TSTP Solution File: SEU332+1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU332+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n005.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 : Thu Aug 31 17:58:16 EDT 2023
% Result : Theorem 0.23s 0.47s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 25
% Syntax : Number of formulae : 179 ( 9 unt; 0 def)
% Number of atoms : 1157 ( 347 equ)
% Maximal formula atoms : 32 ( 6 avg)
% Number of connectives : 1569 ( 591 ~; 697 |; 231 &)
% ( 13 <=>; 35 =>; 0 <=; 2 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 7 con; 0-4 aty)
% Number of variables : 560 (; 405 !; 155 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f559,plain,
$false,
inference(avatar_sat_refutation,[],[f258,f317,f504,f513,f541,f551,f558]) ).
fof(f558,plain,
( ~ spl28_6
| ~ spl28_7
| ~ spl28_10 ),
inference(avatar_contradiction_clause,[],[f557]) ).
fof(f557,plain,
( $false
| ~ spl28_6
| ~ spl28_7
| ~ spl28_10 ),
inference(subsumption_resolution,[],[f556,f441]) ).
fof(f441,plain,
( in(sK5(sK11(sK2,sK3,sK4)),sF25)
| ~ spl28_6
| ~ spl28_7 ),
inference(backward_demodulation,[],[f415,f416]) ).
fof(f416,plain,
( sK5(sK11(sK2,sK3,sK4)) = sK13(sK2,sK3,sK4,sK5(sK11(sK2,sK3,sK4)))
| ~ spl28_6
| ~ spl28_7 ),
inference(subsumption_resolution,[],[f406,f253]) ).
fof(f253,plain,
( sP1(sK2,sK3,sK4)
| ~ spl28_6 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f252,plain,
( spl28_6
<=> sP1(sK2,sK3,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_6])]) ).
fof(f406,plain,
( sK5(sK11(sK2,sK3,sK4)) = sK13(sK2,sK3,sK4,sK5(sK11(sK2,sK3,sK4)))
| ~ sP1(sK2,sK3,sK4)
| ~ spl28_6
| ~ spl28_7 ),
inference(resolution,[],[f393,f146]) ).
fof(f146,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK11(X0,X1,X2))
| sK13(X0,X1,X2,X4) = X4
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK11(X0,X1,X2))
| ! [X5] :
( ! [X6,X7] :
( ( subset_complement(the_carrier(X0),sK12(X0,X6,X7)) != X7
& sK12(X0,X6,X7) = X6
& element(sK12(X0,X6,X7),powerset(the_carrier(X0))) )
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2)) ) )
& ( ( ! [X12] :
( subset_complement(the_carrier(X0),X12) = sK15(X0,X1,X4)
| sK14(X0,X1,X4) != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(sK14(X0,X1,X4),X1)
& ordered_pair(sK14(X0,X1,X4),sK15(X0,X1,X4)) = X4
& sK13(X0,X1,X2,X4) = X4
& in(sK13(X0,X1,X2,X4),cartesian_product2(X1,X2)) )
| ~ in(X4,sK11(X0,X1,X2)) ) )
| ~ sP1(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15])],[f88,f92,f91,f90,f89]) ).
fof(f89,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,X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2)) ) )
& ( ? [X9] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,X1)
& ordered_pair(X10,X11) = X4 )
& X4 = X9
& in(X9,cartesian_product2(X1,X2)) )
| ~ in(X4,X3) ) )
=> ! [X4] :
( ( in(X4,sK11(X0,X1,X2))
| ! [X5] :
( ! [X6,X7] :
( ? [X8] :
( subset_complement(the_carrier(X0),X8) != X7
& X6 = X8
& element(X8,powerset(the_carrier(X0))) )
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2)) ) )
& ( ? [X9] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,X1)
& ordered_pair(X10,X11) = X4 )
& X4 = X9
& in(X9,cartesian_product2(X1,X2)) )
| ~ in(X4,sK11(X0,X1,X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f90,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),sK12(X0,X6,X7)) != X7
& sK12(X0,X6,X7) = X6
& element(sK12(X0,X6,X7),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f91,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,X1)
& ordered_pair(X10,X11) = X4 )
& X4 = X9
& in(X9,cartesian_product2(X1,X2)) )
=> ( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,X1)
& ordered_pair(X10,X11) = X4 )
& sK13(X0,X1,X2,X4) = X4
& in(sK13(X0,X1,X2,X4),cartesian_product2(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0,X1,X4] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,X1)
& ordered_pair(X10,X11) = X4 )
=> ( ! [X12] :
( subset_complement(the_carrier(X0),X12) = sK15(X0,X1,X4)
| sK14(X0,X1,X4) != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(sK14(X0,X1,X4),X1)
& ordered_pair(sK14(X0,X1,X4),sK15(X0,X1,X4)) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f88,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,X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2)) ) )
& ( ? [X9] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,X1)
& ordered_pair(X10,X11) = X4 )
& X4 = X9
& in(X9,cartesian_product2(X1,X2)) )
| ~ in(X4,X3) ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f87]) ).
fof(f87,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,X1)
| ordered_pair(X15,X16) != X13 )
| X13 != X14
| ~ in(X14,cartesian_product2(X1,X2)) ) )
& ( ? [X14] :
( ? [X15,X16] :
( ! [X17] :
( subset_complement(the_carrier(X0),X17) = X16
| X15 != X17
| ~ element(X17,powerset(the_carrier(X0))) )
& in(X15,X1)
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(X1,X2)) )
| ~ in(X13,X12) ) )
| ~ sP1(X0,X1,X2) ),
inference(nnf_transformation,[],[f72]) ).
fof(f72,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,X1)
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(X1,X2)) ) )
| ~ sP1(X0,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f393,plain,
( in(sK5(sK11(sK2,sK3,sK4)),sK11(sK2,sK3,sK4))
| ~ spl28_6
| ~ spl28_7 ),
inference(factoring,[],[f377]) ).
fof(f377,plain,
( ! [X0] :
( in(sK5(X0),sK11(sK2,sK3,sK4))
| in(sK5(X0),X0) )
| ~ spl28_6
| ~ spl28_7 ),
inference(duplicate_literal_removal,[],[f376]) ).
fof(f376,plain,
( ! [X0] :
( in(sK5(X0),sK11(sK2,sK3,sK4))
| in(sK5(X0),X0)
| in(sK5(X0),X0) )
| ~ spl28_6
| ~ spl28_7 ),
inference(superposition,[],[f369,f106]) ).
fof(f106,plain,
! [X3] :
( sK5(X3) = ordered_pair(sK7(X3),sK8(X3))
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
( ! [X3] :
( ( ! [X5,X6] :
( ( subset_complement(the_carrier(sK2),sK6(X5,X6)) != X6
& sK6(X5,X6) = X5
& element(sK6(X5,X6),powerset(the_carrier(sK2))) )
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3) )
| ~ in(sK5(X3),cartesian_product2(sK3,sK4))
| ~ in(sK5(X3),X3) )
& ( ( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = sK8(X3)
| sK7(X3) != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(sK7(X3),sK3)
& sK5(X3) = ordered_pair(sK7(X3),sK8(X3))
& in(sK5(X3),cartesian_product2(sK3,sK4)) )
| in(sK5(X3),X3) ) )
& element(sK3,powerset(powerset(the_carrier(sK2))))
& one_sorted_str(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f76,f81,f80,f79,f78,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,X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(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,X1)
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(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(sK2),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK2))) )
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(sK3,X2))
| ~ in(X4,X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(X8,sK3)
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(sK3,X2)) )
| in(X4,X3) ) )
& element(sK3,powerset(powerset(the_carrier(sK2))))
& one_sorted_str(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
( ? [X2] :
! [X3] :
? [X4] :
( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK2),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK2))) )
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(sK3,X2))
| ~ in(X4,X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(X8,sK3)
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(sK3,X2)) )
| in(X4,X3) ) )
=> ! [X3] :
? [X4] :
( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK2),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK2))) )
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(sK3,sK4))
| ~ in(X4,X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(X8,sK3)
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(sK3,sK4)) )
| in(X4,X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X3] :
( ? [X4] :
( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK2),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK2))) )
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(sK3,sK4))
| ~ in(X4,X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(X8,sK3)
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(sK3,sK4)) )
| in(X4,X3) ) )
=> ( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK2),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK2))) )
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3) )
| ~ in(sK5(X3),cartesian_product2(sK3,sK4))
| ~ in(sK5(X3),X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(X8,sK3)
& ordered_pair(X8,X9) = sK5(X3) )
& in(sK5(X3),cartesian_product2(sK3,sK4)) )
| in(sK5(X3),X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X5,X6] :
( ? [X7] :
( subset_complement(the_carrier(sK2),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK2))) )
=> ( subset_complement(the_carrier(sK2),sK6(X5,X6)) != X6
& sK6(X5,X6) = X5
& element(sK6(X5,X6),powerset(the_carrier(sK2))) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X3] :
( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(X8,sK3)
& ordered_pair(X8,X9) = sK5(X3) )
=> ( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = sK8(X3)
| sK7(X3) != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(sK7(X3),sK3)
& sK5(X3) = ordered_pair(sK7(X3),sK8(X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f76,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,X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(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,X1)
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(X1,X2)) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(rectify,[],[f75]) ).
fof(f75,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,X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(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,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(flattening,[],[f74]) ).
fof(f74,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,X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(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,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(nnf_transformation,[],[f52]) ).
fof(f52,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,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(flattening,[],[f51]) ).
fof(f51,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,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(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,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(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,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ypPuY9dz6I/Vampire---4.8_6584',s1_xboole_0__e4_7_2__tops_2__1) ).
fof(f369,plain,
( ! [X0] :
( in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(sK5(X0),X0) )
| ~ spl28_6
| ~ spl28_7 ),
inference(subsumption_resolution,[],[f368,f186]) ).
fof(f186,plain,
! [X3] :
( in(sK5(X3),sF25)
| in(sK5(X3),X3) ),
inference(definition_folding,[],[f105,f180]) ).
fof(f180,plain,
cartesian_product2(sK3,sK4) = sF25,
introduced(function_definition,[]) ).
fof(f105,plain,
! [X3] :
( in(sK5(X3),cartesian_product2(sK3,sK4))
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f368,plain,
( ! [X0] :
( ~ in(sK5(X0),sF25)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(sK5(X0),X0) )
| ~ spl28_6
| ~ spl28_7 ),
inference(duplicate_literal_removal,[],[f367]) ).
fof(f367,plain,
( ! [X0] :
( ~ in(sK5(X0),sF25)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(sK5(X0),X0)
| in(sK5(X0),X0) )
| ~ spl28_6
| ~ spl28_7 ),
inference(superposition,[],[f366,f106]) ).
fof(f366,plain,
( ! [X0] :
( ~ in(ordered_pair(sK7(X0),sK8(X0)),sF25)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(sK5(X0),X0) )
| ~ spl28_6
| ~ spl28_7 ),
inference(subsumption_resolution,[],[f364,f253]) ).
fof(f364,plain,
( ! [X0] :
( ~ in(ordered_pair(sK7(X0),sK8(X0)),sF25)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(sK5(X0),X0)
| ~ sP1(sK2,sK3,sK4) )
| ~ spl28_6
| ~ spl28_7 ),
inference(duplicate_literal_removal,[],[f363]) ).
fof(f363,plain,
( ! [X0] :
( ~ in(ordered_pair(sK7(X0),sK8(X0)),sF25)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(sK5(X0),X0)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| ~ sP1(sK2,sK3,sK4) )
| ~ spl28_6
| ~ spl28_7 ),
inference(superposition,[],[f361,f180]) ).
fof(f361,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(sK3,X1))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,X1))
| in(sK5(X0),X0)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| ~ sP1(sK2,sK3,X1) )
| ~ spl28_6
| ~ spl28_7 ),
inference(duplicate_literal_removal,[],[f360]) ).
fof(f360,plain,
( ! [X0,X1] :
( in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,X1))
| in(sK5(X0),X0)
| ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(sK3,X1))
| ~ sP1(sK2,sK3,X1)
| in(sK5(X0),X0) )
| ~ spl28_6
| ~ spl28_7 ),
inference(resolution,[],[f352,f107]) ).
fof(f107,plain,
! [X3] :
( in(sK7(X3),sK3)
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f352,plain,
( ! [X2,X0,X1] :
( ~ in(sK7(X0),X1)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,X1,X2))
| in(sK5(X0),X0)
| ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(X1,X2))
| ~ sP1(sK2,X1,X2) )
| ~ spl28_6
| ~ spl28_7 ),
inference(trivial_inequality_removal,[],[f351]) ).
fof(f351,plain,
( ! [X2,X0,X1] :
( sK8(X0) != sK8(X0)
| in(sK5(X0),X0)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,X1,X2))
| ~ in(sK7(X0),X1)
| ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(X1,X2))
| ~ sP1(sK2,X1,X2) )
| ~ spl28_6
| ~ spl28_7 ),
inference(duplicate_literal_removal,[],[f344]) ).
fof(f344,plain,
( ! [X2,X0,X1] :
( sK8(X0) != sK8(X0)
| in(sK5(X0),X0)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,X1,X2))
| ~ in(sK7(X0),X1)
| ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(X1,X2))
| ~ sP1(sK2,X1,X2)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(sK5(X0),X0) )
| ~ spl28_6
| ~ spl28_7 ),
inference(superposition,[],[f318,f343]) ).
fof(f343,plain,
( ! [X0] :
( sK8(X0) = subset_complement(sF24,sK7(X0))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(sK5(X0),X0) )
| ~ spl28_6 ),
inference(subsumption_resolution,[],[f342,f186]) ).
fof(f342,plain,
( ! [X0] :
( ~ in(sK5(X0),sF25)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0) )
| ~ spl28_6 ),
inference(duplicate_literal_removal,[],[f341]) ).
fof(f341,plain,
( ! [X0] :
( ~ in(sK5(X0),sF25)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0)
| in(sK5(X0),X0) )
| ~ spl28_6 ),
inference(superposition,[],[f340,f106]) ).
fof(f340,plain,
( ! [X0] :
( ~ in(ordered_pair(sK7(X0),sK8(X0)),sF25)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0) )
| ~ spl28_6 ),
inference(subsumption_resolution,[],[f338,f253]) ).
fof(f338,plain,
( ! [X0] :
( ~ in(ordered_pair(sK7(X0),sK8(X0)),sF25)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| ~ sP1(sK2,sK3,sK4)
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0) )
| ~ spl28_6 ),
inference(duplicate_literal_removal,[],[f337]) ).
fof(f337,plain,
( ! [X0] :
( ~ in(ordered_pair(sK7(X0),sK8(X0)),sF25)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| ~ sP1(sK2,sK3,sK4)
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0) )
| ~ spl28_6 ),
inference(superposition,[],[f335,f180]) ).
fof(f335,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(sK3,X1))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,X1))
| ~ sP1(sK2,sK3,X1)
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0) )
| ~ spl28_6 ),
inference(subsumption_resolution,[],[f334,f186]) ).
fof(f334,plain,
( ! [X0,X1] :
( ~ in(sK5(X0),sF25)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,X1))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(sK3,X1))
| ~ sP1(sK2,sK3,X1)
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0) )
| ~ spl28_6 ),
inference(duplicate_literal_removal,[],[f333]) ).
fof(f333,plain,
( ! [X0,X1] :
( ~ in(sK5(X0),sF25)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,X1))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(sK3,X1))
| ~ sP1(sK2,sK3,X1)
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0)
| in(sK5(X0),X0) )
| ~ spl28_6 ),
inference(superposition,[],[f332,f106]) ).
fof(f332,plain,
( ! [X2,X0,X1] :
( ~ in(ordered_pair(sK7(X0),X1),sF25)
| in(ordered_pair(sK7(X0),X1),sK11(sK2,sK3,X2))
| in(ordered_pair(sK7(X0),X1),sK11(sK2,sK3,sK4))
| ~ in(ordered_pair(sK7(X0),X1),cartesian_product2(sK3,X2))
| ~ sP1(sK2,sK3,X2)
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0) )
| ~ spl28_6 ),
inference(subsumption_resolution,[],[f330,f253]) ).
fof(f330,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(sK7(X0),X1),sF25)
| ~ sP1(sK2,sK3,sK4)
| in(ordered_pair(sK7(X0),X1),sK11(sK2,sK3,X2))
| in(ordered_pair(sK7(X0),X1),sK11(sK2,sK3,sK4))
| ~ in(ordered_pair(sK7(X0),X1),cartesian_product2(sK3,X2))
| ~ sP1(sK2,sK3,X2)
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0) ),
inference(superposition,[],[f328,f180]) ).
fof(f328,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK7(X0),X1),cartesian_product2(sK3,X2))
| ~ sP1(sK2,sK3,X2)
| in(ordered_pair(sK7(X0),X1),sK11(sK2,sK3,X3))
| in(ordered_pair(sK7(X0),X1),sK11(sK2,sK3,X2))
| ~ in(ordered_pair(sK7(X0),X1),cartesian_product2(sK3,X3))
| ~ sP1(sK2,sK3,X3)
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0) ),
inference(duplicate_literal_removal,[],[f327]) ).
fof(f327,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK7(X0),X1),cartesian_product2(sK3,X2))
| ~ sP1(sK2,sK3,X2)
| in(ordered_pair(sK7(X0),X1),sK11(sK2,sK3,X3))
| in(ordered_pair(sK7(X0),X1),sK11(sK2,sK3,X2))
| ~ in(ordered_pair(sK7(X0),X1),cartesian_product2(sK3,X3))
| ~ sP1(sK2,sK3,X3)
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0)
| in(sK5(X0),X0) ),
inference(resolution,[],[f326,f107]) ).
fof(f326,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(sK7(X0),X3)
| ~ in(ordered_pair(sK7(X0),X1),cartesian_product2(sK3,X2))
| ~ sP1(sK2,sK3,X2)
| in(ordered_pair(sK7(X0),X1),sK11(sK2,X3,X4))
| in(ordered_pair(sK7(X0),X1),sK11(sK2,sK3,X2))
| ~ in(ordered_pair(sK7(X0),X1),cartesian_product2(X3,X4))
| ~ sP1(sK2,X3,X4)
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0) ),
inference(duplicate_literal_removal,[],[f325]) ).
fof(f325,plain,
! [X2,X3,X0,X1,X4] :
( in(ordered_pair(sK7(X0),X1),sK11(sK2,sK3,X2))
| ~ in(ordered_pair(sK7(X0),X1),cartesian_product2(sK3,X2))
| ~ sP1(sK2,sK3,X2)
| in(ordered_pair(sK7(X0),X1),sK11(sK2,X3,X4))
| ~ in(sK7(X0),X3)
| ~ in(ordered_pair(sK7(X0),X1),cartesian_product2(X3,X4))
| ~ sP1(sK2,X3,X4)
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0)
| in(sK5(X0),X0) ),
inference(resolution,[],[f323,f107]) ).
fof(f323,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ in(sK7(X0),X2)
| in(ordered_pair(sK7(X0),X1),sK11(sK2,X2,X3))
| ~ in(ordered_pair(sK7(X0),X1),cartesian_product2(X2,X3))
| ~ sP1(sK2,X2,X3)
| in(ordered_pair(sK7(X0),X1),sK11(sK2,X4,X5))
| ~ in(sK7(X0),X4)
| ~ in(ordered_pair(sK7(X0),X1),cartesian_product2(X4,X5))
| ~ sP1(sK2,X4,X5)
| sK8(X0) = subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0) ),
inference(resolution,[],[f241,f185]) ).
fof(f185,plain,
! [X3] :
( ~ element(sK7(X3),sF26)
| sK8(X3) = subset_complement(sF24,sK7(X3))
| in(sK5(X3),X3) ),
inference(definition_folding,[],[f169,f183,f179,f179]) ).
fof(f179,plain,
the_carrier(sK2) = sF24,
introduced(function_definition,[]) ).
fof(f183,plain,
powerset(sF24) = sF26,
introduced(function_definition,[]) ).
fof(f169,plain,
! [X3] :
( sK8(X3) = subset_complement(the_carrier(sK2),sK7(X3))
| ~ element(sK7(X3),powerset(the_carrier(sK2)))
| in(sK5(X3),X3) ),
inference(equality_resolution,[],[f108]) ).
fof(f108,plain,
! [X3,X10] :
( subset_complement(the_carrier(sK2),X10) = sK8(X3)
| sK7(X3) != X10
| ~ element(X10,powerset(the_carrier(sK2)))
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f241,plain,
! [X2,X3,X0,X1,X4,X5] :
( element(X0,sF26)
| in(ordered_pair(X0,X1),sK11(sK2,X2,X3))
| ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ sP1(sK2,X2,X3)
| in(ordered_pair(X0,X1),sK11(sK2,X4,X5))
| ~ in(X0,X4)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X4,X5))
| ~ sP1(sK2,X4,X5) ),
inference(superposition,[],[f240,f173]) ).
fof(f173,plain,
! [X2,X0,X1,X6,X7] :
( sK12(X0,X6,X7) = X6
| in(ordered_pair(X6,X7),sK11(X0,X1,X2))
| ~ in(X6,X1)
| ~ in(ordered_pair(X6,X7),cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f172]) ).
fof(f172,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(ordered_pair(X6,X7),sK11(X0,X1,X2))
| sK12(X0,X6,X7) = X6
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X5
| ~ in(X5,cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f151]) ).
fof(f151,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK11(X0,X1,X2))
| sK12(X0,X6,X7) = X6
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f240,plain,
! [X2,X3,X0,X1] :
( element(sK12(sK2,X0,X1),sF26)
| in(ordered_pair(X0,X1),sK11(sK2,X2,X3))
| ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ sP1(sK2,X2,X3) ),
inference(forward_demodulation,[],[f239,f183]) ).
fof(f239,plain,
! [X2,X3,X0,X1] :
( element(sK12(sK2,X0,X1),powerset(sF24))
| in(ordered_pair(X0,X1),sK11(sK2,X2,X3))
| ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ sP1(sK2,X2,X3) ),
inference(superposition,[],[f175,f179]) ).
fof(f175,plain,
! [X2,X0,X1,X6,X7] :
( element(sK12(X0,X6,X7),powerset(the_carrier(X0)))
| in(ordered_pair(X6,X7),sK11(X0,X1,X2))
| ~ in(X6,X1)
| ~ in(ordered_pair(X6,X7),cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f174]) ).
fof(f174,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(ordered_pair(X6,X7),sK11(X0,X1,X2))
| element(sK12(X0,X6,X7),powerset(the_carrier(X0)))
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X5
| ~ in(X5,cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f150]) ).
fof(f150,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK11(X0,X1,X2))
| element(sK12(X0,X6,X7),powerset(the_carrier(X0)))
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f318,plain,
( ! [X2,X0,X1] :
( sK8(X0) != subset_complement(sF24,sK7(X0))
| in(sK5(X0),X0)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,X1,X2))
| ~ in(sK7(X0),X1)
| ~ in(ordered_pair(sK7(X0),sK8(X0)),cartesian_product2(X1,X2))
| ~ sP1(sK2,X1,X2) )
| ~ spl28_7 ),
inference(superposition,[],[f257,f173]) ).
fof(f257,plain,
( ! [X0] :
( sK8(X0) != subset_complement(sF24,sK12(sK2,sK7(X0),sK8(X0)))
| in(sK5(X0),X0)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4)) )
| ~ spl28_7 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f256,plain,
( spl28_7
<=> ! [X0] :
( sK8(X0) != subset_complement(sF24,sK12(sK2,sK7(X0),sK8(X0)))
| in(sK5(X0),X0)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_7])]) ).
fof(f415,plain,
( in(sK13(sK2,sK3,sK4,sK5(sK11(sK2,sK3,sK4))),sF25)
| ~ spl28_6
| ~ spl28_7 ),
inference(forward_demodulation,[],[f414,f180]) ).
fof(f414,plain,
( in(sK13(sK2,sK3,sK4,sK5(sK11(sK2,sK3,sK4))),cartesian_product2(sK3,sK4))
| ~ spl28_6
| ~ spl28_7 ),
inference(subsumption_resolution,[],[f405,f253]) ).
fof(f405,plain,
( in(sK13(sK2,sK3,sK4,sK5(sK11(sK2,sK3,sK4))),cartesian_product2(sK3,sK4))
| ~ sP1(sK2,sK3,sK4)
| ~ spl28_6
| ~ spl28_7 ),
inference(resolution,[],[f393,f145]) ).
fof(f145,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK11(X0,X1,X2))
| in(sK13(X0,X1,X2,X4),cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f556,plain,
( ~ in(sK5(sK11(sK2,sK3,sK4)),sF25)
| ~ spl28_6
| ~ spl28_7
| ~ spl28_10 ),
inference(subsumption_resolution,[],[f555,f393]) ).
fof(f555,plain,
( ~ in(sK5(sK11(sK2,sK3,sK4)),sK11(sK2,sK3,sK4))
| ~ in(sK5(sK11(sK2,sK3,sK4)),sF25)
| ~ spl28_10 ),
inference(equality_resolution,[],[f512]) ).
fof(f512,plain,
( ! [X0] :
( sK5(X0) != sK5(sK11(sK2,sK3,sK4))
| ~ in(sK5(X0),X0)
| ~ in(sK5(X0),sF25) )
| ~ spl28_10 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f511,plain,
( spl28_10
<=> ! [X0] :
( sK5(X0) != sK5(sK11(sK2,sK3,sK4))
| ~ in(sK5(X0),X0)
| ~ in(sK5(X0),sF25) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_10])]) ).
fof(f551,plain,
( spl28_10
| ~ spl28_6
| ~ spl28_7
| ~ spl28_9
| spl28_11 ),
inference(avatar_split_clause,[],[f550,f538,f501,f256,f252,f511]) ).
fof(f501,plain,
( spl28_9
<=> sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))) = subset_complement(sF24,sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_9])]) ).
fof(f538,plain,
( spl28_11
<=> sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))) = subset_complement(sF24,sK6(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_11])]) ).
fof(f550,plain,
( ! [X0] :
( sK5(X0) != sK5(sK11(sK2,sK3,sK4))
| ~ in(sK5(X0),sF25)
| ~ in(sK5(X0),X0) )
| ~ spl28_6
| ~ spl28_7
| ~ spl28_9
| spl28_11 ),
inference(forward_demodulation,[],[f549,f413]) ).
fof(f413,plain,
( sK5(sK11(sK2,sK3,sK4)) = ordered_pair(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ spl28_6
| ~ spl28_7 ),
inference(subsumption_resolution,[],[f404,f253]) ).
fof(f404,plain,
( sK5(sK11(sK2,sK3,sK4)) = ordered_pair(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ sP1(sK2,sK3,sK4)
| ~ spl28_6
| ~ spl28_7 ),
inference(resolution,[],[f393,f147]) ).
fof(f147,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK11(X0,X1,X2))
| ordered_pair(sK14(X0,X1,X4),sK15(X0,X1,X4)) = X4
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f549,plain,
( ! [X0] :
( sK5(X0) != ordered_pair(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ in(sK5(X0),sF25)
| ~ in(sK5(X0),X0) )
| ~ spl28_6
| ~ spl28_7
| ~ spl28_9
| spl28_11 ),
inference(subsumption_resolution,[],[f548,f417]) ).
fof(f417,plain,
( in(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK3)
| ~ spl28_6
| ~ spl28_7 ),
inference(subsumption_resolution,[],[f407,f253]) ).
fof(f407,plain,
( in(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK3)
| ~ sP1(sK2,sK3,sK4)
| ~ spl28_6
| ~ spl28_7 ),
inference(resolution,[],[f393,f148]) ).
fof(f148,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK11(X0,X1,X2))
| in(sK14(X0,X1,X4),X1)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f548,plain,
( ! [X0] :
( ~ in(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK3)
| sK5(X0) != ordered_pair(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ in(sK5(X0),sF25)
| ~ in(sK5(X0),X0) )
| ~ spl28_9
| spl28_11 ),
inference(subsumption_resolution,[],[f547,f503]) ).
fof(f503,plain,
( sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))) = subset_complement(sF24,sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ spl28_9 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f547,plain,
( ! [X0] :
( sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))) != subset_complement(sF24,sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ in(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK3)
| sK5(X0) != ordered_pair(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ in(sK5(X0),sF25)
| ~ in(sK5(X0),X0) )
| spl28_11 ),
inference(superposition,[],[f540,f182]) ).
fof(f182,plain,
! [X3,X6,X5] :
( sK6(X5,X6) = X5
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),sF25)
| ~ in(sK5(X3),X3) ),
inference(definition_folding,[],[f110,f180]) ).
fof(f110,plain,
! [X3,X6,X5] :
( sK6(X5,X6) = X5
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),cartesian_product2(sK3,sK4))
| ~ in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f540,plain,
( sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))) != subset_complement(sF24,sK6(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4)))))
| spl28_11 ),
inference(avatar_component_clause,[],[f538]) ).
fof(f541,plain,
( ~ spl28_11
| spl28_10
| ~ spl28_6
| ~ spl28_7 ),
inference(avatar_split_clause,[],[f494,f256,f252,f511,f538]) ).
fof(f494,plain,
( ! [X6] :
( sK5(X6) != sK5(sK11(sK2,sK3,sK4))
| sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))) != subset_complement(sF24,sK6(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4)))))
| ~ in(sK5(X6),sF25)
| ~ in(sK5(X6),X6) )
| ~ spl28_6
| ~ spl28_7 ),
inference(subsumption_resolution,[],[f487,f417]) ).
fof(f487,plain,
( ! [X6] :
( sK5(X6) != sK5(sK11(sK2,sK3,sK4))
| ~ in(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK3)
| sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))) != subset_complement(sF24,sK6(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4)))))
| ~ in(sK5(X6),sF25)
| ~ in(sK5(X6),X6) )
| ~ spl28_6
| ~ spl28_7 ),
inference(superposition,[],[f181,f413]) ).
fof(f181,plain,
! [X3,X6,X5] :
( ordered_pair(X5,X6) != sK5(X3)
| ~ in(X5,sK3)
| subset_complement(sF24,sK6(X5,X6)) != X6
| ~ in(sK5(X3),sF25)
| ~ in(sK5(X3),X3) ),
inference(definition_folding,[],[f111,f180,f179]) ).
fof(f111,plain,
! [X3,X6,X5] :
( subset_complement(the_carrier(sK2),sK6(X5,X6)) != X6
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),cartesian_product2(sK3,sK4))
| ~ in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f513,plain,
( spl28_10
| spl28_10
| ~ spl28_6
| ~ spl28_7
| spl28_8 ),
inference(avatar_split_clause,[],[f509,f497,f256,f252,f511,f511]) ).
fof(f497,plain,
( spl28_8
<=> element(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sF26) ),
introduced(avatar_definition,[new_symbols(naming,[spl28_8])]) ).
fof(f509,plain,
( ! [X0,X1] :
( sK5(X1) != sK5(sK11(sK2,sK3,sK4))
| sK5(X0) != sK5(sK11(sK2,sK3,sK4))
| ~ in(sK5(X0),sF25)
| ~ in(sK5(X0),X0)
| ~ in(sK5(X1),sF25)
| ~ in(sK5(X1),X1) )
| ~ spl28_6
| ~ spl28_7
| spl28_8 ),
inference(subsumption_resolution,[],[f489,f499]) ).
fof(f499,plain,
( ~ element(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sF26)
| spl28_8 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f489,plain,
( ! [X0,X1] :
( sK5(X1) != sK5(sK11(sK2,sK3,sK4))
| sK5(X0) != sK5(sK11(sK2,sK3,sK4))
| element(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sF26)
| ~ in(sK5(X0),sF25)
| ~ in(sK5(X0),X0)
| ~ in(sK5(X1),sF25)
| ~ in(sK5(X1),X1) )
| ~ spl28_6
| ~ spl28_7 ),
inference(forward_demodulation,[],[f488,f413]) ).
fof(f488,plain,
( ! [X0,X1] :
( sK5(X0) != sK5(sK11(sK2,sK3,sK4))
| element(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sF26)
| ~ in(sK5(X0),sF25)
| ~ in(sK5(X0),X0)
| sK5(X1) != ordered_pair(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ in(sK5(X1),sF25)
| ~ in(sK5(X1),X1) )
| ~ spl28_6
| ~ spl28_7 ),
inference(subsumption_resolution,[],[f484,f417]) ).
fof(f484,plain,
( ! [X0,X1] :
( sK5(X0) != sK5(sK11(sK2,sK3,sK4))
| ~ in(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK3)
| element(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sF26)
| ~ in(sK5(X0),sF25)
| ~ in(sK5(X0),X0)
| sK5(X1) != ordered_pair(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ in(sK5(X1),sF25)
| ~ in(sK5(X1),X1) )
| ~ spl28_6
| ~ spl28_7 ),
inference(superposition,[],[f233,f413]) ).
fof(f233,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != sK5(X2)
| ~ in(X0,sK3)
| element(X0,sF26)
| ~ in(sK5(X2),sF25)
| ~ in(sK5(X2),X2)
| sK5(X3) != ordered_pair(X0,X1)
| ~ in(sK5(X3),sF25)
| ~ in(sK5(X3),X3) ),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f232,plain,
! [X2,X3,X0,X1] :
( element(X0,sF26)
| ~ in(X0,sK3)
| ordered_pair(X0,X1) != sK5(X2)
| ~ in(sK5(X2),sF25)
| ~ in(sK5(X2),X2)
| ~ in(X0,sK3)
| sK5(X3) != ordered_pair(X0,X1)
| ~ in(sK5(X3),sF25)
| ~ in(sK5(X3),X3) ),
inference(superposition,[],[f184,f182]) ).
fof(f184,plain,
! [X3,X6,X5] :
( element(sK6(X5,X6),sF26)
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),sF25)
| ~ in(sK5(X3),X3) ),
inference(definition_folding,[],[f109,f180,f183,f179]) ).
fof(f109,plain,
! [X3,X6,X5] :
( element(sK6(X5,X6),powerset(the_carrier(sK2)))
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),cartesian_product2(sK3,sK4))
| ~ in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f504,plain,
( ~ spl28_8
| spl28_9
| ~ spl28_6
| ~ spl28_7 ),
inference(avatar_split_clause,[],[f412,f256,f252,f501,f497]) ).
fof(f412,plain,
( sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))) = subset_complement(sF24,sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ element(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sF26)
| ~ spl28_6
| ~ spl28_7 ),
inference(forward_demodulation,[],[f411,f179]) ).
fof(f411,plain,
( ~ element(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),sF26)
| sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))) = subset_complement(the_carrier(sK2),sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ spl28_6
| ~ spl28_7 ),
inference(forward_demodulation,[],[f410,f183]) ).
fof(f410,plain,
( ~ element(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),powerset(sF24))
| sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))) = subset_complement(the_carrier(sK2),sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ spl28_6
| ~ spl28_7 ),
inference(forward_demodulation,[],[f409,f179]) ).
fof(f409,plain,
( ~ element(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),powerset(the_carrier(sK2)))
| sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))) = subset_complement(the_carrier(sK2),sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ spl28_6
| ~ spl28_7 ),
inference(subsumption_resolution,[],[f403,f253]) ).
fof(f403,plain,
( ~ element(sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))),powerset(the_carrier(sK2)))
| sK15(sK2,sK3,sK5(sK11(sK2,sK3,sK4))) = subset_complement(the_carrier(sK2),sK14(sK2,sK3,sK5(sK11(sK2,sK3,sK4))))
| ~ sP1(sK2,sK3,sK4)
| ~ spl28_6
| ~ spl28_7 ),
inference(resolution,[],[f393,f176]) ).
fof(f176,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK11(X0,X1,X2))
| ~ element(sK14(X0,X1,X4),powerset(the_carrier(X0)))
| sK15(X0,X1,X4) = subset_complement(the_carrier(X0),sK14(X0,X1,X4))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f149]) ).
fof(f149,plain,
! [X2,X0,X1,X4,X12] :
( subset_complement(the_carrier(X0),X12) = sK15(X0,X1,X4)
| sK14(X0,X1,X4) != X12
| ~ element(X12,powerset(the_carrier(X0)))
| ~ in(X4,sK11(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
fof(f317,plain,
spl28_6,
inference(avatar_contradiction_clause,[],[f316]) ).
fof(f316,plain,
( $false
| spl28_6 ),
inference(resolution,[],[f315,f254]) ).
fof(f254,plain,
( ~ sP1(sK2,sK3,sK4)
| spl28_6 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f315,plain,
( ! [X0] : sP1(sK2,sK3,X0)
| spl28_6 ),
inference(subsumption_resolution,[],[f314,f188]) ).
fof(f188,plain,
element(sK3,sF27),
inference(definition_folding,[],[f104,f187,f183,f179]) ).
fof(f187,plain,
powerset(sF26) = sF27,
introduced(function_definition,[]) ).
fof(f104,plain,
element(sK3,powerset(powerset(the_carrier(sK2)))),
inference(cnf_transformation,[],[f82]) ).
fof(f314,plain,
( ! [X0] :
( ~ element(sK3,sF27)
| sP1(sK2,sK3,X0) )
| spl28_6 ),
inference(forward_demodulation,[],[f313,f187]) ).
fof(f313,plain,
( ! [X0] :
( ~ element(sK3,powerset(sF26))
| sP1(sK2,sK3,X0) )
| spl28_6 ),
inference(forward_demodulation,[],[f312,f183]) ).
fof(f312,plain,
( ! [X0] :
( ~ element(sK3,powerset(powerset(sF24)))
| sP1(sK2,sK3,X0) )
| spl28_6 ),
inference(forward_demodulation,[],[f311,f179]) ).
fof(f311,plain,
( ! [X0] :
( sP1(sK2,sK3,X0)
| ~ element(sK3,powerset(powerset(the_carrier(sK2)))) )
| spl28_6 ),
inference(subsumption_resolution,[],[f310,f103]) ).
fof(f103,plain,
one_sorted_str(sK2),
inference(cnf_transformation,[],[f82]) ).
fof(f310,plain,
( ! [X0] :
( sP1(sK2,sK3,X0)
| ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| ~ one_sorted_str(sK2) )
| spl28_6 ),
inference(trivial_inequality_removal,[],[f309]) ).
fof(f309,plain,
( ! [X0] :
( sK19(sK2,sK3) != sK19(sK2,sK3)
| sP1(sK2,sK3,X0)
| ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| ~ one_sorted_str(sK2) )
| spl28_6 ),
inference(superposition,[],[f162,f306]) ).
fof(f306,plain,
( sK20(sK2,sK3) = sK19(sK2,sK3)
| spl28_6 ),
inference(backward_demodulation,[],[f282,f287]) ).
fof(f287,plain,
( sK18(sK2,sK3) = sK19(sK2,sK3)
| spl28_6 ),
inference(subsumption_resolution,[],[f286,f188]) ).
fof(f286,plain,
( ~ element(sK3,sF27)
| sK18(sK2,sK3) = sK19(sK2,sK3)
| spl28_6 ),
inference(forward_demodulation,[],[f285,f187]) ).
fof(f285,plain,
( ~ element(sK3,powerset(sF26))
| sK18(sK2,sK3) = sK19(sK2,sK3)
| spl28_6 ),
inference(forward_demodulation,[],[f284,f183]) ).
fof(f284,plain,
( ~ element(sK3,powerset(powerset(sF24)))
| sK18(sK2,sK3) = sK19(sK2,sK3)
| spl28_6 ),
inference(forward_demodulation,[],[f283,f179]) ).
fof(f283,plain,
( sK18(sK2,sK3) = sK19(sK2,sK3)
| ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| spl28_6 ),
inference(subsumption_resolution,[],[f262,f103]) ).
fof(f262,plain,
( sK18(sK2,sK3) = sK19(sK2,sK3)
| ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| ~ one_sorted_str(sK2)
| spl28_6 ),
inference(resolution,[],[f254,f156]) ).
fof(f156,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| sK18(X0,X1) = sK19(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ! [X2] :
( sP1(X0,X1,X2)
| ( sK19(X0,X1) != sK20(X0,X1)
& ! [X8] :
( subset_complement(the_carrier(X0),X8) = sK22(X0,X1)
| sK21(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(sK21(X0,X1),X1)
& sK20(X0,X1) = ordered_pair(sK21(X0,X1),sK22(X0,X1))
& sK18(X0,X1) = sK20(X0,X1)
& sP0(X0,X1,sK19(X0,X1))
& sK18(X0,X1) = sK19(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])],[f73,f99,f98]) ).
fof(f98,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,X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& sP0(X0,X1,X4)
& X3 = X4 )
=> ( sK19(X0,X1) != sK20(X0,X1)
& ? [X7,X6] :
( ! [X8] :
( subset_complement(the_carrier(X0),X8) = X7
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(X6,X1)
& ordered_pair(X6,X7) = sK20(X0,X1) )
& sK18(X0,X1) = sK20(X0,X1)
& sP0(X0,X1,sK19(X0,X1))
& sK18(X0,X1) = sK19(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
! [X0,X1] :
( ? [X7,X6] :
( ! [X8] :
( subset_complement(the_carrier(X0),X8) = X7
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(X6,X1)
& ordered_pair(X6,X7) = sK20(X0,X1) )
=> ( ! [X8] :
( subset_complement(the_carrier(X0),X8) = sK22(X0,X1)
| sK21(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(sK21(X0,X1),X1)
& sK20(X0,X1) = ordered_pair(sK21(X0,X1),sK22(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1] :
( ! [X2] :
( sP1(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,X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& sP0(X0,X1,X4)
& X3 = X4 ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(definition_folding,[],[f70,f72,f71]) ).
fof(f71,plain,
! [X0,X1,X4] :
( ? [X9,X10] :
( ! [X11] :
( subset_complement(the_carrier(X0),X11) = X10
| X9 != X11
| ~ element(X11,powerset(the_carrier(X0))) )
& in(X9,X1)
& ordered_pair(X9,X10) = X4 )
| ~ sP0(X0,X1,X4) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f70,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,X1)
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(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,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,X1)
& ordered_pair(X9,X10) = X4 )
& X3 = X4 ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f69]) ).
fof(f69,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,X1)
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(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,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,X1)
& ordered_pair(X9,X10) = X4 )
& X3 = X4 ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,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,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,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,X1)
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(X1,X2)) ) ) ) ),
inference(rectify,[],[f33]) ).
fof(f33,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,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,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,X1)
& ordered_pair(X12,X13) = X4 )
& X4 = X5
& in(X5,cartesian_product2(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ypPuY9dz6I/Vampire---4.8_6584',s1_tarski__e4_7_2__tops_2__2) ).
fof(f282,plain,
( sK20(sK2,sK3) = sK18(sK2,sK3)
| spl28_6 ),
inference(subsumption_resolution,[],[f281,f188]) ).
fof(f281,plain,
( ~ element(sK3,sF27)
| sK20(sK2,sK3) = sK18(sK2,sK3)
| spl28_6 ),
inference(forward_demodulation,[],[f280,f187]) ).
fof(f280,plain,
( ~ element(sK3,powerset(sF26))
| sK20(sK2,sK3) = sK18(sK2,sK3)
| spl28_6 ),
inference(forward_demodulation,[],[f279,f183]) ).
fof(f279,plain,
( ~ element(sK3,powerset(powerset(sF24)))
| sK20(sK2,sK3) = sK18(sK2,sK3)
| spl28_6 ),
inference(forward_demodulation,[],[f278,f179]) ).
fof(f278,plain,
( sK20(sK2,sK3) = sK18(sK2,sK3)
| ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| spl28_6 ),
inference(subsumption_resolution,[],[f261,f103]) ).
fof(f261,plain,
( sK20(sK2,sK3) = sK18(sK2,sK3)
| ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| ~ one_sorted_str(sK2)
| spl28_6 ),
inference(resolution,[],[f254,f158]) ).
fof(f158,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| sK18(X0,X1) = sK20(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f162,plain,
! [X2,X0,X1] :
( sK19(X0,X1) != sK20(X0,X1)
| sP1(X0,X1,X2)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f258,plain,
( ~ spl28_6
| spl28_7 ),
inference(avatar_split_clause,[],[f249,f256,f252]) ).
fof(f249,plain,
! [X0] :
( sK8(X0) != subset_complement(sF24,sK12(sK2,sK7(X0),sK8(X0)))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(sK2,sK3,sK4))
| ~ sP1(sK2,sK3,sK4)
| in(sK5(X0),X0) ),
inference(superposition,[],[f246,f179]) ).
fof(f246,plain,
! [X0,X1] :
( sK8(X0) != subset_complement(the_carrier(X1),sK12(X1,sK7(X0),sK8(X0)))
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(X1,sK3,sK4))
| ~ sP1(X1,sK3,sK4)
| in(sK5(X0),X0) ),
inference(subsumption_resolution,[],[f245,f107]) ).
fof(f245,plain,
! [X0,X1] :
( sK8(X0) != subset_complement(the_carrier(X1),sK12(X1,sK7(X0),sK8(X0)))
| ~ in(sK7(X0),sK3)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(X1,sK3,sK4))
| ~ sP1(X1,sK3,sK4)
| in(sK5(X0),X0) ),
inference(subsumption_resolution,[],[f244,f186]) ).
fof(f244,plain,
! [X0,X1] :
( ~ in(sK5(X0),sF25)
| sK8(X0) != subset_complement(the_carrier(X1),sK12(X1,sK7(X0),sK8(X0)))
| ~ in(sK7(X0),sK3)
| in(ordered_pair(sK7(X0),sK8(X0)),sK11(X1,sK3,sK4))
| ~ sP1(X1,sK3,sK4)
| in(sK5(X0),X0) ),
inference(superposition,[],[f243,f106]) ).
fof(f243,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X0,X1),sF25)
| subset_complement(the_carrier(X2),sK12(X2,X0,X1)) != X1
| ~ in(X0,sK3)
| in(ordered_pair(X0,X1),sK11(X2,sK3,sK4))
| ~ sP1(X2,sK3,sK4) ),
inference(superposition,[],[f171,f180]) ).
fof(f171,plain,
! [X2,X0,X1,X6,X7] :
( ~ in(ordered_pair(X6,X7),cartesian_product2(X1,X2))
| subset_complement(the_carrier(X0),sK12(X0,X6,X7)) != X7
| ~ in(X6,X1)
| in(ordered_pair(X6,X7),sK11(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f170]) ).
fof(f170,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(ordered_pair(X6,X7),sK11(X0,X1,X2))
| subset_complement(the_carrier(X0),sK12(X0,X6,X7)) != X7
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X5
| ~ in(X5,cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f152]) ).
fof(f152,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK11(X0,X1,X2))
| subset_complement(the_carrier(X0),sK12(X0,X6,X7)) != X7
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU332+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.37 % Computer : n005.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Wed Aug 23 14:20:23 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.14/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.37 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.ypPuY9dz6I/Vampire---4.8_6584
% 0.14/0.37 % (6860)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.44 % (6866)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.23/0.44 % (6861)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.23/0.44 % (6864)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.23/0.44 % (6863)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.23/0.44 % (6867)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.23/0.44 % (6865)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.23/0.44 % (6862)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.23/0.46 % (6866)First to succeed.
% 0.23/0.47 % (6866)Refutation found. Thanks to Tanya!
% 0.23/0.47 % SZS status Theorem for Vampire---4
% 0.23/0.47 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.47 % (6866)------------------------------
% 0.23/0.47 % (6866)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.47 % (6866)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.47 % (6866)Termination reason: Refutation
% 0.23/0.47
% 0.23/0.47 % (6866)Memory used [KB]: 6012
% 0.23/0.47 % (6866)Time elapsed: 0.032 s
% 0.23/0.47 % (6866)------------------------------
% 0.23/0.47 % (6866)------------------------------
% 0.23/0.47 % (6860)Success in time 0.095 s
% 0.23/0.47 6862 Aborted by signal SIGHUP on /export/starexec/sandbox/tmp/tmp.ypPuY9dz6I/Vampire---4.8_6584
% 0.23/0.47 % (6862)------------------------------
% 0.23/0.47 % (6862)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.47 6863 Aborted by signal SIGHUP on /export/starexec/sandbox/tmp/tmp.ypPuY9dz6I/Vampire---4.8_6584
% 0.23/0.47 % (6863)------------------------------
% 0.23/0.47 % (6863)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.47 % (6862)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.47 % (6863)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.47 % (6862)Termination reason: Unknown
% 0.23/0.47 % (6863)Termination reason: Unknown
% 0.23/0.47 % (6862)Termination phase: Saturation
% 0.23/0.47 % (6863)Termination phase: Saturation
% 0.23/0.47
% 0.23/0.47
% 0.23/0.47 % (6862)Memory used [KB]: 1023
% 0.23/0.47 % (6863)Memory used [KB]: 1279
% 0.23/0.47 % (6862)Time elapsed: 0.033 s
% 0.23/0.47 % (6863)Time elapsed: 0.036 s
% 0.23/0.47 % (6862)------------------------------
% 0.23/0.47 % (6862)------------------------------
% 0.23/0.47 % (6863)------------------------------
% 0.23/0.47 % (6863)------------------------------
% 0.23/0.47 % Vampire---4.8 exiting
%------------------------------------------------------------------------------