| ~ sP1(X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ( v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) )
| ~ element(X1,powerset(X0)) )
| ~ v5_membered(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( v5_membered(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> ( v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc20_membered) ).
fof(f200,plain,
! [X0] :
( ~ in(X0,sK9(X0))
| element(sK10(X0),powerset(the_carrier(sK7))) ),
inference(resolution,[],[f119,f158]) ).
fof(f197,plain,
! [X0] :
( ~ in(X0,sK9(X0))
| in(sK9(X0),powerset(the_carrier(sK7))) ),
inference(resolution,[],[f118,f158]) ).
fof(f196,plain,
! [X0] :
( ~ in(powerset(the_carrier(sK7)),sK9(X0))
| in(sK9(X0),X0) ),
inference(resolution,[],[f118,f158]) ).
fof(f119,plain,
! [X2] :
( element(sK10(X2),powerset(the_carrier(sK7)))
| in(sK9(X2),X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f199,plain,
~ in(powerset(the_carrier(sK7)),sK9(powerset(the_carrier(sK7)))),
inference(resolution,[],[f198,f158]) ).
fof(f198,plain,
in(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7))),
inference(factoring,[],[f118]) ).
fof(f118,plain,
! [X2] :
( in(sK9(X2),powerset(the_carrier(sK7)))
| in(sK9(X2),X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1,X2)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f125,plain,
! [X0] :
( element(sK11(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( ( ~ empty(sK11(X0))
& element(sK11(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f51,f84]) ).
fof(f84,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK11(X0))
& element(sK11(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f195,plain,
! [X0] :
( ~ in(X0,sK9(X0))
| sK9(X0) = sK10(X0) ),
inference(resolution,[],[f120,f158]) ).
fof(f120,plain,
! [X2] :
( in(sK9(X2),X2)
| sK9(X2) = sK10(X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f194,plain,
! [X0] :
( ~ in(X0,sK9(X0))
| subset(sK8,sK9(X0)) ),
inference(resolution,[],[f122,f158]) ).
fof(f193,plain,
! [X0] :
( ~ in(X0,sK9(X0))
| closed_subset(sK10(X0),sK7) ),
inference(resolution,[],[f121,f158]) ).
fof(f122,plain,
! [X2] :
( subset(sK8,sK9(X2))
| in(sK9(X2),X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f121,plain,
! [X2] :
( closed_subset(sK10(X2),sK7)
| in(sK9(X2),X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f158,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f155,plain,
! [X0] : element(sK13(X0),powerset(X0)),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( empty(sK13(X0))
& element(sK13(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f20,f91]) ).
fof(f91,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK13(X0))
& element(sK13(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f126,plain,
! [X0] :
( ~ empty(sK11(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f192,plain,
! [X0] : v5_membered(sK13(X0)),
inference(resolution,[],[f191,f156]) ).
fof(f191,plain,
! [X0] :
( ~ empty(X0)
| v5_membered(X0) ),
inference(resolution,[],[f132,f131]) ).
fof(f138,plain,
! [X0] :
( ~ sP1(X0)
| v5_membered(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0) )
| ~ sP1(X0) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
! [X1] :
( ( v5_membered(X1)
& v4_membered(X1)
& v3_membered(X1)
& v2_membered(X1)
& v1_membered(X1) )
| ~ sP1(X1) ),
inference(nnf_transformation,[],[f69]) ).
fof(f132,plain,
! [X0] :
( sP0(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( sP0(X0)
| ~ empty(X0) ),
inference(definition_folding,[],[f52,f67]) ).
fof(f67,plain,
! [X0] :
( ( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f52,plain,
! [X0] :
( ( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( empty(X0)
=> ( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc15_membered) ).
fof(f131,plain,
! [X0] :
( ~ sP0(X0)
| v5_membered(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f67]) ).
fof(f117,plain,
element(sK8,powerset(the_carrier(sK7))),
inference(cnf_transformation,[],[f83]) ).
fof(f157,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f156,plain,
! [X0] : empty(sK13(X0)),
inference(cnf_transformation,[],[f92]) ).
fof(f124,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f187,plain,
v5_membered(sK22),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
( v5_membered(sK22)
& v4_membered(sK22)
& v3_membered(sK22)
& v2_membered(sK22)
& v1_membered(sK22)
& ~ empty(sK22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f7,f113]) ).
fof(f113,plain,
( ? [X0] :
( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0)
& ~ empty(X0) )
=> ( v5_membered(sK22)
& v4_membered(sK22)
& v3_membered(sK22)
& v2_membered(sK22)
& v1_membered(sK22)
& ~ empty(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f7,axiom,
? [X0] :
( v5_membered(X0)
& v4_membered(X0)
& v3_membered(X0)
& v2_membered(X0)
& v1_membered(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_membered) ).
fof(f182,plain,
~ empty(sK22),
inference(cnf_transformation,[],[f114]) ).
fof(f116,plain,
top_str(sK7),
inference(cnf_transformation,[],[f83]) ).
fof(f115,plain,
topological_space(sK7),
inference(cnf_transformation,[],[f83]) ).
fof(f543,plain,
( ~ spl23_3
| ~ spl23_8
| ~ spl23_10
| ~ spl23_11 ),
inference(avatar_contradiction_clause,[],[f542]) ).
fof(f542,plain,
( $false
| ~ spl23_3
| ~ spl23_8
| ~ spl23_10
| ~ spl23_11 ),
inference(subsumption_resolution,[],[f541,f254]) ).
fof(f254,plain,
( sP6(sK7,sK8)
| ~ spl23_3 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f252,plain,
( spl23_3
<=> sP6(sK7,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_3])]) ).
fof(f541,plain,
( ~ sP6(sK7,sK8)
| ~ spl23_8
| ~ spl23_10
| ~ spl23_11 ),
inference(subsumption_resolution,[],[f535,f369]) ).
fof(f535,plain,
( ~ sP4(sK9(sK14(sK7,sK8)),sK8,sK7)
| ~ sP6(sK7,sK8)
| ~ spl23_8
| ~ spl23_10
| ~ spl23_11 ),
inference(resolution,[],[f526,f160]) ).
fof(f526,plain,
( ~ in(sK9(sK14(sK7,sK8)),sK14(sK7,sK8))
| ~ spl23_8
| ~ spl23_10
| ~ spl23_11 ),
inference(global_subsumption,[],[f115,f116,f182,f187,f124,f156,f157,f117,f131,f132,f138,f191,f192,f126,f155,f158,f121,f122,f193,f194,f120,f195,f125,f171,f176,f180,f118,f198,f199,f119,f196,f197,f200,f139,f202,f201,f154,f204,f203,f215,f162,f216,f164,f217,f153,f161,f163,f165,f167,f169,f170,f174,f175,f178,f179,f218,f221,f159,f160,f166,f168,f173,f177,f228,f230,f231,f232,f233,f235,f236,f237,f181,f248,f250,f260,f246,f225,f264,f265,f226,f268,f188,f277,f278,f279,f280,f219,f220,f222,f288,f286,f223,f297,f300,f299,f294,f242,f224,f302,f303,f190,f305,f306,f307,f308,f309,f310,f311,f312,f313,f314,f281,f262,f263,f266,f267,f292,f261,f329,f330,f240,f304,f284,f335,f285,f339,f295,f343,f341,f296,f347,f345,f342,f346,f234,f301,f349,f350,f351,f352,f353,f357,f365,f366,f243,f432,f374,f244,f455,f245,f478,f369,f516,f515,f519,f520,f525]) ).
fof(f525,plain,
( ~ element(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| ~ in(sK9(sK14(sK7,sK8)),sK14(sK7,sK8))
| ~ spl23_10
| ~ spl23_11 ),
inference(subsumption_resolution,[],[f524,f516]) ).
fof(f524,plain,
( ~ element(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(sK14(sK7,sK8)))
| ~ in(sK9(sK14(sK7,sK8)),sK14(sK7,sK8))
| ~ spl23_10
| ~ spl23_11 ),
inference(subsumption_resolution,[],[f521,f374]) ).
fof(f521,plain,
( ~ closed_subset(sK9(sK14(sK7,sK8)),sK7)
| ~ element(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| ~ subset(sK8,sK9(sK14(sK7,sK8)))
| ~ in(sK9(sK14(sK7,sK8)),sK14(sK7,sK8))
| ~ spl23_10 ),
inference(resolution,[],[f520,f188]) ).
fof(f374,plain,
( closed_subset(sK9(sK14(sK7,sK8)),sK7)
| ~ spl23_11 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f372,plain,
( spl23_11
<=> closed_subset(sK9(sK14(sK7,sK8)),sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_11])]) ).
fof(f366,plain,
( closed_subset(sK9(sK14(sK7,sK8)),sK7)
| ~ sP4(sK9(sK14(sK7,sK8)),sK8,sK7)
| ~ spl23_8 ),
inference(superposition,[],[f170,f357]) ).
fof(f365,plain,
( element(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| ~ sP4(sK9(sK14(sK7,sK8)),sK8,sK7)
| ~ spl23_8 ),
inference(superposition,[],[f168,f357]) ).
fof(f357,plain,
( sK9(sK14(sK7,sK8)) = sK19(sK9(sK14(sK7,sK8)),sK8,sK7)
| ~ spl23_8 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f499,plain,
( ~ spl23_3
| spl23_4
| ~ spl23_9
| spl23_10
| ~ spl23_11 ),
inference(avatar_contradiction_clause,[],[f498]) ).
fof(f498,plain,
( $false
| ~ spl23_3
| spl23_4
| ~ spl23_9
| spl23_10
| ~ spl23_11 ),
inference(subsumption_resolution,[],[f487,f254]) ).
fof(f487,plain,
( ~ sP6(sK7,sK8)
| ~ spl23_3
| spl23_4
| ~ spl23_9
| spl23_10
| ~ spl23_11 ),
inference(resolution,[],[f483,f265]) ).
fof(f483,plain,
( ~ subset(sK8,sK9(sK14(sK7,sK8)))
| ~ spl23_3
| spl23_4
| ~ spl23_9
| spl23_10
| ~ spl23_11 ),
inference(resolution,[],[f468,f370]) ).
fof(f370,plain,
( ~ sP4(sK9(sK14(sK7,sK8)),sK8,sK7)
| spl23_10 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f468,plain,
( ! [X0] :
( sP4(sK9(sK14(sK7,sK8)),X0,sK7)
| ~ subset(X0,sK9(sK14(sK7,sK8))) )
| ~ spl23_3
| spl23_4
| ~ spl23_9
| spl23_10
| ~ spl23_11 ),
inference(subsumption_resolution,[],[f467,f411]) ).
fof(f411,plain,
( element(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| ~ spl23_3
| ~ spl23_9
| spl23_10 ),
inference(subsumption_resolution,[],[f410,f254]) ).
fof(f410,plain,
( element(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| ~ sP6(sK7,sK8)
| ~ spl23_9
| spl23_10 ),
inference(subsumption_resolution,[],[f398,f370]) ).
fof(f398,plain,
( element(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| sP4(sK9(sK14(sK7,sK8)),sK8,sK7)
| ~ sP6(sK7,sK8)
| ~ spl23_9 ),
inference(superposition,[],[f222,f361]) ).
fof(f361,plain,
( sK9(sK14(sK7,sK8)) = sK10(sK14(sK7,sK8))
| ~ spl23_9 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f359,plain,
( spl23_9
<=> sK9(sK14(sK7,sK8)) = sK10(sK14(sK7,sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_9])]) ).
fof(f467,plain,
( ! [X0] :
( ~ subset(X0,sK9(sK14(sK7,sK8)))
| ~ element(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| sP4(sK9(sK14(sK7,sK8)),X0,sK7) )
| spl23_4
| spl23_10
| ~ spl23_11 ),
inference(subsumption_resolution,[],[f463,f374]) ).
fof(f463,plain,
( ! [X0] :
( ~ subset(X0,sK9(sK14(sK7,sK8)))
| ~ closed_subset(sK9(sK14(sK7,sK8)),sK7)
| ~ element(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| sP4(sK9(sK14(sK7,sK8)),X0,sK7) )
| spl23_4
| spl23_10 ),
inference(resolution,[],[f447,f190]) ).
fof(f447,plain,
( in(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| spl23_4
| spl23_10 ),
inference(global_subsumption,[],[f115,f116,f182,f187,f124,f156,f157,f117,f131,f132,f138,f191,f192,f126,f155,f158,f121,f122,f193,f194,f120,f195,f125,f171,f176,f180,f118,f198,f199,f119,f196,f197,f200,f139,f202,f201,f154,f204,f203,f215,f162,f216,f164,f217,f153,f161,f163,f165,f167,f169,f170,f174,f175,f178,f179,f218,f221,f159,f160,f166,f168,f173,f177,f228,f230,f231,f232,f233,f235,f236,f237,f181,f244,f245,f248,f257,f250,f260,f246,f225,f264,f265,f226,f268,f188,f277,f278,f279,f280,f219,f220,f222,f288,f286,f223,f297,f300,f299,f294,f242,f224,f302,f303,f190,f305,f306,f307,f308,f309,f310,f311,f312,f313,f314,f281,f262,f263,f266,f267,f292,f261,f329,f330,f240,f304,f284,f335,f285,f339,f295,f343,f341,f296,f347,f345,f342,f346,f234,f301,f349,f350,f351,f352,f353,f370,f243,f432,f378]) ).
fof(f378,plain,
( in(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| ~ sP6(sK7,sK8)
| spl23_10 ),
inference(resolution,[],[f370,f223]) ).
fof(f257,plain,
( ~ sP5(sK7,sK8)
| spl23_4 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f256,plain,
( spl23_4
<=> sP5(sK7,sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_4])]) ).
fof(f477,plain,
( spl23_12
| spl23_13
| spl23_4
| ~ spl23_9
| spl23_10 ),
inference(avatar_split_clause,[],[f446,f368,f359,f256,f474,f470]) ).
fof(f470,plain,
( spl23_12
<=> sP5(sK7,sK9(sK14(sK7,sK8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_12])]) ).
fof(f474,plain,
( spl23_13
<=> sP6(sK7,sK9(sK14(sK7,sK8))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_13])]) ).
fof(f446,plain,
( sP6(sK7,sK9(sK14(sK7,sK8)))
| sP5(sK7,sK9(sK14(sK7,sK8)))
| spl23_4
| ~ spl23_9
| spl23_10 ),
inference(global_subsumption,[],[f115,f116,f182,f187,f124,f156,f157,f117,f131,f132,f138,f191,f192,f126,f155,f158,f121,f122,f193,f194,f120,f195,f125,f171,f176,f180,f118,f198,f199,f119,f196,f197,f200,f139,f202,f201,f154,f204,f203,f215,f162,f216,f164,f217,f153,f161,f163,f165,f167,f169,f170,f174,f175,f178,f179,f218,f221,f159,f160,f166,f168,f173,f177,f228,f230,f231,f232,f233,f235,f236,f237,f181,f244,f245,f248,f257,f250,f260,f246,f225,f264,f265,f226,f268,f188,f277,f278,f279,f280,f219,f220,f222,f288,f286,f223,f297,f300,f299,f294,f242,f224,f302,f303,f190,f305,f306,f307,f308,f309,f310,f311,f312,f313,f314,f281,f262,f263,f266,f267,f292,f261,f329,f330,f240,f304,f284,f335,f285,f339,f295,f343,f341,f296,f347,f345,f342,f346,f234,f301,f349,f350,f351,f352,f353,f370,f361,f416,f406,f402,f410,f422,f378,f243,f432,f426]) ).
fof(f426,plain,
( sP6(sK7,sK9(sK14(sK7,sK8)))
| sP5(sK7,sK9(sK14(sK7,sK8)))
| ~ sP6(sK7,sK8)
| ~ spl23_9
| spl23_10 ),
inference(forward_demodulation,[],[f425,f361]) ).
fof(f425,plain,
( sP5(sK7,sK9(sK14(sK7,sK8)))
| sP6(sK7,sK10(sK14(sK7,sK8)))
| ~ sP6(sK7,sK8)
| ~ spl23_9
| spl23_10 ),
inference(forward_demodulation,[],[f376,f361]) ).
fof(f376,plain,
( sP5(sK7,sK10(sK14(sK7,sK8)))
| sP6(sK7,sK10(sK14(sK7,sK8)))
| ~ sP6(sK7,sK8)
| spl23_10 ),
inference(resolution,[],[f370,f261]) ).
fof(f422,plain,
( element(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| ~ sP6(sK7,sK8)
| ~ spl23_9
| spl23_10 ),
inference(forward_demodulation,[],[f379,f361]) ).
fof(f379,plain,
( element(sK10(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| ~ sP6(sK7,sK8)
| spl23_10 ),
inference(resolution,[],[f370,f222]) ).
fof(f402,plain,
( element(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| ~ sP6(sK7,sK8)
| sK9(sK14(sK7,sK8)) = sK18(sK9(sK14(sK7,sK8)),sK8,sK7)
| ~ spl23_9 ),
inference(superposition,[],[f285,f361]) ).
fof(f406,plain,
( element(sK9(sK14(sK7,sK8)),powerset(the_carrier(sK7)))
| in(sK9(sK14(sK7,sK8)),sK14(sK7,sK8))
| ~ spl23_9 ),
inference(superposition,[],[f119,f361]) ).
fof(f416,plain,
( sP5(sK7,sK9(sK14(sK7,sK8)))
| sP6(sK7,sK9(sK14(sK7,sK8)))
| in(sK9(sK14(sK7,sK8)),sK14(sK7,sK8))
| ~ spl23_9 ),
inference(forward_demodulation,[],[f405,f361]) ).
fof(f405,plain,
( sP6(sK7,sK9(sK14(sK7,sK8)))
| in(sK9(sK14(sK7,sK8)),sK14(sK7,sK8))
| sP5(sK7,sK10(sK14(sK7,sK8)))
| ~ spl23_9 ),
inference(superposition,[],[f250,f361]) ).
fof(f445,plain,
~ spl23_4,
inference(avatar_contradiction_clause,[],[f444]) ).
fof(f444,plain,
( $false
| ~ spl23_4 ),
inference(global_subsumption,[],[f115,f116,f182,f187,f124,f156,f157,f117,f131,f132,f138,f191,f192,f126,f155,f158,f121,f122,f193,f194,f120,f195,f125,f171,f176,f180,f118,f198,f199,f119,f196,f197,f200,f139,f202,f201,f154,f204,f203,f215,f162,f216,f164,f217,f153,f161,f163,f165,f167,f169,f170,f174,f175,f178,f179,f218,f221,f159,f160,f166,f168,f173,f177,f228,f230,f231,f232,f233,f235,f236,f237,f181,f244,f245,f248,f250,f260,f246,f225,f264,f265,f226,f268,f188,f277,f278,f279,f280,f219,f220,f222,f288,f286,f223,f297,f300,f299,f294,f242,f224,f302,f303,f190,f305,f306,f307,f308,f309,f310,f311,f312,f313,f314,f281,f262,f263,f266,f267,f292,f261,f329,f330,f240,f304,f284,f335,f285,f339,f295,f343,f341,f296,f347,f345,f342,f346,f234,f301,f349,f350,f351,f352,f353,f258,f428,f429,f431,f243,f432,f430,f437,f440,f443]) ).
fof(f443,plain,
( sP3(sK15(sK7,sK8),sK8,sK7)
| ~ spl23_4 ),
inference(subsumption_resolution,[],[f436,f258]) ).
fof(f436,plain,
( sP3(sK15(sK7,sK8),sK8,sK7)
| ~ sP5(sK7,sK8)
| ~ spl23_4 ),
inference(superposition,[],[f164,f430]) ).
fof(f440,plain,
( subset(sK8,sK15(sK7,sK8))
| ~ spl23_4 ),
inference(subsumption_resolution,[],[f435,f258]) ).
fof(f435,plain,
( subset(sK8,sK15(sK7,sK8))
| ~ sP5(sK7,sK8)
| ~ spl23_4 ),
inference(superposition,[],[f217,f430]) ).
fof(f437,plain,
( sK16(sK7,sK8) != sK15(sK7,sK8)
| ~ spl23_4 ),
inference(subsumption_resolution,[],[f434,f258]) ).
fof(f434,plain,
( sK16(sK7,sK8) != sK15(sK7,sK8)
| ~ sP5(sK7,sK8)
| ~ spl23_4 ),
inference(superposition,[],[f165,f430]) ).
fof(f430,plain,
( sK17(sK7,sK8) = sK15(sK7,sK8)
| ~ spl23_4 ),
inference(resolution,[],[f258,f163]) ).
fof(f431,plain,
( sK16(sK7,sK8) = sK15(sK7,sK8)
| ~ spl23_4 ),
inference(resolution,[],[f258,f161]) ).
fof(f429,plain,
( sK17(sK7,sK8) = sK20(sK17(sK7,sK8),sK8,sK7)
| ~ spl23_4 ),
inference(resolution,[],[f258,f219]) ).
fof(f428,plain,
( sK16(sK7,sK8) = sK21(sK16(sK7,sK8),sK8,sK7)
| ~ spl23_4 ),
inference(resolution,[],[f258,f220]) ).
fof(f258,plain,
( sP5(sK7,sK8)
| ~ spl23_4 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f442,plain,
~ spl23_4,
inference(avatar_contradiction_clause,[],[f441]) ).
fof(f441,plain,
( $false
| ~ spl23_4 ),
inference(global_subsumption,[],[f115,f116,f182,f187,f124,f156,f157,f117,f131,f132,f138,f191,f192,f126,f155,f158,f121,f122,f193,f194,f120,f195,f125,f171,f176,f180,f118,f198,f199,f119,f196,f197,f200,f139,f202,f201,f154,f204,f203,f215,f162,f216,f164,f217,f153,f161,f163,f165,f167,f169,f170,f174,f175,f178,f179,f218,f221,f159,f160,f166,f168,f173,f177,f228,f230,f231,f232,f233,f235,f236,f237,f181,f244,f245,f248,f250,f260,f246,f225,f264,f265,f226,f268,f188,f277,f278,f279,f280,f219,f220,f222,f288,f286,f223,f297,f300,f299,f294,f242,f224,f302,f303,f190,f305,f306,f307,f308,f309,f310,f311,f312,f313,f314,f281,f262,f263,f266,f267,f292,f261,f329,f330,f240,f304,f284,f335,f285,f339,f295,f343,f341,f296,f347,f345,f342,f346,f234,f301,f349,f350,f351,f352,f353,f258,f428,f429,f431,f243,f432,f430,f437,f440]) ).
fof(f439,plain,
~ spl23_4,
inference(avatar_contradiction_clause,[],[f438]) ).
fof(f438,plain,
( $false
| ~ spl23_4 ),
inference(global_subsumption,[],[f115,f116,f182,f187,f124,f156,f157,f117,f131,f132,f138,f191,f192,f126,f155,f158,f121,f122,f193,f194,f120,f195,f125,f171,f176,f180,f118,f198,f199,f119,f196,f197,f200,f139,f202,f201,f154,f204,f203,f215,f162,f216,f164,f217,f153,f161,f163,f165,f167,f169,f170,f174,f175,f178,f179,f218,f221,f159,f160,f166,f168,f173,f177,f228,f230,f231,f232,f233,f235,f236,f237,f181,f244,f245,f248,f250,f260,f246,f225,f264,f265,f226,f268,f188,f277,f278,f279,f280,f219,f220,f222,f288,f286,f223,f297,f300,f299,f294,f242,f224,f302,f303,f190,f305,f306,f307,f308,f309,f310,f311,f312,f313,f314,f281,f262,f263,f266,f267,f292,f261,f329,f330,f240,f304,f284,f335,f285,f339,f295,f343,f341,f296,f347,f345,f342,f346,f234,f301,f349,f350,f351,f352,f353,f258,f428,f429,f431,f243,f432,f430,f437]) ).
fof(f409,plain,
( ~ spl23_3
| ~ spl23_9
| spl23_10
| spl23_11 ),
inference(avatar_contradiction_clause,[],[f408]) ).
fof(f408,plain,
( $false
| ~ spl23_3
| ~ spl23_9
| spl23_10
| spl23_11 ),
inference(subsumption_resolution,[],[f397,f373]) ).
fof(f373,plain,
( ~ closed_subset(sK9(sK14(sK7,sK8)),sK7)
| spl23_11 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f397,plain,
( closed_subset(sK9(sK14(sK7,sK8)),sK7)
| ~ spl23_3
| ~ spl23_9
| spl23_10 ),
inference(superposition,[],[f388,f361]) ).
fof(f388,plain,
( closed_subset(sK10(sK14(sK7,sK8)),sK7)
| ~ spl23_3
| spl23_10 ),
inference(subsumption_resolution,[],[f380,f254]) ).
fof(f380,plain,
( ~ sP6(sK7,sK8)
| closed_subset(sK10(sK14(sK7,sK8)),sK7)
| spl23_10 ),
inference(resolution,[],[f370,f226]) ).
fof(f385,plain,
( ~ spl23_3
| spl23_9
| spl23_10 ),
inference(avatar_contradiction_clause,[],[f384]) ).
fof(f384,plain,
( $false
| ~ spl23_3
| spl23_9
| spl23_10 ),
inference(subsumption_resolution,[],[f383,f360]) ).
fof(f360,plain,
( sK9(sK14(sK7,sK8)) != sK10(sK14(sK7,sK8))
| spl23_9 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f383,plain,
( sK9(sK14(sK7,sK8)) = sK10(sK14(sK7,sK8))
| ~ spl23_3
| spl23_10 ),
inference(subsumption_resolution,[],[f377,f254]) ).
fof(f377,plain,
( ~ sP6(sK7,sK8)
| sK9(sK14(sK7,sK8)) = sK10(sK14(sK7,sK8))
| spl23_10 ),
inference(resolution,[],[f370,f224]) ).
fof(f375,plain,
( ~ spl23_10
| spl23_11
| ~ spl23_8 ),
inference(avatar_split_clause,[],[f366,f355,f372,f368]) ).
fof(f362,plain,
( spl23_8
| spl23_9
| ~ spl23_3 ),
inference(avatar_split_clause,[],[f348,f252,f359,f355]) ).
fof(f348,plain,
( sK9(sK14(sK7,sK8)) = sK10(sK14(sK7,sK8))
| sK9(sK14(sK7,sK8)) = sK19(sK9(sK14(sK7,sK8)),sK8,sK7)
| ~ spl23_3 ),
inference(resolution,[],[f301,f254]) ).
fof(f327,plain,
( ~ spl23_5
| ~ spl23_6
| ~ spl23_7 ),
inference(avatar_split_clause,[],[f281,f324,f320,f316]) ).
fof(f316,plain,
( spl23_5
<=> subset(sK8,sK9(powerset(the_carrier(sK7)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_5])]) ).
fof(f320,plain,
( spl23_6
<=> element(sK9(powerset(the_carrier(sK7))),powerset(the_carrier(sK7))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_6])]) ).
fof(f324,plain,
( spl23_7
<=> closed_subset(sK9(powerset(the_carrier(sK7))),sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_7])]) ).
fof(f259,plain,
( spl23_3
| spl23_4 ),
inference(avatar_split_clause,[],[f248,f256,f252]) ).
fof(f213,plain,
( ~ spl23_1
| spl23_2 ),
inference(avatar_split_clause,[],[f201,f210,f206]) ).
fof(f206,plain,
( spl23_1
<=> v5_membered(the_carrier(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_1])]) ).
fof(f210,plain,
( spl23_2
<=> sP1(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_2])]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SEU314+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.08 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.26 % Computer : n016.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Apr 29 21:31:25 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % (9514)Running in auto input_syntax mode. Trying TPTP
% 0.07/0.27 % (9518)WARNING: value z3 for option sas not known
% 0.07/0.28 % (9517)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.07/0.28 % (9519)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.07/0.28 % (9516)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.07/0.28 % (9518)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.07/0.28 % (9520)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.07/0.28 % (9521)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.07/0.28 % (9522)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.07/0.28 TRYING [1]
% 0.07/0.28 TRYING [2]
% 0.07/0.28 TRYING [3]
% 0.07/0.28 TRYING [4]
% 0.11/0.29 % (9518)First to succeed.
% 0.11/0.29 % (9518)Refutation found. Thanks to Tanya!
% 0.11/0.29 % SZS status Theorem for theBenchmark
% 0.11/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.29 % (9518)------------------------------
% 0.11/0.29 % (9518)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.11/0.29 % (9518)Termination reason: Refutation
% 0.11/0.29
% 0.11/0.29 % (9518)Memory used [KB]: 1092
% 0.11/0.29 % (9518)Time elapsed: 0.017 s
% 0.11/0.29 % (9518)Instructions burned: 44 (million)
% 0.11/0.29 % (9518)------------------------------
% 0.11/0.29 % (9518)------------------------------
% 0.11/0.29 % (9514)Success in time 0.024 s
%------------------------------------------------------------------------------