TSTP Solution File: SEU329+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU329+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n006.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 : Sun May 5 09:22:22 EDT 2024
% Result : Theorem 0.58s 0.77s
% Output : Refutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 35
% Syntax : Number of formulae : 171 ( 5 unt; 0 def)
% Number of atoms : 1264 ( 324 equ)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 1692 ( 599 ~; 771 |; 257 &)
% ( 27 <=>; 36 =>; 0 <=; 2 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 26 ( 24 usr; 21 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 3 con; 0-4 aty)
% Number of variables : 607 ( 432 !; 175 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f515,plain,
$false,
inference(avatar_sat_refutation,[],[f230,f257,f259,f270,f277,f339,f346,f378,f388,f393,f398,f403,f459,f464,f479,f482,f485,f487,f509,f511,f514]) ).
fof(f514,plain,
( ~ spl23_12
| ~ spl23_28 ),
inference(avatar_contradiction_clause,[],[f512]) ).
fof(f512,plain,
( $false
| ~ spl23_12
| ~ spl23_28 ),
inference(resolution,[],[f468,f360]) ).
fof(f360,plain,
( in(sK4(sK18(sK1,sK2,sK3)),sK18(sK1,sK2,sK3))
| ~ spl23_12 ),
inference(factoring,[],[f354]) ).
fof(f354,plain,
( ! [X0] :
( in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),X0) )
| ~ spl23_12 ),
inference(duplicate_literal_removal,[],[f351]) ).
fof(f351,plain,
( ! [X0] :
( in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),X0)
| in(sK4(X0),X0) )
| ~ spl23_12 ),
inference(resolution,[],[f350,f107]) ).
fof(f107,plain,
! [X3] :
( in(sK4(X3),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
( ! [X3] :
( ( ! [X5,X6] :
( ( subset_complement(the_carrier(sK1),sK5(X5,X6)) != X6
& sK5(X5,X6) = X5
& element(sK5(X5,X6),powerset(the_carrier(sK1))) )
| ~ in(X5,complements_of_subsets(the_carrier(sK1),sK2))
| ordered_pair(X5,X6) != sK4(X3) )
| ~ in(sK4(X3),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ in(sK4(X3),X3) )
& ( ( ! [X10] :
( subset_complement(the_carrier(sK1),X10) = sK7(X3)
| sK6(X3) != X10
| ~ element(X10,powerset(the_carrier(sK1))) )
& in(sK6(X3),complements_of_subsets(the_carrier(sK1),sK2))
& sK4(X3) = ordered_pair(sK6(X3),sK7(X3))
& in(sK4(X3),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3)) )
| in(sK4(X3),X3) ) )
& element(sK2,powerset(powerset(the_carrier(sK1))))
& one_sorted_str(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f79,f84,f83,f82,f81,f80]) ).
fof(f80,plain,
( ? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ! [X5,X6] :
( ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) )
| ~ in(X5,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| ~ in(X4,X3) )
& ( ( ? [X8,X9] :
( ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) )
& in(X8,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) )
=> ( ? [X2] :
! [X3] :
? [X4] :
( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK1),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK1))) )
| ~ in(X5,complements_of_subsets(the_carrier(sK1),sK2))
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X2))
| ~ in(X4,X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK1),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK1))) )
& in(X8,complements_of_subsets(the_carrier(sK1),sK2))
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X2)) )
| in(X4,X3) ) )
& element(sK2,powerset(powerset(the_carrier(sK1))))
& one_sorted_str(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
( ? [X2] :
! [X3] :
? [X4] :
( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK1),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK1))) )
| ~ in(X5,complements_of_subsets(the_carrier(sK1),sK2))
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X2))
| ~ in(X4,X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK1),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK1))) )
& in(X8,complements_of_subsets(the_carrier(sK1),sK2))
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X2)) )
| in(X4,X3) ) )
=> ! [X3] :
? [X4] :
( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK1),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK1))) )
| ~ in(X5,complements_of_subsets(the_carrier(sK1),sK2))
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ in(X4,X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK1),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK1))) )
& in(X8,complements_of_subsets(the_carrier(sK1),sK2))
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3)) )
| in(X4,X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
! [X3] :
( ? [X4] :
( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK1),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK1))) )
| ~ in(X5,complements_of_subsets(the_carrier(sK1),sK2))
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ in(X4,X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK1),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK1))) )
& in(X8,complements_of_subsets(the_carrier(sK1),sK2))
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3)) )
| in(X4,X3) ) )
=> ( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK1),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK1))) )
| ~ in(X5,complements_of_subsets(the_carrier(sK1),sK2))
| ordered_pair(X5,X6) != sK4(X3) )
| ~ in(sK4(X3),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ in(sK4(X3),X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK1),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK1))) )
& in(X8,complements_of_subsets(the_carrier(sK1),sK2))
& ordered_pair(X8,X9) = sK4(X3) )
& in(sK4(X3),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3)) )
| in(sK4(X3),X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X5,X6] :
( ? [X7] :
( subset_complement(the_carrier(sK1),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK1))) )
=> ( subset_complement(the_carrier(sK1),sK5(X5,X6)) != X6
& sK5(X5,X6) = X5
& element(sK5(X5,X6),powerset(the_carrier(sK1))) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
! [X3] :
( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK1),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK1))) )
& in(X8,complements_of_subsets(the_carrier(sK1),sK2))
& ordered_pair(X8,X9) = sK4(X3) )
=> ( ! [X10] :
( subset_complement(the_carrier(sK1),X10) = sK7(X3)
| sK6(X3) != X10
| ~ element(X10,powerset(the_carrier(sK1))) )
& in(sK6(X3),complements_of_subsets(the_carrier(sK1),sK2))
& sK4(X3) = ordered_pair(sK6(X3),sK7(X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ! [X5,X6] :
( ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) )
| ~ in(X5,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| ~ in(X4,X3) )
& ( ( ? [X8,X9] :
( ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) )
& in(X8,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ! [X5,X6] :
( ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) )
| ~ in(X5,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| ~ in(X4,X3) )
& ( ( ? [X5,X6] :
( ! [X7] :
( subset_complement(the_carrier(X0),X7) = X6
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(X5,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ! [X5,X6] :
( ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) )
| ~ in(X5,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| ~ in(X4,X3) )
& ( ( ? [X5,X6] :
( ! [X7] :
( subset_complement(the_carrier(X0),X7) = X6
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(X5,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(nnf_transformation,[],[f54]) ).
fof(f54,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( in(X4,X3)
<~> ( ? [X5,X6] :
( ! [X7] :
( subset_complement(the_carrier(X0),X7) = X6
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(X5,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( in(X4,X3)
<~> ( ? [X5,X6] :
( ! [X7] :
( subset_complement(the_carrier(X0),X7) = X6
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(X5,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) )
=> ! [X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( ! [X7] :
( element(X7,powerset(the_carrier(X0)))
=> ( X5 = X7
=> subset_complement(the_carrier(X0),X7) = X6 ) )
& in(X5,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) )
=> ! [X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( ! [X7] :
( element(X7,powerset(the_carrier(X0)))
=> ( X5 = X7
=> subset_complement(the_carrier(X0),X7) = X6 ) )
& in(X5,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kl8RzQtopJ/Vampire---4.8_10303',s1_xboole_0__e4_7_1__tops_2__1) ).
fof(f350,plain,
( ! [X0,X1] :
( ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),sK18(sK1,sK2,X1))
| in(sK4(X0),X0) )
| ~ spl23_12 ),
inference(duplicate_literal_removal,[],[f347]) ).
fof(f347,plain,
( ! [X0,X1] :
( in(sK4(X0),X0)
| in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),sK18(sK1,sK2,X1))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| in(sK4(X0),X0) )
| ~ spl23_12 ),
inference(resolution,[],[f345,f107]) ).
fof(f345,plain,
( ! [X2,X0,X1] :
( ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X2))
| in(sK4(X0),X0)
| in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),sK18(sK1,sK2,X2))
| in(sK4(X0),sK18(sK1,sK2,X1))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1)) )
| ~ spl23_12 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f344,plain,
( spl23_12
<=> ! [X2,X0,X1] :
( in(sK4(X0),X0)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X2))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),sK18(sK1,sK2,X2))
| in(sK4(X0),sK18(sK1,sK2,X1))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_12])]) ).
fof(f468,plain,
( ! [X0] : ~ in(sK4(sK18(sK1,sK2,sK3)),sK18(sK1,sK2,X0))
| ~ spl23_28 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f467,plain,
( spl23_28
<=> ! [X0] : ~ in(sK4(sK18(sK1,sK2,sK3)),sK18(sK1,sK2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_28])]) ).
fof(f511,plain,
( ~ spl23_1
| ~ spl23_3
| spl23_4
| spl23_28
| spl23_23
| ~ spl23_22 ),
inference(avatar_split_clause,[],[f488,f439,f444,f467,f251,f247,f224]) ).
fof(f224,plain,
( spl23_1
<=> one_sorted_str(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_1])]) ).
fof(f247,plain,
( spl23_3
<=> element(sK2,powerset(powerset(the_carrier(sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_3])]) ).
fof(f251,plain,
( spl23_4
<=> sP0(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_4])]) ).
fof(f444,plain,
( spl23_23
<=> sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3))) = subset_complement(the_carrier(sK1),sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_23])]) ).
fof(f439,plain,
( spl23_22
<=> element(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),powerset(the_carrier(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_22])]) ).
fof(f488,plain,
( ! [X0] :
( sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3))) = subset_complement(the_carrier(sK1),sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))))
| ~ in(sK4(sK18(sK1,sK2,sK3)),sK18(sK1,sK2,X0))
| sP0(sK1,sK2)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| ~ one_sorted_str(sK1) )
| ~ spl23_22 ),
inference(resolution,[],[f441,f181]) ).
fof(f181,plain,
! [X2,X0,X1,X4] :
( ~ element(sK21(X0,X1,X4),powerset(the_carrier(X0)))
| sK22(X0,X1,X4) = subset_complement(the_carrier(X0),sK21(X0,X1,X4))
| ~ in(X4,sK18(X0,X1,X2))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(equality_resolution,[],[f168]) ).
fof(f168,plain,
! [X2,X0,X1,X4,X12] :
( subset_complement(the_carrier(X0),X12) = sK22(X0,X1,X4)
| sK21(X0,X1,X4) != X12
| ~ element(X12,powerset(the_carrier(X0)))
| ~ in(X4,sK18(X0,X1,X2))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ! [X2] :
( ! [X4] :
( ( in(X4,sK18(X0,X1,X2))
| ! [X5] :
( ! [X6,X7] :
( ( subset_complement(the_carrier(X0),sK19(X0,X6,X7)) != X7
& sK19(X0,X6,X7) = X6
& element(sK19(X0,X6,X7),powerset(the_carrier(X0))) )
| ~ in(X6,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) )
& ( ( ! [X12] :
( subset_complement(the_carrier(X0),X12) = sK22(X0,X1,X4)
| sK21(X0,X1,X4) != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(sK21(X0,X1,X4),complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(sK21(X0,X1,X4),sK22(X0,X1,X4)) = X4
& sK20(X0,X1,X2,X4) = X4
& in(sK20(X0,X1,X2,X4),cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) )
| ~ in(X4,sK18(X0,X1,X2)) ) )
| sP0(X0,X1) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21,sK22])],[f99,f103,f102,f101,f100]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ! [X6,X7] :
( ? [X8] :
( subset_complement(the_carrier(X0),X8) != X7
& X6 = X8
& element(X8,powerset(the_carrier(X0))) )
| ~ in(X6,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) )
& ( ? [X9] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X10,X11) = X4 )
& X4 = X9
& in(X9,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) )
| ~ in(X4,X3) ) )
=> ! [X4] :
( ( in(X4,sK18(X0,X1,X2))
| ! [X5] :
( ! [X6,X7] :
( ? [X8] :
( subset_complement(the_carrier(X0),X8) != X7
& X6 = X8
& element(X8,powerset(the_carrier(X0))) )
| ~ in(X6,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) )
& ( ? [X9] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X10,X11) = X4 )
& X4 = X9
& in(X9,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) )
| ~ in(X4,sK18(X0,X1,X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X6,X7] :
( ? [X8] :
( subset_complement(the_carrier(X0),X8) != X7
& X6 = X8
& element(X8,powerset(the_carrier(X0))) )
=> ( subset_complement(the_carrier(X0),sK19(X0,X6,X7)) != X7
& sK19(X0,X6,X7) = X6
& element(sK19(X0,X6,X7),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1,X2,X4] :
( ? [X9] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X10,X11) = X4 )
& X4 = X9
& in(X9,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) )
=> ( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X10,X11) = X4 )
& sK20(X0,X1,X2,X4) = X4
& in(sK20(X0,X1,X2,X4),cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0,X1,X4] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X10,X11) = X4 )
=> ( ! [X12] :
( subset_complement(the_carrier(X0),X12) = sK22(X0,X1,X4)
| sK21(X0,X1,X4) != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(sK21(X0,X1,X4),complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(sK21(X0,X1,X4),sK22(X0,X1,X4)) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
! [X0,X1] :
( ! [X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ! [X6,X7] :
( ? [X8] :
( subset_complement(the_carrier(X0),X8) != X7
& X6 = X8
& element(X8,powerset(the_carrier(X0))) )
| ~ in(X6,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) )
& ( ? [X9] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X10,X11) = X4 )
& X4 = X9
& in(X9,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) )
| ~ in(X4,X3) ) )
| sP0(X0,X1) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(rectify,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ! [X2] :
( ? [X12] :
! [X13] :
( ( in(X13,X12)
| ! [X14] :
( ! [X15,X16] :
( ? [X17] :
( subset_complement(the_carrier(X0),X17) != X16
& X15 = X17
& element(X17,powerset(the_carrier(X0))) )
| ~ in(X15,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X15,X16) != X13 )
| X13 != X14
| ~ in(X14,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) )
& ( ? [X14] :
( ? [X15,X16] :
( ! [X17] :
( subset_complement(the_carrier(X0),X17) = X16
| X15 != X17
| ~ element(X17,powerset(the_carrier(X0))) )
& in(X15,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) )
| ~ in(X13,X12) ) )
| sP0(X0,X1) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ! [X2] :
( ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( ? [X15,X16] :
( ! [X17] :
( subset_complement(the_carrier(X0),X17) = X16
| X15 != X17
| ~ element(X17,powerset(the_carrier(X0))) )
& in(X15,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) )
| sP0(X0,X1) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(definition_folding,[],[f74,f75]) ).
fof(f75,plain,
! [X0,X1] :
( ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( ! [X8] :
( subset_complement(the_carrier(X0),X8) = X7
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(X6,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X9,X10] :
( ! [X11] :
( subset_complement(the_carrier(X0),X11) = X10
| X9 != X11
| ~ element(X11,powerset(the_carrier(X0))) )
& in(X9,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X9,X10) = X4 )
& X3 = X4 )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f74,plain,
! [X0,X1] :
( ! [X2] :
( ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( ? [X15,X16] :
( ! [X17] :
( subset_complement(the_carrier(X0),X17) = X16
| X15 != X17
| ~ element(X17,powerset(the_carrier(X0))) )
& in(X15,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) )
| ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( ! [X8] :
( subset_complement(the_carrier(X0),X8) = X7
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(X6,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X9,X10] :
( ! [X11] :
( subset_complement(the_carrier(X0),X11) = X10
| X9 != X11
| ~ element(X11,powerset(the_carrier(X0))) )
& in(X9,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X9,X10) = X4 )
& X3 = X4 ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ! [X2] :
( ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( ? [X15,X16] :
( ! [X17] :
( subset_complement(the_carrier(X0),X17) = X16
| X15 != X17
| ~ element(X17,powerset(the_carrier(X0))) )
& in(X15,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) )
| ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( ! [X8] :
( subset_complement(the_carrier(X0),X8) = X7
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(X6,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X9,X10] :
( ! [X11] :
( subset_complement(the_carrier(X0),X11) = X10
| X9 != X11
| ~ element(X11,powerset(the_carrier(X0))) )
& in(X9,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X9,X10) = X4 )
& X3 = X4 ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) )
=> ! [X2] :
( ! [X3,X4,X5] :
( ( ? [X6,X7] :
( ! [X8] :
( element(X8,powerset(the_carrier(X0)))
=> ( X6 = X8
=> subset_complement(the_carrier(X0),X8) = X7 ) )
& in(X6,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X9,X10] :
( ! [X11] :
( element(X11,powerset(the_carrier(X0)))
=> ( X9 = X11
=> subset_complement(the_carrier(X0),X11) = X10 ) )
& in(X9,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X9,X10) = X4 )
& X3 = X4 )
=> X4 = X5 )
=> ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( ? [X15,X16] :
( ! [X17] :
( element(X17,powerset(the_carrier(X0)))
=> ( X15 = X17
=> subset_complement(the_carrier(X0),X17) = X16 ) )
& in(X15,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) ) ) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) )
=> ! [X2] :
( ! [X3,X4,X5] :
( ( ? [X9,X10] :
( ! [X11] :
( element(X11,powerset(the_carrier(X0)))
=> ( X9 = X11
=> subset_complement(the_carrier(X0),X11) = X10 ) )
& in(X9,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X9,X10) = X5 )
& X3 = X5
& ? [X6,X7] :
( ! [X8] :
( element(X8,powerset(the_carrier(X0)))
=> ( X6 = X8
=> subset_complement(the_carrier(X0),X8) = X7 ) )
& in(X6,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X6,X7) = X4 )
& X3 = X4 )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( ? [X12,X13] :
( ! [X14] :
( element(X14,powerset(the_carrier(X0)))
=> ( X12 = X14
=> subset_complement(the_carrier(X0),X14) = X13 ) )
& in(X12,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X12,X13) = X4 )
& X4 = X5
& in(X5,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.kl8RzQtopJ/Vampire---4.8_10303',s1_tarski__e4_7_1__tops_2__2) ).
fof(f441,plain,
( element(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),powerset(the_carrier(sK1)))
| ~ spl23_22 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f509,plain,
( ~ spl23_19
| ~ spl23_23
| spl23_26
| ~ spl23_18
| ~ spl23_27 ),
inference(avatar_split_clause,[],[f508,f461,f390,f457,f444,f395]) ).
fof(f395,plain,
( spl23_19
<=> in(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),complements_of_subsets(the_carrier(sK1),sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_19])]) ).
fof(f457,plain,
( spl23_26
<=> ! [X0] :
( sK4(X0) != sK4(sK18(sK1,sK2,sK3))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_26])]) ).
fof(f390,plain,
( spl23_18
<=> sK4(sK18(sK1,sK2,sK3)) = ordered_pair(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_18])]) ).
fof(f461,plain,
( spl23_27
<=> sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))) = sK5(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_27])]) ).
fof(f508,plain,
( ! [X0] :
( sK4(X0) != sK4(sK18(sK1,sK2,sK3))
| sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3))) != subset_complement(the_carrier(sK1),sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))))
| ~ in(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),complements_of_subsets(the_carrier(sK1),sK2))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ in(sK4(X0),X0) )
| ~ spl23_18
| ~ spl23_27 ),
inference(forward_demodulation,[],[f503,f392]) ).
fof(f392,plain,
( sK4(sK18(sK1,sK2,sK3)) = ordered_pair(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3))))
| ~ spl23_18 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f503,plain,
( ! [X0] :
( sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3))) != subset_complement(the_carrier(sK1),sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))))
| ~ in(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),complements_of_subsets(the_carrier(sK1),sK2))
| sK4(X0) != ordered_pair(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3))))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ in(sK4(X0),X0) )
| ~ spl23_27 ),
inference(superposition,[],[f113,f463]) ).
fof(f463,plain,
( sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))) = sK5(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3))))
| ~ spl23_27 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f113,plain,
! [X3,X6,X5] :
( subset_complement(the_carrier(sK1),sK5(X5,X6)) != X6
| ~ in(X5,complements_of_subsets(the_carrier(sK1),sK2))
| ordered_pair(X5,X6) != sK4(X3)
| ~ in(sK4(X3),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f487,plain,
( spl23_22
| ~ spl23_25
| ~ spl23_27 ),
inference(avatar_split_clause,[],[f486,f461,f453,f439]) ).
fof(f453,plain,
( spl23_25
<=> element(sK5(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3)))),powerset(the_carrier(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_25])]) ).
fof(f486,plain,
( element(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),powerset(the_carrier(sK1)))
| ~ spl23_25
| ~ spl23_27 ),
inference(forward_demodulation,[],[f455,f463]) ).
fof(f455,plain,
( element(sK5(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3)))),powerset(the_carrier(sK1)))
| ~ spl23_25 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f485,plain,
( ~ spl23_17
| ~ spl23_20
| spl23_29 ),
inference(avatar_contradiction_clause,[],[f483]) ).
fof(f483,plain,
( $false
| ~ spl23_17
| ~ spl23_20
| spl23_29 ),
inference(resolution,[],[f474,f404]) ).
fof(f404,plain,
( in(sK4(sK18(sK1,sK2,sK3)),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ spl23_17
| ~ spl23_20 ),
inference(forward_demodulation,[],[f387,f402]) ).
fof(f402,plain,
( sK4(sK18(sK1,sK2,sK3)) = sK20(sK1,sK2,sK3,sK4(sK18(sK1,sK2,sK3)))
| ~ spl23_20 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f400,plain,
( spl23_20
<=> sK4(sK18(sK1,sK2,sK3)) = sK20(sK1,sK2,sK3,sK4(sK18(sK1,sK2,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_20])]) ).
fof(f387,plain,
( in(sK20(sK1,sK2,sK3,sK4(sK18(sK1,sK2,sK3))),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ spl23_17 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f385,plain,
( spl23_17
<=> in(sK20(sK1,sK2,sK3,sK4(sK18(sK1,sK2,sK3))),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_17])]) ).
fof(f474,plain,
( ~ in(sK4(sK18(sK1,sK2,sK3)),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| spl23_29 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f472,plain,
( spl23_29
<=> in(sK4(sK18(sK1,sK2,sK3)),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_29])]) ).
fof(f482,plain,
( ~ spl23_12
| spl23_30 ),
inference(avatar_contradiction_clause,[],[f480]) ).
fof(f480,plain,
( $false
| ~ spl23_12
| spl23_30 ),
inference(resolution,[],[f478,f360]) ).
fof(f478,plain,
( ~ in(sK4(sK18(sK1,sK2,sK3)),sK18(sK1,sK2,sK3))
| spl23_30 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f476,plain,
( spl23_30
<=> in(sK4(sK18(sK1,sK2,sK3)),sK18(sK1,sK2,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_30])]) ).
fof(f479,plain,
( ~ spl23_29
| ~ spl23_30
| ~ spl23_26 ),
inference(avatar_split_clause,[],[f470,f457,f476,f472]) ).
fof(f470,plain,
( ~ in(sK4(sK18(sK1,sK2,sK3)),sK18(sK1,sK2,sK3))
| ~ in(sK4(sK18(sK1,sK2,sK3)),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ spl23_26 ),
inference(equality_resolution,[],[f458]) ).
fof(f458,plain,
( ! [X0] :
( sK4(X0) != sK4(sK18(sK1,sK2,sK3))
| ~ in(sK4(X0),X0)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3)) )
| ~ spl23_26 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f464,plain,
( spl23_27
| ~ spl23_19
| spl23_26
| ~ spl23_18 ),
inference(avatar_split_clause,[],[f434,f390,f457,f395,f461]) ).
fof(f434,plain,
( ! [X0] :
( sK4(X0) != sK4(sK18(sK1,sK2,sK3))
| ~ in(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),complements_of_subsets(the_carrier(sK1),sK2))
| sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))) = sK5(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3))))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ in(sK4(X0),X0) )
| ~ spl23_18 ),
inference(superposition,[],[f112,f392]) ).
fof(f112,plain,
! [X3,X6,X5] :
( ordered_pair(X5,X6) != sK4(X3)
| ~ in(X5,complements_of_subsets(the_carrier(sK1),sK2))
| sK5(X5,X6) = X5
| ~ in(sK4(X3),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f459,plain,
( spl23_25
| ~ spl23_19
| spl23_26
| ~ spl23_18 ),
inference(avatar_split_clause,[],[f433,f390,f457,f395,f453]) ).
fof(f433,plain,
( ! [X0] :
( sK4(X0) != sK4(sK18(sK1,sK2,sK3))
| ~ in(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),complements_of_subsets(the_carrier(sK1),sK2))
| element(sK5(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3)))),powerset(the_carrier(sK1)))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ in(sK4(X0),X0) )
| ~ spl23_18 ),
inference(superposition,[],[f111,f392]) ).
fof(f111,plain,
! [X3,X6,X5] :
( ordered_pair(X5,X6) != sK4(X3)
| ~ in(X5,complements_of_subsets(the_carrier(sK1),sK2))
| element(sK5(X5,X6),powerset(the_carrier(sK1)))
| ~ in(sK4(X3),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| ~ in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f403,plain,
( ~ spl23_1
| ~ spl23_3
| spl23_4
| spl23_20
| ~ spl23_12 ),
inference(avatar_split_clause,[],[f382,f344,f400,f251,f247,f224]) ).
fof(f382,plain,
( sK4(sK18(sK1,sK2,sK3)) = sK20(sK1,sK2,sK3,sK4(sK18(sK1,sK2,sK3)))
| sP0(sK1,sK2)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| ~ one_sorted_str(sK1)
| ~ spl23_12 ),
inference(resolution,[],[f360,f165]) ).
fof(f165,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK18(X0,X1,X2))
| sK20(X0,X1,X2,X4) = X4
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f398,plain,
( ~ spl23_1
| ~ spl23_3
| spl23_4
| spl23_19
| ~ spl23_12 ),
inference(avatar_split_clause,[],[f381,f344,f395,f251,f247,f224]) ).
fof(f381,plain,
( in(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),complements_of_subsets(the_carrier(sK1),sK2))
| sP0(sK1,sK2)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| ~ one_sorted_str(sK1)
| ~ spl23_12 ),
inference(resolution,[],[f360,f167]) ).
fof(f167,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK18(X0,X1,X2))
| in(sK21(X0,X1,X4),complements_of_subsets(the_carrier(X0),X1))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f393,plain,
( ~ spl23_1
| ~ spl23_3
| spl23_4
| spl23_18
| ~ spl23_12 ),
inference(avatar_split_clause,[],[f380,f344,f390,f251,f247,f224]) ).
fof(f380,plain,
( sK4(sK18(sK1,sK2,sK3)) = ordered_pair(sK21(sK1,sK2,sK4(sK18(sK1,sK2,sK3))),sK22(sK1,sK2,sK4(sK18(sK1,sK2,sK3))))
| sP0(sK1,sK2)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| ~ one_sorted_str(sK1)
| ~ spl23_12 ),
inference(resolution,[],[f360,f166]) ).
fof(f166,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK18(X0,X1,X2))
| ordered_pair(sK21(X0,X1,X4),sK22(X0,X1,X4)) = X4
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f388,plain,
( ~ spl23_1
| ~ spl23_3
| spl23_4
| spl23_17
| ~ spl23_12 ),
inference(avatar_split_clause,[],[f379,f344,f385,f251,f247,f224]) ).
fof(f379,plain,
( in(sK20(sK1,sK2,sK3,sK4(sK18(sK1,sK2,sK3))),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),sK3))
| sP0(sK1,sK2)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| ~ one_sorted_str(sK1)
| ~ spl23_12 ),
inference(resolution,[],[f360,f164]) ).
fof(f164,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK18(X0,X1,X2))
| in(sK20(X0,X1,X2,X4),cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f378,plain,
spl23_1,
inference(avatar_contradiction_clause,[],[f377]) ).
fof(f377,plain,
( $false
| spl23_1 ),
inference(resolution,[],[f226,f105]) ).
fof(f105,plain,
one_sorted_str(sK1),
inference(cnf_transformation,[],[f85]) ).
fof(f226,plain,
( ~ one_sorted_str(sK1)
| spl23_1 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f346,plain,
( ~ spl23_3
| spl23_4
| spl23_12
| ~ spl23_11 ),
inference(avatar_split_clause,[],[f342,f337,f344,f251,f247]) ).
fof(f337,plain,
( spl23_11
<=> ! [X0,X3,X2,X1] :
( in(sK4(X0),X0)
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X2))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X2),X3))
| sP0(sK1,X2)
| ~ element(X2,powerset(powerset(the_carrier(sK1))))
| in(sK4(X0),sK18(sK1,X2,X3))
| in(sK4(X0),sK18(sK1,sK2,X1))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_11])]) ).
fof(f342,plain,
( ! [X2,X0,X1] :
( in(sK4(X0),X0)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| sP0(sK1,sK2)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| in(sK4(X0),sK18(sK1,sK2,X1))
| in(sK4(X0),sK18(sK1,sK2,X2))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X2)) )
| ~ spl23_11 ),
inference(duplicate_literal_removal,[],[f340]) ).
fof(f340,plain,
( ! [X2,X0,X1] :
( in(sK4(X0),X0)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| sP0(sK1,sK2)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| in(sK4(X0),sK18(sK1,sK2,X1))
| in(sK4(X0),sK18(sK1,sK2,X2))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X2))
| in(sK4(X0),X0) )
| ~ spl23_11 ),
inference(resolution,[],[f338,f109]) ).
fof(f109,plain,
! [X3] :
( in(sK6(X3),complements_of_subsets(the_carrier(sK1),sK2))
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f338,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X2))
| in(sK4(X0),X0)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X2),X3))
| sP0(sK1,X2)
| ~ element(X2,powerset(powerset(the_carrier(sK1))))
| in(sK4(X0),sK18(sK1,X2,X3))
| in(sK4(X0),sK18(sK1,sK2,X1))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1)) )
| ~ spl23_11 ),
inference(avatar_component_clause,[],[f337]) ).
fof(f339,plain,
( ~ spl23_3
| spl23_4
| spl23_11
| ~ spl23_2
| ~ spl23_6 ),
inference(avatar_split_clause,[],[f335,f275,f228,f337,f251,f247]) ).
fof(f228,plain,
( spl23_2
<=> ! [X2,X3,X4,X0,X5,X1] :
( subset_complement(the_carrier(sK1),X0) != X1
| ~ element(X4,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X4)
| ~ in(ordered_pair(X0,X1),cartesian_product2(complements_of_subsets(the_carrier(sK1),X4),X5))
| ~ in(X0,complements_of_subsets(the_carrier(sK1),X4))
| in(ordered_pair(X0,X1),sK18(sK1,X4,X5))
| in(ordered_pair(X0,X1),sK18(sK1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(complements_of_subsets(the_carrier(sK1),X2),X3))
| ~ in(X0,complements_of_subsets(the_carrier(sK1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_2])]) ).
fof(f275,plain,
( spl23_6
<=> ! [X2,X0,X1] :
( in(sK4(X0),X0)
| in(sK4(X0),sK18(sK1,sK2,X2))
| element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),sK18(sK1,sK2,X1))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X2))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_6])]) ).
fof(f335,plain,
( ! [X2,X3,X0,X1] :
( in(sK4(X0),X0)
| sP0(sK1,sK2)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),sK18(sK1,sK2,X1))
| in(sK4(X0),sK18(sK1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X2)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X2),X3))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X2))
| ~ element(sK2,powerset(powerset(the_carrier(sK1)))) )
| ~ spl23_2
| ~ spl23_6 ),
inference(duplicate_literal_removal,[],[f333]) ).
fof(f333,plain,
( ! [X2,X3,X0,X1] :
( in(sK4(X0),X0)
| sP0(sK1,sK2)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),sK18(sK1,sK2,X1))
| in(sK4(X0),sK18(sK1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X2)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X2),X3))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X2))
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| in(sK4(X0),X0) )
| ~ spl23_2
| ~ spl23_6 ),
inference(resolution,[],[f289,f109]) ).
fof(f289,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X1))
| in(sK4(X0),X0)
| sP0(sK1,X1)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X1),X2))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),sK18(sK1,X1,X2))
| in(sK4(X0),sK18(sK1,X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X3)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X3),X4))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X3))
| ~ element(X1,powerset(powerset(the_carrier(sK1)))) )
| ~ spl23_2
| ~ spl23_6 ),
inference(duplicate_literal_removal,[],[f286]) ).
fof(f286,plain,
( ! [X2,X3,X0,X1,X4] :
( in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),X0)
| sP0(sK1,X1)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X1),X2))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X1))
| in(sK4(X0),sK18(sK1,X1,X2))
| in(sK4(X0),sK18(sK1,X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X3)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X3),X4))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X3))
| in(sK4(X0),X0)
| ~ element(X1,powerset(powerset(the_carrier(sK1)))) )
| ~ spl23_2
| ~ spl23_6 ),
inference(resolution,[],[f284,f235]) ).
fof(f235,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ element(sK6(X0),powerset(the_carrier(sK1)))
| sP0(sK1,X1)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X1),X2))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X1))
| in(sK4(X0),sK18(sK1,X1,X2))
| in(sK4(X0),sK18(sK1,X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X3)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X3),X4))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X3))
| in(sK4(X0),X0)
| ~ element(X1,powerset(powerset(the_carrier(sK1)))) )
| ~ spl23_2 ),
inference(trivial_inequality_removal,[],[f234]) ).
fof(f234,plain,
( ! [X2,X3,X0,X1,X4] :
( sK7(X0) != sK7(X0)
| ~ element(X1,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X1)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X1),X2))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X1))
| in(sK4(X0),sK18(sK1,X1,X2))
| in(sK4(X0),sK18(sK1,X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X3)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X3),X4))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X3))
| in(sK4(X0),X0)
| ~ element(sK6(X0),powerset(the_carrier(sK1))) )
| ~ spl23_2 ),
inference(duplicate_literal_removal,[],[f233]) ).
fof(f233,plain,
( ! [X2,X3,X0,X1,X4] :
( sK7(X0) != sK7(X0)
| ~ element(X1,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X1)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X1),X2))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X1))
| in(sK4(X0),sK18(sK1,X1,X2))
| in(sK4(X0),sK18(sK1,X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X3)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X3),X4))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X3))
| in(sK4(X0),X0)
| ~ element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),X0) )
| ~ spl23_2 ),
inference(superposition,[],[f231,f172]) ).
fof(f172,plain,
! [X3] :
( sK7(X3) = subset_complement(the_carrier(sK1),sK6(X3))
| ~ element(sK6(X3),powerset(the_carrier(sK1)))
| in(sK4(X3),X3) ),
inference(equality_resolution,[],[f110]) ).
fof(f110,plain,
! [X3,X10] :
( subset_complement(the_carrier(sK1),X10) = sK7(X3)
| sK6(X3) != X10
| ~ element(X10,powerset(the_carrier(sK1)))
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f231,plain,
( ! [X2,X3,X0,X1,X4] :
( sK7(X0) != subset_complement(the_carrier(sK1),sK6(X0))
| ~ element(X1,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X1)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X1),X2))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X1))
| in(sK4(X0),sK18(sK1,X1,X2))
| in(sK4(X0),sK18(sK1,X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X3)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X3),X4))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X3))
| in(sK4(X0),X0) )
| ~ spl23_2 ),
inference(superposition,[],[f229,f108]) ).
fof(f108,plain,
! [X3] :
( sK4(X3) = ordered_pair(sK6(X3),sK7(X3))
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f85]) ).
fof(f229,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(complements_of_subsets(the_carrier(sK1),X4),X5))
| ~ element(X4,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X4)
| subset_complement(the_carrier(sK1),X0) != X1
| ~ in(X0,complements_of_subsets(the_carrier(sK1),X4))
| in(ordered_pair(X0,X1),sK18(sK1,X4,X5))
| in(ordered_pair(X0,X1),sK18(sK1,X2,X3))
| ~ element(X2,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(complements_of_subsets(the_carrier(sK1),X2),X3))
| ~ in(X0,complements_of_subsets(the_carrier(sK1),X2)) )
| ~ spl23_2 ),
inference(avatar_component_clause,[],[f228]) ).
fof(f284,plain,
( ! [X0] :
( element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),X0) )
| ~ spl23_6 ),
inference(duplicate_literal_removal,[],[f281]) ).
fof(f281,plain,
( ! [X0] :
( element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),X0)
| in(sK4(X0),X0) )
| ~ spl23_6 ),
inference(resolution,[],[f280,f107]) ).
fof(f280,plain,
( ! [X0,X1] :
( ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| in(sK4(X0),sK18(sK1,sK2,X1))
| in(sK4(X0),X0) )
| ~ spl23_6 ),
inference(duplicate_literal_removal,[],[f278]) ).
fof(f278,plain,
( ! [X0,X1] :
( in(sK4(X0),sK18(sK1,sK2,X1))
| element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),sK18(sK1,sK2,sK3))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| in(sK4(X0),X0)
| in(sK4(X0),X0) )
| ~ spl23_6 ),
inference(resolution,[],[f276,f107]) ).
fof(f276,plain,
( ! [X2,X0,X1] :
( ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| in(sK4(X0),sK18(sK1,sK2,X2))
| element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),sK18(sK1,sK2,X1))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X2))
| in(sK4(X0),X0) )
| ~ spl23_6 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f277,plain,
( spl23_4
| ~ spl23_3
| spl23_6
| ~ spl23_5 ),
inference(avatar_split_clause,[],[f273,f255,f275,f247,f251]) ).
fof(f255,plain,
( spl23_5
<=> ! [X0,X3,X2,X1] :
( ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| in(sK4(X0),X0)
| ~ element(X2,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X2)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X2),X3))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X2))
| in(sK4(X0),sK18(sK1,X2,X3))
| element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),sK18(sK1,sK2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl23_5])]) ).
fof(f273,plain,
( ! [X2,X0,X1] :
( in(sK4(X0),X0)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,sK2)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X2))
| in(sK4(X0),sK18(sK1,sK2,X1))
| element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),sK18(sK1,sK2,X2)) )
| ~ spl23_5 ),
inference(duplicate_literal_removal,[],[f271]) ).
fof(f271,plain,
( ! [X2,X0,X1] :
( in(sK4(X0),X0)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,sK2)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X2))
| in(sK4(X0),sK18(sK1,sK2,X1))
| element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),sK18(sK1,sK2,X2))
| in(sK4(X0),X0) )
| ~ spl23_5 ),
inference(resolution,[],[f256,f109]) ).
fof(f256,plain,
( ! [X2,X3,X0,X1] :
( ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X2))
| in(sK4(X0),X0)
| ~ element(X2,powerset(powerset(the_carrier(sK1))))
| sP0(sK1,X2)
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X2),X3))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| in(sK4(X0),sK18(sK1,X2,X3))
| element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),sK18(sK1,sK2,X1)) )
| ~ spl23_5 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f270,plain,
( ~ spl23_4
| ~ spl23_4 ),
inference(avatar_split_clause,[],[f269,f251,f251]) ).
fof(f269,plain,
( ~ sP0(sK1,sK2)
| ~ spl23_4 ),
inference(trivial_inequality_removal,[],[f268]) ).
fof(f268,plain,
( sK12(sK1,sK2) != sK12(sK1,sK2)
| ~ sP0(sK1,sK2)
| ~ spl23_4 ),
inference(superposition,[],[f163,f266]) ).
fof(f266,plain,
( sK13(sK1,sK2) = sK12(sK1,sK2)
| ~ spl23_4 ),
inference(superposition,[],[f265,f264]) ).
fof(f264,plain,
( sK13(sK1,sK2) = sK11(sK1,sK2)
| ~ spl23_4 ),
inference(resolution,[],[f253,f159]) ).
fof(f159,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK11(X0,X1) = sK13(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( ( sK12(X0,X1) != sK13(X0,X1)
& ! [X7] :
( subset_complement(the_carrier(X0),X7) = sK15(X0,X1)
| sK14(X0,X1) != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(sK14(X0,X1),complements_of_subsets(the_carrier(X0),X1))
& sK13(X0,X1) = ordered_pair(sK14(X0,X1),sK15(X0,X1))
& sK11(X0,X1) = sK13(X0,X1)
& ! [X10] :
( subset_complement(the_carrier(X0),X10) = sK17(X0,X1)
| sK16(X0,X1) != X10
| ~ element(X10,powerset(the_carrier(X0))) )
& in(sK16(X0,X1),complements_of_subsets(the_carrier(X0),X1))
& sK12(X0,X1) = ordered_pair(sK16(X0,X1),sK17(X0,X1))
& sK11(X0,X1) = sK12(X0,X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15,sK16,sK17])],[f93,f96,f95,f94]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5,X6] :
( ! [X7] :
( subset_complement(the_carrier(X0),X7) = X6
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(X5,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& ? [X8,X9] :
( ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) )
& in(X8,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X8,X9) = X3 )
& X2 = X3 )
=> ( sK12(X0,X1) != sK13(X0,X1)
& ? [X6,X5] :
( ! [X7] :
( subset_complement(the_carrier(X0),X7) = X6
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(X5,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X5,X6) = sK13(X0,X1) )
& sK11(X0,X1) = sK13(X0,X1)
& ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) )
& in(X8,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X8,X9) = sK12(X0,X1) )
& sK11(X0,X1) = sK12(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X0,X1] :
( ? [X6,X5] :
( ! [X7] :
( subset_complement(the_carrier(X0),X7) = X6
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(X5,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X5,X6) = sK13(X0,X1) )
=> ( ! [X7] :
( subset_complement(the_carrier(X0),X7) = sK15(X0,X1)
| sK14(X0,X1) != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(sK14(X0,X1),complements_of_subsets(the_carrier(X0),X1))
& sK13(X0,X1) = ordered_pair(sK14(X0,X1),sK15(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0,X1] :
( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) )
& in(X8,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X8,X9) = sK12(X0,X1) )
=> ( ! [X10] :
( subset_complement(the_carrier(X0),X10) = sK17(X0,X1)
| sK16(X0,X1) != X10
| ~ element(X10,powerset(the_carrier(X0))) )
& in(sK16(X0,X1),complements_of_subsets(the_carrier(X0),X1))
& sK12(X0,X1) = ordered_pair(sK16(X0,X1),sK17(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& ? [X5,X6] :
( ! [X7] :
( subset_complement(the_carrier(X0),X7) = X6
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(X5,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X5,X6) = X4 )
& X2 = X4
& ? [X8,X9] :
( ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) )
& in(X8,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X8,X9) = X3 )
& X2 = X3 )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f92]) ).
fof(f92,plain,
! [X0,X1] :
( ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( ! [X8] :
( subset_complement(the_carrier(X0),X8) = X7
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(X6,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X9,X10] :
( ! [X11] :
( subset_complement(the_carrier(X0),X11) = X10
| X9 != X11
| ~ element(X11,powerset(the_carrier(X0))) )
& in(X9,complements_of_subsets(the_carrier(X0),X1))
& ordered_pair(X9,X10) = X4 )
& X3 = X4 )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f75]) ).
fof(f253,plain,
( sP0(sK1,sK2)
| ~ spl23_4 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f265,plain,
( sK12(sK1,sK2) = sK11(sK1,sK2)
| ~ spl23_4 ),
inference(resolution,[],[f253,f155]) ).
fof(f155,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK11(X0,X1) = sK12(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f163,plain,
! [X0,X1] :
( sK12(X0,X1) != sK13(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f97]) ).
fof(f259,plain,
spl23_3,
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f258,plain,
( $false
| spl23_3 ),
inference(resolution,[],[f249,f106]) ).
fof(f106,plain,
element(sK2,powerset(powerset(the_carrier(sK1)))),
inference(cnf_transformation,[],[f85]) ).
fof(f249,plain,
( ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| spl23_3 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f257,plain,
( ~ spl23_3
| spl23_4
| spl23_5 ),
inference(avatar_split_clause,[],[f245,f255,f251,f247]) ).
fof(f245,plain,
! [X2,X3,X0,X1] :
( ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| in(sK4(X0),sK18(sK1,sK2,X1))
| sP0(sK1,sK2)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),sK18(sK1,X2,X3))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X2))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X2),X3))
| sP0(sK1,X2)
| ~ element(X2,powerset(powerset(the_carrier(sK1))))
| in(sK4(X0),X0) ),
inference(duplicate_literal_removal,[],[f243]) ).
fof(f243,plain,
! [X2,X3,X0,X1] :
( ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),sK2),X1))
| in(sK4(X0),sK18(sK1,sK2,X1))
| sP0(sK1,sK2)
| ~ element(sK2,powerset(powerset(the_carrier(sK1))))
| element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),sK18(sK1,X2,X3))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X2))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X2),X3))
| sP0(sK1,X2)
| ~ element(X2,powerset(powerset(the_carrier(sK1))))
| in(sK4(X0),X0)
| in(sK4(X0),X0) ),
inference(resolution,[],[f241,f109]) ).
fof(f241,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X1))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X1),X2))
| in(sK4(X0),sK18(sK1,X1,X2))
| sP0(sK1,X1)
| ~ element(X1,powerset(powerset(the_carrier(sK1))))
| element(sK6(X0),powerset(the_carrier(sK1)))
| in(sK4(X0),sK18(sK1,X3,X4))
| ~ in(sK6(X0),complements_of_subsets(the_carrier(sK1),X3))
| ~ in(sK4(X0),cartesian_product2(complements_of_subsets(the_carrier(sK1),X3),X4))
| sP0(sK1,X3)
| ~ element(X3,powerset(powerset(the_carrier(sK1))))
| in(sK4(X0),X0) ),
inference(superposition,[],[f240,f108]) ).
fof(f240,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(complements_of_subsets(the_carrier(sK1),X2),X3))
| ~ in(X0,complements_of_subsets(the_carrier(sK1),X2))
| in(ordered_pair(X0,X1),sK18(sK1,X2,X3))
| sP0(sK1,X2)
| ~ element(X2,powerset(powerset(the_carrier(sK1))))
| element(X0,powerset(the_carrier(sK1)))
| in(ordered_pair(X0,X1),sK18(sK1,X4,X5))
| ~ in(X0,complements_of_subsets(the_carrier(sK1),X4))
| ~ in(ordered_pair(X0,X1),cartesian_product2(complements_of_subsets(the_carrier(sK1),X4),X5))
| sP0(sK1,X4)
| ~ element(X4,powerset(powerset(the_carrier(sK1)))) ),
inference(resolution,[],[f220,f105]) ).
fof(f220,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ one_sorted_str(X0)
| in(ordered_pair(X1,X2),sK18(X0,X3,X4))
| ~ in(X1,complements_of_subsets(the_carrier(X0),X3))
| ~ in(ordered_pair(X1,X2),cartesian_product2(complements_of_subsets(the_carrier(X0),X3),X4))
| sP0(X0,X3)
| ~ element(X3,powerset(powerset(the_carrier(X0))))
| element(X1,powerset(the_carrier(X0)))
| in(ordered_pair(X1,X2),sK18(X0,X5,X6))
| ~ in(X1,complements_of_subsets(the_carrier(X0),X5))
| ~ in(ordered_pair(X1,X2),cartesian_product2(complements_of_subsets(the_carrier(X0),X5),X6))
| sP0(X0,X5)
| ~ element(X5,powerset(powerset(the_carrier(X0)))) ),
inference(duplicate_literal_removal,[],[f219]) ).
fof(f219,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( element(X1,powerset(the_carrier(X0)))
| in(ordered_pair(X1,X2),sK18(X0,X3,X4))
| ~ in(X1,complements_of_subsets(the_carrier(X0),X3))
| ~ in(ordered_pair(X1,X2),cartesian_product2(complements_of_subsets(the_carrier(X0),X3),X4))
| sP0(X0,X3)
| ~ element(X3,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0)
| in(ordered_pair(X1,X2),sK18(X0,X5,X6))
| ~ in(X1,complements_of_subsets(the_carrier(X0),X5))
| ~ in(ordered_pair(X1,X2),cartesian_product2(complements_of_subsets(the_carrier(X0),X5),X6))
| sP0(X0,X5)
| ~ element(X5,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(superposition,[],[f180,f178]) ).
fof(f178,plain,
! [X2,X0,X1,X6,X7] :
( sK19(X0,X6,X7) = X6
| in(ordered_pair(X6,X7),sK18(X0,X1,X2))
| ~ in(X6,complements_of_subsets(the_carrier(X0),X1))
| ~ in(ordered_pair(X6,X7),cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(equality_resolution,[],[f177]) ).
fof(f177,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(ordered_pair(X6,X7),sK18(X0,X1,X2))
| sK19(X0,X6,X7) = X6
| ~ in(X6,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X6,X7) != X5
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(equality_resolution,[],[f170]) ).
fof(f170,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK18(X0,X1,X2))
| sK19(X0,X6,X7) = X6
| ~ in(X6,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f180,plain,
! [X2,X0,X1,X6,X7] :
( element(sK19(X0,X6,X7),powerset(the_carrier(X0)))
| in(ordered_pair(X6,X7),sK18(X0,X1,X2))
| ~ in(X6,complements_of_subsets(the_carrier(X0),X1))
| ~ in(ordered_pair(X6,X7),cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(equality_resolution,[],[f179]) ).
fof(f179,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(ordered_pair(X6,X7),sK18(X0,X1,X2))
| element(sK19(X0,X6,X7),powerset(the_carrier(X0)))
| ~ in(X6,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X6,X7) != X5
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(equality_resolution,[],[f169]) ).
fof(f169,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK18(X0,X1,X2))
| element(sK19(X0,X6,X7),powerset(the_carrier(X0)))
| ~ in(X6,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f230,plain,
( ~ spl23_1
| spl23_2 ),
inference(avatar_split_clause,[],[f222,f228,f224]) ).
fof(f222,plain,
! [X2,X3,X0,X1,X4,X5] :
( subset_complement(the_carrier(sK1),X0) != X1
| ~ in(X0,complements_of_subsets(the_carrier(sK1),X2))
| ~ in(ordered_pair(X0,X1),cartesian_product2(complements_of_subsets(the_carrier(sK1),X2),X3))
| sP0(sK1,X2)
| ~ element(X2,powerset(powerset(the_carrier(sK1))))
| in(ordered_pair(X0,X1),sK18(sK1,X2,X3))
| in(ordered_pair(X0,X1),sK18(sK1,X4,X5))
| ~ in(X0,complements_of_subsets(the_carrier(sK1),X4))
| ~ in(ordered_pair(X0,X1),cartesian_product2(complements_of_subsets(the_carrier(sK1),X4),X5))
| sP0(sK1,X4)
| ~ element(X4,powerset(powerset(the_carrier(sK1))))
| ~ one_sorted_str(sK1) ),
inference(superposition,[],[f221,f178]) ).
fof(f221,plain,
! [X2,X3,X0,X1] :
( subset_complement(the_carrier(sK1),sK19(sK1,X0,X1)) != X1
| ~ in(X0,complements_of_subsets(the_carrier(sK1),X2))
| ~ in(ordered_pair(X0,X1),cartesian_product2(complements_of_subsets(the_carrier(sK1),X2),X3))
| sP0(sK1,X2)
| ~ element(X2,powerset(powerset(the_carrier(sK1))))
| in(ordered_pair(X0,X1),sK18(sK1,X2,X3)) ),
inference(resolution,[],[f176,f105]) ).
fof(f176,plain,
! [X2,X0,X1,X6,X7] :
( ~ one_sorted_str(X0)
| subset_complement(the_carrier(X0),sK19(X0,X6,X7)) != X7
| ~ in(X6,complements_of_subsets(the_carrier(X0),X1))
| ~ in(ordered_pair(X6,X7),cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| in(ordered_pair(X6,X7),sK18(X0,X1,X2)) ),
inference(equality_resolution,[],[f175]) ).
fof(f175,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(ordered_pair(X6,X7),sK18(X0,X1,X2))
| subset_complement(the_carrier(X0),sK19(X0,X6,X7)) != X7
| ~ in(X6,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X6,X7) != X5
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(equality_resolution,[],[f171]) ).
fof(f171,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK18(X0,X1,X2))
| subset_complement(the_carrier(X0),sK19(X0,X6,X7)) != X7
| ~ in(X6,complements_of_subsets(the_carrier(X0),X1))
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(complements_of_subsets(the_carrier(X0),X1),X2))
| sP0(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU329+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 3 11:36:04 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.kl8RzQtopJ/Vampire---4.8_10303
% 0.58/0.74 % (10517)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.58/0.74 % (10518)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.58/0.74 % (10511)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.58/0.74 % (10514)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.58/0.74 % (10512)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.58/0.74 % (10513)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.58/0.74 % (10515)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.58/0.74 % (10516)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.58/0.75 % (10515)Refutation not found, incomplete strategy% (10515)------------------------------
% 0.58/0.75 % (10515)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.75 % (10515)Termination reason: Refutation not found, incomplete strategy
% 0.58/0.75
% 0.58/0.75 % (10515)Memory used [KB]: 1201
% 0.58/0.75 % (10515)Time elapsed: 0.009 s
% 0.58/0.75 % (10515)Instructions burned: 12 (million)
% 0.58/0.75 % (10515)------------------------------
% 0.58/0.75 % (10515)------------------------------
% 0.58/0.76 % (10519)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.58/0.76 % (10514)Instruction limit reached!
% 0.58/0.76 % (10514)------------------------------
% 0.58/0.76 % (10514)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.76 % (10514)Termination reason: Unknown
% 0.58/0.76 % (10514)Termination phase: Saturation
% 0.58/0.76
% 0.58/0.76 % (10514)Memory used [KB]: 1474
% 0.58/0.76 % (10514)Time elapsed: 0.018 s
% 0.58/0.76 % (10514)Instructions burned: 33 (million)
% 0.58/0.76 % (10514)------------------------------
% 0.58/0.76 % (10514)------------------------------
% 0.58/0.76 % (10512)First to succeed.
% 0.58/0.76 % (10511)Instruction limit reached!
% 0.58/0.76 % (10511)------------------------------
% 0.58/0.76 % (10511)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.76 % (10511)Termination reason: Unknown
% 0.58/0.76 % (10511)Termination phase: Saturation
% 0.58/0.76
% 0.58/0.76 % (10511)Memory used [KB]: 1513
% 0.58/0.76 % (10511)Time elapsed: 0.020 s
% 0.58/0.76 % (10511)Instructions burned: 35 (million)
% 0.58/0.76 % (10511)------------------------------
% 0.58/0.76 % (10511)------------------------------
% 0.58/0.76 % (10520)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.58/0.77 % (10521)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/208Mi)
% 0.58/0.77 % (10516)Refutation not found, incomplete strategy% (10516)------------------------------
% 0.58/0.77 % (10516)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.77 % (10516)Termination reason: Refutation not found, incomplete strategy
% 0.58/0.77
% 0.58/0.77 % (10516)Memory used [KB]: 1303
% 0.58/0.77 % (10516)Time elapsed: 0.024 s
% 0.58/0.77 % (10516)Instructions burned: 38 (million)
% 0.58/0.77 % (10516)------------------------------
% 0.58/0.77 % (10516)------------------------------
% 0.58/0.77 % (10512)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-10510"
% 0.58/0.77 % (10517)Instruction limit reached!
% 0.58/0.77 % (10517)------------------------------
% 0.58/0.77 % (10517)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.77 % (10517)Termination reason: Unknown
% 0.58/0.77 % (10517)Termination phase: Saturation
% 0.58/0.77
% 0.58/0.77 % (10517)Memory used [KB]: 2336
% 0.58/0.77 % (10517)Time elapsed: 0.026 s
% 0.58/0.77 % (10517)Instructions burned: 83 (million)
% 0.58/0.77 % (10517)------------------------------
% 0.58/0.77 % (10517)------------------------------
% 0.58/0.77 % (10512)Refutation found. Thanks to Tanya!
% 0.58/0.77 % SZS status Theorem for Vampire---4
% 0.58/0.77 % SZS output start Proof for Vampire---4
% See solution above
% 0.58/0.77 % (10512)------------------------------
% 0.58/0.77 % (10512)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.77 % (10512)Termination reason: Refutation
% 0.58/0.77
% 0.58/0.77 % (10512)Memory used [KB]: 1355
% 0.58/0.77 % (10512)Time elapsed: 0.025 s
% 0.58/0.77 % (10512)Instructions burned: 41 (million)
% 0.58/0.77 % (10510)Success in time 0.388 s
% 0.58/0.77 % Vampire---4.8 exiting
%------------------------------------------------------------------------------