TSTP Solution File: SEU297+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU297+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 18:33:04 EDT 2022
% Result : Theorem 0.18s 0.52s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 101 ( 11 unt; 0 def)
% Number of atoms : 479 ( 66 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 583 ( 205 ~; 231 |; 117 &)
% ( 14 <=>; 14 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 203 ( 142 !; 61 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f639,plain,
$false,
inference(avatar_sat_refutation,[],[f520,f549,f580,f592,f600,f610,f638]) ).
fof(f638,plain,
( ~ spl30_15
| ~ spl30_19
| ~ spl30_20
| ~ spl30_21 ),
inference(avatar_contradiction_clause,[],[f637]) ).
fof(f637,plain,
( $false
| ~ spl30_15
| ~ spl30_19
| ~ spl30_20
| ~ spl30_21 ),
inference(subsumption_resolution,[],[f636,f558]) ).
fof(f558,plain,
( in(sK6(sK23(sK3,sK5)),sK23(sK3,sK5))
| ~ spl30_15 ),
inference(factoring,[],[f516]) ).
fof(f516,plain,
( ! [X0] :
( in(sK6(X0),sK23(sK3,sK5))
| in(sK6(X0),X0) )
| ~ spl30_15 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f515,plain,
( spl30_15
<=> ! [X0] :
( in(sK6(X0),sK23(sK3,sK5))
| in(sK6(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_15])]) ).
fof(f636,plain,
( ~ in(sK6(sK23(sK3,sK5)),sK23(sK3,sK5))
| ~ spl30_19
| ~ spl30_20
| ~ spl30_21 ),
inference(subsumption_resolution,[],[f633,f611]) ).
fof(f611,plain,
( in(sK6(sK23(sK3,sK5)),sF27)
| ~ spl30_19
| ~ spl30_21 ),
inference(forward_demodulation,[],[f609,f591]) ).
fof(f591,plain,
( sK24(sK3,sK5,sK6(sK23(sK3,sK5))) = sK6(sK23(sK3,sK5))
| ~ spl30_19 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f589,plain,
( spl30_19
<=> sK24(sK3,sK5,sK6(sK23(sK3,sK5))) = sK6(sK23(sK3,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_19])]) ).
fof(f609,plain,
( in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),sF27)
| ~ spl30_21 ),
inference(avatar_component_clause,[],[f607]) ).
fof(f607,plain,
( spl30_21
<=> in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),sF27) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_21])]) ).
fof(f633,plain,
( ~ in(sK6(sK23(sK3,sK5)),sF27)
| ~ in(sK6(sK23(sK3,sK5)),sK23(sK3,sK5))
| ~ spl30_20 ),
inference(resolution,[],[f599,f213]) ).
fof(f213,plain,
! [X3] :
( ~ in(relation_image(sK3,sK6(X3)),sK5)
| ~ in(sK6(X3),sF27)
| ~ in(sK6(X3),X3) ),
inference(definition_folding,[],[f146,f212,f211]) ).
fof(f211,plain,
sF26 = relation_dom(sK3),
introduced(function_definition,[]) ).
fof(f212,plain,
sF27 = powerset(sF26),
introduced(function_definition,[]) ).
fof(f146,plain,
! [X3] :
( ~ in(sK6(X3),X3)
| ~ in(sK6(X3),powerset(relation_dom(sK3)))
| ~ in(relation_image(sK3,sK6(X3)),sK5) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
( ! [X3] :
( ( ~ in(sK6(X3),X3)
| ~ in(sK6(X3),powerset(relation_dom(sK3)))
| ~ in(relation_image(sK3,sK6(X3)),sK5) )
& ( in(sK6(X3),X3)
| ( in(sK6(X3),powerset(relation_dom(sK3)))
& in(relation_image(sK3,sK6(X3)),sK5) ) ) )
& function(sK3)
& relation(sK3)
& element(sK5,powerset(powerset(sK4))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6])],[f82,f84,f83]) ).
fof(f83,plain,
( ? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,powerset(relation_dom(X0)))
| ~ in(relation_image(X0,X4),X2) )
& ( in(X4,X3)
| ( in(X4,powerset(relation_dom(X0)))
& in(relation_image(X0,X4),X2) ) ) )
& function(X0)
& relation(X0)
& element(X2,powerset(powerset(X1))) )
=> ( ! [X3] :
? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,powerset(relation_dom(sK3)))
| ~ in(relation_image(sK3,X4),sK5) )
& ( in(X4,X3)
| ( in(X4,powerset(relation_dom(sK3)))
& in(relation_image(sK3,X4),sK5) ) ) )
& function(sK3)
& relation(sK3)
& element(sK5,powerset(powerset(sK4))) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X3] :
( ? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,powerset(relation_dom(sK3)))
| ~ in(relation_image(sK3,X4),sK5) )
& ( in(X4,X3)
| ( in(X4,powerset(relation_dom(sK3)))
& in(relation_image(sK3,X4),sK5) ) ) )
=> ( ( ~ in(sK6(X3),X3)
| ~ in(sK6(X3),powerset(relation_dom(sK3)))
| ~ in(relation_image(sK3,sK6(X3)),sK5) )
& ( in(sK6(X3),X3)
| ( in(sK6(X3),powerset(relation_dom(sK3)))
& in(relation_image(sK3,sK6(X3)),sK5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,powerset(relation_dom(X0)))
| ~ in(relation_image(X0,X4),X2) )
& ( in(X4,X3)
| ( in(X4,powerset(relation_dom(X0)))
& in(relation_image(X0,X4),X2) ) ) )
& function(X0)
& relation(X0)
& element(X2,powerset(powerset(X1))) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ~ in(X4,X3)
| ~ in(X4,powerset(relation_dom(X0)))
| ~ in(relation_image(X0,X4),X2) )
& ( in(X4,X3)
| ( in(X4,powerset(relation_dom(X0)))
& in(relation_image(X0,X4),X2) ) ) )
& function(X0)
& relation(X0)
& element(X2,powerset(powerset(X1))) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( in(X4,powerset(relation_dom(X0)))
& in(relation_image(X0,X4),X2) )
<~> in(X4,X3) )
& function(X0)
& relation(X0)
& element(X2,powerset(powerset(X1))) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
? [X0,X2,X1] :
( ! [X3] :
? [X4] :
( ( in(X4,powerset(relation_dom(X0)))
& in(relation_image(X0,X4),X2) )
<~> in(X4,X3) )
& function(X0)
& relation(X0)
& element(X2,powerset(powerset(X1))) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,plain,
~ ! [X0,X2,X1] :
( ( function(X0)
& relation(X0)
& element(X2,powerset(powerset(X1))) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,powerset(relation_dom(X0)))
& in(relation_image(X0,X4),X2) ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X2,X0,X1] :
( ( relation(X2)
& element(X1,powerset(powerset(X0)))
& function(X2) )
=> ? [X3] :
! [X4] :
( ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) )
<=> in(X4,X3) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X2,X0,X1] :
( ( relation(X2)
& element(X1,powerset(powerset(X0)))
& function(X2) )
=> ? [X3] :
! [X4] :
( ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) )
<=> in(X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_27__finset_1) ).
fof(f599,plain,
( in(relation_image(sK3,sK6(sK23(sK3,sK5))),sK5)
| ~ spl30_20 ),
inference(avatar_component_clause,[],[f597]) ).
fof(f597,plain,
( spl30_20
<=> in(relation_image(sK3,sK6(sK23(sK3,sK5))),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_20])]) ).
fof(f610,plain,
( spl30_21
| spl30_16
| spl30_14
| ~ spl30_15 ),
inference(avatar_split_clause,[],[f605,f515,f511,f518,f607]) ).
fof(f518,plain,
( spl30_16
<=> ! [X1] : ~ element(sK5,powerset(powerset(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_16])]) ).
fof(f511,plain,
( spl30_14
<=> sP0(sK5,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_14])]) ).
fof(f605,plain,
( ! [X0] :
( ~ element(sK5,powerset(powerset(X0)))
| in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),sF27) )
| spl30_14
| ~ spl30_15 ),
inference(forward_demodulation,[],[f604,f212]) ).
fof(f604,plain,
( ! [X0] :
( in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),powerset(sF26))
| ~ element(sK5,powerset(powerset(X0))) )
| spl30_14
| ~ spl30_15 ),
inference(forward_demodulation,[],[f603,f211]) ).
fof(f603,plain,
( ! [X0] :
( in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),powerset(relation_dom(sK3)))
| ~ element(sK5,powerset(powerset(X0))) )
| spl30_14
| ~ spl30_15 ),
inference(subsumption_resolution,[],[f602,f512]) ).
fof(f512,plain,
( ~ sP0(sK5,sK3)
| spl30_14 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f602,plain,
( ! [X0] :
( sP0(sK5,sK3)
| ~ element(sK5,powerset(powerset(X0)))
| in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),powerset(relation_dom(sK3))) )
| ~ spl30_15 ),
inference(subsumption_resolution,[],[f601,f143]) ).
fof(f143,plain,
function(sK3),
inference(cnf_transformation,[],[f85]) ).
fof(f601,plain,
( ! [X0] :
( ~ function(sK3)
| ~ element(sK5,powerset(powerset(X0)))
| sP0(sK5,sK3)
| in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),powerset(relation_dom(sK3))) )
| ~ spl30_15 ),
inference(subsumption_resolution,[],[f581,f142]) ).
fof(f142,plain,
relation(sK3),
inference(cnf_transformation,[],[f85]) ).
fof(f581,plain,
( ! [X0] :
( in(sK24(sK3,sK5,sK6(sK23(sK3,sK5))),powerset(relation_dom(sK3)))
| ~ relation(sK3)
| sP0(sK5,sK3)
| ~ element(sK5,powerset(powerset(X0)))
| ~ function(sK3) )
| ~ spl30_15 ),
inference(resolution,[],[f558,f202]) ).
fof(f202,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK23(X0,X2))
| sP0(X2,X0)
| ~ element(X2,powerset(powerset(X1)))
| in(sK24(X0,X2,X4),powerset(relation_dom(X0)))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2] :
( sP0(X2,X0)
| ~ element(X2,powerset(powerset(X1)))
| ~ function(X0)
| ~ relation(X0)
| ! [X4] :
( ( ( sK24(X0,X2,X4) = X4
& in(sK24(X0,X2,X4),powerset(relation_dom(X0)))
& in(relation_image(X0,X4),X2) )
| ~ in(X4,sK23(X0,X2)) )
& ( in(X4,sK23(X0,X2))
| ! [X6] :
( X4 != X6
| ~ in(X6,powerset(relation_dom(X0)))
| ~ in(relation_image(X0,X4),X2) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f117,f119,f118]) ).
fof(f118,plain,
! [X0,X2] :
( ? [X3] :
! [X4] :
( ( ? [X5] :
( X4 = X5
& in(X5,powerset(relation_dom(X0)))
& in(relation_image(X0,X4),X2) )
| ~ in(X4,X3) )
& ( in(X4,X3)
| ! [X6] :
( X4 != X6
| ~ in(X6,powerset(relation_dom(X0)))
| ~ in(relation_image(X0,X4),X2) ) ) )
=> ! [X4] :
( ( ? [X5] :
( X4 = X5
& in(X5,powerset(relation_dom(X0)))
& in(relation_image(X0,X4),X2) )
| ~ in(X4,sK23(X0,X2)) )
& ( in(X4,sK23(X0,X2))
| ! [X6] :
( X4 != X6
| ~ in(X6,powerset(relation_dom(X0)))
| ~ in(relation_image(X0,X4),X2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
! [X0,X2,X4] :
( ? [X5] :
( X4 = X5
& in(X5,powerset(relation_dom(X0)))
& in(relation_image(X0,X4),X2) )
=> ( sK24(X0,X2,X4) = X4
& in(sK24(X0,X2,X4),powerset(relation_dom(X0)))
& in(relation_image(X0,X4),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
! [X0,X1,X2] :
( sP0(X2,X0)
| ~ element(X2,powerset(powerset(X1)))
| ~ function(X0)
| ~ relation(X0)
| ? [X3] :
! [X4] :
( ( ? [X5] :
( X4 = X5
& in(X5,powerset(relation_dom(X0)))
& in(relation_image(X0,X4),X2) )
| ~ in(X4,X3) )
& ( in(X4,X3)
| ! [X6] :
( X4 != X6
| ~ in(X6,powerset(relation_dom(X0)))
| ~ in(relation_image(X0,X4),X2) ) ) ) ),
inference(rectify,[],[f116]) ).
fof(f116,plain,
! [X2,X0,X1] :
( sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ function(X2)
| ~ relation(X2)
| ? [X6] :
! [X7] :
( ( ? [X8] :
( X7 = X8
& in(X8,powerset(relation_dom(X2)))
& in(relation_image(X2,X7),X1) )
| ~ in(X7,X6) )
& ( in(X7,X6)
| ! [X8] :
( X7 != X8
| ~ in(X8,powerset(relation_dom(X2)))
| ~ in(relation_image(X2,X7),X1) ) ) ) ),
inference(nnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X2,X0,X1] :
( sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ function(X2)
| ~ relation(X2)
| ? [X6] :
! [X7] :
( ? [X8] :
( X7 = X8
& in(X8,powerset(relation_dom(X2)))
& in(relation_image(X2,X7),X1) )
<=> in(X7,X6) ) ),
inference(definition_folding,[],[f64,f75]) ).
fof(f75,plain,
! [X1,X2] :
( ? [X5,X4,X3] :
( in(relation_image(X2,X3),X1)
& X3 = X4
& X4 = X5
& in(relation_image(X2,X5),X1)
& X3 != X5 )
| ~ sP0(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ? [X5,X4,X3] :
( in(relation_image(X2,X3),X1)
& X3 = X4
& X4 = X5
& in(relation_image(X2,X5),X1)
& X3 != X5 )
| ~ element(X1,powerset(powerset(X0)))
| ~ function(X2)
| ~ relation(X2)
| ? [X6] :
! [X7] :
( ? [X8] :
( X7 = X8
& in(X8,powerset(relation_dom(X2)))
& in(relation_image(X2,X7),X1) )
<=> in(X7,X6) ) ),
inference(flattening,[],[f63]) ).
fof(f63,plain,
! [X2,X1,X0] :
( ? [X6] :
! [X7] :
( ? [X8] :
( X7 = X8
& in(X8,powerset(relation_dom(X2)))
& in(relation_image(X2,X7),X1) )
<=> in(X7,X6) )
| ? [X3,X4,X5] :
( X3 != X5
& X3 = X4
& in(relation_image(X2,X5),X1)
& in(relation_image(X2,X3),X1)
& X4 = X5 )
| ~ relation(X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ function(X2) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,plain,
! [X2,X1,X0] :
( ( relation(X2)
& element(X1,powerset(powerset(X0)))
& function(X2) )
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& in(relation_image(X2,X5),X1)
& in(relation_image(X2,X3),X1)
& X4 = X5 )
=> X3 = X5 )
=> ? [X6] :
! [X7] :
( ? [X8] :
( X7 = X8
& in(X8,powerset(relation_dom(X2)))
& in(relation_image(X2,X7),X1) )
<=> in(X7,X6) ) ) ),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X0,X1,X2] :
( ( relation(X2)
& element(X1,powerset(powerset(X0)))
& function(X2) )
=> ( ! [X5,X3,X4] :
( ( X3 = X5
& in(relation_image(X2,X4),X1)
& X3 = X4
& in(relation_image(X2,X5),X1) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( X4 = X5
& in(X5,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_27__finset_1__1) ).
fof(f600,plain,
( spl30_16
| spl30_20
| spl30_14
| ~ spl30_15 ),
inference(avatar_split_clause,[],[f595,f515,f511,f597,f518]) ).
fof(f595,plain,
( ! [X2] :
( in(relation_image(sK3,sK6(sK23(sK3,sK5))),sK5)
| ~ element(sK5,powerset(powerset(X2))) )
| spl30_14
| ~ spl30_15 ),
inference(subsumption_resolution,[],[f594,f512]) ).
fof(f594,plain,
( ! [X2] :
( in(relation_image(sK3,sK6(sK23(sK3,sK5))),sK5)
| sP0(sK5,sK3)
| ~ element(sK5,powerset(powerset(X2))) )
| ~ spl30_15 ),
inference(subsumption_resolution,[],[f593,f142]) ).
fof(f593,plain,
( ! [X2] :
( in(relation_image(sK3,sK6(sK23(sK3,sK5))),sK5)
| ~ relation(sK3)
| sP0(sK5,sK3)
| ~ element(sK5,powerset(powerset(X2))) )
| ~ spl30_15 ),
inference(subsumption_resolution,[],[f583,f143]) ).
fof(f583,plain,
( ! [X2] :
( in(relation_image(sK3,sK6(sK23(sK3,sK5))),sK5)
| ~ function(sK3)
| ~ relation(sK3)
| sP0(sK5,sK3)
| ~ element(sK5,powerset(powerset(X2))) )
| ~ spl30_15 ),
inference(resolution,[],[f558,f201]) ).
fof(f201,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK23(X0,X2))
| sP0(X2,X0)
| ~ relation(X0)
| ~ function(X0)
| ~ element(X2,powerset(powerset(X1)))
| in(relation_image(X0,X4),X2) ),
inference(cnf_transformation,[],[f120]) ).
fof(f592,plain,
( spl30_16
| spl30_19
| spl30_14
| ~ spl30_15 ),
inference(avatar_split_clause,[],[f587,f515,f511,f589,f518]) ).
fof(f587,plain,
( ! [X1] :
( sK24(sK3,sK5,sK6(sK23(sK3,sK5))) = sK6(sK23(sK3,sK5))
| ~ element(sK5,powerset(powerset(X1))) )
| spl30_14
| ~ spl30_15 ),
inference(subsumption_resolution,[],[f586,f143]) ).
fof(f586,plain,
( ! [X1] :
( sK24(sK3,sK5,sK6(sK23(sK3,sK5))) = sK6(sK23(sK3,sK5))
| ~ element(sK5,powerset(powerset(X1)))
| ~ function(sK3) )
| spl30_14
| ~ spl30_15 ),
inference(subsumption_resolution,[],[f585,f142]) ).
fof(f585,plain,
( ! [X1] :
( ~ element(sK5,powerset(powerset(X1)))
| sK24(sK3,sK5,sK6(sK23(sK3,sK5))) = sK6(sK23(sK3,sK5))
| ~ relation(sK3)
| ~ function(sK3) )
| spl30_14
| ~ spl30_15 ),
inference(subsumption_resolution,[],[f582,f512]) ).
fof(f582,plain,
( ! [X1] :
( sP0(sK5,sK3)
| ~ function(sK3)
| sK24(sK3,sK5,sK6(sK23(sK3,sK5))) = sK6(sK23(sK3,sK5))
| ~ relation(sK3)
| ~ element(sK5,powerset(powerset(X1))) )
| ~ spl30_15 ),
inference(resolution,[],[f558,f203]) ).
fof(f203,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK23(X0,X2))
| ~ relation(X0)
| ~ element(X2,powerset(powerset(X1)))
| ~ function(X0)
| sP0(X2,X0)
| sK24(X0,X2,X4) = X4 ),
inference(cnf_transformation,[],[f120]) ).
fof(f580,plain,
~ spl30_16,
inference(avatar_contradiction_clause,[],[f579]) ).
fof(f579,plain,
( $false
| ~ spl30_16 ),
inference(subsumption_resolution,[],[f578,f217]) ).
fof(f217,plain,
element(sK5,sF29),
inference(definition_folding,[],[f141,f216,f215]) ).
fof(f215,plain,
powerset(sK4) = sF28,
introduced(function_definition,[]) ).
fof(f216,plain,
sF29 = powerset(sF28),
introduced(function_definition,[]) ).
fof(f141,plain,
element(sK5,powerset(powerset(sK4))),
inference(cnf_transformation,[],[f85]) ).
fof(f578,plain,
( ~ element(sK5,sF29)
| ~ spl30_16 ),
inference(forward_demodulation,[],[f576,f216]) ).
fof(f576,plain,
( ~ element(sK5,powerset(sF28))
| ~ spl30_16 ),
inference(superposition,[],[f519,f215]) ).
fof(f519,plain,
( ! [X1] : ~ element(sK5,powerset(powerset(X1)))
| ~ spl30_16 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f549,plain,
~ spl30_14,
inference(avatar_contradiction_clause,[],[f548]) ).
fof(f548,plain,
( $false
| ~ spl30_14 ),
inference(subsumption_resolution,[],[f547,f513]) ).
fof(f513,plain,
( sP0(sK5,sK3)
| ~ spl30_14 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f547,plain,
( ~ sP0(sK5,sK3)
| ~ spl30_14 ),
inference(trivial_inequality_removal,[],[f546]) ).
fof(f546,plain,
( ~ sP0(sK5,sK3)
| sK20(sK5,sK3) != sK20(sK5,sK3)
| ~ spl30_14 ),
inference(superposition,[],[f195,f523]) ).
fof(f523,plain,
( sK22(sK5,sK3) = sK20(sK5,sK3)
| ~ spl30_14 ),
inference(backward_demodulation,[],[f521,f522]) ).
fof(f522,plain,
( sK20(sK5,sK3) = sK21(sK5,sK3)
| ~ spl30_14 ),
inference(resolution,[],[f513,f197]) ).
fof(f197,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK21(X0,X1) = sK20(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ( in(relation_image(X1,sK22(X0,X1)),X0)
& sK22(X0,X1) = sK21(X0,X1)
& sK21(X0,X1) = sK20(X0,X1)
& in(relation_image(X1,sK20(X0,X1)),X0)
& sK22(X0,X1) != sK20(X0,X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22])],[f113,f114]) ).
fof(f114,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( in(relation_image(X1,X4),X0)
& X3 = X4
& X2 = X3
& in(relation_image(X1,X2),X0)
& X2 != X4 )
=> ( in(relation_image(X1,sK22(X0,X1)),X0)
& sK22(X0,X1) = sK21(X0,X1)
& sK21(X0,X1) = sK20(X0,X1)
& in(relation_image(X1,sK20(X0,X1)),X0)
& sK22(X0,X1) != sK20(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f113,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( in(relation_image(X1,X4),X0)
& X3 = X4
& X2 = X3
& in(relation_image(X1,X2),X0)
& X2 != X4 )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f112]) ).
fof(f112,plain,
! [X1,X2] :
( ? [X5,X4,X3] :
( in(relation_image(X2,X3),X1)
& X3 = X4
& X4 = X5
& in(relation_image(X2,X5),X1)
& X3 != X5 )
| ~ sP0(X1,X2) ),
inference(nnf_transformation,[],[f75]) ).
fof(f521,plain,
( sK22(sK5,sK3) = sK21(sK5,sK3)
| ~ spl30_14 ),
inference(resolution,[],[f513,f198]) ).
fof(f198,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK22(X0,X1) = sK21(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f195,plain,
! [X0,X1] :
( sK22(X0,X1) != sK20(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f115]) ).
fof(f520,plain,
( spl30_14
| spl30_15
| spl30_16 ),
inference(avatar_split_clause,[],[f509,f518,f515,f511]) ).
fof(f509,plain,
! [X0,X1] :
( ~ element(sK5,powerset(powerset(X1)))
| in(sK6(X0),sK23(sK3,sK5))
| sP0(sK5,sK3)
| in(sK6(X0),X0) ),
inference(subsumption_resolution,[],[f508,f214]) ).
fof(f214,plain,
! [X3] :
( in(sK6(X3),sF27)
| in(sK6(X3),X3) ),
inference(definition_folding,[],[f145,f212,f211]) ).
fof(f145,plain,
! [X3] :
( in(sK6(X3),X3)
| in(sK6(X3),powerset(relation_dom(sK3))) ),
inference(cnf_transformation,[],[f85]) ).
fof(f508,plain,
! [X0,X1] :
( ~ element(sK5,powerset(powerset(X1)))
| ~ in(sK6(X0),sF27)
| in(sK6(X0),X0)
| sP0(sK5,sK3)
| in(sK6(X0),sK23(sK3,sK5)) ),
inference(forward_demodulation,[],[f507,f212]) ).
fof(f507,plain,
! [X0,X1] :
( in(sK6(X0),X0)
| in(sK6(X0),sK23(sK3,sK5))
| ~ element(sK5,powerset(powerset(X1)))
| sP0(sK5,sK3)
| ~ in(sK6(X0),powerset(sF26)) ),
inference(forward_demodulation,[],[f506,f211]) ).
fof(f506,plain,
! [X0,X1] :
( ~ element(sK5,powerset(powerset(X1)))
| sP0(sK5,sK3)
| in(sK6(X0),X0)
| in(sK6(X0),sK23(sK3,sK5))
| ~ in(sK6(X0),powerset(relation_dom(sK3))) ),
inference(subsumption_resolution,[],[f505,f143]) ).
fof(f505,plain,
! [X0,X1] :
( ~ in(sK6(X0),powerset(relation_dom(sK3)))
| ~ element(sK5,powerset(powerset(X1)))
| in(sK6(X0),X0)
| in(sK6(X0),sK23(sK3,sK5))
| ~ function(sK3)
| sP0(sK5,sK3) ),
inference(subsumption_resolution,[],[f502,f142]) ).
fof(f502,plain,
! [X0,X1] :
( ~ in(sK6(X0),powerset(relation_dom(sK3)))
| in(sK6(X0),X0)
| ~ element(sK5,powerset(powerset(X1)))
| ~ relation(sK3)
| ~ function(sK3)
| in(sK6(X0),sK23(sK3,sK5))
| sP0(sK5,sK3) ),
inference(resolution,[],[f210,f144]) ).
fof(f144,plain,
! [X3] :
( in(sK6(X3),X3)
| in(relation_image(sK3,sK6(X3)),sK5) ),
inference(cnf_transformation,[],[f85]) ).
fof(f210,plain,
! [X2,X0,X1,X6] :
( ~ in(relation_image(X0,X6),X2)
| ~ relation(X0)
| ~ in(X6,powerset(relation_dom(X0)))
| in(X6,sK23(X0,X2))
| ~ element(X2,powerset(powerset(X1)))
| sP0(X2,X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f200]) ).
fof(f200,plain,
! [X2,X0,X1,X6,X4] :
( sP0(X2,X0)
| ~ element(X2,powerset(powerset(X1)))
| ~ function(X0)
| ~ relation(X0)
| in(X4,sK23(X0,X2))
| X4 != X6
| ~ in(X6,powerset(relation_dom(X0)))
| ~ in(relation_image(X0,X4),X2) ),
inference(cnf_transformation,[],[f120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU297+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.32 % Computer : n028.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 15:15:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.49 % (9507)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.18/0.49 % (9492)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.49 % (9499)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.50 % (9486)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.18/0.50 % (9487)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.50 % (9490)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.51 % (9508)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.18/0.51 % (9495)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.18/0.51 % (9489)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.18/0.51 % (9489)Instruction limit reached!
% 0.18/0.51 % (9489)------------------------------
% 0.18/0.51 % (9489)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.51 % (9489)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.51 % (9489)Termination reason: Unknown
% 0.18/0.51 % (9489)Termination phase: Unused predicate definition removal
% 0.18/0.51
% 0.18/0.51 % (9489)Memory used [KB]: 895
% 0.18/0.51 % (9489)Time elapsed: 0.003 s
% 0.18/0.51 % (9489)Instructions burned: 2 (million)
% 0.18/0.51 % (9489)------------------------------
% 0.18/0.51 % (9489)------------------------------
% 0.18/0.51 % (9482)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.18/0.51 % (9506)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.18/0.51 % (9481)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.18/0.51 % (9485)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.51 % (9500)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.51 % (9503)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.18/0.51 % (9483)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.18/0.51 % (9488)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.18/0.52 % (9484)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.52 % (9493)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.18/0.52 TRYING [1]
% 0.18/0.52 % (9509)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.18/0.52 % (9488)Instruction limit reached!
% 0.18/0.52 % (9488)------------------------------
% 0.18/0.52 % (9488)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52 % (9488)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52 % (9488)Termination reason: Unknown
% 0.18/0.52 % (9488)Termination phase: Saturation
% 0.18/0.52
% 0.18/0.52 % (9488)Memory used [KB]: 5628
% 0.18/0.52 % (9488)Time elapsed: 0.093 s
% 0.18/0.52 % (9488)Instructions burned: 8 (million)
% 0.18/0.52 % (9488)------------------------------
% 0.18/0.52 % (9488)------------------------------
% 0.18/0.52 % (9504)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.18/0.52 % (9498)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.18/0.52 TRYING [2]
% 0.18/0.52 % (9501)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.18/0.52 % (9496)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.18/0.52 % (9499)First to succeed.
% 0.18/0.52 % (9511)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.18/0.52 TRYING [1]
% 0.18/0.52 % (9499)Refutation found. Thanks to Tanya!
% 0.18/0.52 % SZS status Theorem for theBenchmark
% 0.18/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.52 % (9499)------------------------------
% 0.18/0.52 % (9499)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.52 % (9499)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.52 % (9499)Termination reason: Refutation
% 0.18/0.52
% 0.18/0.52 % (9499)Memory used [KB]: 5756
% 0.18/0.52 % (9499)Time elapsed: 0.142 s
% 0.18/0.52 % (9499)Instructions burned: 18 (million)
% 0.18/0.52 % (9499)------------------------------
% 0.18/0.52 % (9499)------------------------------
% 0.18/0.52 % (9480)Success in time 0.187 s
%------------------------------------------------------------------------------