TSTP Solution File: SEU094+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU094+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.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 15:22:07 EDT 2024
% Result : Theorem 0.14s 0.42s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 73
% Syntax : Number of formulae : 294 ( 91 unt; 0 def)
% Number of atoms : 806 ( 13 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 746 ( 234 ~; 192 |; 267 &)
% ( 10 <=>; 42 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 7 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 17 con; 0-1 aty)
% Number of variables : 267 ( 209 !; 58 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f643,plain,
$false,
inference(avatar_sat_refutation,[],[f318,f434,f479,f566,f627,f642]) ).
fof(f642,plain,
( ~ spl29_1
| spl29_2 ),
inference(avatar_contradiction_clause,[],[f641]) ).
fof(f641,plain,
( $false
| ~ spl29_1
| spl29_2 ),
inference(subsumption_resolution,[],[f640,f313]) ).
fof(f313,plain,
( finite(sK0)
| ~ spl29_1 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f311,plain,
( spl29_1
<=> finite(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_1])]) ).
fof(f640,plain,
( ~ finite(sK0)
| ~ spl29_1
| spl29_2 ),
inference(subsumption_resolution,[],[f639,f316]) ).
fof(f316,plain,
( ~ finite(union(sK0))
| spl29_2 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f315,plain,
( spl29_2
<=> finite(union(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_2])]) ).
fof(f639,plain,
( finite(union(sK0))
| ~ finite(sK0)
| ~ spl29_1
| spl29_2 ),
inference(resolution,[],[f637,f222]) ).
fof(f222,plain,
! [X0] :
( ~ finite(sK4(X0))
| finite(union(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0] :
( finite(union(X0))
| ( ~ finite(sK4(X0))
& in(sK4(X0),X0) )
| ~ finite(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f98,f127]) ).
fof(f127,plain,
! [X0] :
( ? [X1] :
( ~ finite(X1)
& in(X1,X0) )
=> ( ~ finite(sK4(X0))
& in(sK4(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f98,plain,
! [X0] :
( finite(union(X0))
| ? [X1] :
( ~ finite(X1)
& in(X1,X0) )
| ~ finite(X0) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0] :
( finite(union(X0))
| ? [X1] :
( ~ finite(X1)
& in(X1,X0) )
| ~ finite(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ( ! [X1] :
( in(X1,X0)
=> finite(X1) )
& finite(X0) )
=> finite(union(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l22_finset_1) ).
fof(f637,plain,
( finite(sK4(sK0))
| ~ spl29_1
| spl29_2 ),
inference(subsumption_resolution,[],[f636,f313]) ).
fof(f636,plain,
( finite(sK4(sK0))
| ~ finite(sK0)
| spl29_2 ),
inference(subsumption_resolution,[],[f634,f316]) ).
fof(f634,plain,
( finite(sK4(sK0))
| finite(union(sK0))
| ~ finite(sK0) ),
inference(resolution,[],[f631,f221]) ).
fof(f221,plain,
! [X0] :
( in(sK4(X0),X0)
| finite(union(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f631,plain,
! [X2] :
( ~ in(X2,sK0)
| finite(X2) ),
inference(subsumption_resolution,[],[f180,f428]) ).
fof(f428,plain,
! [X0,X1] :
( ~ finite(union(X0))
| finite(X1)
| ~ in(X1,X0) ),
inference(resolution,[],[f247,f245]) ).
fof(f245,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f247,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ finite(X1)
| finite(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( finite(X0)
| ~ finite(X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0,X1] :
( ( finite(X1)
& subset(X0,X1) )
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
fof(f180,plain,
! [X2] :
( finite(union(sK0))
| finite(X2)
| ~ in(X2,sK0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
( ( ~ finite(union(sK0))
| ( ~ finite(sK1)
& in(sK1,sK0) )
| ~ finite(sK0) )
& ( finite(union(sK0))
| ( ! [X2] :
( finite(X2)
| ~ in(X2,sK0) )
& finite(sK0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f119,f121,f120]) ).
fof(f120,plain,
( ? [X0] :
( ( ~ finite(union(X0))
| ? [X1] :
( ~ finite(X1)
& in(X1,X0) )
| ~ finite(X0) )
& ( finite(union(X0))
| ( ! [X2] :
( finite(X2)
| ~ in(X2,X0) )
& finite(X0) ) ) )
=> ( ( ~ finite(union(sK0))
| ? [X1] :
( ~ finite(X1)
& in(X1,sK0) )
| ~ finite(sK0) )
& ( finite(union(sK0))
| ( ! [X2] :
( finite(X2)
| ~ in(X2,sK0) )
& finite(sK0) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f121,plain,
( ? [X1] :
( ~ finite(X1)
& in(X1,sK0) )
=> ( ~ finite(sK1)
& in(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
? [X0] :
( ( ~ finite(union(X0))
| ? [X1] :
( ~ finite(X1)
& in(X1,X0) )
| ~ finite(X0) )
& ( finite(union(X0))
| ( ! [X2] :
( finite(X2)
| ~ in(X2,X0) )
& finite(X0) ) ) ),
inference(rectify,[],[f118]) ).
fof(f118,plain,
? [X0] :
( ( ~ finite(union(X0))
| ? [X1] :
( ~ finite(X1)
& in(X1,X0) )
| ~ finite(X0) )
& ( finite(union(X0))
| ( ! [X1] :
( finite(X1)
| ~ in(X1,X0) )
& finite(X0) ) ) ),
inference(flattening,[],[f117]) ).
fof(f117,plain,
? [X0] :
( ( ~ finite(union(X0))
| ? [X1] :
( ~ finite(X1)
& in(X1,X0) )
| ~ finite(X0) )
& ( finite(union(X0))
| ( ! [X1] :
( finite(X1)
| ~ in(X1,X0) )
& finite(X0) ) ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f83,plain,
? [X0] :
( ( ! [X1] :
( finite(X1)
| ~ in(X1,X0) )
& finite(X0) )
<~> finite(union(X0)) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,negated_conjecture,
~ ! [X0] :
( ( ! [X1] :
( in(X1,X0)
=> finite(X1) )
& finite(X0) )
<=> finite(union(X0)) ),
inference(negated_conjecture,[],[f52]) ).
fof(f52,conjecture,
! [X0] :
( ( ! [X1] :
( in(X1,X0)
=> finite(X1) )
& finite(X0) )
<=> finite(union(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_finset_1) ).
fof(f627,plain,
~ spl29_2,
inference(avatar_contradiction_clause,[],[f626]) ).
fof(f626,plain,
( $false
| ~ spl29_2 ),
inference(subsumption_resolution,[],[f623,f438]) ).
fof(f438,plain,
( ~ finite(sK1)
| ~ spl29_2 ),
inference(global_subsumption,[],[f182,f181,f180,f185,f187,f191,f202,f222,f221,f232,f234,f246,f249,f248,f250,f252,f253,f183,f184,f192,f193,f194,f254,f255,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f268,f270,f271,f272,f273,f274,f275,f293,f294,f295,f296,f298,f301,f302,f303,f304,f306,f307,f308,f309,f195,f233,f235,f238,f239,f240,f241,f242,f300,f305,f179,f317,f203,f207,f323,f324,f326,f321,f208,f331,f332,f334,f329,f209,f339,f340,f342,f337,f231,f196,f198,f200,f201,f206,f347,f348,f349,f350,f351,f368,f345,f346,f212,f377,f213,f214,f229,f230,f384,f251,f226,f243,f244,f197,f199,f215,f401,f403,f404,f400,f216,f409,f411,f412,f408,f417,f217,f419,f421,f422,f245,f247,f428,f427,f429,f432,f431,f435,f436,f437]) ).
fof(f437,plain,
( ~ finite(sK1)
| ~ finite(sK0)
| ~ spl29_2 ),
inference(subsumption_resolution,[],[f182,f317]) ).
fof(f436,plain,
( in(sK1,sK0)
| ~ spl29_2 ),
inference(global_subsumption,[],[f182,f181,f180,f185,f187,f191,f202,f222,f221,f232,f234,f246,f249,f248,f250,f252,f253,f183,f184,f192,f193,f194,f254,f255,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f266,f268,f270,f271,f272,f273,f274,f275,f293,f294,f295,f296,f298,f301,f302,f303,f304,f306,f307,f308,f309,f195,f233,f235,f238,f239,f240,f241,f242,f300,f305,f179,f317,f203,f207,f323,f324,f326,f321,f208,f331,f332,f334,f329,f209,f339,f340,f342,f337,f231,f196,f198,f200,f201,f206,f347,f348,f349,f350,f351,f368,f345,f346,f212,f377,f213,f214,f229,f230,f384,f251,f226,f243,f244,f197,f199,f215,f401,f403,f404,f400,f216,f409,f411,f412,f408,f417,f217,f419,f421,f422,f245,f247,f428,f427,f429,f432,f431,f435]) ).
fof(f435,plain,
( in(sK1,sK0)
| ~ finite(sK0)
| ~ spl29_2 ),
inference(subsumption_resolution,[],[f181,f317]) ).
fof(f431,plain,
( finite(sK0)
| ~ spl29_2 ),
inference(resolution,[],[f429,f317]) ).
fof(f432,plain,
! [X0] :
( ~ empty(union(X0))
| finite(X0) ),
inference(resolution,[],[f429,f203]) ).
fof(f429,plain,
! [X0] :
( ~ finite(union(X0))
| finite(X0) ),
inference(resolution,[],[f427,f229]) ).
fof(f427,plain,
! [X0] :
( ~ finite(powerset(union(X0)))
| finite(X0) ),
inference(resolution,[],[f247,f196]) ).
fof(f422,plain,
! [X0] :
( ordinal(sK3(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f217,f199]) ).
fof(f421,plain,
! [X0] :
( ordinal(sK2(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f217,f197]) ).
fof(f419,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ ordinal(X1)
| ordinal(X0) ),
inference(resolution,[],[f217,f244]) ).
fof(f217,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ordinal(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) )
| ~ element(X1,X0) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ordinal(X0)
=> ! [X1] :
( element(X1,X0)
=> ( ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_arytm_3) ).
fof(f417,plain,
! [X0] :
( ordinal(sK5(X0))
| ~ ordinal(X0) ),
inference(subsumption_resolution,[],[f416,f400]) ).
fof(f416,plain,
! [X0] :
( ~ ordinal(X0)
| ordinal(sK5(X0))
| ~ epsilon_transitive(sK5(X0)) ),
inference(resolution,[],[f408,f226]) ).
fof(f408,plain,
! [X0] :
( epsilon_connected(sK5(X0))
| ~ ordinal(X0) ),
inference(resolution,[],[f216,f231]) ).
fof(f412,plain,
! [X0] :
( epsilon_connected(sK3(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f216,f199]) ).
fof(f411,plain,
! [X0] :
( epsilon_connected(sK2(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f216,f197]) ).
fof(f409,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ ordinal(X1)
| epsilon_connected(X0) ),
inference(resolution,[],[f216,f244]) ).
fof(f216,plain,
! [X0,X1] :
( ~ element(X1,X0)
| epsilon_connected(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f400,plain,
! [X0] :
( epsilon_transitive(sK5(X0))
| ~ ordinal(X0) ),
inference(resolution,[],[f215,f231]) ).
fof(f404,plain,
! [X0] :
( epsilon_transitive(sK3(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f215,f199]) ).
fof(f403,plain,
! [X0] :
( epsilon_transitive(sK2(X0))
| ~ ordinal(powerset(X0))
| empty(X0) ),
inference(resolution,[],[f215,f197]) ).
fof(f401,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ ordinal(X1)
| epsilon_transitive(X0) ),
inference(resolution,[],[f215,f244]) ).
fof(f215,plain,
! [X0,X1] :
( ~ element(X1,X0)
| epsilon_transitive(X1)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f199,plain,
! [X0] :
( element(sK3(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ( finite(sK3(X0))
& ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f85,f125]) ).
fof(f125,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK3(X0))
& ~ empty(sK3(X0))
& element(sK3(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( finite(X1)
& ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(f197,plain,
! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0] :
( ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f84,f123]) ).
fof(f123,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f244,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f243,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f226,plain,
! [X0] :
( ~ epsilon_connected(X0)
| ordinal(X0)
| ~ epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(flattening,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ordinal(X0)
| ~ epsilon_connected(X0)
| ~ epsilon_transitive(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ( epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ordinal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(f251,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f384,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(forward_demodulation,[],[f232,f345]) ).
fof(f230,plain,
! [X0] :
( ~ finite(powerset(X0))
| finite(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0] :
( ( finite(X0)
| ~ finite(powerset(X0)) )
& ( finite(powerset(X0))
| ~ finite(X0) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( finite(X0)
<=> finite(powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_finset_1) ).
fof(f229,plain,
! [X0] :
( finite(powerset(X0))
| ~ finite(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f214,plain,
! [X0] :
( ordinal(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] :
( ( ordinal(union(X0))
& epsilon_connected(union(X0))
& epsilon_transitive(union(X0)) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ordinal(X0)
=> ( ordinal(union(X0))
& epsilon_connected(union(X0))
& epsilon_transitive(union(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_ordinal1) ).
fof(f213,plain,
! [X0] :
( epsilon_connected(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f377,plain,
finite(empty_set),
inference(superposition,[],[f241,f346]) ).
fof(f212,plain,
! [X0] :
( epsilon_transitive(union(X0))
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f346,plain,
! [X0] : empty_set = sK7(X0),
inference(resolution,[],[f206,f235]) ).
fof(f345,plain,
! [X0] : empty_set = sK6(X0),
inference(resolution,[],[f206,f233]) ).
fof(f368,plain,
element(empty_set,positive_rationals),
inference(superposition,[],[f305,f351]) ).
fof(f351,plain,
empty_set = sK28,
inference(resolution,[],[f206,f306]) ).
fof(f350,plain,
empty_set = sK26,
inference(resolution,[],[f206,f298]) ).
fof(f349,plain,
empty_set = sK25,
inference(resolution,[],[f206,f293]) ).
fof(f348,plain,
empty_set = sK14,
inference(resolution,[],[f206,f268]) ).
fof(f347,plain,
empty_set = sK9,
inference(resolution,[],[f206,f255]) ).
fof(f206,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f201,plain,
! [X0] :
( finite(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f200,plain,
! [X0] :
( ~ empty(sK3(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f198,plain,
! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f196,plain,
! [X0] : subset(X0,powerset(union(X0))),
inference(cnf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] : subset(X0,powerset(union(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_zfmisc_1) ).
fof(f231,plain,
! [X0] : element(sK5(X0),X0),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0] : element(sK5(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f13,f130]) ).
fof(f130,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK5(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f13,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f337,plain,
! [X0] : ordinal(sK6(X0)),
inference(resolution,[],[f209,f233]) ).
fof(f342,plain,
ordinal(sK26),
inference(resolution,[],[f209,f298]) ).
fof(f340,plain,
ordinal(sK14),
inference(resolution,[],[f209,f268]) ).
fof(f339,plain,
ordinal(sK9),
inference(resolution,[],[f209,f255]) ).
fof(f209,plain,
! [X0] :
( ~ empty(X0)
| ordinal(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( empty(X0)
=> ( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(f329,plain,
! [X0] : epsilon_connected(sK6(X0)),
inference(resolution,[],[f208,f233]) ).
fof(f334,plain,
epsilon_connected(sK26),
inference(resolution,[],[f208,f298]) ).
fof(f332,plain,
epsilon_connected(sK14),
inference(resolution,[],[f208,f268]) ).
fof(f331,plain,
epsilon_connected(sK9),
inference(resolution,[],[f208,f255]) ).
fof(f208,plain,
! [X0] :
( ~ empty(X0)
| epsilon_connected(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f321,plain,
! [X0] : epsilon_transitive(sK6(X0)),
inference(resolution,[],[f207,f233]) ).
fof(f326,plain,
epsilon_transitive(sK26),
inference(resolution,[],[f207,f298]) ).
fof(f324,plain,
epsilon_transitive(sK14),
inference(resolution,[],[f207,f268]) ).
fof(f323,plain,
epsilon_transitive(sK9),
inference(resolution,[],[f207,f255]) ).
fof(f207,plain,
! [X0] :
( ~ empty(X0)
| epsilon_transitive(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f203,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0] :
( finite(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> finite(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(f317,plain,
( finite(union(sK0))
| ~ spl29_2 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f179,plain,
( finite(union(sK0))
| finite(sK0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f305,plain,
element(sK28,positive_rationals),
inference(cnf_transformation,[],[f178]) ).
fof(f178,plain,
( ordinal(sK28)
& epsilon_connected(sK28)
& epsilon_transitive(sK28)
& empty(sK28)
& element(sK28,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f78,f177]) ).
fof(f177,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) )
=> ( ordinal(sK28)
& epsilon_connected(sK28)
& epsilon_transitive(sK28)
& empty(sK28)
& element(sK28,positive_rationals) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) ),
inference(pure_predicate_removal,[],[f39]) ).
fof(f39,axiom,
? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& element(X0,positive_rationals) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_arytm_3) ).
fof(f300,plain,
element(sK27,positive_rationals),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
( ordinal(sK27)
& epsilon_connected(sK27)
& epsilon_transitive(sK27)
& ~ empty(sK27)
& element(sK27,positive_rationals) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f31,f175]) ).
fof(f175,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0)
& element(X0,positive_rationals) )
=> ( ordinal(sK27)
& epsilon_connected(sK27)
& epsilon_transitive(sK27)
& ~ empty(sK27)
& element(sK27,positive_rationals) ) ),
introduced(choice_axiom,[]) ).
fof(f31,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0)
& element(X0,positive_rationals) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_arytm_3) ).
fof(f242,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f47]) ).
fof(f47,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f241,plain,
! [X0] : finite(sK7(X0)),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0] :
( finite(sK7(X0))
& ordinal(sK7(X0))
& epsilon_connected(sK7(X0))
& epsilon_transitive(sK7(X0))
& function(sK7(X0))
& relation(sK7(X0))
& empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f80,f134]) ).
fof(f134,plain,
! [X0] :
( ? [X1] :
( finite(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) )
=> ( finite(sK7(X0))
& ordinal(sK7(X0))
& epsilon_connected(sK7(X0))
& epsilon_transitive(sK7(X0))
& function(sK7(X0))
& relation(sK7(X0))
& empty(sK7(X0))
& element(sK7(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0] :
? [X1] :
( finite(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f77]) ).
fof(f77,plain,
! [X0] :
? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
inference(pure_predicate_removal,[],[f32]) ).
fof(f32,axiom,
! [X0] :
? [X1] :
( finite(X1)
& natural(X1)
& ordinal(X1)
& epsilon_connected(X1)
& epsilon_transitive(X1)
& one_to_one(X1)
& function(X1)
& relation(X1)
& empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
fof(f240,plain,
! [X0] : ordinal(sK7(X0)),
inference(cnf_transformation,[],[f135]) ).
fof(f239,plain,
! [X0] : epsilon_connected(sK7(X0)),
inference(cnf_transformation,[],[f135]) ).
fof(f238,plain,
! [X0] : epsilon_transitive(sK7(X0)),
inference(cnf_transformation,[],[f135]) ).
fof(f235,plain,
! [X0] : empty(sK7(X0)),
inference(cnf_transformation,[],[f135]) ).
fof(f233,plain,
! [X0] : empty(sK6(X0)),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0] :
( empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f37,f132]) ).
fof(f132,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f37,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f195,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f309,plain,
ordinal(sK28),
inference(cnf_transformation,[],[f178]) ).
fof(f308,plain,
epsilon_connected(sK28),
inference(cnf_transformation,[],[f178]) ).
fof(f307,plain,
epsilon_transitive(sK28),
inference(cnf_transformation,[],[f178]) ).
fof(f306,plain,
empty(sK28),
inference(cnf_transformation,[],[f178]) ).
fof(f304,plain,
ordinal(sK27),
inference(cnf_transformation,[],[f176]) ).
fof(f303,plain,
epsilon_connected(sK27),
inference(cnf_transformation,[],[f176]) ).
fof(f302,plain,
epsilon_transitive(sK27),
inference(cnf_transformation,[],[f176]) ).
fof(f301,plain,
~ empty(sK27),
inference(cnf_transformation,[],[f176]) ).
fof(f298,plain,
empty(sK26),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
( function(sK26)
& empty(sK26)
& relation(sK26) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f33,f173]) ).
fof(f173,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK26)
& empty(sK26)
& relation(sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f33,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f296,plain,
ordinal(sK25),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
( ordinal(sK25)
& epsilon_connected(sK25)
& epsilon_transitive(sK25)
& empty(sK25)
& function(sK25)
& relation(sK25) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f76,f171]) ).
fof(f171,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK25)
& epsilon_connected(sK25)
& epsilon_transitive(sK25)
& empty(sK25)
& function(sK25)
& relation(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f34]) ).
fof(f34,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f295,plain,
epsilon_connected(sK25),
inference(cnf_transformation,[],[f172]) ).
fof(f294,plain,
epsilon_transitive(sK25),
inference(cnf_transformation,[],[f172]) ).
fof(f293,plain,
empty(sK25),
inference(cnf_transformation,[],[f172]) ).
fof(f275,plain,
ordinal(sK16),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
( ordinal(sK16)
& epsilon_connected(sK16)
& epsilon_transitive(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f67,f153]) ).
fof(f153,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK16)
& epsilon_connected(sK16)
& epsilon_transitive(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
inference(pure_predicate_removal,[],[f27]) ).
fof(f27,axiom,
? [X0] :
( being_limit_ordinal(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal2) ).
fof(f274,plain,
epsilon_connected(sK16),
inference(cnf_transformation,[],[f154]) ).
fof(f273,plain,
epsilon_transitive(sK16),
inference(cnf_transformation,[],[f154]) ).
fof(f272,plain,
ordinal(sK15),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
( ordinal(sK15)
& epsilon_connected(sK15)
& epsilon_transitive(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f26,f151]) ).
fof(f151,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) )
=> ( ordinal(sK15)
& epsilon_connected(sK15)
& epsilon_transitive(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(f271,plain,
epsilon_connected(sK15),
inference(cnf_transformation,[],[f152]) ).
fof(f270,plain,
epsilon_transitive(sK15),
inference(cnf_transformation,[],[f152]) ).
fof(f268,plain,
empty(sK14),
inference(cnf_transformation,[],[f150]) ).
fof(f150,plain,
( relation(sK14)
& empty(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f28,f149]) ).
fof(f149,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK14)
& empty(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f266,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
( relation(sK13)
& ~ empty(sK13) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f36,f147]) ).
fof(f147,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK13)
& ~ empty(sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f36,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f265,plain,
ordinal(sK12),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& ~ empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f81,f145]) ).
fof(f145,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& ~ empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
inference(pure_predicate_removal,[],[f22]) ).
fof(f22,axiom,
? [X0] :
( natural(X0)
& ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(f264,plain,
epsilon_connected(sK12),
inference(cnf_transformation,[],[f146]) ).
fof(f263,plain,
epsilon_transitive(sK12),
inference(cnf_transformation,[],[f146]) ).
fof(f262,plain,
~ empty(sK12),
inference(cnf_transformation,[],[f146]) ).
fof(f261,plain,
ordinal(sK11),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11)
& ~ empty(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f42,f143]) ).
fof(f143,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11)
& ~ empty(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f42,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f260,plain,
epsilon_connected(sK11),
inference(cnf_transformation,[],[f144]) ).
fof(f259,plain,
epsilon_transitive(sK11),
inference(cnf_transformation,[],[f144]) ).
fof(f258,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f144]) ).
fof(f257,plain,
finite(sK10),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
( finite(sK10)
& ~ empty(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f23,f141]) ).
fof(f141,plain,
( ? [X0] :
( finite(X0)
& ~ empty(X0) )
=> ( finite(sK10)
& ~ empty(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] :
( finite(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(f256,plain,
~ empty(sK10),
inference(cnf_transformation,[],[f142]) ).
fof(f255,plain,
empty(sK9),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
empty(sK9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f30,f139]) ).
fof(f139,plain,
( ? [X0] : empty(X0)
=> empty(sK9) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f254,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
~ empty(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f38,f137]) ).
fof(f137,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK8) ),
introduced(choice_axiom,[]) ).
fof(f38,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f194,plain,
ordinal(empty_set),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f71]) ).
fof(f71,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation(empty_set) ),
inference(pure_predicate_removal,[],[f17]) ).
fof(f17,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f193,plain,
epsilon_connected(empty_set),
inference(cnf_transformation,[],[f74]) ).
fof(f192,plain,
epsilon_transitive(empty_set),
inference(cnf_transformation,[],[f74]) ).
fof(f184,plain,
empty(empty_set),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f183,plain,
~ empty(positive_rationals),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
~ empty(positive_rationals),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_arytm_3) ).
fof(f253,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f252,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f250,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f248,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f249,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f246,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f234,plain,
! [X0] : element(sK7(X0),powerset(X0)),
inference(cnf_transformation,[],[f135]) ).
fof(f232,plain,
! [X0] : element(sK6(X0),powerset(X0)),
inference(cnf_transformation,[],[f133]) ).
fof(f202,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| finite(X1)
| ~ finite(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( finite(X1)
| ~ element(X1,powerset(X0)) )
| ~ finite(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( finite(X0)
=> ! [X1] :
( element(X1,powerset(X0))
=> finite(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(f191,plain,
empty(empty_set),
inference(cnf_transformation,[],[f74]) ).
fof(f187,plain,
empty(empty_set),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(pure_predicate_removal,[],[f14]) ).
fof(f14,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f185,plain,
empty(empty_set),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f181,plain,
( ~ finite(union(sK0))
| in(sK1,sK0)
| ~ finite(sK0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f182,plain,
( ~ finite(union(sK0))
| ~ finite(sK1)
| ~ finite(sK0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f623,plain,
( finite(sK1)
| ~ spl29_2 ),
inference(resolution,[],[f619,f436]) ).
fof(f619,plain,
( ! [X0] :
( ~ in(X0,sK0)
| finite(X0) )
| ~ spl29_2 ),
inference(resolution,[],[f428,f317]) ).
fof(f566,plain,
( spl29_5
| spl29_6 ),
inference(avatar_split_clause,[],[f554,f564,f561]) ).
fof(f561,plain,
( spl29_5
<=> ! [X1] : ~ in(X1,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_5])]) ).
fof(f564,plain,
( spl29_6
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_6])]) ).
fof(f554,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,empty_set) ),
inference(resolution,[],[f253,f384]) ).
fof(f479,plain,
( spl29_3
| ~ spl29_4
| ~ spl29_2 ),
inference(avatar_split_clause,[],[f470,f315,f476,f472]) ).
fof(f472,plain,
( spl29_3
<=> epsilon_transitive(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_3])]) ).
fof(f476,plain,
( spl29_4
<=> ordinal(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl29_4])]) ).
fof(f470,plain,
( ~ ordinal(sK0)
| epsilon_transitive(sK1)
| ~ spl29_2 ),
inference(resolution,[],[f401,f436]) ).
fof(f434,plain,
( spl29_1
| ~ spl29_2 ),
inference(avatar_contradiction_clause,[],[f433]) ).
fof(f433,plain,
( $false
| spl29_1
| ~ spl29_2 ),
inference(subsumption_resolution,[],[f431,f312]) ).
fof(f312,plain,
( ~ finite(sK0)
| spl29_1 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f318,plain,
( spl29_1
| spl29_2 ),
inference(avatar_split_clause,[],[f179,f315,f311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU094+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n022.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 20:42:28 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (26496)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (26500)WARNING: value z3 for option sas not known
% 0.14/0.39 % (26501)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (26500)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)
% 0.14/0.39 TRYING [1]
% 0.14/0.40 TRYING [2]
% 0.14/0.40 % (26503)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)
% 0.14/0.40 % (26504)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)
% 0.14/0.40 % (26502)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)
% 0.14/0.40 TRYING [3]
% 0.14/0.40 TRYING [4]
% 0.14/0.40 TRYING [5]
% 0.14/0.41 % (26500)First to succeed.
% 0.14/0.41 TRYING [6]
% 0.14/0.42 % (26500)Refutation found. Thanks to Tanya!
% 0.14/0.42 % SZS status Theorem for theBenchmark
% 0.14/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.42 % (26500)------------------------------
% 0.14/0.42 % (26500)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.42 % (26500)Termination reason: Refutation
% 0.14/0.42
% 0.14/0.42 % (26500)Memory used [KB]: 1017
% 0.14/0.42 % (26500)Time elapsed: 0.025 s
% 0.14/0.42 % (26500)Instructions burned: 25 (million)
% 0.14/0.42 % (26500)------------------------------
% 0.14/0.42 % (26500)------------------------------
% 0.14/0.42 % (26496)Success in time 0.051 s
%------------------------------------------------------------------------------