%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU335+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:24 PM UTC 2026
% Result : Theorem 16.94s 3.72s
% Output : Refutation 20.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 99
% Syntax : Number of formulae : 899 ( 30 unt; 87 def)
% Number of atoms : 4233 ( 610 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 5701 (2367 ~;2996 |; 176 &)
% ( 97 <=>; 64 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 95 ( 93 usr; 86 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 2 con; 0-3 aty)
% Number of variables : 776 ( 0 sgn 702 !; 74 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f18,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ! [X2] :
( element(X2,powerset(powerset(X0)))
=> ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( element(X3,powerset(X0))
=> ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f24,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f25,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f34,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f35,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f40,axiom,
! [X0,X1] :
( ( one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( ( ! [X2,X3,X4] :
( ( in(X2,complements_of_subsets(the_carrier(X0),X1))
& ! [X5] :
( element(X5,powerset(the_carrier(X0)))
=> ( X5 = X2
=> X3 = subset_complement(the_carrier(X0),X5) ) )
& ! [X6] :
( element(X6,powerset(the_carrier(X0)))
=> ( X6 = X2
=> X4 = subset_complement(the_carrier(X0),X6) ) ) )
=> X3 = X4 )
& ! [X2] :
~ ( in(X2,complements_of_subsets(the_carrier(X0),X1))
& ! [X3] :
~ ! [X7] :
( element(X7,powerset(the_carrier(X0)))
=> ( X7 = X2
=> X3 = subset_complement(the_carrier(X0),X7) ) ) ) )
=> ? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = complements_of_subsets(the_carrier(X0),X1)
& ! [X3] :
( in(X3,complements_of_subsets(the_carrier(X0),X1))
=> ! [X8] :
( element(X8,powerset(the_carrier(X0)))
=> ( X8 = X3
=> apply(X2,X3) = subset_complement(the_carrier(X0),X8) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e4_7_1__tops_2) ).
fof(f41,axiom,
! [X0,X1] :
( ( one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( ( ! [X2,X3,X4] :
( ( in(X2,X1)
& ! [X5] :
( element(X5,powerset(the_carrier(X0)))
=> ( X5 = X2
=> X3 = subset_complement(the_carrier(X0),X5) ) )
& ! [X6] :
( element(X6,powerset(the_carrier(X0)))
=> ( X6 = X2
=> X4 = subset_complement(the_carrier(X0),X6) ) ) )
=> X3 = X4 )
& ! [X2] :
~ ( in(X2,X1)
& ! [X3] :
~ ! [X7] :
( element(X7,powerset(the_carrier(X0)))
=> ( X7 = X2
=> X3 = subset_complement(the_carrier(X0),X7) ) ) ) )
=> ? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> ! [X8] :
( element(X8,powerset(the_carrier(X0)))
=> ( X8 = X3
=> apply(X2,X3) = subset_complement(the_carrier(X0),X8) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e4_7_2__tops_2) ).
fof(f42,conjecture,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( finite(complements_of_subsets(the_carrier(X0),X1))
<=> finite(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_tops_2) ).
fof(f43,negated_conjecture,
~ ! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( finite(complements_of_subsets(the_carrier(X0),X1))
<=> finite(X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f44,axiom,
! [X0] :
( relation(X0)
=> relation_image(X0,relation_dom(X0)) = relation_rng(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_relat_1) ).
fof(f45,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( finite(X0)
=> finite(relation_image(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finset_1) ).
fof(f50,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f56,plain,
! [X0,X1] :
( ( one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( ( ! [X2,X3,X4] :
( ( in(X2,complements_of_subsets(the_carrier(X0),X1))
& ! [X5] :
( element(X5,powerset(the_carrier(X0)))
=> ( X5 = X2
=> X3 = subset_complement(the_carrier(X0),X5) ) )
& ! [X6] :
( element(X6,powerset(the_carrier(X0)))
=> ( X6 = X2
=> X4 = subset_complement(the_carrier(X0),X6) ) ) )
=> X3 = X4 )
& ! [X7] :
~ ( in(X7,complements_of_subsets(the_carrier(X0),X1))
& ! [X8] :
~ ! [X9] :
( element(X9,powerset(the_carrier(X0)))
=> ( X7 = X9
=> subset_complement(the_carrier(X0),X9) = X8 ) ) ) )
=> ? [X10] :
( relation(X10)
& function(X10)
& complements_of_subsets(the_carrier(X0),X1) = relation_dom(X10)
& ! [X11] :
( in(X11,complements_of_subsets(the_carrier(X0),X1))
=> ! [X12] :
( element(X12,powerset(the_carrier(X0)))
=> ( X11 = X12
=> apply(X10,X11) = subset_complement(the_carrier(X0),X12) ) ) ) ) ) ),
inference(rectify,[],[f40]) ).
fof(f57,plain,
! [X0,X1] :
( ( one_sorted_str(X0)
& element(X1,powerset(powerset(the_carrier(X0)))) )
=> ( ( ! [X2,X3,X4] :
( ( in(X2,X1)
& ! [X5] :
( element(X5,powerset(the_carrier(X0)))
=> ( X5 = X2
=> X3 = subset_complement(the_carrier(X0),X5) ) )
& ! [X6] :
( element(X6,powerset(the_carrier(X0)))
=> ( X6 = X2
=> X4 = subset_complement(the_carrier(X0),X6) ) ) )
=> X3 = X4 )
& ! [X7] :
~ ( in(X7,X1)
& ! [X8] :
~ ! [X9] :
( element(X9,powerset(the_carrier(X0)))
=> ( X7 = X9
=> subset_complement(the_carrier(X0),X9) = X8 ) ) ) )
=> ? [X10] :
( relation(X10)
& function(X10)
& relation_dom(X10) = X1
& ! [X11] :
( in(X11,X1)
=> ! [X12] :
( element(X12,powerset(the_carrier(X0)))
=> ( X11 = X12
=> apply(X10,X11) = subset_complement(the_carrier(X0),X12) ) ) ) ) ) ),
inference(rectify,[],[f41]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f86,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) )
| ~ element(X3,powerset(X0)) ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f18]) ).
fof(f88,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f89,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f25]) ).
fof(f90,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f34]) ).
fof(f91,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f35]) ).
fof(f93,plain,
! [X0,X1] :
( ? [X10] :
( relation(X10)
& function(X10)
& complements_of_subsets(the_carrier(X0),X1) = relation_dom(X10)
& ! [X11] :
( ! [X12] :
( apply(X10,X11) = subset_complement(the_carrier(X0),X12)
| X11 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
| ~ in(X11,complements_of_subsets(the_carrier(X0),X1)) ) )
| ? [X2,X3,X4] :
( X3 != X4
& in(X2,complements_of_subsets(the_carrier(X0),X1))
& ! [X5] :
( X3 = subset_complement(the_carrier(X0),X5)
| X2 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
& ! [X6] :
( X4 = subset_complement(the_carrier(X0),X6)
| X2 != X6
| ~ element(X6,powerset(the_carrier(X0))) ) )
| ? [X7] :
( in(X7,complements_of_subsets(the_carrier(X0),X1))
& ! [X8] :
? [X9] :
( subset_complement(the_carrier(X0),X9) != X8
& X7 = X9
& element(X9,powerset(the_carrier(X0))) ) )
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(ennf_transformation,[],[f56]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X10] :
( relation(X10)
& function(X10)
& complements_of_subsets(the_carrier(X0),X1) = relation_dom(X10)
& ! [X11] :
( ! [X12] :
( apply(X10,X11) = subset_complement(the_carrier(X0),X12)
| X11 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
| ~ in(X11,complements_of_subsets(the_carrier(X0),X1)) ) )
| ? [X2,X3,X4] :
( X3 != X4
& in(X2,complements_of_subsets(the_carrier(X0),X1))
& ! [X5] :
( X3 = subset_complement(the_carrier(X0),X5)
| X2 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
& ! [X6] :
( X4 = subset_complement(the_carrier(X0),X6)
| X2 != X6
| ~ element(X6,powerset(the_carrier(X0))) ) )
| ? [X7] :
( in(X7,complements_of_subsets(the_carrier(X0),X1))
& ! [X8] :
? [X9] :
( subset_complement(the_carrier(X0),X9) != X8
& X7 = X9
& element(X9,powerset(the_carrier(X0))) ) )
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ? [X10] :
( relation(X10)
& function(X10)
& relation_dom(X10) = X1
& ! [X11] :
( ! [X12] :
( apply(X10,X11) = subset_complement(the_carrier(X0),X12)
| X11 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
| ~ in(X11,X1) ) )
| ? [X2,X3,X4] :
( X3 != X4
& in(X2,X1)
& ! [X5] :
( X3 = subset_complement(the_carrier(X0),X5)
| X2 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
& ! [X6] :
( X4 = subset_complement(the_carrier(X0),X6)
| X2 != X6
| ~ element(X6,powerset(the_carrier(X0))) ) )
| ? [X7] :
( in(X7,X1)
& ! [X8] :
? [X9] :
( subset_complement(the_carrier(X0),X9) != X8
& X7 = X9
& element(X9,powerset(the_carrier(X0))) ) )
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(ennf_transformation,[],[f57]) ).
fof(f96,plain,
! [X0,X1] :
( ? [X10] :
( relation(X10)
& function(X10)
& relation_dom(X10) = X1
& ! [X11] :
( ! [X12] :
( apply(X10,X11) = subset_complement(the_carrier(X0),X12)
| X11 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
| ~ in(X11,X1) ) )
| ? [X2,X3,X4] :
( X3 != X4
& in(X2,X1)
& ! [X5] :
( X3 = subset_complement(the_carrier(X0),X5)
| X2 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
& ! [X6] :
( X4 = subset_complement(the_carrier(X0),X6)
| X2 != X6
| ~ element(X6,powerset(the_carrier(X0))) ) )
| ? [X7] :
( in(X7,X1)
& ! [X8] :
? [X9] :
( subset_complement(the_carrier(X0),X9) != X8
& X7 = X9
& element(X9,powerset(the_carrier(X0))) ) )
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(flattening,[],[f95]) ).
fof(f97,plain,
? [X0] :
( ? [X1] :
( ( finite(complements_of_subsets(the_carrier(X0),X1))
<~> finite(X1) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f98,plain,
! [X0] :
( relation_image(X0,relation_dom(X0)) = relation_rng(X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f99,plain,
! [X0,X1] :
( finite(relation_image(X1,X0))
| ~ finite(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f100,plain,
! [X0,X1] :
( finite(relation_image(X1,X0))
| ~ finite(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f99]) ).
fof(f106,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f50]) ).
fof(f107,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f106]) ).
fof(f112,definition,
! [X1,X0] :
( ? [X7] :
( in(X7,complements_of_subsets(the_carrier(X0),X1))
& ! [X8] :
? [X9] :
( subset_complement(the_carrier(X0),X9) != X8
& X7 = X9
& element(X9,powerset(the_carrier(X0))) ) )
| ~ sP0(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f113,plain,
! [X0,X1] :
( ? [X10] :
( relation(X10)
& function(X10)
& complements_of_subsets(the_carrier(X0),X1) = relation_dom(X10)
& ! [X11] :
( ! [X12] :
( apply(X10,X11) = subset_complement(the_carrier(X0),X12)
| X11 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
| ~ in(X11,complements_of_subsets(the_carrier(X0),X1)) ) )
| ? [X2,X3,X4] :
( X3 != X4
& in(X2,complements_of_subsets(the_carrier(X0),X1))
& ! [X5] :
( X3 = subset_complement(the_carrier(X0),X5)
| X2 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
& ! [X6] :
( X4 = subset_complement(the_carrier(X0),X6)
| X2 != X6
| ~ element(X6,powerset(the_carrier(X0))) ) )
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(definition_folding,[],[f94,f112]) ).
fof(f114,definition,
! [X1,X0] :
( ? [X7] :
( in(X7,X1)
& ! [X8] :
? [X9] :
( subset_complement(the_carrier(X0),X9) != X8
& X7 = X9
& element(X9,powerset(the_carrier(X0))) ) )
| ~ sP1(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f115,plain,
! [X0,X1] :
( ? [X10] :
( relation(X10)
& function(X10)
& relation_dom(X10) = X1
& ! [X11] :
( ! [X12] :
( apply(X10,X11) = subset_complement(the_carrier(X0),X12)
| X11 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
| ~ in(X11,X1) ) )
| ? [X2,X3,X4] :
( X3 != X4
& in(X2,X1)
& ! [X5] :
( X3 = subset_complement(the_carrier(X0),X5)
| X2 != X5
| ~ element(X5,powerset(the_carrier(X0))) )
& ! [X6] :
( X4 = subset_complement(the_carrier(X0),X6)
| X2 != X6
| ~ element(X6,powerset(the_carrier(X0))) ) )
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(definition_folding,[],[f96,f114]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f86]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& apply(X0,X4) = X2 )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( in(X7,relation_dom(X0))
& apply(X0,X7) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f116]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK2(X0,X1) )
| ~ in(sK2(X0,X1),X1) )
& ( ( in(sK3(X0,X1),relation_dom(X0))
& sK2(X0,X1) = apply(X0,sK3(X0,X1)) )
| in(sK2(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK4(X0,X5),relation_dom(X0))
& apply(X0,sK4(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X2,sK2(X0,X1)),skolemize(X4,sK3(X0,X1)),skolemize(X7,sK4(X0,X5))],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(nnf_transformation,[],[f87]) ).
fof(f120,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X0,X4),X1) )
& ( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ( ( ~ in(subset_complement(X0,sK5(X0,X1,X2)),X1)
| ~ in(sK5(X0,X1,X2),X2) )
& ( in(subset_complement(X0,sK5(X0,X1,X2)),X1)
| in(sK5(X0,X1,X2),X2) )
& element(sK5(X0,X1,X2),powerset(X0)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X0,X4),X1) )
& ( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f121]) ).
fof(f128,plain,
! [X1,X0] :
( ? [X7] :
( in(X7,complements_of_subsets(the_carrier(X0),X1))
& ! [X8] :
? [X9] :
( subset_complement(the_carrier(X0),X9) != X8
& X7 = X9
& element(X9,powerset(the_carrier(X0))) ) )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f112]) ).
fof(f129,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,complements_of_subsets(the_carrier(X1),X0))
& ! [X3] :
? [X4] :
( subset_complement(the_carrier(X1),X4) != X3
& X2 = X4
& element(X4,powerset(the_carrier(X1))) ) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( ( in(sK11(X0,X1),complements_of_subsets(the_carrier(X1),X0))
& ! [X3] :
( subset_complement(the_carrier(X1),sK12(X0,X1,X3)) != X3
& sK11(X0,X1) = sK12(X0,X1,X3)
& element(sK12(X0,X1,X3),powerset(the_carrier(X1))) ) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X2,sK11(X0,X1)),skolemize(X4,sK12(X0,X1,X3))],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( ? [X2] :
( relation(X2)
& function(X2)
& complements_of_subsets(the_carrier(X0),X1) = relation_dom(X2)
& ! [X3] :
( ! [X4] :
( apply(X2,X3) = subset_complement(the_carrier(X0),X4)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,complements_of_subsets(the_carrier(X0),X1)) ) )
| ? [X5,X6,X7] :
( X6 != X7
& in(X5,complements_of_subsets(the_carrier(X0),X1))
& ! [X8] :
( subset_complement(the_carrier(X0),X8) = X6
| X5 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& ! [X9] :
( subset_complement(the_carrier(X0),X9) = X7
| X5 != X9
| ~ element(X9,powerset(the_carrier(X0))) ) )
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(rectify,[],[f113]) ).
fof(f132,plain,
! [X0,X1] :
( ( relation(sK13(X0,X1))
& function(sK13(X0,X1))
& complements_of_subsets(the_carrier(X0),X1) = relation_dom(sK13(X0,X1))
& ! [X3] :
( ! [X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK13(X0,X1),X3)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,complements_of_subsets(the_carrier(X0),X1)) ) )
| ( sK15(X0,X1) != sK16(X0,X1)
& in(sK14(X0,X1),complements_of_subsets(the_carrier(X0),X1))
& ! [X8] :
( subset_complement(the_carrier(X0),X8) = sK15(X0,X1)
| sK14(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& ! [X9] :
( subset_complement(the_carrier(X0),X9) = sK16(X0,X1)
| sK14(X0,X1) != X9
| ~ element(X9,powerset(the_carrier(X0))) ) )
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16]),skolemize(X2,sK13(X0,X1)),skolemize(X5,sK14(X0,X1)),skolemize(X6,sK15(X0,X1)),skolemize(X7,sK16(X0,X1))],[f131]) ).
fof(f133,plain,
! [X1,X0] :
( ? [X7] :
( in(X7,X1)
& ! [X8] :
? [X9] :
( subset_complement(the_carrier(X0),X9) != X8
& X7 = X9
& element(X9,powerset(the_carrier(X0))) ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f114]) ).
fof(f134,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X0)
& ! [X3] :
? [X4] :
( subset_complement(the_carrier(X1),X4) != X3
& X2 = X4
& element(X4,powerset(the_carrier(X1))) ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f133]) ).
fof(f135,plain,
! [X0,X1] :
( ( in(sK17(X0,X1),X0)
& ! [X3] :
( subset_complement(the_carrier(X1),sK18(X0,X1,X3)) != X3
& sK17(X0,X1) = sK18(X0,X1,X3)
& element(sK18(X0,X1,X3),powerset(the_carrier(X1))) ) )
| ~ sP1(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X2,sK17(X0,X1)),skolemize(X4,sK18(X0,X1,X3))],[f134]) ).
fof(f136,plain,
! [X0,X1] :
( ? [X2] :
( relation(X2)
& function(X2)
& relation_dom(X2) = X1
& ! [X3] :
( ! [X4] :
( apply(X2,X3) = subset_complement(the_carrier(X0),X4)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X1) ) )
| ? [X5,X6,X7] :
( X6 != X7
& in(X5,X1)
& ! [X8] :
( subset_complement(the_carrier(X0),X8) = X6
| X5 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& ! [X9] :
( subset_complement(the_carrier(X0),X9) = X7
| X5 != X9
| ~ element(X9,powerset(the_carrier(X0))) ) )
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(rectify,[],[f115]) ).
fof(f137,plain,
! [X0,X1] :
( ( relation(sK19(X0,X1))
& function(sK19(X0,X1))
& relation_dom(sK19(X0,X1)) = X1
& ! [X3] :
( ! [X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK19(X0,X1),X3)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0))) )
| ~ in(X3,X1) ) )
| ( sK21(X0,X1) != sK22(X0,X1)
& in(sK20(X0,X1),X1)
& ! [X8] :
( subset_complement(the_carrier(X0),X8) = sK21(X0,X1)
| sK20(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& ! [X9] :
( subset_complement(the_carrier(X0),X9) = sK22(X0,X1)
| sK20(X0,X1) != X9
| ~ element(X9,powerset(the_carrier(X0))) ) )
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21,sK22]),skolemize(X2,sK19(X0,X1)),skolemize(X5,sK20(X0,X1)),skolemize(X6,sK21(X0,X1)),skolemize(X7,sK22(X0,X1))],[f136]) ).
fof(f138,plain,
? [X0] :
( ? [X1] :
( ( ~ finite(X1)
| ~ finite(complements_of_subsets(the_carrier(X0),X1)) )
& ( finite(X1)
| finite(complements_of_subsets(the_carrier(X0),X1)) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& one_sorted_str(X0) ),
inference(nnf_transformation,[],[f97]) ).
fof(f139,plain,
? [X0] :
( ? [X1] :
( ( ~ finite(X1)
| ~ finite(complements_of_subsets(the_carrier(X0),X1)) )
& ( finite(X1)
| finite(complements_of_subsets(the_carrier(X0),X1)) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& one_sorted_str(X0) ),
inference(flattening,[],[f138]) ).
fof(f140,plain,
( ( ~ finite(sK24)
| ~ finite(complements_of_subsets(the_carrier(sK23),sK24)) )
& ( finite(sK24)
| finite(complements_of_subsets(the_carrier(sK23),sK24)) )
& element(sK24,powerset(powerset(the_carrier(sK23))))
& one_sorted_str(sK23) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23,sK24]),skolemize(X0,sK23),skolemize(X1,sK24)],[f139]) ).
fof(f168,plain,
! [X0,X1,X5] :
( apply(X0,sK4(X0,X5)) = X5
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f169,plain,
! [X0,X1,X5] :
( in(sK4(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f170,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f171,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| sK2(X0,X1) = apply(X0,sK3(X0,X1))
| in(sK2(X0,X1),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f172,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(sK3(X0,X1),relation_dom(X0))
| in(sK2(X0,X1),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f173,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK2(X0,X1)
| ~ in(sK2(X0,X1),X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f174,plain,
! [X2,X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2)
| ~ element(X4,powerset(X0))
| complements_of_subsets(X0,X1) != X2
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f122]) ).
fof(f179,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f88]) ).
fof(f180,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f89]) ).
fof(f190,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f191,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f91]) ).
fof(f204,plain,
! [X3,X0,X1] :
( sK11(X0,X1) = sK12(X0,X1,X3)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f205,plain,
! [X3,X0,X1] :
( subset_complement(the_carrier(X1),sK12(X0,X1,X3)) != X3
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f207,plain,
! [X3,X0,X1,X9,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK13(X0,X1),X3)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X3,complements_of_subsets(the_carrier(X0),X1))
| subset_complement(the_carrier(X0),X9) = sK16(X0,X1)
| sK14(X0,X1) != X9
| ~ element(X9,powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f208,plain,
! [X3,X0,X1,X8,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK13(X0,X1),X3)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X3,complements_of_subsets(the_carrier(X0),X1))
| subset_complement(the_carrier(X0),X8) = sK15(X0,X1)
| sK14(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f209,plain,
! [X3,X0,X1,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK13(X0,X1),X3)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X3,complements_of_subsets(the_carrier(X0),X1))
| in(sK14(X0,X1),complements_of_subsets(the_carrier(X0),X1))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f210,plain,
! [X3,X0,X1,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK13(X0,X1),X3)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X3,complements_of_subsets(the_carrier(X0),X1))
| sK15(X0,X1) != sK16(X0,X1)
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f211,plain,
! [X0,X1,X9] :
( complements_of_subsets(the_carrier(X0),X1) = relation_dom(sK13(X0,X1))
| subset_complement(the_carrier(X0),X9) = sK16(X0,X1)
| sK14(X0,X1) != X9
| ~ element(X9,powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f212,plain,
! [X0,X1,X8] :
( complements_of_subsets(the_carrier(X0),X1) = relation_dom(sK13(X0,X1))
| subset_complement(the_carrier(X0),X8) = sK15(X0,X1)
| sK14(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f213,plain,
! [X0,X1] :
( complements_of_subsets(the_carrier(X0),X1) = relation_dom(sK13(X0,X1))
| in(sK14(X0,X1),complements_of_subsets(the_carrier(X0),X1))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f214,plain,
! [X0,X1] :
( complements_of_subsets(the_carrier(X0),X1) = relation_dom(sK13(X0,X1))
| sK15(X0,X1) != sK16(X0,X1)
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f215,plain,
! [X0,X1,X9] :
( function(sK13(X0,X1))
| subset_complement(the_carrier(X0),X9) = sK16(X0,X1)
| sK14(X0,X1) != X9
| ~ element(X9,powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f216,plain,
! [X0,X1,X8] :
( function(sK13(X0,X1))
| subset_complement(the_carrier(X0),X8) = sK15(X0,X1)
| sK14(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f217,plain,
! [X0,X1] :
( function(sK13(X0,X1))
| in(sK14(X0,X1),complements_of_subsets(the_carrier(X0),X1))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f218,plain,
! [X0,X1] :
( function(sK13(X0,X1))
| sK15(X0,X1) != sK16(X0,X1)
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f219,plain,
! [X0,X1,X9] :
( relation(sK13(X0,X1))
| subset_complement(the_carrier(X0),X9) = sK16(X0,X1)
| sK14(X0,X1) != X9
| ~ element(X9,powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f220,plain,
! [X0,X1,X8] :
( relation(sK13(X0,X1))
| subset_complement(the_carrier(X0),X8) = sK15(X0,X1)
| sK14(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f221,plain,
! [X0,X1] :
( relation(sK13(X0,X1))
| in(sK14(X0,X1),complements_of_subsets(the_carrier(X0),X1))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f222,plain,
! [X0,X1] :
( relation(sK13(X0,X1))
| sK15(X0,X1) != sK16(X0,X1)
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f132]) ).
fof(f224,plain,
! [X3,X0,X1] :
( sK17(X0,X1) = sK18(X0,X1,X3)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f225,plain,
! [X3,X0,X1] :
( subset_complement(the_carrier(X1),sK18(X0,X1,X3)) != X3
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f227,plain,
! [X3,X0,X1,X9,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK19(X0,X1),X3)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X3,X1)
| subset_complement(the_carrier(X0),X9) = sK22(X0,X1)
| sK20(X0,X1) != X9
| ~ element(X9,powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f228,plain,
! [X3,X0,X1,X8,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK19(X0,X1),X3)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X3,X1)
| subset_complement(the_carrier(X0),X8) = sK21(X0,X1)
| sK20(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f229,plain,
! [X3,X0,X1,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK19(X0,X1),X3)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X3,X1)
| in(sK20(X0,X1),X1)
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f230,plain,
! [X3,X0,X1,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK19(X0,X1),X3)
| X3 != X4
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X3,X1)
| sK21(X0,X1) != sK22(X0,X1)
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f231,plain,
! [X0,X1,X9] :
( relation_dom(sK19(X0,X1)) = X1
| subset_complement(the_carrier(X0),X9) = sK22(X0,X1)
| sK20(X0,X1) != X9
| ~ element(X9,powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f232,plain,
! [X0,X1,X8] :
( relation_dom(sK19(X0,X1)) = X1
| subset_complement(the_carrier(X0),X8) = sK21(X0,X1)
| sK20(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f233,plain,
! [X0,X1] :
( relation_dom(sK19(X0,X1)) = X1
| in(sK20(X0,X1),X1)
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f234,plain,
! [X0,X1] :
( relation_dom(sK19(X0,X1)) = X1
| sK21(X0,X1) != sK22(X0,X1)
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f235,plain,
! [X0,X1,X9] :
( function(sK19(X0,X1))
| subset_complement(the_carrier(X0),X9) = sK22(X0,X1)
| sK20(X0,X1) != X9
| ~ element(X9,powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f236,plain,
! [X0,X1,X8] :
( function(sK19(X0,X1))
| subset_complement(the_carrier(X0),X8) = sK21(X0,X1)
| sK20(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f237,plain,
! [X0,X1] :
( function(sK19(X0,X1))
| in(sK20(X0,X1),X1)
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f238,plain,
! [X0,X1] :
( function(sK19(X0,X1))
| sK21(X0,X1) != sK22(X0,X1)
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f239,plain,
! [X0,X1,X9] :
( relation(sK19(X0,X1))
| subset_complement(the_carrier(X0),X9) = sK22(X0,X1)
| sK20(X0,X1) != X9
| ~ element(X9,powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f240,plain,
! [X0,X1,X8] :
( relation(sK19(X0,X1))
| subset_complement(the_carrier(X0),X8) = sK21(X0,X1)
| sK20(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f241,plain,
! [X0,X1] :
( relation(sK19(X0,X1))
| in(sK20(X0,X1),X1)
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f242,plain,
! [X0,X1] :
( relation(sK19(X0,X1))
| sK21(X0,X1) != sK22(X0,X1)
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(cnf_transformation,[],[f137]) ).
fof(f243,plain,
one_sorted_str(sK23),
inference(cnf_transformation,[],[f140]) ).
fof(f244,plain,
element(sK24,powerset(powerset(the_carrier(sK23)))),
inference(cnf_transformation,[],[f140]) ).
fof(f245,plain,
( finite(sK24)
| finite(complements_of_subsets(the_carrier(sK23),sK24)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f246,plain,
( ~ finite(sK24)
| ~ finite(complements_of_subsets(the_carrier(sK23),sK24)) ),
inference(cnf_transformation,[],[f140]) ).
fof(f247,plain,
! [X0] :
( relation_rng(X0) = relation_image(X0,relation_dom(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f248,plain,
! [X0,X1] :
( finite(relation_image(X1,X0))
| ~ finite(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f254,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f259,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f170]) ).
fof(f260,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f259]) ).
fof(f261,plain,
! [X0,X5] :
( in(sK4(X0,X5),relation_dom(X0))
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f169]) ).
fof(f262,plain,
! [X0,X5] :
( apply(X0,sK4(X0,X5)) = X5
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f168]) ).
fof(f264,plain,
! [X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,complements_of_subsets(X0,X1))
| ~ element(X4,powerset(X0))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(equality_resolution,[],[f174]) ).
fof(f265,plain,
! [X0,X1] :
( relation(sK13(X0,X1))
| sK15(X0,X1) = subset_complement(the_carrier(X0),sK14(X0,X1))
| ~ element(sK14(X0,X1),powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f220]) ).
fof(f266,plain,
! [X0,X1] :
( relation(sK13(X0,X1))
| sK16(X0,X1) = subset_complement(the_carrier(X0),sK14(X0,X1))
| ~ element(sK14(X0,X1),powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f219]) ).
fof(f267,plain,
! [X0,X1] :
( function(sK13(X0,X1))
| sK15(X0,X1) = subset_complement(the_carrier(X0),sK14(X0,X1))
| ~ element(sK14(X0,X1),powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f216]) ).
fof(f268,plain,
! [X0,X1] :
( function(sK13(X0,X1))
| sK16(X0,X1) = subset_complement(the_carrier(X0),sK14(X0,X1))
| ~ element(sK14(X0,X1),powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f215]) ).
fof(f269,plain,
! [X0,X1] :
( complements_of_subsets(the_carrier(X0),X1) = relation_dom(sK13(X0,X1))
| sK15(X0,X1) = subset_complement(the_carrier(X0),sK14(X0,X1))
| ~ element(sK14(X0,X1),powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f212]) ).
fof(f270,plain,
! [X0,X1] :
( complements_of_subsets(the_carrier(X0),X1) = relation_dom(sK13(X0,X1))
| sK16(X0,X1) = subset_complement(the_carrier(X0),sK14(X0,X1))
| ~ element(sK14(X0,X1),powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f211]) ).
fof(f271,plain,
! [X0,X1,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK13(X0,X1),X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,complements_of_subsets(the_carrier(X0),X1))
| sK15(X0,X1) != sK16(X0,X1)
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f210]) ).
fof(f272,plain,
! [X0,X1,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK13(X0,X1),X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,complements_of_subsets(the_carrier(X0),X1))
| in(sK14(X0,X1),complements_of_subsets(the_carrier(X0),X1))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f209]) ).
fof(f273,plain,
! [X0,X1,X8,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK13(X0,X1),X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,complements_of_subsets(the_carrier(X0),X1))
| subset_complement(the_carrier(X0),X8) = sK15(X0,X1)
| sK14(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f208]) ).
fof(f274,plain,
! [X0,X1,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK13(X0,X1),X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,complements_of_subsets(the_carrier(X0),X1))
| sK15(X0,X1) = subset_complement(the_carrier(X0),sK14(X0,X1))
| ~ element(sK14(X0,X1),powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f273]) ).
fof(f275,plain,
! [X0,X1,X9,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK13(X0,X1),X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,complements_of_subsets(the_carrier(X0),X1))
| subset_complement(the_carrier(X0),X9) = sK16(X0,X1)
| sK14(X0,X1) != X9
| ~ element(X9,powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f207]) ).
fof(f276,plain,
! [X0,X1,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK13(X0,X1),X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,complements_of_subsets(the_carrier(X0),X1))
| sK16(X0,X1) = subset_complement(the_carrier(X0),sK14(X0,X1))
| ~ element(sK14(X0,X1),powerset(the_carrier(X0)))
| sP0(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f275]) ).
fof(f277,plain,
! [X0,X1] :
( relation(sK19(X0,X1))
| sK21(X0,X1) = subset_complement(the_carrier(X0),sK20(X0,X1))
| ~ element(sK20(X0,X1),powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f240]) ).
fof(f278,plain,
! [X0,X1] :
( relation(sK19(X0,X1))
| sK22(X0,X1) = subset_complement(the_carrier(X0),sK20(X0,X1))
| ~ element(sK20(X0,X1),powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f239]) ).
fof(f279,plain,
! [X0,X1] :
( function(sK19(X0,X1))
| sK21(X0,X1) = subset_complement(the_carrier(X0),sK20(X0,X1))
| ~ element(sK20(X0,X1),powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f236]) ).
fof(f280,plain,
! [X0,X1] :
( function(sK19(X0,X1))
| sK22(X0,X1) = subset_complement(the_carrier(X0),sK20(X0,X1))
| ~ element(sK20(X0,X1),powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f235]) ).
fof(f281,plain,
! [X0,X1] :
( relation_dom(sK19(X0,X1)) = X1
| sK21(X0,X1) = subset_complement(the_carrier(X0),sK20(X0,X1))
| ~ element(sK20(X0,X1),powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f232]) ).
fof(f282,plain,
! [X0,X1] :
( relation_dom(sK19(X0,X1)) = X1
| sK22(X0,X1) = subset_complement(the_carrier(X0),sK20(X0,X1))
| ~ element(sK20(X0,X1),powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f231]) ).
fof(f283,plain,
! [X0,X1,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK19(X0,X1),X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,X1)
| sK21(X0,X1) != sK22(X0,X1)
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f230]) ).
fof(f284,plain,
! [X0,X1,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK19(X0,X1),X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,X1)
| in(sK20(X0,X1),X1)
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f229]) ).
fof(f285,plain,
! [X0,X1,X8,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK19(X0,X1),X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,X1)
| subset_complement(the_carrier(X0),X8) = sK21(X0,X1)
| sK20(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f228]) ).
fof(f286,plain,
! [X0,X1,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK19(X0,X1),X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,X1)
| sK21(X0,X1) = subset_complement(the_carrier(X0),sK20(X0,X1))
| ~ element(sK20(X0,X1),powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f285]) ).
fof(f287,plain,
! [X0,X1,X9,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK19(X0,X1),X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,X1)
| subset_complement(the_carrier(X0),X9) = sK22(X0,X1)
| sK20(X0,X1) != X9
| ~ element(X9,powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f227]) ).
fof(f288,plain,
! [X0,X1,X4] :
( subset_complement(the_carrier(X0),X4) = apply(sK19(X0,X1),X4)
| ~ element(X4,powerset(the_carrier(X0)))
| ~ in(X4,X1)
| sK22(X0,X1) = subset_complement(the_carrier(X0),sK20(X0,X1))
| ~ element(sK20(X0,X1),powerset(the_carrier(X0)))
| sP1(X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0)))) ),
inference(equality_resolution,[],[f287]) ).
fof(f292,definition,
( spl27_1
<=> finite(complements_of_subsets(the_carrier(sK23),sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f293,plain,
( finite(complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f294,plain,
( ~ finite(complements_of_subsets(the_carrier(sK23),sK24))
| spl27_1 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f296,definition,
( spl27_2
<=> finite(sK24) ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
fof(f297,plain,
( finite(sK24)
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f298,plain,
( ~ finite(sK24)
| spl27_2 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f299,plain,
( ~ spl27_1
| ~ spl27_2 ),
inference(avatar_split_clause,[],[f246,f296,f292]) ).
fof(f300,plain,
( finite(sK24)
| spl27_1 ),
inference(backward_subsumption_resolution,[],[f245,f294]) ).
fof(f308,definition,
( spl27_3
<=> one_sorted_str(sK23) ),
introduced(definition,[new_symbols(definition,[spl27_3])],[avatar_definition]) ).
fof(f310,plain,
( one_sorted_str(sK23)
| ~ spl27_3 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f311,plain,
spl27_3,
inference(avatar_split_clause,[],[f243,f308]) ).
fof(f339,plain,
( ! [X0] :
( relation_dom(sK19(sK23,X0)) = X0
| sK22(sK23,X0) = subset_complement(the_carrier(sK23),sK20(sK23,X0))
| ~ element(sK20(sK23,X0),powerset(the_carrier(sK23)))
| sP1(X0,sK23)
| ~ element(X0,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_3 ),
inference(resolution,[],[f310,f282]) ).
fof(f340,plain,
( ! [X0,X1] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,X1),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,X1)
| sK21(sK23,X1) != sK22(sK23,X1)
| sP1(X1,sK23)
| ~ element(X1,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_3 ),
inference(resolution,[],[f310,f283]) ).
fof(f347,plain,
( ! [X0,X1] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,X1),X0)
| ~ in(X0,X1)
| sK21(sK23,X1) != sK22(sK23,X1)
| sP1(X1,sK23)
| ~ element(X1,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_3 ),
inference(forward_subsumption_resolution,[],[f340,f254]) ).
fof(f349,definition,
( spl27_4
<=> element(sK24,powerset(powerset(the_carrier(sK23)))) ),
introduced(definition,[new_symbols(definition,[spl27_4])],[avatar_definition]) ).
fof(f351,plain,
( element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ spl27_4 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f352,plain,
spl27_4,
inference(avatar_split_clause,[],[f244,f349]) ).
fof(f353,plain,
( complements_of_subsets(the_carrier(sK23),sK24) = relation_dom(sK13(sK23,sK24))
| in(sK14(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f213]) ).
fof(f354,plain,
( complements_of_subsets(the_carrier(sK23),sK24) = relation_dom(sK13(sK23,sK24))
| sK15(sK23,sK24) != sK16(sK23,sK24)
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f214]) ).
fof(f355,plain,
( function(sK13(sK23,sK24))
| in(sK14(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f217]) ).
fof(f356,plain,
( function(sK13(sK23,sK24))
| sK15(sK23,sK24) != sK16(sK23,sK24)
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f218]) ).
fof(f358,plain,
( relation(sK13(sK23,sK24))
| sK15(sK23,sK24) != sK16(sK23,sK24)
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f222]) ).
fof(f361,plain,
( function(sK19(sK23,sK24))
| in(sK20(sK23,sK24),sK24)
| sP1(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f237]) ).
fof(f363,plain,
( relation(sK19(sK23,sK24))
| in(sK20(sK23,sK24),sK24)
| sP1(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f241]) ).
fof(f365,plain,
( relation(sK13(sK23,sK24))
| sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f265]) ).
fof(f366,plain,
( relation(sK13(sK23,sK24))
| sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f266]) ).
fof(f367,plain,
( function(sK13(sK23,sK24))
| sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f267]) ).
fof(f368,plain,
( function(sK13(sK23,sK24))
| sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f268]) ).
fof(f369,plain,
( complements_of_subsets(the_carrier(sK23),sK24) = relation_dom(sK13(sK23,sK24))
| sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f269]) ).
fof(f370,plain,
( complements_of_subsets(the_carrier(sK23),sK24) = relation_dom(sK13(sK23,sK24))
| sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f270]) ).
fof(f371,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| sK15(sK23,sK24) != sK16(sK23,sK24)
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23) )
| ~ spl27_4 ),
inference(resolution,[],[f351,f271]) ).
fof(f372,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| in(sK14(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23) )
| ~ spl27_4 ),
inference(resolution,[],[f351,f272]) ).
fof(f373,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23) )
| ~ spl27_4 ),
inference(resolution,[],[f351,f274]) ).
fof(f374,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23) )
| ~ spl27_4 ),
inference(resolution,[],[f351,f276]) ).
fof(f375,plain,
( relation(sK19(sK23,sK24))
| sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| sP1(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f277]) ).
fof(f377,plain,
( function(sK19(sK23,sK24))
| sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| sP1(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ spl27_4 ),
inference(resolution,[],[f351,f279]) ).
fof(f382,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,sK24)
| in(sK20(sK23,sK24),sK24)
| sP1(sK24,sK23)
| ~ one_sorted_str(sK23) )
| ~ spl27_4 ),
inference(resolution,[],[f351,f284]) ).
fof(f383,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,sK24)
| sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| sP1(sK24,sK23)
| ~ one_sorted_str(sK23) )
| ~ spl27_4 ),
inference(resolution,[],[f351,f286]) ).
fof(f384,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,sK24)
| sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| sP1(sK24,sK23)
| ~ one_sorted_str(sK23) )
| ~ spl27_4 ),
inference(resolution,[],[f351,f288]) ).
fof(f391,plain,
( element(complements_of_subsets(the_carrier(sK23),sK24),powerset(powerset(the_carrier(sK23))))
| ~ spl27_4 ),
inference(resolution,[],[f351,f180]) ).
fof(f392,plain,
( sK24 = complements_of_subsets(the_carrier(sK23),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_4 ),
inference(resolution,[],[f351,f191]) ).
fof(f394,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),sK24)
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ element(complements_of_subsets(the_carrier(sK23),sK24),powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_4 ),
inference(resolution,[],[f351,f264]) ).
fof(f412,plain,
( ! [X0] :
( element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,sK24) )
| ~ spl27_4 ),
inference(resolution,[],[f351,f254]) ).
fof(f420,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),sK24)
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(complements_of_subsets(the_carrier(sK23),sK24),powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f394,f254]) ).
fof(f422,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24)
| sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| sP1(sK24,sK23)
| ~ one_sorted_str(sK23) )
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f384,f412]) ).
fof(f423,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24)
| sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| sP1(sK24,sK23)
| ~ one_sorted_str(sK23) )
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f383,f412]) ).
fof(f424,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,sK24)
| in(sK20(sK23,sK24),sK24)
| sP1(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f382,f310]) ).
fof(f429,plain,
( function(sK19(sK23,sK24))
| sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| sP1(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f377,f310]) ).
fof(f431,plain,
( relation(sK19(sK23,sK24))
| sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| sP1(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f375,f310]) ).
fof(f432,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f374,f310]) ).
fof(f433,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f373,f310]) ).
fof(f434,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| in(sK14(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| sP0(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f372,f310]) ).
fof(f435,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| sK15(sK23,sK24) != sK16(sK23,sK24)
| sP0(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f371,f310]) ).
fof(f436,plain,
( complements_of_subsets(the_carrier(sK23),sK24) = relation_dom(sK13(sK23,sK24))
| sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f370,f310]) ).
fof(f437,plain,
( complements_of_subsets(the_carrier(sK23),sK24) = relation_dom(sK13(sK23,sK24))
| sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f369,f310]) ).
fof(f438,plain,
( function(sK13(sK23,sK24))
| sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f368,f310]) ).
fof(f439,plain,
( function(sK13(sK23,sK24))
| sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f367,f310]) ).
fof(f440,plain,
( relation(sK13(sK23,sK24))
| sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f366,f310]) ).
fof(f441,plain,
( relation(sK13(sK23,sK24))
| sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| sP0(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f365,f310]) ).
fof(f443,plain,
( relation(sK19(sK23,sK24))
| in(sK20(sK23,sK24),sK24)
| sP1(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f363,f310]) ).
fof(f445,plain,
( function(sK19(sK23,sK24))
| in(sK20(sK23,sK24),sK24)
| sP1(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f361,f310]) ).
fof(f448,plain,
( relation(sK13(sK23,sK24))
| sK15(sK23,sK24) != sK16(sK23,sK24)
| sP0(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f358,f310]) ).
fof(f450,plain,
( function(sK13(sK23,sK24))
| sK15(sK23,sK24) != sK16(sK23,sK24)
| sP0(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f356,f310]) ).
fof(f451,plain,
( function(sK13(sK23,sK24))
| in(sK14(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| sP0(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f355,f310]) ).
fof(f452,plain,
( complements_of_subsets(the_carrier(sK23),sK24) = relation_dom(sK13(sK23,sK24))
| sK15(sK23,sK24) != sK16(sK23,sK24)
| sP0(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f354,f310]) ).
fof(f453,plain,
( complements_of_subsets(the_carrier(sK23),sK24) = relation_dom(sK13(sK23,sK24))
| in(sK14(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| sP0(sK24,sK23)
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f353,f310]) ).
fof(f454,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),sK24)
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) )
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f420,f391]) ).
fof(f455,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24)
| sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| sP1(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f422,f310]) ).
fof(f456,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24)
| sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| sP1(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f423,f310]) ).
fof(f457,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24)
| in(sK20(sK23,sK24),sK24)
| sP1(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4 ),
inference(forward_subsumption_resolution,[],[f424,f412]) ).
fof(f460,definition,
( spl27_5
<=> sP0(sK24,sK23) ),
introduced(definition,[new_symbols(definition,[spl27_5])],[avatar_definition]) ).
fof(f461,plain,
( ~ sP0(sK24,sK23)
| spl27_5 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f462,plain,
( sP0(sK24,sK23)
| ~ spl27_5 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f464,definition,
( spl27_6
<=> in(sK14(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_6])],[avatar_definition]) ).
fof(f465,plain,
( ~ in(sK14(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| spl27_6 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f466,plain,
( in(sK14(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_6 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f468,definition,
( spl27_7
<=> complements_of_subsets(the_carrier(sK23),sK24) = relation_dom(sK13(sK23,sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_7])],[avatar_definition]) ).
fof(f470,plain,
( complements_of_subsets(the_carrier(sK23),sK24) = relation_dom(sK13(sK23,sK24))
| ~ spl27_7 ),
inference(avatar_component_clause,[],[f468]) ).
fof(f471,plain,
( spl27_5
| spl27_6
| spl27_7
| ~ spl27_3
| ~ spl27_4 ),
inference(avatar_split_clause,[],[f453,f349,f308,f468,f464,f460]) ).
fof(f482,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23))) )
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(backward_subsumption_resolution,[],[f432,f461]) ).
fof(f483,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23))) )
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(backward_subsumption_resolution,[],[f433,f461]) ).
fof(f485,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| sK15(sK23,sK24) != sK16(sK23,sK24) )
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(backward_subsumption_resolution,[],[f435,f461]) ).
fof(f486,plain,
( complements_of_subsets(the_carrier(sK23),sK24) = relation_dom(sK13(sK23,sK24))
| sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(backward_subsumption_resolution,[],[f436,f461]) ).
fof(f487,plain,
( complements_of_subsets(the_carrier(sK23),sK24) = relation_dom(sK13(sK23,sK24))
| sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(backward_subsumption_resolution,[],[f437,f461]) ).
fof(f488,plain,
( function(sK13(sK23,sK24))
| sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(backward_subsumption_resolution,[],[f438,f461]) ).
fof(f489,plain,
( function(sK13(sK23,sK24))
| sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(backward_subsumption_resolution,[],[f439,f461]) ).
fof(f490,plain,
( relation(sK13(sK23,sK24))
| sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(backward_subsumption_resolution,[],[f440,f461]) ).
fof(f491,plain,
( relation(sK13(sK23,sK24))
| sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(backward_subsumption_resolution,[],[f441,f461]) ).
fof(f492,plain,
( relation(sK13(sK23,sK24))
| sK15(sK23,sK24) != sK16(sK23,sK24)
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(backward_subsumption_resolution,[],[f448,f461]) ).
fof(f494,plain,
( function(sK13(sK23,sK24))
| sK15(sK23,sK24) != sK16(sK23,sK24)
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(backward_subsumption_resolution,[],[f450,f461]) ).
fof(f495,plain,
( function(sK13(sK23,sK24))
| in(sK14(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(backward_subsumption_resolution,[],[f451,f461]) ).
fof(f496,plain,
( complements_of_subsets(the_carrier(sK23),sK24) = relation_dom(sK13(sK23,sK24))
| sK15(sK23,sK24) != sK16(sK23,sK24)
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(backward_subsumption_resolution,[],[f452,f461]) ).
fof(f548,definition,
( spl27_9
<=> sK15(sK23,sK24) = sK16(sK23,sK24) ),
introduced(definition,[new_symbols(definition,[spl27_9])],[avatar_definition]) ).
fof(f550,plain,
( sK15(sK23,sK24) != sK16(sK23,sK24)
| spl27_9 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f551,plain,
( ~ spl27_9
| spl27_7
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(avatar_split_clause,[],[f496,f460,f349,f308,f468,f548]) ).
fof(f553,definition,
( spl27_10
<=> ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(X0,powerset(the_carrier(sK23))) ) ),
introduced(definition,[new_symbols(definition,[spl27_10])],[avatar_definition]) ).
fof(f554,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(X0,powerset(the_carrier(sK23))) )
| ~ spl27_10 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f555,plain,
( ~ spl27_9
| spl27_10
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(avatar_split_clause,[],[f485,f460,f349,f308,f553,f548]) ).
fof(f557,definition,
( spl27_11
<=> element(sK14(sK23,sK24),powerset(the_carrier(sK23))) ),
introduced(definition,[new_symbols(definition,[spl27_11])],[avatar_definition]) ).
fof(f559,plain,
( ~ element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| spl27_11 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f574,definition,
( spl27_14
<=> sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_14])],[avatar_definition]) ).
fof(f576,plain,
( sK15(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ spl27_14 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f577,plain,
( ~ spl27_11
| spl27_14
| spl27_7
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(avatar_split_clause,[],[f487,f460,f349,f308,f468,f574,f557]) ).
fof(f579,definition,
( spl27_15
<=> sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_15])],[avatar_definition]) ).
fof(f581,plain,
( sK16(sK23,sK24) = subset_complement(the_carrier(sK23),sK14(sK23,sK24))
| ~ spl27_15 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f582,plain,
( ~ spl27_11
| spl27_15
| spl27_7
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(avatar_split_clause,[],[f486,f460,f349,f308,f468,f579,f557]) ).
fof(f585,plain,
( ~ spl27_11
| spl27_14
| spl27_10
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(avatar_split_clause,[],[f483,f460,f349,f308,f553,f574,f557]) ).
fof(f586,plain,
( ~ spl27_11
| spl27_15
| spl27_10
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(avatar_split_clause,[],[f482,f460,f349,f308,f553,f579,f557]) ).
fof(f588,definition,
( spl27_16
<=> sK24 = complements_of_subsets(the_carrier(sK23),complements_of_subsets(the_carrier(sK23),sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_16])],[avatar_definition]) ).
fof(f590,plain,
( sK24 = complements_of_subsets(the_carrier(sK23),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_16 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f591,plain,
( spl27_16
| ~ spl27_4 ),
inference(avatar_split_clause,[],[f392,f349,f588]) ).
fof(f614,plain,
( ! [X0] :
( ~ in(X0,sK24)
| in(subset_complement(the_carrier(sK23),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ element(complements_of_subsets(the_carrier(sK23),sK24),powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_16 ),
inference(superposition,[],[f264,f590]) ).
fof(f615,plain,
( ! [X0] :
( ~ in(X0,sK24)
| in(subset_complement(the_carrier(sK23),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ element(complements_of_subsets(the_carrier(sK23),sK24),powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_16 ),
inference(forward_subsumption_resolution,[],[f614,f254]) ).
fof(f636,plain,
( ! [X0] :
( ~ in(X0,sK24)
| in(subset_complement(the_carrier(sK23),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(sK24,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_16 ),
inference(forward_subsumption_resolution,[],[f615,f180]) ).
fof(f648,plain,
( ! [X0] :
( ~ in(X0,sK24)
| in(subset_complement(the_carrier(sK23),X0),complements_of_subsets(the_carrier(sK23),sK24)) )
| ~ spl27_4
| ~ spl27_16 ),
inference(forward_subsumption_resolution,[],[f636,f351]) ).
fof(f733,definition,
( spl27_18
<=> ! [X0] :
( ~ in(X0,sK24)
| in(subset_complement(the_carrier(sK23),X0),complements_of_subsets(the_carrier(sK23),sK24)) ) ),
introduced(definition,[new_symbols(definition,[spl27_18])],[avatar_definition]) ).
fof(f734,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ in(X0,sK24) )
| ~ spl27_18 ),
inference(avatar_component_clause,[],[f733]) ).
fof(f735,plain,
( spl27_18
| ~ spl27_4
| ~ spl27_16 ),
inference(avatar_split_clause,[],[f648,f588,f349,f733]) ).
fof(f842,definition,
( spl27_21
<=> ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),sK24)
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) ) ),
introduced(definition,[new_symbols(definition,[spl27_21])],[avatar_definition]) ).
fof(f843,plain,
( ! [X0] :
( ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| in(subset_complement(the_carrier(sK23),X0),sK24) )
| ~ spl27_21 ),
inference(avatar_component_clause,[],[f842]) ).
fof(f844,plain,
( spl27_21
| ~ spl27_4 ),
inference(avatar_split_clause,[],[f454,f349,f842]) ).
fof(f877,definition,
( spl27_22
<=> sP1(sK24,sK23) ),
introduced(definition,[new_symbols(definition,[spl27_22])],[avatar_definition]) ).
fof(f878,plain,
( ~ sP1(sK24,sK23)
| spl27_22 ),
inference(avatar_component_clause,[],[f877]) ).
fof(f879,plain,
( sP1(sK24,sK23)
| ~ spl27_22 ),
inference(avatar_component_clause,[],[f877]) ).
fof(f881,definition,
( spl27_23
<=> sK21(sK23,sK24) = sK22(sK23,sK24) ),
introduced(definition,[new_symbols(definition,[spl27_23])],[avatar_definition]) ).
fof(f882,plain,
( sK21(sK23,sK24) = sK22(sK23,sK24)
| ~ spl27_23 ),
inference(avatar_component_clause,[],[f881]) ).
fof(f883,plain,
( sK21(sK23,sK24) != sK22(sK23,sK24)
| spl27_23 ),
inference(avatar_component_clause,[],[f881]) ).
fof(f885,definition,
( spl27_24
<=> sK24 = relation_dom(sK19(sK23,sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_24])],[avatar_definition]) ).
fof(f886,plain,
( sK24 != relation_dom(sK19(sK23,sK24))
| spl27_24 ),
inference(avatar_component_clause,[],[f885]) ).
fof(f887,plain,
( sK24 = relation_dom(sK19(sK23,sK24))
| ~ spl27_24 ),
inference(avatar_component_clause,[],[f885]) ).
fof(f992,definition,
( spl27_27
<=> element(sK20(sK23,sK24),powerset(the_carrier(sK23))) ),
introduced(definition,[new_symbols(definition,[spl27_27])],[avatar_definition]) ).
fof(f993,plain,
( element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| ~ spl27_27 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f994,plain,
( ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| spl27_27 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f996,definition,
( spl27_28
<=> sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_28])],[avatar_definition]) ).
fof(f997,plain,
( sK21(sK23,sK24) != subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| spl27_28 ),
inference(avatar_component_clause,[],[f996]) ).
fof(f998,plain,
( sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ spl27_28 ),
inference(avatar_component_clause,[],[f996]) ).
fof(f1009,definition,
( spl27_30
<=> in(sK20(sK23,sK24),sK24) ),
introduced(definition,[new_symbols(definition,[spl27_30])],[avatar_definition]) ).
fof(f1010,plain,
( ~ in(sK20(sK23,sK24),sK24)
| spl27_30 ),
inference(avatar_component_clause,[],[f1009]) ).
fof(f1014,plain,
( ! [X0] : sK18(sK24,sK23,X0) = sK17(sK24,sK23)
| ~ spl27_22 ),
inference(resolution,[],[f879,f224]) ).
fof(f1019,definition,
( spl27_31
<=> ! [X0] : sK18(sK24,sK23,X0) = sK17(sK24,sK23) ),
introduced(definition,[new_symbols(definition,[spl27_31])],[avatar_definition]) ).
fof(f1020,plain,
( ! [X0] : sK18(sK24,sK23,X0) = sK17(sK24,sK23)
| ~ spl27_31 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f1021,plain,
( spl27_31
| ~ spl27_22 ),
inference(avatar_split_clause,[],[f1014,f877,f1019]) ).
fof(f1027,plain,
( relation(sK19(sK23,sK24))
| in(sK20(sK23,sK24),sK24)
| ~ spl27_3
| ~ spl27_4
| spl27_22 ),
inference(backward_subsumption_resolution,[],[f443,f878]) ).
fof(f1029,plain,
( function(sK19(sK23,sK24))
| in(sK20(sK23,sK24),sK24)
| ~ spl27_3
| ~ spl27_4
| spl27_22 ),
inference(backward_subsumption_resolution,[],[f445,f878]) ).
fof(f1034,plain,
( relation_rng(sK19(sK23,sK24)) = relation_image(sK19(sK23,sK24),sK24)
| ~ relation(sK19(sK23,sK24))
| ~ spl27_24 ),
inference(superposition,[],[f247,f887]) ).
fof(f1039,plain,
( sK24 = relation_dom(sK19(sK23,sK24))
| in(sK20(sK23,sK24),sK24)
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_22 ),
inference(resolution,[],[f878,f233]) ).
fof(f1058,definition,
( spl27_32
<=> ! [X0] :
( element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,sK24) ) ),
introduced(definition,[new_symbols(definition,[spl27_32])],[avatar_definition]) ).
fof(f1059,plain,
( ! [X0] :
( element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,sK24) )
| ~ spl27_32 ),
inference(avatar_component_clause,[],[f1058]) ).
fof(f1060,plain,
( spl27_32
| ~ spl27_4 ),
inference(avatar_split_clause,[],[f412,f349,f1058]) ).
fof(f1107,plain,
( ~ in(sK20(sK23,sK24),sK24)
| spl27_27
| ~ spl27_32 ),
inference(resolution,[],[f1059,f994]) ).
fof(f1111,plain,
( function(sK19(sK23,sK24))
| ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_27
| ~ spl27_32 ),
inference(backward_subsumption_resolution,[],[f1029,f1107]) ).
fof(f1112,plain,
( relation(sK19(sK23,sK24))
| ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_27
| ~ spl27_32 ),
inference(backward_subsumption_resolution,[],[f1027,f1107]) ).
fof(f1139,plain,
( relation_rng(sK19(sK23,sK24)) = relation_image(sK19(sK23,sK24),sK24)
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32 ),
inference(backward_subsumption_resolution,[],[f1034,f1112]) ).
fof(f1147,definition,
( spl27_33
<=> relation_rng(sK19(sK23,sK24)) = relation_image(sK19(sK23,sK24),sK24) ),
introduced(definition,[new_symbols(definition,[spl27_33])],[avatar_definition]) ).
fof(f1148,plain,
( relation_rng(sK19(sK23,sK24)) != relation_image(sK19(sK23,sK24),sK24)
| spl27_33 ),
inference(avatar_component_clause,[],[f1147]) ).
fof(f1149,plain,
( relation_rng(sK19(sK23,sK24)) = relation_image(sK19(sK23,sK24),sK24)
| ~ spl27_33 ),
inference(avatar_component_clause,[],[f1147]) ).
fof(f1150,plain,
( spl27_33
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32 ),
inference(avatar_split_clause,[],[f1139,f1058,f992,f885,f877,f349,f308,f1147]) ).
fof(f1313,definition,
( spl27_39
<=> relation(sK13(sK23,sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_39])],[avatar_definition]) ).
fof(f1314,plain,
( ~ relation(sK13(sK23,sK24))
| spl27_39 ),
inference(avatar_component_clause,[],[f1313]) ).
fof(f1315,plain,
( relation(sK13(sK23,sK24))
| ~ spl27_39 ),
inference(avatar_component_clause,[],[f1313]) ).
fof(f1316,plain,
( ~ spl27_9
| spl27_39
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(avatar_split_clause,[],[f492,f460,f349,f308,f1313,f548]) ).
fof(f1327,plain,
( in(sK20(sK23,sK24),sK24)
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_22
| spl27_24 ),
inference(forward_subsumption_resolution,[],[f1039,f886]) ).
fof(f1328,plain,
( ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_22
| spl27_24
| spl27_27
| ~ spl27_32 ),
inference(forward_subsumption_resolution,[],[f1327,f1107]) ).
fof(f1329,plain,
( ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ spl27_3
| spl27_22
| spl27_24
| spl27_27
| ~ spl27_32 ),
inference(forward_subsumption_resolution,[],[f1328,f310]) ).
fof(f1330,plain,
( $false
| ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_24
| spl27_27
| ~ spl27_32 ),
inference(forward_subsumption_resolution,[],[f1329,f351]) ).
fof(f1331,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_24
| spl27_27
| ~ spl27_32 ),
inference(avatar_contradiction_clause,[],[f1330]) ).
fof(f1346,plain,
( ! [X0] : subset_complement(the_carrier(sK23),sK18(sK24,sK23,X0)) != X0
| ~ spl27_22 ),
inference(resolution,[],[f879,f225]) ).
fof(f1348,plain,
( ! [X0] : subset_complement(the_carrier(sK23),sK17(sK24,sK23)) != X0
| ~ spl27_22
| ~ spl27_31 ),
inference(forward_demodulation,[],[f1346,f1020]) ).
fof(f1352,plain,
( ~ spl27_30
| spl27_27
| ~ spl27_32 ),
inference(avatar_split_clause,[],[f1107,f1058,f992,f1009]) ).
fof(f1364,definition,
( spl27_42
<=> ! [X0] : subset_complement(the_carrier(sK23),sK17(sK24,sK23)) != X0 ),
introduced(definition,[new_symbols(definition,[spl27_42])],[avatar_definition]) ).
fof(f1365,plain,
( ! [X0] : subset_complement(the_carrier(sK23),sK17(sK24,sK23)) != X0
| ~ spl27_42 ),
inference(avatar_component_clause,[],[f1364]) ).
fof(f1366,plain,
( spl27_42
| ~ spl27_22
| ~ spl27_31 ),
inference(avatar_split_clause,[],[f1348,f1019,f877,f1364]) ).
fof(f1367,plain,
( $false
| ~ spl27_42 ),
inference(equality_resolution,[],[f1365]) ).
fof(f1368,plain,
~ spl27_42,
inference(avatar_contradiction_clause,[],[f1367]) ).
fof(f1369,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24)
| sP1(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4
| spl27_30 ),
inference(forward_subsumption_resolution,[],[f457,f1010]) ).
fof(f1371,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_30 ),
inference(forward_subsumption_resolution,[],[f1369,f878]) ).
fof(f1373,plain,
( relation_rng(sK19(sK23,sK24)) = relation_image(sK19(sK23,sK24),sK24)
| ~ relation(sK19(sK23,sK24))
| ~ spl27_24 ),
inference(superposition,[],[f247,f887]) ).
fof(f1374,plain,
( ! [X0] :
( in(sK4(sK19(sK23,sK24),X0),sK24)
| ~ in(X0,relation_rng(sK19(sK23,sK24)))
| ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_24 ),
inference(superposition,[],[f261,f887]) ).
fof(f1376,plain,
( ! [X0] :
( in(sK3(sK19(sK23,sK24),X0),sK24)
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0)
| ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_24 ),
inference(superposition,[],[f172,f887]) ).
fof(f1379,plain,
( ! [X0] :
( in(sK3(sK19(sK23,sK24),X0),sK24)
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0)
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32 ),
inference(forward_subsumption_resolution,[],[f1376,f1112]) ).
fof(f1381,plain,
( ! [X0] :
( in(sK4(sK19(sK23,sK24),X0),sK24)
| ~ in(X0,relation_rng(sK19(sK23,sK24)))
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32 ),
inference(forward_subsumption_resolution,[],[f1374,f1112]) ).
fof(f1383,plain,
( ! [X0] :
( in(sK3(sK19(sK23,sK24),X0),sK24)
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32 ),
inference(forward_subsumption_resolution,[],[f1379,f1111]) ).
fof(f1385,plain,
( ! [X0] :
( in(sK4(sK19(sK23,sK24),X0),sK24)
| ~ in(X0,relation_rng(sK19(sK23,sK24))) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32 ),
inference(forward_subsumption_resolution,[],[f1381,f1111]) ).
fof(f1389,plain,
( function(sK19(sK23,sK24))
| sK21(sK23,sK24) != sK22(sK23,sK24)
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_22 ),
inference(resolution,[],[f878,f238]) ).
fof(f1391,plain,
( relation(sK19(sK23,sK24))
| sK21(sK23,sK24) != sK22(sK23,sK24)
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_22 ),
inference(resolution,[],[f878,f242]) ).
fof(f1407,definition,
( spl27_43
<=> ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24) ) ),
introduced(definition,[new_symbols(definition,[spl27_43])],[avatar_definition]) ).
fof(f1408,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24) )
| ~ spl27_43 ),
inference(avatar_component_clause,[],[f1407]) ).
fof(f1409,plain,
( spl27_43
| ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_30 ),
inference(avatar_split_clause,[],[f1371,f1009,f877,f349,f308,f1407]) ).
fof(f1412,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),relation_rng(sK19(sK23,sK24)))
| ~ in(X0,relation_dom(sK19(sK23,sK24)))
| ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24))
| ~ in(X0,sK24) )
| ~ spl27_43 ),
inference(superposition,[],[f260,f1408]) ).
fof(f1414,plain,
( ! [X0] :
( sK2(sK19(sK23,sK24),X0) = subset_complement(the_carrier(sK23),sK3(sK19(sK23,sK24),X0))
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0)
| ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24))
| ~ in(sK3(sK19(sK23,sK24),X0),sK24) )
| ~ spl27_43 ),
inference(superposition,[],[f171,f1408]) ).
fof(f1415,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),sK4(sK19(sK23,sK24),X0)) = X0
| ~ in(X0,relation_rng(sK19(sK23,sK24)))
| ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24))
| ~ in(sK4(sK19(sK23,sK24),X0),sK24) )
| ~ spl27_43 ),
inference(superposition,[],[f262,f1408]) ).
fof(f1416,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),sK4(sK19(sK23,sK24),X0)) = X0
| ~ in(X0,relation_rng(sK19(sK23,sK24)))
| ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43 ),
inference(forward_subsumption_resolution,[],[f1415,f1385]) ).
fof(f1417,plain,
( ! [X0] :
( sK2(sK19(sK23,sK24),X0) = subset_complement(the_carrier(sK23),sK3(sK19(sK23,sK24),X0))
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0)
| ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43 ),
inference(forward_subsumption_resolution,[],[f1414,f1383]) ).
fof(f1419,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),relation_rng(sK19(sK23,sK24)))
| ~ in(X0,relation_dom(sK19(sK23,sK24)))
| ~ function(sK19(sK23,sK24))
| ~ in(X0,sK24) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_27
| ~ spl27_32
| ~ spl27_43 ),
inference(forward_subsumption_resolution,[],[f1412,f1112]) ).
fof(f1422,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),sK4(sK19(sK23,sK24),X0)) = X0
| ~ in(X0,relation_rng(sK19(sK23,sK24)))
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43 ),
inference(forward_subsumption_resolution,[],[f1416,f1112]) ).
fof(f1423,plain,
( ! [X0] :
( sK2(sK19(sK23,sK24),X0) = subset_complement(the_carrier(sK23),sK3(sK19(sK23,sK24),X0))
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0)
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43 ),
inference(forward_subsumption_resolution,[],[f1417,f1112]) ).
fof(f1425,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),relation_rng(sK19(sK23,sK24)))
| ~ in(X0,relation_dom(sK19(sK23,sK24)))
| ~ in(X0,sK24) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_27
| ~ spl27_32
| ~ spl27_43 ),
inference(forward_subsumption_resolution,[],[f1419,f1111]) ).
fof(f1428,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),sK4(sK19(sK23,sK24),X0)) = X0
| ~ in(X0,relation_rng(sK19(sK23,sK24))) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43 ),
inference(forward_subsumption_resolution,[],[f1422,f1111]) ).
fof(f1429,plain,
( ! [X0] :
( sK2(sK19(sK23,sK24),X0) = subset_complement(the_carrier(sK23),sK3(sK19(sK23,sK24),X0))
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43 ),
inference(forward_subsumption_resolution,[],[f1423,f1111]) ).
fof(f1432,plain,
( ! [X0] :
( ~ in(X0,sK24)
| in(subset_complement(the_carrier(sK23),X0),relation_rng(sK19(sK23,sK24)))
| ~ in(X0,sK24) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43 ),
inference(forward_demodulation,[],[f1425,f887]) ).
fof(f1433,plain,
( ! [X0] :
( ~ in(X0,sK24)
| in(subset_complement(the_carrier(sK23),X0),relation_rng(sK19(sK23,sK24))) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43 ),
inference(duplicate_literal_removal,[],[f1432]) ).
fof(f1438,definition,
( spl27_44
<=> ! [X0] :
( in(sK3(sK19(sK23,sK24),X0),sK24)
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_44])],[avatar_definition]) ).
fof(f1439,plain,
( ! [X0] :
( in(sK3(sK19(sK23,sK24),X0),sK24)
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_44 ),
inference(avatar_component_clause,[],[f1438]) ).
fof(f1440,plain,
( spl27_44
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32 ),
inference(avatar_split_clause,[],[f1383,f1058,f992,f885,f877,f349,f308,f1438]) ).
fof(f1465,plain,
( ~ spl27_11
| spl27_14
| spl27_39
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(avatar_split_clause,[],[f491,f460,f349,f308,f1313,f574,f557]) ).
fof(f1467,definition,
( spl27_45
<=> function(sK13(sK23,sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_45])],[avatar_definition]) ).
fof(f1469,plain,
( function(sK13(sK23,sK24))
| ~ spl27_45 ),
inference(avatar_component_clause,[],[f1467]) ).
fof(f1470,plain,
( ~ spl27_9
| spl27_45
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(avatar_split_clause,[],[f494,f460,f349,f308,f1467,f548]) ).
fof(f1471,plain,
( ~ spl27_11
| spl27_15
| spl27_39
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(avatar_split_clause,[],[f490,f460,f349,f308,f1313,f579,f557]) ).
fof(f1495,plain,
( ~ spl27_11
| spl27_14
| spl27_45
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(avatar_split_clause,[],[f489,f460,f349,f308,f1467,f574,f557]) ).
fof(f1496,plain,
( ~ spl27_11
| spl27_15
| spl27_45
| ~ spl27_3
| ~ spl27_4
| spl27_5 ),
inference(avatar_split_clause,[],[f488,f460,f349,f308,f1467,f579,f557]) ).
fof(f1498,definition,
( spl27_47
<=> ! [X0] :
( sK2(sK19(sK23,sK24),X0) = subset_complement(the_carrier(sK23),sK3(sK19(sK23,sK24),X0))
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_47])],[avatar_definition]) ).
fof(f1499,plain,
( ! [X0] :
( sK2(sK19(sK23,sK24),X0) = subset_complement(the_carrier(sK23),sK3(sK19(sK23,sK24),X0))
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_47 ),
inference(avatar_component_clause,[],[f1498]) ).
fof(f1500,plain,
( spl27_47
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43 ),
inference(avatar_split_clause,[],[f1429,f1407,f1058,f992,f885,f877,f349,f308,f1498]) ).
fof(f1502,definition,
( spl27_48
<=> ! [X0] :
( ~ in(X0,sK24)
| in(subset_complement(the_carrier(sK23),X0),relation_rng(sK19(sK23,sK24))) ) ),
introduced(definition,[new_symbols(definition,[spl27_48])],[avatar_definition]) ).
fof(f1503,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),relation_rng(sK19(sK23,sK24)))
| ~ in(X0,sK24) )
| ~ spl27_48 ),
inference(avatar_component_clause,[],[f1502]) ).
fof(f1504,plain,
( spl27_48
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43 ),
inference(avatar_split_clause,[],[f1433,f1407,f1058,f992,f885,f877,f349,f308,f1502]) ).
fof(f1515,definition,
( spl27_51
<=> ! [X0] :
( in(sK4(sK19(sK23,sK24),X0),sK24)
| ~ in(X0,relation_rng(sK19(sK23,sK24))) ) ),
introduced(definition,[new_symbols(definition,[spl27_51])],[avatar_definition]) ).
fof(f1516,plain,
( ! [X0] :
( in(sK4(sK19(sK23,sK24),X0),sK24)
| ~ in(X0,relation_rng(sK19(sK23,sK24))) )
| ~ spl27_51 ),
inference(avatar_component_clause,[],[f1515]) ).
fof(f1529,plain,
( ! [X0] :
( in(sK2(sK19(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ in(sK3(sK19(sK23,sK24),X0),sK24)
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_18
| ~ spl27_47 ),
inference(superposition,[],[f734,f1499]) ).
fof(f1537,plain,
( ! [X0] :
( in(sK2(sK19(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_18
| ~ spl27_44
| ~ spl27_47 ),
inference(forward_subsumption_resolution,[],[f1529,f1439]) ).
fof(f1595,plain,
( ! [X0] :
( in(X0,relation_rng(sK19(sK23,sK24)))
| ~ in(subset_complement(the_carrier(sK23),X0),sK24)
| ~ element(X0,powerset(the_carrier(sK23))) )
| ~ spl27_48 ),
inference(superposition,[],[f1503,f190]) ).
fof(f1654,definition,
( spl27_54
<=> element(complements_of_subsets(the_carrier(sK23),sK24),powerset(powerset(the_carrier(sK23)))) ),
introduced(definition,[new_symbols(definition,[spl27_54])],[avatar_definition]) ).
fof(f1656,plain,
( element(complements_of_subsets(the_carrier(sK23),sK24),powerset(powerset(the_carrier(sK23))))
| ~ spl27_54 ),
inference(avatar_component_clause,[],[f1654]) ).
fof(f1657,plain,
( spl27_54
| ~ spl27_4 ),
inference(avatar_split_clause,[],[f391,f349,f1654]) ).
fof(f1719,plain,
( ! [X0] :
( element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) )
| ~ spl27_54 ),
inference(resolution,[],[f1656,f254]) ).
fof(f1850,definition,
( spl27_56
<=> ! [X0] :
( subset_complement(the_carrier(sK23),sK4(sK19(sK23,sK24),X0)) = X0
| ~ in(X0,relation_rng(sK19(sK23,sK24))) ) ),
introduced(definition,[new_symbols(definition,[spl27_56])],[avatar_definition]) ).
fof(f1851,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),sK4(sK19(sK23,sK24),X0)) = X0
| ~ in(X0,relation_rng(sK19(sK23,sK24))) )
| ~ spl27_56 ),
inference(avatar_component_clause,[],[f1850]) ).
fof(f1852,plain,
( spl27_56
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43 ),
inference(avatar_split_clause,[],[f1428,f1407,f1058,f992,f885,f877,f349,f308,f1850]) ).
fof(f1929,definition,
( spl27_59
<=> ! [X0] :
( in(sK2(sK19(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_59])],[avatar_definition]) ).
fof(f1930,plain,
( ! [X0] :
( in(sK2(sK19(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| relation_rng(sK19(sK23,sK24)) = X0
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_59 ),
inference(avatar_component_clause,[],[f1929]) ).
fof(f1931,plain,
( spl27_59
| ~ spl27_18
| ~ spl27_44
| ~ spl27_47 ),
inference(avatar_split_clause,[],[f1537,f1498,f1438,f733,f1929]) ).
fof(f1949,plain,
( in(sK2(sK19(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24)),complements_of_subsets(the_carrier(sK23),sK24))
| complements_of_subsets(the_carrier(sK23),sK24) = relation_rng(sK19(sK23,sK24))
| ~ spl27_59 ),
inference(factoring,[],[f1930]) ).
fof(f2026,definition,
( spl27_64
<=> relation(sK19(sK23,sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_64])],[avatar_definition]) ).
fof(f2027,plain,
( ~ relation(sK19(sK23,sK24))
| spl27_64 ),
inference(avatar_component_clause,[],[f2026]) ).
fof(f2028,plain,
( relation(sK19(sK23,sK24))
| ~ spl27_64 ),
inference(avatar_component_clause,[],[f2026]) ).
fof(f2029,plain,
( spl27_64
| ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_27
| ~ spl27_32 ),
inference(avatar_split_clause,[],[f1112,f1058,f992,f877,f349,f308,f2026]) ).
fof(f2051,definition,
( spl27_65
<=> ! [X0] :
( finite(relation_image(sK19(sK23,sK24),X0))
| ~ finite(X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_65])],[avatar_definition]) ).
fof(f2052,plain,
( ! [X0] :
( finite(relation_image(sK19(sK23,sK24),X0))
| ~ finite(X0) )
| ~ spl27_65 ),
inference(avatar_component_clause,[],[f2051]) ).
fof(f2055,plain,
( finite(relation_rng(sK19(sK23,sK24)))
| ~ finite(sK24)
| ~ spl27_33
| ~ spl27_65 ),
inference(superposition,[],[f2052,f1149]) ).
fof(f2311,definition,
( spl27_72
<=> function(sK19(sK23,sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_72])],[avatar_definition]) ).
fof(f2312,plain,
( ~ function(sK19(sK23,sK24))
| spl27_72 ),
inference(avatar_component_clause,[],[f2311]) ).
fof(f2313,plain,
( function(sK19(sK23,sK24))
| ~ spl27_72 ),
inference(avatar_component_clause,[],[f2311]) ).
fof(f2314,plain,
( spl27_72
| ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_27
| ~ spl27_32 ),
inference(avatar_split_clause,[],[f1111,f1058,f992,f877,f349,f308,f2311]) ).
fof(f2347,plain,
( function(sK13(sK23,sK24))
| ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_6 ),
inference(forward_subsumption_resolution,[],[f495,f465]) ).
fof(f2661,plain,
( relation_rng(sK13(sK23,sK24)) = relation_image(sK13(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| ~ relation(sK13(sK23,sK24))
| ~ spl27_7 ),
inference(superposition,[],[f247,f470]) ).
fof(f2662,plain,
( ! [X0] :
( in(sK4(sK13(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ in(X0,relation_rng(sK13(sK23,sK24)))
| ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24)) )
| ~ spl27_7 ),
inference(superposition,[],[f261,f470]) ).
fof(f2976,plain,
( ! [X0] : sK12(sK24,sK23,X0) = sK11(sK24,sK23)
| ~ spl27_5 ),
inference(resolution,[],[f462,f204]) ).
fof(f2977,plain,
( ! [X0] : subset_complement(the_carrier(sK23),sK12(sK24,sK23,X0)) != X0
| ~ spl27_5 ),
inference(resolution,[],[f462,f205]) ).
fof(f2981,definition,
( spl27_76
<=> ! [X0] : subset_complement(the_carrier(sK23),sK12(sK24,sK23,X0)) != X0 ),
introduced(definition,[new_symbols(definition,[spl27_76])],[avatar_definition]) ).
fof(f2982,plain,
( ! [X0] : subset_complement(the_carrier(sK23),sK12(sK24,sK23,X0)) != X0
| ~ spl27_76 ),
inference(avatar_component_clause,[],[f2981]) ).
fof(f2983,plain,
( spl27_76
| ~ spl27_5 ),
inference(avatar_split_clause,[],[f2977,f460,f2981]) ).
fof(f2984,plain,
( ! [X0] : subset_complement(the_carrier(sK23),sK11(sK24,sK23)) != X0
| ~ spl27_5
| ~ spl27_76 ),
inference(forward_demodulation,[],[f2982,f2976]) ).
fof(f2986,definition,
( spl27_77
<=> ! [X0] : subset_complement(the_carrier(sK23),sK11(sK24,sK23)) != X0 ),
introduced(definition,[new_symbols(definition,[spl27_77])],[avatar_definition]) ).
fof(f2987,plain,
( ! [X0] : subset_complement(the_carrier(sK23),sK11(sK24,sK23)) != X0
| ~ spl27_77 ),
inference(avatar_component_clause,[],[f2986]) ).
fof(f2988,plain,
( spl27_77
| ~ spl27_5
| ~ spl27_76 ),
inference(avatar_split_clause,[],[f2984,f2981,f460,f2986]) ).
fof(f2989,plain,
( $false
| ~ spl27_77 ),
inference(equality_resolution,[],[f2987]) ).
fof(f2990,plain,
~ spl27_77,
inference(avatar_contradiction_clause,[],[f2989]) ).
fof(f2991,plain,
( sK15(sK23,sK24) = sK16(sK23,sK24)
| ~ spl27_14
| ~ spl27_15 ),
inference(forward_demodulation,[],[f581,f576]) ).
fof(f3012,plain,
( $false
| spl27_9
| ~ spl27_14
| ~ spl27_15 ),
inference(forward_subsumption_resolution,[],[f2991,f550]) ).
fof(f3013,plain,
( spl27_9
| ~ spl27_14
| ~ spl27_15 ),
inference(avatar_contradiction_clause,[],[f3012]) ).
fof(f3102,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) )
| ~ spl27_10
| ~ spl27_54 ),
inference(forward_subsumption_resolution,[],[f554,f1719]) ).
fof(f3114,plain,
( ! [X0] :
( in(sK4(sK13(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ in(X0,relation_rng(sK13(sK23,sK24)))
| ~ function(sK13(sK23,sK24)) )
| ~ spl27_7
| ~ spl27_39 ),
inference(forward_subsumption_resolution,[],[f2662,f1315]) ).
fof(f3115,plain,
( relation_rng(sK13(sK23,sK24)) = relation_image(sK13(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_7
| ~ spl27_39 ),
inference(forward_subsumption_resolution,[],[f2661,f1315]) ).
fof(f3125,plain,
( ! [X0] :
( in(sK4(sK13(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ in(X0,relation_rng(sK13(sK23,sK24))) )
| ~ spl27_7
| ~ spl27_39
| ~ spl27_45 ),
inference(forward_subsumption_resolution,[],[f3114,f1469]) ).
fof(f3234,definition,
( spl27_81
<=> ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) ) ),
introduced(definition,[new_symbols(definition,[spl27_81])],[avatar_definition]) ).
fof(f3235,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) )
| ~ spl27_81 ),
inference(avatar_component_clause,[],[f3234]) ).
fof(f3236,plain,
( spl27_81
| ~ spl27_10
| ~ spl27_54 ),
inference(avatar_split_clause,[],[f3102,f1654,f553,f3234]) ).
fof(f3239,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),relation_rng(sK13(sK23,sK24)))
| ~ in(X0,relation_dom(sK13(sK23,sK24)))
| ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) )
| ~ spl27_81 ),
inference(superposition,[],[f260,f3235]) ).
fof(f3246,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),relation_rng(sK13(sK23,sK24)))
| ~ in(X0,relation_dom(sK13(sK23,sK24)))
| ~ function(sK13(sK23,sK24))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) )
| ~ spl27_39
| ~ spl27_81 ),
inference(forward_subsumption_resolution,[],[f3239,f1315]) ).
fof(f3252,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),relation_rng(sK13(sK23,sK24)))
| ~ in(X0,relation_dom(sK13(sK23,sK24)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) )
| ~ spl27_39
| ~ spl27_45
| ~ spl27_81 ),
inference(forward_subsumption_resolution,[],[f3246,f1469]) ).
fof(f3259,plain,
( ! [X0] :
( ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| in(subset_complement(the_carrier(sK23),X0),relation_rng(sK13(sK23,sK24)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) )
| ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| ~ spl27_81 ),
inference(forward_demodulation,[],[f3252,f470]) ).
fof(f3260,plain,
( ! [X0] :
( ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| in(subset_complement(the_carrier(sK23),X0),relation_rng(sK13(sK23,sK24))) )
| ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| ~ spl27_81 ),
inference(duplicate_literal_removal,[],[f3259]) ).
fof(f3376,definition,
( spl27_86
<=> relation_rng(sK13(sK23,sK24)) = relation_image(sK13(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_86])],[avatar_definition]) ).
fof(f3378,plain,
( relation_rng(sK13(sK23,sK24)) = relation_image(sK13(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_86 ),
inference(avatar_component_clause,[],[f3376]) ).
fof(f3379,plain,
( spl27_86
| ~ spl27_7
| ~ spl27_39 ),
inference(avatar_split_clause,[],[f3115,f1313,f468,f3376]) ).
fof(f3383,plain,
( finite(relation_rng(sK13(sK23,sK24)))
| ~ finite(complements_of_subsets(the_carrier(sK23),sK24))
| ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24))
| ~ spl27_86 ),
inference(superposition,[],[f248,f3378]) ).
fof(f3384,plain,
( finite(relation_rng(sK13(sK23,sK24)))
| ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24))
| ~ spl27_1
| ~ spl27_86 ),
inference(forward_subsumption_resolution,[],[f3383,f293]) ).
fof(f3388,plain,
( finite(relation_rng(sK13(sK23,sK24)))
| ~ function(sK13(sK23,sK24))
| ~ spl27_1
| ~ spl27_39
| ~ spl27_86 ),
inference(forward_subsumption_resolution,[],[f3384,f1315]) ).
fof(f3389,plain,
( finite(relation_rng(sK13(sK23,sK24)))
| ~ spl27_1
| ~ spl27_39
| ~ spl27_45
| ~ spl27_86 ),
inference(forward_subsumption_resolution,[],[f3388,f1469]) ).
fof(f3456,plain,
( relation_rng(sK13(sK23,sK24)) = relation_image(sK13(sK23,sK24),relation_dom(sK13(sK23,sK24)))
| ~ spl27_39 ),
inference(resolution,[],[f1315,f247]) ).
fof(f3457,plain,
( ! [X0] :
( finite(relation_image(sK13(sK23,sK24),X0))
| ~ finite(X0)
| ~ function(sK13(sK23,sK24)) )
| ~ spl27_39 ),
inference(resolution,[],[f1315,f248]) ).
fof(f3460,plain,
( ! [X0] :
( apply(sK13(sK23,sK24),sK4(sK13(sK23,sK24),X0)) = X0
| ~ in(X0,relation_rng(sK13(sK23,sK24)))
| ~ function(sK13(sK23,sK24)) )
| ~ spl27_39 ),
inference(resolution,[],[f1315,f262]) ).
fof(f3461,plain,
( ! [X0] :
( apply(sK13(sK23,sK24),sK4(sK13(sK23,sK24),X0)) = X0
| ~ in(X0,relation_rng(sK13(sK23,sK24))) )
| ~ spl27_39
| ~ spl27_45 ),
inference(forward_subsumption_resolution,[],[f3460,f1469]) ).
fof(f3464,plain,
( ! [X0] :
( finite(relation_image(sK13(sK23,sK24),X0))
| ~ finite(X0) )
| ~ spl27_39
| ~ spl27_45 ),
inference(forward_subsumption_resolution,[],[f3457,f1469]) ).
fof(f3474,definition,
( spl27_89
<=> ! [X0] :
( finite(relation_image(sK13(sK23,sK24),X0))
| ~ finite(X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_89])],[avatar_definition]) ).
fof(f3475,plain,
( ! [X0] :
( finite(relation_image(sK13(sK23,sK24),X0))
| ~ finite(X0) )
| ~ spl27_89 ),
inference(avatar_component_clause,[],[f3474]) ).
fof(f3476,plain,
( spl27_89
| ~ spl27_39
| ~ spl27_45 ),
inference(avatar_split_clause,[],[f3464,f1467,f1313,f3474]) ).
fof(f3478,plain,
( finite(relation_rng(sK13(sK23,sK24)))
| ~ finite(complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_86
| ~ spl27_89 ),
inference(superposition,[],[f3475,f3378]) ).
fof(f3516,definition,
( spl27_90
<=> finite(relation_rng(sK13(sK23,sK24))) ),
introduced(definition,[new_symbols(definition,[spl27_90])],[avatar_definition]) ).
fof(f3517,plain,
( ~ finite(relation_rng(sK13(sK23,sK24)))
| spl27_90 ),
inference(avatar_component_clause,[],[f3516]) ).
fof(f3518,plain,
( finite(relation_rng(sK13(sK23,sK24)))
| ~ spl27_90 ),
inference(avatar_component_clause,[],[f3516]) ).
fof(f3519,plain,
( spl27_90
| ~ spl27_1
| ~ spl27_39
| ~ spl27_45
| ~ spl27_86 ),
inference(avatar_split_clause,[],[f3389,f3376,f1467,f1313,f292,f3516]) ).
fof(f3571,definition,
( spl27_92
<=> ! [X0] :
( apply(sK13(sK23,sK24),sK4(sK13(sK23,sK24),X0)) = X0
| ~ in(X0,relation_rng(sK13(sK23,sK24))) ) ),
introduced(definition,[new_symbols(definition,[spl27_92])],[avatar_definition]) ).
fof(f3572,plain,
( ! [X0] :
( apply(sK13(sK23,sK24),sK4(sK13(sK23,sK24),X0)) = X0
| ~ in(X0,relation_rng(sK13(sK23,sK24))) )
| ~ spl27_92 ),
inference(avatar_component_clause,[],[f3571]) ).
fof(f3573,plain,
( spl27_92
| ~ spl27_39
| ~ spl27_45 ),
inference(avatar_split_clause,[],[f3461,f1467,f1313,f3571]) ).
fof(f3649,definition,
( spl27_95
<=> ! [X0] :
( ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| in(subset_complement(the_carrier(sK23),X0),relation_rng(sK13(sK23,sK24))) ) ),
introduced(definition,[new_symbols(definition,[spl27_95])],[avatar_definition]) ).
fof(f3650,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),relation_rng(sK13(sK23,sK24)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) )
| ~ spl27_95 ),
inference(avatar_component_clause,[],[f3649]) ).
fof(f3651,plain,
( spl27_95
| ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| ~ spl27_81 ),
inference(avatar_split_clause,[],[f3260,f3234,f1467,f1313,f468,f3649]) ).
fof(f3686,plain,
( ! [X0] :
( in(X0,relation_rng(sK13(sK23,sK24)))
| ~ in(subset_complement(the_carrier(sK23),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(X0,powerset(the_carrier(sK23))) )
| ~ spl27_95 ),
inference(superposition,[],[f3650,f190]) ).
fof(f3791,definition,
( spl27_96
<=> ! [X0] :
( in(sK4(sK13(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ in(X0,relation_rng(sK13(sK23,sK24))) ) ),
introduced(definition,[new_symbols(definition,[spl27_96])],[avatar_definition]) ).
fof(f3792,plain,
( ! [X0] :
( in(sK4(sK13(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ in(X0,relation_rng(sK13(sK23,sK24))) )
| ~ spl27_96 ),
inference(avatar_component_clause,[],[f3791]) ).
fof(f3793,plain,
( spl27_96
| ~ spl27_7
| ~ spl27_39
| ~ spl27_45 ),
inference(avatar_split_clause,[],[f3125,f1467,f1313,f468,f3791]) ).
fof(f4114,plain,
( ! [X0] :
( finite(X0)
| in(sK3(sK13(sK23,sK24),X0),relation_dom(sK13(sK23,sK24)))
| in(sK2(sK13(sK23,sK24),X0),X0)
| ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24)) )
| ~ spl27_90 ),
inference(superposition,[],[f3518,f172]) ).
fof(f4115,plain,
( ! [X0,X1] :
( finite(X0)
| ~ in(X1,relation_dom(sK13(sK23,sK24)))
| sK2(sK13(sK23,sK24),X0) != apply(sK13(sK23,sK24),X1)
| ~ in(sK2(sK13(sK23,sK24),X0),X0)
| ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24)) )
| ~ spl27_90 ),
inference(superposition,[],[f3518,f173]) ).
fof(f4116,plain,
( ! [X0,X1] :
( finite(X0)
| ~ in(X1,relation_dom(sK13(sK23,sK24)))
| sK2(sK13(sK23,sK24),X0) != apply(sK13(sK23,sK24),X1)
| ~ in(sK2(sK13(sK23,sK24),X0),X0)
| ~ function(sK13(sK23,sK24)) )
| ~ spl27_39
| ~ spl27_90 ),
inference(forward_subsumption_resolution,[],[f4115,f1315]) ).
fof(f4117,plain,
( ! [X0] :
( finite(X0)
| in(sK3(sK13(sK23,sK24),X0),relation_dom(sK13(sK23,sK24)))
| in(sK2(sK13(sK23,sK24),X0),X0)
| ~ function(sK13(sK23,sK24)) )
| ~ spl27_39
| ~ spl27_90 ),
inference(forward_subsumption_resolution,[],[f4114,f1315]) ).
fof(f4119,plain,
( ! [X0,X1] :
( finite(X0)
| ~ in(X1,relation_dom(sK13(sK23,sK24)))
| sK2(sK13(sK23,sK24),X0) != apply(sK13(sK23,sK24),X1)
| ~ in(sK2(sK13(sK23,sK24),X0),X0) )
| ~ spl27_39
| ~ spl27_45
| ~ spl27_90 ),
inference(forward_subsumption_resolution,[],[f4116,f1469]) ).
fof(f4120,plain,
( ! [X0] :
( finite(X0)
| in(sK3(sK13(sK23,sK24),X0),relation_dom(sK13(sK23,sK24)))
| in(sK2(sK13(sK23,sK24),X0),X0) )
| ~ spl27_39
| ~ spl27_45
| ~ spl27_90 ),
inference(forward_subsumption_resolution,[],[f4117,f1469]) ).
fof(f4122,plain,
( ! [X0,X1] :
( ~ in(X1,complements_of_subsets(the_carrier(sK23),sK24))
| finite(X0)
| sK2(sK13(sK23,sK24),X0) != apply(sK13(sK23,sK24),X1)
| ~ in(sK2(sK13(sK23,sK24),X0),X0) )
| ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| ~ spl27_90 ),
inference(forward_demodulation,[],[f4119,f470]) ).
fof(f4123,plain,
( ! [X0] :
( in(sK3(sK13(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| finite(X0)
| in(sK2(sK13(sK23,sK24),X0),X0) )
| ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| ~ spl27_90 ),
inference(forward_demodulation,[],[f4120,f470]) ).
fof(f4125,definition,
( spl27_106
<=> ! [X0] :
( in(sK3(sK13(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| finite(X0)
| in(sK2(sK13(sK23,sK24),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_106])],[avatar_definition]) ).
fof(f4126,plain,
( ! [X0] :
( in(sK3(sK13(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| finite(X0)
| in(sK2(sK13(sK23,sK24),X0),X0) )
| ~ spl27_106 ),
inference(avatar_component_clause,[],[f4125]) ).
fof(f4127,plain,
( spl27_106
| ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| ~ spl27_90 ),
inference(avatar_split_clause,[],[f4123,f3516,f1467,f1313,f468,f4125]) ).
fof(f4128,plain,
( ! [X0] :
( finite(X0)
| in(sK2(sK13(sK23,sK24),X0),X0)
| in(subset_complement(the_carrier(sK23),sK3(sK13(sK23,sK24),X0)),sK24) )
| ~ spl27_21
| ~ spl27_106 ),
inference(resolution,[],[f4126,f843]) ).
fof(f4177,definition,
( spl27_108
<=> ! [X0,X1] :
( ~ in(X1,complements_of_subsets(the_carrier(sK23),sK24))
| finite(X0)
| sK2(sK13(sK23,sK24),X0) != apply(sK13(sK23,sK24),X1)
| ~ in(sK2(sK13(sK23,sK24),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_108])],[avatar_definition]) ).
fof(f4178,plain,
( ! [X0,X1] :
( sK2(sK13(sK23,sK24),X0) != apply(sK13(sK23,sK24),X1)
| finite(X0)
| ~ in(X1,complements_of_subsets(the_carrier(sK23),sK24))
| ~ in(sK2(sK13(sK23,sK24),X0),X0) )
| ~ spl27_108 ),
inference(avatar_component_clause,[],[f4177]) ).
fof(f4179,plain,
( spl27_108
| ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| ~ spl27_90 ),
inference(avatar_split_clause,[],[f4122,f3516,f1467,f1313,f468,f4177]) ).
fof(f4189,plain,
( ! [X0,X1] :
( sK2(sK13(sK23,sK24),X1) != X0
| finite(X1)
| ~ in(sK4(sK13(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ in(sK2(sK13(sK23,sK24),X1),X1)
| ~ in(X0,relation_rng(sK13(sK23,sK24))) )
| ~ spl27_92
| ~ spl27_108 ),
inference(superposition,[],[f4178,f3572]) ).
fof(f4202,plain,
( ! [X0,X1] :
( sK2(sK13(sK23,sK24),X1) != X0
| finite(X1)
| ~ in(sK2(sK13(sK23,sK24),X1),X1)
| ~ in(X0,relation_rng(sK13(sK23,sK24))) )
| ~ spl27_92
| ~ spl27_96
| ~ spl27_108 ),
inference(forward_subsumption_resolution,[],[f4189,f3792]) ).
fof(f4217,plain,
( finite(relation_rng(sK19(sK23,sK24)))
| spl27_1
| ~ spl27_33
| ~ spl27_65 ),
inference(forward_subsumption_resolution,[],[f2055,f300]) ).
fof(f4278,plain,
( spl27_2
| spl27_1 ),
inference(avatar_split_clause,[],[f300,f292,f296]) ).
fof(f4371,definition,
( spl27_111
<=> ! [X0,X1] :
( sK2(sK13(sK23,sK24),X1) != X0
| finite(X1)
| ~ in(sK2(sK13(sK23,sK24),X1),X1)
| ~ in(X0,relation_rng(sK13(sK23,sK24))) ) ),
introduced(definition,[new_symbols(definition,[spl27_111])],[avatar_definition]) ).
fof(f4372,plain,
( ! [X0,X1] :
( sK2(sK13(sK23,sK24),X1) != X0
| finite(X1)
| ~ in(sK2(sK13(sK23,sK24),X1),X1)
| ~ in(X0,relation_rng(sK13(sK23,sK24))) )
| ~ spl27_111 ),
inference(avatar_component_clause,[],[f4371]) ).
fof(f4373,plain,
( spl27_111
| ~ spl27_92
| ~ spl27_96
| ~ spl27_108 ),
inference(avatar_split_clause,[],[f4202,f4177,f3791,f3571,f4371]) ).
fof(f4374,plain,
( ! [X0] :
( finite(X0)
| ~ in(sK2(sK13(sK23,sK24),X0),X0)
| ~ in(sK2(sK13(sK23,sK24),X0),relation_rng(sK13(sK23,sK24))) )
| ~ spl27_111 ),
inference(equality_resolution,[],[f4372]) ).
fof(f4376,definition,
( spl27_112
<=> ! [X0] :
( finite(X0)
| ~ in(sK2(sK13(sK23,sK24),X0),X0)
| ~ in(sK2(sK13(sK23,sK24),X0),relation_rng(sK13(sK23,sK24))) ) ),
introduced(definition,[new_symbols(definition,[spl27_112])],[avatar_definition]) ).
fof(f4377,plain,
( ! [X0] :
( ~ in(sK2(sK13(sK23,sK24),X0),relation_rng(sK13(sK23,sK24)))
| ~ in(sK2(sK13(sK23,sK24),X0),X0)
| finite(X0) )
| ~ spl27_112 ),
inference(avatar_component_clause,[],[f4376]) ).
fof(f4378,plain,
( spl27_112
| ~ spl27_111 ),
inference(avatar_split_clause,[],[f4374,f4371,f4376]) ).
fof(f4547,plain,
( ! [X0] :
( finite(relation_image(X0,sK24))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl27_2 ),
inference(resolution,[],[f297,f248]) ).
fof(f4561,definition,
( spl27_118
<=> finite(relation_rng(sK19(sK23,sK24))) ),
introduced(definition,[new_symbols(definition,[spl27_118])],[avatar_definition]) ).
fof(f4562,plain,
( ~ finite(relation_rng(sK19(sK23,sK24)))
| spl27_118 ),
inference(avatar_component_clause,[],[f4561]) ).
fof(f4563,plain,
( finite(relation_rng(sK19(sK23,sK24)))
| ~ spl27_118 ),
inference(avatar_component_clause,[],[f4561]) ).
fof(f4564,plain,
( spl27_118
| spl27_1
| ~ spl27_33
| ~ spl27_65 ),
inference(avatar_split_clause,[],[f4217,f2051,f1147,f292,f4561]) ).
fof(f4596,definition,
( spl27_120
<=> ! [X0] :
( finite(relation_image(X0,sK24))
| ~ relation(X0)
| ~ function(X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_120])],[avatar_definition]) ).
fof(f4597,plain,
( ! [X0] :
( finite(relation_image(X0,sK24))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl27_120 ),
inference(avatar_component_clause,[],[f4596]) ).
fof(f4598,plain,
( spl27_120
| ~ spl27_2 ),
inference(avatar_split_clause,[],[f4547,f296,f4596]) ).
fof(f4600,plain,
( finite(relation_rng(sK19(sK23,sK24)))
| ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24))
| ~ spl27_33
| ~ spl27_120 ),
inference(superposition,[],[f4597,f1149]) ).
fof(f5144,plain,
( ! [X0] :
( finite(X0)
| sK2(sK19(sK23,sK24),X0) = apply(sK19(sK23,sK24),sK3(sK19(sK23,sK24),X0))
| in(sK2(sK19(sK23,sK24),X0),X0)
| ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_118 ),
inference(superposition,[],[f4563,f171]) ).
fof(f5145,plain,
( ! [X0] :
( finite(X0)
| in(sK3(sK19(sK23,sK24),X0),relation_dom(sK19(sK23,sK24)))
| in(sK2(sK19(sK23,sK24),X0),X0)
| ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_118 ),
inference(superposition,[],[f4563,f172]) ).
fof(f5146,plain,
( ! [X0,X1] :
( finite(X0)
| ~ in(X1,relation_dom(sK19(sK23,sK24)))
| sK2(sK19(sK23,sK24),X0) != apply(sK19(sK23,sK24),X1)
| ~ in(sK2(sK19(sK23,sK24),X0),X0)
| ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_118 ),
inference(superposition,[],[f4563,f173]) ).
fof(f5147,plain,
( ! [X0,X1] :
( finite(X0)
| ~ in(X1,relation_dom(sK19(sK23,sK24)))
| sK2(sK19(sK23,sK24),X0) != apply(sK19(sK23,sK24),X1)
| ~ in(sK2(sK19(sK23,sK24),X0),X0)
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_64
| ~ spl27_118 ),
inference(forward_subsumption_resolution,[],[f5146,f2028]) ).
fof(f5148,plain,
( ! [X0] :
( finite(X0)
| in(sK3(sK19(sK23,sK24),X0),relation_dom(sK19(sK23,sK24)))
| in(sK2(sK19(sK23,sK24),X0),X0)
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_64
| ~ spl27_118 ),
inference(forward_subsumption_resolution,[],[f5145,f2028]) ).
fof(f5149,plain,
( ! [X0] :
( finite(X0)
| sK2(sK19(sK23,sK24),X0) = apply(sK19(sK23,sK24),sK3(sK19(sK23,sK24),X0))
| in(sK2(sK19(sK23,sK24),X0),X0)
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_64
| ~ spl27_118 ),
inference(forward_subsumption_resolution,[],[f5144,f2028]) ).
fof(f5150,plain,
( ! [X0,X1] :
( finite(X0)
| ~ in(X1,relation_dom(sK19(sK23,sK24)))
| sK2(sK19(sK23,sK24),X0) != apply(sK19(sK23,sK24),X1)
| ~ in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_64
| ~ spl27_72
| ~ spl27_118 ),
inference(forward_subsumption_resolution,[],[f5147,f2313]) ).
fof(f5151,plain,
( ! [X0] :
( finite(X0)
| in(sK3(sK19(sK23,sK24),X0),relation_dom(sK19(sK23,sK24)))
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_64
| ~ spl27_72
| ~ spl27_118 ),
inference(forward_subsumption_resolution,[],[f5148,f2313]) ).
fof(f5152,plain,
( ! [X0] :
( finite(X0)
| sK2(sK19(sK23,sK24),X0) = apply(sK19(sK23,sK24),sK3(sK19(sK23,sK24),X0))
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_64
| ~ spl27_72
| ~ spl27_118 ),
inference(forward_subsumption_resolution,[],[f5149,f2313]) ).
fof(f5153,plain,
( ! [X0,X1] :
( ~ in(X1,sK24)
| finite(X0)
| sK2(sK19(sK23,sK24),X0) != apply(sK19(sK23,sK24),X1)
| ~ in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_24
| ~ spl27_64
| ~ spl27_72
| ~ spl27_118 ),
inference(forward_demodulation,[],[f5150,f887]) ).
fof(f5154,plain,
( ! [X0] :
( in(sK3(sK19(sK23,sK24),X0),sK24)
| finite(X0)
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_24
| ~ spl27_64
| ~ spl27_72
| ~ spl27_118 ),
inference(forward_demodulation,[],[f5151,f887]) ).
fof(f5156,definition,
( spl27_134
<=> ! [X0] :
( in(sK3(sK19(sK23,sK24),X0),sK24)
| finite(X0)
| in(sK2(sK19(sK23,sK24),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_134])],[avatar_definition]) ).
fof(f5157,plain,
( ! [X0] :
( in(sK3(sK19(sK23,sK24),X0),sK24)
| finite(X0)
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_134 ),
inference(avatar_component_clause,[],[f5156]) ).
fof(f5158,plain,
( spl27_134
| ~ spl27_24
| ~ spl27_64
| ~ spl27_72
| ~ spl27_118 ),
inference(avatar_split_clause,[],[f5154,f4561,f2311,f2026,f885,f5156]) ).
fof(f5170,definition,
( spl27_135
<=> ! [X0,X1] :
( ~ in(X1,sK24)
| finite(X0)
| sK2(sK19(sK23,sK24),X0) != apply(sK19(sK23,sK24),X1)
| ~ in(sK2(sK19(sK23,sK24),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_135])],[avatar_definition]) ).
fof(f5171,plain,
( ! [X0,X1] :
( sK2(sK19(sK23,sK24),X0) != apply(sK19(sK23,sK24),X1)
| finite(X0)
| ~ in(X1,sK24)
| ~ in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_135 ),
inference(avatar_component_clause,[],[f5170]) ).
fof(f5172,plain,
( spl27_135
| ~ spl27_24
| ~ spl27_64
| ~ spl27_72
| ~ spl27_118 ),
inference(avatar_split_clause,[],[f5153,f4561,f2311,f2026,f885,f5170]) ).
fof(f5173,plain,
( ! [X0,X1] :
( subset_complement(the_carrier(sK23),X0) != sK2(sK19(sK23,sK24),X1)
| finite(X1)
| ~ in(X0,sK24)
| ~ in(sK2(sK19(sK23,sK24),X1),X1)
| ~ in(X0,sK24) )
| ~ spl27_43
| ~ spl27_135 ),
inference(superposition,[],[f5171,f1408]) ).
fof(f5186,plain,
( ! [X0,X1] :
( subset_complement(the_carrier(sK23),X0) != sK2(sK19(sK23,sK24),X1)
| finite(X1)
| ~ in(X0,sK24)
| ~ in(sK2(sK19(sK23,sK24),X1),X1) )
| ~ spl27_43
| ~ spl27_135 ),
inference(duplicate_literal_removal,[],[f5173]) ).
fof(f5221,definition,
( spl27_138
<=> ! [X0,X1] :
( subset_complement(the_carrier(sK23),X0) != sK2(sK19(sK23,sK24),X1)
| finite(X1)
| ~ in(X0,sK24)
| ~ in(sK2(sK19(sK23,sK24),X1),X1) ) ),
introduced(definition,[new_symbols(definition,[spl27_138])],[avatar_definition]) ).
fof(f5222,plain,
( ! [X0,X1] :
( subset_complement(the_carrier(sK23),X0) != sK2(sK19(sK23,sK24),X1)
| finite(X1)
| ~ in(X0,sK24)
| ~ in(sK2(sK19(sK23,sK24),X1),X1) )
| ~ spl27_138 ),
inference(avatar_component_clause,[],[f5221]) ).
fof(f5223,plain,
( spl27_138
| ~ spl27_43
| ~ spl27_135 ),
inference(avatar_split_clause,[],[f5186,f5170,f1407,f5221]) ).
fof(f5246,plain,
( ! [X0,X1] :
( sK2(sK19(sK23,sK24),X1) != X0
| finite(X1)
| ~ in(subset_complement(the_carrier(sK23),X0),sK24)
| ~ in(sK2(sK19(sK23,sK24),X1),X1)
| ~ element(X0,powerset(the_carrier(sK23))) )
| ~ spl27_138 ),
inference(superposition,[],[f5222,f190]) ).
fof(f5283,definition,
( spl27_139
<=> ! [X0] :
( finite(X0)
| sK2(sK19(sK23,sK24),X0) = apply(sK19(sK23,sK24),sK3(sK19(sK23,sK24),X0))
| in(sK2(sK19(sK23,sK24),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_139])],[avatar_definition]) ).
fof(f5284,plain,
( ! [X0] :
( sK2(sK19(sK23,sK24),X0) = apply(sK19(sK23,sK24),sK3(sK19(sK23,sK24),X0))
| finite(X0)
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_139 ),
inference(avatar_component_clause,[],[f5283]) ).
fof(f5285,plain,
( spl27_139
| ~ spl27_64
| ~ spl27_72
| ~ spl27_118 ),
inference(avatar_split_clause,[],[f5152,f4561,f2311,f2026,f5283]) ).
fof(f5295,plain,
( ! [X0] :
( sK2(sK19(sK23,sK24),X0) = subset_complement(the_carrier(sK23),sK3(sK19(sK23,sK24),X0))
| ~ in(sK3(sK19(sK23,sK24),X0),sK24)
| finite(X0)
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_43
| ~ spl27_139 ),
inference(superposition,[],[f1408,f5284]) ).
fof(f5307,plain,
( ! [X0] :
( sK2(sK19(sK23,sK24),X0) = subset_complement(the_carrier(sK23),sK3(sK19(sK23,sK24),X0))
| finite(X0)
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_43
| ~ spl27_134
| ~ spl27_139 ),
inference(forward_subsumption_resolution,[],[f5295,f5157]) ).
fof(f5323,definition,
( spl27_140
<=> ! [X0] :
( sK2(sK19(sK23,sK24),X0) = subset_complement(the_carrier(sK23),sK3(sK19(sK23,sK24),X0))
| finite(X0)
| in(sK2(sK19(sK23,sK24),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_140])],[avatar_definition]) ).
fof(f5324,plain,
( ! [X0] :
( sK2(sK19(sK23,sK24),X0) = subset_complement(the_carrier(sK23),sK3(sK19(sK23,sK24),X0))
| finite(X0)
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_140 ),
inference(avatar_component_clause,[],[f5323]) ).
fof(f5325,plain,
( spl27_140
| ~ spl27_43
| ~ spl27_134
| ~ spl27_139 ),
inference(avatar_split_clause,[],[f5307,f5283,f5156,f1407,f5323]) ).
fof(f5349,definition,
( spl27_141
<=> ! [X0] :
( in(sK2(sK19(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| finite(X0)
| in(sK2(sK19(sK23,sK24),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_141])],[avatar_definition]) ).
fof(f5350,plain,
( ! [X0] :
( in(sK2(sK19(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| finite(X0)
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_141 ),
inference(avatar_component_clause,[],[f5349]) ).
fof(f5369,plain,
( in(sK2(sK19(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24)),complements_of_subsets(the_carrier(sK23),sK24))
| finite(complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_141 ),
inference(factoring,[],[f5350]) ).
fof(f5374,plain,
( in(sK2(sK19(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24)),complements_of_subsets(the_carrier(sK23),sK24))
| spl27_1
| ~ spl27_141 ),
inference(forward_subsumption_resolution,[],[f5369,f294]) ).
fof(f5377,definition,
( spl27_142
<=> in(sK2(sK19(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24)),complements_of_subsets(the_carrier(sK23),sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_142])],[avatar_definition]) ).
fof(f5379,plain,
( in(sK2(sK19(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24)),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_142 ),
inference(avatar_component_clause,[],[f5377]) ).
fof(f5380,plain,
( spl27_142
| spl27_1
| ~ spl27_141 ),
inference(avatar_split_clause,[],[f5374,f5349,f292,f5377]) ).
fof(f5382,plain,
( in(subset_complement(the_carrier(sK23),sK2(sK19(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))),sK24)
| ~ spl27_21
| ~ spl27_142 ),
inference(resolution,[],[f5379,f843]) ).
fof(f5491,definition,
( spl27_151
<=> in(subset_complement(the_carrier(sK23),sK2(sK19(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))),sK24) ),
introduced(definition,[new_symbols(definition,[spl27_151])],[avatar_definition]) ).
fof(f5493,plain,
( in(subset_complement(the_carrier(sK23),sK2(sK19(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))),sK24)
| ~ spl27_151 ),
inference(avatar_component_clause,[],[f5491]) ).
fof(f5494,plain,
( spl27_151
| ~ spl27_21
| ~ spl27_142 ),
inference(avatar_split_clause,[],[f5382,f5377,f842,f5491]) ).
fof(f5516,definition,
( spl27_153
<=> ! [X0,X1] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,X1),X0)
| ~ in(X0,X1)
| sK21(sK23,X1) != sK22(sK23,X1)
| sP1(X1,sK23)
| ~ element(X1,powerset(powerset(the_carrier(sK23)))) ) ),
introduced(definition,[new_symbols(definition,[spl27_153])],[avatar_definition]) ).
fof(f5517,plain,
( ! [X0,X1] :
( sK21(sK23,X1) != sK22(sK23,X1)
| ~ in(X0,X1)
| subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,X1),X0)
| sP1(X1,sK23)
| ~ element(X1,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_153 ),
inference(avatar_component_clause,[],[f5516]) ).
fof(f5518,plain,
( spl27_153
| ~ spl27_3 ),
inference(avatar_split_clause,[],[f347,f308,f5516]) ).
fof(f5777,definition,
( spl27_164
<=> ! [X0,X1] :
( sK2(sK19(sK23,sK24),X1) != X0
| finite(X1)
| ~ in(subset_complement(the_carrier(sK23),X0),sK24)
| ~ in(sK2(sK19(sK23,sK24),X1),X1)
| ~ element(X0,powerset(the_carrier(sK23))) ) ),
introduced(definition,[new_symbols(definition,[spl27_164])],[avatar_definition]) ).
fof(f5778,plain,
( ! [X0,X1] :
( sK2(sK19(sK23,sK24),X1) != X0
| finite(X1)
| ~ in(subset_complement(the_carrier(sK23),X0),sK24)
| ~ in(sK2(sK19(sK23,sK24),X1),X1)
| ~ element(X0,powerset(the_carrier(sK23))) )
| ~ spl27_164 ),
inference(avatar_component_clause,[],[f5777]) ).
fof(f5779,plain,
( spl27_164
| ~ spl27_138 ),
inference(avatar_split_clause,[],[f5246,f5221,f5777]) ).
fof(f5780,plain,
( ! [X0] :
( finite(X0)
| ~ in(subset_complement(the_carrier(sK23),sK2(sK19(sK23,sK24),X0)),sK24)
| ~ in(sK2(sK19(sK23,sK24),X0),X0)
| ~ element(sK2(sK19(sK23,sK24),X0),powerset(the_carrier(sK23))) )
| ~ spl27_164 ),
inference(equality_resolution,[],[f5778]) ).
fof(f5897,definition,
( spl27_172
<=> ! [X0] :
( finite(X0)
| in(sK2(sK13(sK23,sK24),X0),X0)
| in(subset_complement(the_carrier(sK23),sK3(sK13(sK23,sK24),X0)),sK24) ) ),
introduced(definition,[new_symbols(definition,[spl27_172])],[avatar_definition]) ).
fof(f5898,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),sK3(sK13(sK23,sK24),X0)),sK24)
| in(sK2(sK13(sK23,sK24),X0),X0)
| finite(X0) )
| ~ spl27_172 ),
inference(avatar_component_clause,[],[f5897]) ).
fof(f5899,plain,
( spl27_172
| ~ spl27_21
| ~ spl27_106 ),
inference(avatar_split_clause,[],[f4128,f4125,f842,f5897]) ).
fof(f7033,definition,
( spl27_209
<=> complements_of_subsets(the_carrier(sK23),sK24) = relation_rng(sK19(sK23,sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_209])],[avatar_definition]) ).
fof(f7035,plain,
( complements_of_subsets(the_carrier(sK23),sK24) = relation_rng(sK19(sK23,sK24))
| ~ spl27_209 ),
inference(avatar_component_clause,[],[f7033]) ).
fof(f7036,plain,
( spl27_209
| spl27_142
| ~ spl27_59 ),
inference(avatar_split_clause,[],[f1949,f1929,f5377,f7033]) ).
fof(f7185,definition,
( spl27_213
<=> ! [X0] :
( relation_dom(sK19(sK23,X0)) = X0
| sK22(sK23,X0) = subset_complement(the_carrier(sK23),sK20(sK23,X0))
| ~ element(sK20(sK23,X0),powerset(the_carrier(sK23)))
| sP1(X0,sK23)
| ~ element(X0,powerset(powerset(the_carrier(sK23)))) ) ),
introduced(definition,[new_symbols(definition,[spl27_213])],[avatar_definition]) ).
fof(f7186,plain,
( ! [X0] :
( sK22(sK23,X0) = subset_complement(the_carrier(sK23),sK20(sK23,X0))
| relation_dom(sK19(sK23,X0)) = X0
| ~ element(sK20(sK23,X0),powerset(the_carrier(sK23)))
| sP1(X0,sK23)
| ~ element(X0,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_213 ),
inference(avatar_component_clause,[],[f7185]) ).
fof(f7187,plain,
( spl27_213
| ~ spl27_3 ),
inference(avatar_split_clause,[],[f339,f308,f7185]) ).
fof(f7212,plain,
( ! [X0] :
( sK21(sK23,X0) = sK22(sK23,X0)
| relation_dom(sK19(sK23,X0)) = X0
| ~ element(sK20(sK23,X0),powerset(the_carrier(sK23)))
| sP1(X0,sK23)
| ~ one_sorted_str(sK23)
| ~ element(X0,powerset(powerset(the_carrier(sK23))))
| relation_dom(sK19(sK23,X0)) = X0
| ~ element(sK20(sK23,X0),powerset(the_carrier(sK23)))
| sP1(X0,sK23)
| ~ element(X0,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_213 ),
inference(superposition,[],[f281,f7186]) ).
fof(f7223,plain,
( ! [X0] :
( sK21(sK23,X0) = sK22(sK23,X0)
| relation_dom(sK19(sK23,X0)) = X0
| ~ element(sK20(sK23,X0),powerset(the_carrier(sK23)))
| sP1(X0,sK23)
| ~ one_sorted_str(sK23)
| ~ element(X0,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_213 ),
inference(duplicate_literal_removal,[],[f7212]) ).
fof(f7239,plain,
( ! [X0] :
( relation_dom(sK19(sK23,X0)) = X0
| ~ element(sK20(sK23,X0),powerset(the_carrier(sK23)))
| sP1(X0,sK23)
| ~ one_sorted_str(sK23)
| ~ element(X0,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_213 ),
inference(forward_subsumption_resolution,[],[f7223,f234]) ).
fof(f7260,plain,
( ! [X0] :
( relation_dom(sK19(sK23,X0)) = X0
| ~ element(sK20(sK23,X0),powerset(the_carrier(sK23)))
| sP1(X0,sK23)
| ~ element(X0,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_3
| ~ spl27_213 ),
inference(forward_subsumption_resolution,[],[f7239,f310]) ).
fof(f7269,definition,
( spl27_214
<=> ! [X0] :
( relation_dom(sK19(sK23,X0)) = X0
| ~ element(sK20(sK23,X0),powerset(the_carrier(sK23)))
| sP1(X0,sK23)
| ~ element(X0,powerset(powerset(the_carrier(sK23)))) ) ),
introduced(definition,[new_symbols(definition,[spl27_214])],[avatar_definition]) ).
fof(f7270,plain,
( ! [X0] :
( ~ element(sK20(sK23,X0),powerset(the_carrier(sK23)))
| relation_dom(sK19(sK23,X0)) = X0
| sP1(X0,sK23)
| ~ element(X0,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_214 ),
inference(avatar_component_clause,[],[f7269]) ).
fof(f7271,plain,
( spl27_214
| ~ spl27_3
| ~ spl27_213 ),
inference(avatar_split_clause,[],[f7260,f7185,f308,f7269]) ).
fof(f7378,definition,
( spl27_220
<=> sK14(sK23,sK24) = subset_complement(the_carrier(sK23),sK4(sK19(sK23,sK24),sK14(sK23,sK24))) ),
introduced(definition,[new_symbols(definition,[spl27_220])],[avatar_definition]) ).
fof(f7379,plain,
( sK14(sK23,sK24) != subset_complement(the_carrier(sK23),sK4(sK19(sK23,sK24),sK14(sK23,sK24)))
| spl27_220 ),
inference(avatar_component_clause,[],[f7378]) ).
fof(f7380,plain,
( sK14(sK23,sK24) = subset_complement(the_carrier(sK23),sK4(sK19(sK23,sK24),sK14(sK23,sK24)))
| ~ spl27_220 ),
inference(avatar_component_clause,[],[f7378]) ).
fof(f7393,definition,
( spl27_221
<=> in(sK4(sK19(sK23,sK24),sK14(sK23,sK24)),sK24) ),
introduced(definition,[new_symbols(definition,[spl27_221])],[avatar_definition]) ).
fof(f7394,plain,
( ~ in(sK4(sK19(sK23,sK24),sK14(sK23,sK24)),sK24)
| spl27_221 ),
inference(avatar_component_clause,[],[f7393]) ).
fof(f7395,plain,
( in(sK4(sK19(sK23,sK24),sK14(sK23,sK24)),sK24)
| ~ spl27_221 ),
inference(avatar_component_clause,[],[f7393]) ).
fof(f7402,definition,
( spl27_223
<=> in(sK14(sK23,sK24),relation_rng(sK19(sK23,sK24))) ),
introduced(definition,[new_symbols(definition,[spl27_223])],[avatar_definition]) ).
fof(f7403,plain,
( ~ in(sK14(sK23,sK24),relation_rng(sK19(sK23,sK24)))
| spl27_223 ),
inference(avatar_component_clause,[],[f7402]) ).
fof(f7404,plain,
( in(sK14(sK23,sK24),relation_rng(sK19(sK23,sK24)))
| ~ spl27_223 ),
inference(avatar_component_clause,[],[f7402]) ).
fof(f8121,plain,
( ! [X0] :
( in(sK2(sK19(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ in(sK3(sK19(sK23,sK24),X0),sK24)
| finite(X0)
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_18
| ~ spl27_140 ),
inference(superposition,[],[f734,f5324]) ).
fof(f9284,plain,
( sK14(sK23,sK24) != sK14(sK23,sK24)
| ~ in(sK14(sK23,sK24),relation_rng(sK19(sK23,sK24)))
| ~ spl27_56
| spl27_220 ),
inference(superposition,[],[f7379,f1851]) ).
fof(f9285,plain,
( ~ in(sK14(sK23,sK24),relation_rng(sK19(sK23,sK24)))
| ~ spl27_56
| spl27_220 ),
inference(trivial_inequality_removal,[],[f9284]) ).
fof(f9529,definition,
( spl27_227
<=> ! [X0] :
( finite(X0)
| ~ in(subset_complement(the_carrier(sK23),sK2(sK19(sK23,sK24),X0)),sK24)
| ~ in(sK2(sK19(sK23,sK24),X0),X0)
| ~ element(sK2(sK19(sK23,sK24),X0),powerset(the_carrier(sK23))) ) ),
introduced(definition,[new_symbols(definition,[spl27_227])],[avatar_definition]) ).
fof(f9530,plain,
( ! [X0] :
( ~ in(subset_complement(the_carrier(sK23),sK2(sK19(sK23,sK24),X0)),sK24)
| finite(X0)
| ~ in(sK2(sK19(sK23,sK24),X0),X0)
| ~ element(sK2(sK19(sK23,sK24),X0),powerset(the_carrier(sK23))) )
| ~ spl27_227 ),
inference(avatar_component_clause,[],[f9529]) ).
fof(f9531,plain,
( spl27_227
| ~ spl27_164 ),
inference(avatar_split_clause,[],[f5780,f5777,f9529]) ).
fof(f9532,plain,
( finite(complements_of_subsets(the_carrier(sK23),sK24))
| ~ in(sK2(sK19(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24)),complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(sK2(sK19(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24)),powerset(the_carrier(sK23)))
| ~ spl27_151
| ~ spl27_227 ),
inference(resolution,[],[f9530,f5493]) ).
fof(f9540,plain,
( finite(complements_of_subsets(the_carrier(sK23),sK24))
| ~ in(sK2(sK19(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24)),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_54
| ~ spl27_151
| ~ spl27_227 ),
inference(forward_subsumption_resolution,[],[f9532,f1719]) ).
fof(f9542,plain,
( ~ in(sK2(sK19(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24)),complements_of_subsets(the_carrier(sK23),sK24))
| spl27_1
| ~ spl27_54
| ~ spl27_151
| ~ spl27_227 ),
inference(forward_subsumption_resolution,[],[f9540,f294]) ).
fof(f9645,plain,
( ! [X0] :
( finite(relation_image(X0,complements_of_subsets(the_carrier(sK23),sK24)))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl27_1 ),
inference(resolution,[],[f293,f248]) ).
fof(f9707,definition,
( spl27_231
<=> ! [X0] :
( finite(relation_image(X0,complements_of_subsets(the_carrier(sK23),sK24)))
| ~ relation(X0)
| ~ function(X0) ) ),
introduced(definition,[new_symbols(definition,[spl27_231])],[avatar_definition]) ).
fof(f9708,plain,
( ! [X0] :
( finite(relation_image(X0,complements_of_subsets(the_carrier(sK23),sK24)))
| ~ relation(X0)
| ~ function(X0) )
| ~ spl27_231 ),
inference(avatar_component_clause,[],[f9707]) ).
fof(f9709,plain,
( spl27_231
| ~ spl27_1 ),
inference(avatar_split_clause,[],[f9645,f292,f9707]) ).
fof(f9869,definition,
( spl27_237
<=> ! [X0] :
( in(X0,relation_rng(sK19(sK23,sK24)))
| ~ in(subset_complement(the_carrier(sK23),X0),sK24)
| ~ element(X0,powerset(the_carrier(sK23))) ) ),
introduced(definition,[new_symbols(definition,[spl27_237])],[avatar_definition]) ).
fof(f9870,plain,
( ! [X0] :
( ~ in(subset_complement(the_carrier(sK23),X0),sK24)
| in(X0,relation_rng(sK19(sK23,sK24)))
| ~ element(X0,powerset(the_carrier(sK23))) )
| ~ spl27_237 ),
inference(avatar_component_clause,[],[f9869]) ).
fof(f9871,plain,
( spl27_237
| ~ spl27_48 ),
inference(avatar_split_clause,[],[f1595,f1502,f9869]) ).
fof(f9877,plain,
( ! [X0] :
( in(X0,relation_rng(sK19(sK23,sK24)))
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ element(complements_of_subsets(the_carrier(sK23),sK24),powerset(powerset(the_carrier(sK23))))
| ~ element(sK24,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_237 ),
inference(resolution,[],[f9870,f264]) ).
fof(f9931,plain,
( ! [X0] :
( in(X0,relation_rng(sK19(sK23,sK24)))
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(complements_of_subsets(the_carrier(sK23),sK24),powerset(powerset(the_carrier(sK23))))
| ~ element(sK24,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_237 ),
inference(duplicate_literal_removal,[],[f9877]) ).
fof(f9945,plain,
( ! [X0] :
( in(X0,relation_rng(sK19(sK23,sK24)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(complements_of_subsets(the_carrier(sK23),sK24),powerset(powerset(the_carrier(sK23))))
| ~ element(sK24,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_237 ),
inference(forward_subsumption_resolution,[],[f9931,f254]) ).
fof(f9948,plain,
( ! [X0] :
( in(X0,relation_rng(sK19(sK23,sK24)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(sK24,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_237 ),
inference(forward_subsumption_resolution,[],[f9945,f180]) ).
fof(f9950,plain,
( ! [X0] :
( in(X0,relation_rng(sK19(sK23,sK24)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) )
| ~ spl27_4
| ~ spl27_237 ),
inference(forward_subsumption_resolution,[],[f9948,f351]) ).
fof(f9952,definition,
( spl27_238
<=> ! [X0] :
( in(X0,relation_rng(sK19(sK23,sK24)))
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) ) ),
introduced(definition,[new_symbols(definition,[spl27_238])],[avatar_definition]) ).
fof(f9953,plain,
( ! [X0] :
( ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| in(X0,relation_rng(sK19(sK23,sK24))) )
| ~ spl27_238 ),
inference(avatar_component_clause,[],[f9952]) ).
fof(f9954,plain,
( spl27_238
| ~ spl27_4
| ~ spl27_237 ),
inference(avatar_split_clause,[],[f9950,f9869,f349,f9952]) ).
fof(f12118,definition,
( spl27_282
<=> ! [X0] :
( finite(X0)
| ~ in(sK2(sK13(sK23,sK24),X0),X0)
| ~ in(sK2(sK13(sK23,sK24),X0),sK24) ) ),
introduced(definition,[new_symbols(definition,[spl27_282])],[avatar_definition]) ).
fof(f12119,plain,
( ! [X0] :
( ~ in(sK2(sK13(sK23,sK24),X0),sK24)
| ~ in(sK2(sK13(sK23,sK24),X0),X0)
| finite(X0) )
| ~ spl27_282 ),
inference(avatar_component_clause,[],[f12118]) ).
fof(f12121,plain,
( ~ in(sK2(sK13(sK23,sK24),sK24),sK24)
| finite(sK24)
| sK24 = relation_rng(sK13(sK23,sK24))
| sK2(sK13(sK23,sK24),sK24) = apply(sK13(sK23,sK24),sK3(sK13(sK23,sK24),sK24))
| ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24))
| ~ spl27_282 ),
inference(resolution,[],[f12119,f171]) ).
fof(f12122,plain,
( ~ in(sK2(sK13(sK23,sK24),sK24),sK24)
| finite(sK24)
| sK24 = relation_rng(sK13(sK23,sK24))
| in(sK3(sK13(sK23,sK24),sK24),relation_dom(sK13(sK23,sK24)))
| ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24))
| ~ spl27_282 ),
inference(resolution,[],[f12119,f172]) ).
fof(f12125,plain,
( finite(sK24)
| sK24 = relation_rng(sK13(sK23,sK24))
| in(sK3(sK13(sK23,sK24),sK24),relation_dom(sK13(sK23,sK24)))
| ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24))
| ~ spl27_282 ),
inference(forward_subsumption_resolution,[],[f12122,f172]) ).
fof(f12126,plain,
( finite(sK24)
| sK24 = relation_rng(sK13(sK23,sK24))
| sK2(sK13(sK23,sK24),sK24) = apply(sK13(sK23,sK24),sK3(sK13(sK23,sK24),sK24))
| ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24))
| ~ spl27_282 ),
inference(forward_subsumption_resolution,[],[f12121,f171]) ).
fof(f12127,plain,
( sK24 = relation_rng(sK13(sK23,sK24))
| in(sK3(sK13(sK23,sK24),sK24),relation_dom(sK13(sK23,sK24)))
| ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24))
| spl27_2
| ~ spl27_282 ),
inference(forward_subsumption_resolution,[],[f12125,f298]) ).
fof(f12128,plain,
( sK24 = relation_rng(sK13(sK23,sK24))
| sK2(sK13(sK23,sK24),sK24) = apply(sK13(sK23,sK24),sK3(sK13(sK23,sK24),sK24))
| ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24))
| spl27_2
| ~ spl27_282 ),
inference(forward_subsumption_resolution,[],[f12126,f298]) ).
fof(f12129,plain,
( sK24 = relation_rng(sK13(sK23,sK24))
| in(sK3(sK13(sK23,sK24),sK24),relation_dom(sK13(sK23,sK24)))
| ~ function(sK13(sK23,sK24))
| spl27_2
| ~ spl27_39
| ~ spl27_282 ),
inference(forward_subsumption_resolution,[],[f12127,f1315]) ).
fof(f12130,plain,
( sK24 = relation_rng(sK13(sK23,sK24))
| sK2(sK13(sK23,sK24),sK24) = apply(sK13(sK23,sK24),sK3(sK13(sK23,sK24),sK24))
| ~ function(sK13(sK23,sK24))
| spl27_2
| ~ spl27_39
| ~ spl27_282 ),
inference(forward_subsumption_resolution,[],[f12128,f1315]) ).
fof(f12131,plain,
( sK24 = relation_rng(sK13(sK23,sK24))
| in(sK3(sK13(sK23,sK24),sK24),relation_dom(sK13(sK23,sK24)))
| spl27_2
| ~ spl27_39
| ~ spl27_45
| ~ spl27_282 ),
inference(forward_subsumption_resolution,[],[f12129,f1469]) ).
fof(f12132,plain,
( sK24 = relation_rng(sK13(sK23,sK24))
| sK2(sK13(sK23,sK24),sK24) = apply(sK13(sK23,sK24),sK3(sK13(sK23,sK24),sK24))
| spl27_2
| ~ spl27_39
| ~ spl27_45
| ~ spl27_282 ),
inference(forward_subsumption_resolution,[],[f12130,f1469]) ).
fof(f12133,plain,
( in(sK3(sK13(sK23,sK24),sK24),complements_of_subsets(the_carrier(sK23),sK24))
| sK24 = relation_rng(sK13(sK23,sK24))
| spl27_2
| ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| ~ spl27_282 ),
inference(forward_demodulation,[],[f12131,f470]) ).
fof(f12185,definition,
( spl27_284
<=> sK24 = relation_rng(sK13(sK23,sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_284])],[avatar_definition]) ).
fof(f12187,plain,
( sK24 = relation_rng(sK13(sK23,sK24))
| ~ spl27_284 ),
inference(avatar_component_clause,[],[f12185]) ).
fof(f12189,definition,
( spl27_285
<=> in(sK3(sK13(sK23,sK24),sK24),complements_of_subsets(the_carrier(sK23),sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_285])],[avatar_definition]) ).
fof(f12191,plain,
( in(sK3(sK13(sK23,sK24),sK24),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_285 ),
inference(avatar_component_clause,[],[f12189]) ).
fof(f12192,plain,
( spl27_284
| spl27_285
| spl27_2
| ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| ~ spl27_282 ),
inference(avatar_split_clause,[],[f12133,f12118,f1467,f1313,f468,f296,f12189,f12185]) ).
fof(f12244,definition,
( spl27_289
<=> sK2(sK13(sK23,sK24),sK24) = apply(sK13(sK23,sK24),sK3(sK13(sK23,sK24),sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_289])],[avatar_definition]) ).
fof(f12246,plain,
( sK2(sK13(sK23,sK24),sK24) = apply(sK13(sK23,sK24),sK3(sK13(sK23,sK24),sK24))
| ~ spl27_289 ),
inference(avatar_component_clause,[],[f12244]) ).
fof(f12247,plain,
( spl27_289
| spl27_284
| spl27_2
| ~ spl27_39
| ~ spl27_45
| ~ spl27_282 ),
inference(avatar_split_clause,[],[f12132,f12118,f1467,f1313,f296,f12185,f12244]) ).
fof(f12358,plain,
( sK2(sK13(sK23,sK24),sK24) = subset_complement(the_carrier(sK23),sK3(sK13(sK23,sK24),sK24))
| ~ in(sK3(sK13(sK23,sK24),sK24),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_81
| ~ spl27_289 ),
inference(superposition,[],[f12246,f3235]) ).
fof(f12385,definition,
( spl27_291
<=> in(sK2(sK13(sK23,sK24),sK24),sK24) ),
introduced(definition,[new_symbols(definition,[spl27_291])],[avatar_definition]) ).
fof(f12386,plain,
( in(sK2(sK13(sK23,sK24),sK24),sK24)
| ~ spl27_291 ),
inference(avatar_component_clause,[],[f12385]) ).
fof(f12387,plain,
( ~ in(sK2(sK13(sK23,sK24),sK24),sK24)
| spl27_291 ),
inference(avatar_component_clause,[],[f12385]) ).
fof(f12398,definition,
( spl27_292
<=> sK2(sK13(sK23,sK24),sK24) = subset_complement(the_carrier(sK23),sK3(sK13(sK23,sK24),sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_292])],[avatar_definition]) ).
fof(f12399,plain,
( sK2(sK13(sK23,sK24),sK24) != subset_complement(the_carrier(sK23),sK3(sK13(sK23,sK24),sK24))
| spl27_292 ),
inference(avatar_component_clause,[],[f12398]) ).
fof(f12400,plain,
( sK2(sK13(sK23,sK24),sK24) = subset_complement(the_carrier(sK23),sK3(sK13(sK23,sK24),sK24))
| ~ spl27_292 ),
inference(avatar_component_clause,[],[f12398]) ).
fof(f12773,definition,
( spl27_308
<=> ! [X0] :
( in(X0,relation_rng(sK13(sK23,sK24)))
| ~ in(subset_complement(the_carrier(sK23),X0),complements_of_subsets(the_carrier(sK23),sK24))
| ~ element(X0,powerset(the_carrier(sK23))) ) ),
introduced(definition,[new_symbols(definition,[spl27_308])],[avatar_definition]) ).
fof(f12774,plain,
( ! [X0] :
( ~ in(subset_complement(the_carrier(sK23),X0),complements_of_subsets(the_carrier(sK23),sK24))
| in(X0,relation_rng(sK13(sK23,sK24)))
| ~ element(X0,powerset(the_carrier(sK23))) )
| ~ spl27_308 ),
inference(avatar_component_clause,[],[f12773]) ).
fof(f12775,plain,
( spl27_308
| ~ spl27_95 ),
inference(avatar_split_clause,[],[f3686,f3649,f12773]) ).
fof(f12776,plain,
( ! [X0] :
( in(X0,relation_rng(sK13(sK23,sK24)))
| ~ element(X0,powerset(the_carrier(sK23)))
| ~ in(X0,sK24) )
| ~ spl27_18
| ~ spl27_308 ),
inference(resolution,[],[f12774,f734]) ).
fof(f12865,plain,
( ! [X0] :
( in(X0,relation_rng(sK13(sK23,sK24)))
| ~ in(X0,sK24) )
| ~ spl27_18
| ~ spl27_32
| ~ spl27_308 ),
inference(forward_subsumption_resolution,[],[f12776,f1059]) ).
fof(f12874,definition,
( spl27_309
<=> ! [X0] :
( in(X0,relation_rng(sK13(sK23,sK24)))
| ~ in(X0,sK24) ) ),
introduced(definition,[new_symbols(definition,[spl27_309])],[avatar_definition]) ).
fof(f12875,plain,
( ! [X0] :
( in(X0,relation_rng(sK13(sK23,sK24)))
| ~ in(X0,sK24) )
| ~ spl27_309 ),
inference(avatar_component_clause,[],[f12874]) ).
fof(f12876,plain,
( spl27_309
| ~ spl27_18
| ~ spl27_32
| ~ spl27_308 ),
inference(avatar_split_clause,[],[f12865,f12773,f1058,f733,f12874]) ).
fof(f12892,plain,
( ! [X0] :
( ~ in(sK2(sK13(sK23,sK24),X0),sK24)
| ~ in(sK2(sK13(sK23,sK24),X0),X0)
| finite(X0) )
| ~ spl27_112
| ~ spl27_309 ),
inference(resolution,[],[f12875,f4377]) ).
fof(f13212,plain,
( finite(complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_118
| ~ spl27_209 ),
inference(superposition,[],[f4563,f7035]) ).
fof(f13377,plain,
( in(sK2(sK13(sK23,sK24),sK24),sK24)
| in(sK2(sK13(sK23,sK24),sK24),sK24)
| finite(sK24)
| ~ spl27_172
| ~ spl27_292 ),
inference(superposition,[],[f5898,f12400]) ).
fof(f13378,plain,
( in(sK2(sK13(sK23,sK24),sK24),sK24)
| finite(sK24)
| ~ spl27_172
| ~ spl27_292 ),
inference(duplicate_literal_removal,[],[f13377]) ).
fof(f13380,plain,
( finite(sK24)
| ~ spl27_172
| spl27_291
| ~ spl27_292 ),
inference(forward_subsumption_resolution,[],[f13378,f12387]) ).
fof(f13383,plain,
( $false
| spl27_2
| ~ spl27_172
| spl27_291
| ~ spl27_292 ),
inference(forward_subsumption_resolution,[],[f13380,f298]) ).
fof(f13384,plain,
( spl27_2
| ~ spl27_172
| spl27_291
| ~ spl27_292 ),
inference(avatar_contradiction_clause,[],[f13383]) ).
fof(f13400,plain,
( ~ in(sK3(sK13(sK23,sK24),sK24),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_81
| ~ spl27_289
| spl27_292 ),
inference(forward_subsumption_resolution,[],[f12358,f12399]) ).
fof(f13413,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),relation_rng(sK19(sK23,sK24)))
| ~ in(X0,relation_dom(sK19(sK23,sK24)))
| ~ function(sK19(sK23,sK24))
| ~ in(X0,sK24) )
| ~ spl27_43
| ~ spl27_64 ),
inference(forward_subsumption_resolution,[],[f1412,f2028]) ).
fof(f13453,plain,
( $false
| ~ spl27_81
| ~ spl27_285
| ~ spl27_289
| spl27_292 ),
inference(forward_subsumption_resolution,[],[f13400,f12191]) ).
fof(f13454,plain,
( ~ spl27_81
| ~ spl27_285
| ~ spl27_289
| spl27_292 ),
inference(avatar_contradiction_clause,[],[f13453]) ).
fof(f13464,plain,
( ! [X0] :
( in(subset_complement(the_carrier(sK23),X0),relation_rng(sK19(sK23,sK24)))
| ~ in(X0,relation_dom(sK19(sK23,sK24)))
| ~ in(X0,sK24) )
| ~ spl27_43
| ~ spl27_64
| ~ spl27_72 ),
inference(forward_subsumption_resolution,[],[f13413,f2313]) ).
fof(f13539,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| in(sK14(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| sP0(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4
| ~ spl27_54 ),
inference(forward_subsumption_resolution,[],[f434,f1719]) ).
fof(f13573,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24))
| sP0(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4
| spl27_6
| ~ spl27_54 ),
inference(forward_subsumption_resolution,[],[f13539,f465]) ).
fof(f13595,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK13(sK23,sK24),X0)
| ~ in(X0,complements_of_subsets(the_carrier(sK23),sK24)) )
| ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_6
| ~ spl27_54 ),
inference(forward_subsumption_resolution,[],[f13573,f461]) ).
fof(f13626,plain,
( sK24 = relation_dom(sK19(sK23,sK24))
| sP1(sK24,sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ spl27_27
| ~ spl27_214 ),
inference(resolution,[],[f993,f7270]) ).
fof(f13628,plain,
( relation(sK19(sK23,sK24))
| sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| sP1(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ spl27_27 ),
inference(resolution,[],[f993,f278]) ).
fof(f13630,plain,
( function(sK19(sK23,sK24))
| sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| sP1(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ spl27_27 ),
inference(resolution,[],[f993,f280]) ).
fof(f13670,plain,
( spl27_81
| ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_6
| ~ spl27_54 ),
inference(avatar_split_clause,[],[f13595,f1654,f464,f460,f349,f308,f3234]) ).
fof(f14120,definition,
( spl27_328
<=> relation_rng(sK13(sK23,sK24)) = relation_image(sK13(sK23,sK24),relation_dom(sK13(sK23,sK24))) ),
introduced(definition,[new_symbols(definition,[spl27_328])],[avatar_definition]) ).
fof(f14122,plain,
( relation_rng(sK13(sK23,sK24)) = relation_image(sK13(sK23,sK24),relation_dom(sK13(sK23,sK24)))
| ~ spl27_328 ),
inference(avatar_component_clause,[],[f14120]) ).
fof(f14123,plain,
( spl27_328
| ~ spl27_39 ),
inference(avatar_split_clause,[],[f3456,f1313,f14120]) ).
fof(f14141,plain,
( in(sK14(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| sP0(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_39 ),
inference(resolution,[],[f1314,f221]) ).
fof(f14291,plain,
( element(sK14(sK23,sK24),powerset(the_carrier(sK23)))
| ~ element(sK4(sK19(sK23,sK24),sK14(sK23,sK24)),powerset(the_carrier(sK23)))
| ~ spl27_220 ),
inference(superposition,[],[f179,f7380]) ).
fof(f14296,plain,
( ~ element(sK4(sK19(sK23,sK24),sK14(sK23,sK24)),powerset(the_carrier(sK23)))
| spl27_11
| ~ spl27_220 ),
inference(forward_subsumption_resolution,[],[f14291,f559]) ).
fof(f14348,plain,
( ! [X0] :
( ~ in(X0,sK24)
| in(subset_complement(the_carrier(sK23),X0),relation_rng(sK19(sK23,sK24)))
| ~ in(X0,sK24) )
| ~ spl27_24
| ~ spl27_43
| ~ spl27_64
| ~ spl27_72 ),
inference(forward_demodulation,[],[f13464,f887]) ).
fof(f14349,plain,
( ! [X0] :
( ~ in(X0,sK24)
| in(subset_complement(the_carrier(sK23),X0),relation_rng(sK19(sK23,sK24))) )
| ~ spl27_24
| ~ spl27_43
| ~ spl27_64
| ~ spl27_72 ),
inference(duplicate_literal_removal,[],[f14348]) ).
fof(f14351,plain,
( spl27_48
| ~ spl27_24
| ~ spl27_43
| ~ spl27_64
| ~ spl27_72 ),
inference(avatar_split_clause,[],[f14349,f2311,f2026,f1407,f885,f1502]) ).
fof(f14352,plain,
( sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| sP1(sK24,sK23)
| ~ spl27_3
| ~ spl27_4
| spl27_72 ),
inference(forward_subsumption_resolution,[],[f429,f2312]) ).
fof(f14359,plain,
( sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| sP1(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ spl27_27
| spl27_72 ),
inference(forward_subsumption_resolution,[],[f13630,f2312]) ).
fof(f14367,plain,
( sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| sP1(sK24,sK23)
| ~ spl27_3
| ~ spl27_4
| ~ spl27_27
| spl27_72 ),
inference(forward_subsumption_resolution,[],[f14352,f993]) ).
fof(f14374,plain,
( sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_22
| ~ spl27_27
| spl27_72 ),
inference(forward_subsumption_resolution,[],[f14359,f878]) ).
fof(f14382,plain,
( sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_27
| spl27_72 ),
inference(forward_subsumption_resolution,[],[f14367,f878]) ).
fof(f14390,plain,
( sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ spl27_3
| spl27_22
| ~ spl27_27
| spl27_72 ),
inference(forward_subsumption_resolution,[],[f14374,f310]) ).
fof(f14404,plain,
( sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_27
| spl27_72 ),
inference(forward_subsumption_resolution,[],[f14390,f351]) ).
fof(f14414,plain,
( sK21(sK23,sK24) = sK22(sK23,sK24)
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_27
| spl27_72 ),
inference(forward_demodulation,[],[f14404,f14382]) ).
fof(f14423,plain,
( $false
| ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_23
| ~ spl27_27
| spl27_72 ),
inference(forward_subsumption_resolution,[],[f14414,f883]) ).
fof(f14424,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_23
| ~ spl27_27
| spl27_72 ),
inference(avatar_contradiction_clause,[],[f14423]) ).
fof(f14453,plain,
( sK21(sK23,sK24) != sK22(sK23,sK24)
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_22
| spl27_72 ),
inference(forward_subsumption_resolution,[],[f1389,f2312]) ).
fof(f14458,plain,
( ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_22
| ~ spl27_23
| spl27_72 ),
inference(forward_subsumption_resolution,[],[f14453,f882]) ).
fof(f14461,plain,
( ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ spl27_3
| spl27_22
| ~ spl27_23
| spl27_72 ),
inference(forward_subsumption_resolution,[],[f14458,f310]) ).
fof(f14462,plain,
( $false
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_23
| spl27_72 ),
inference(forward_subsumption_resolution,[],[f14461,f351]) ).
fof(f14463,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_23
| spl27_72 ),
inference(avatar_contradiction_clause,[],[f14462]) ).
fof(f14468,plain,
( sK21(sK23,sK24) != sK22(sK23,sK24)
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_22
| spl27_64 ),
inference(forward_subsumption_resolution,[],[f1391,f2027]) ).
fof(f14481,plain,
( ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_22
| ~ spl27_23
| spl27_64 ),
inference(forward_subsumption_resolution,[],[f14468,f882]) ).
fof(f14494,plain,
( ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ spl27_3
| spl27_22
| ~ spl27_23
| spl27_64 ),
inference(forward_subsumption_resolution,[],[f14481,f310]) ).
fof(f14506,plain,
( $false
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_23
| spl27_64 ),
inference(forward_subsumption_resolution,[],[f14494,f351]) ).
fof(f14507,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_23
| spl27_64 ),
inference(avatar_contradiction_clause,[],[f14506]) ).
fof(f14641,plain,
( ! [X0] :
( sK21(sK23,sK24) != sK21(sK23,sK24)
| ~ in(X0,sK24)
| subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| sP1(sK24,sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_23
| ~ spl27_153 ),
inference(superposition,[],[f5517,f882]) ).
fof(f14689,plain,
( in(sK14(sK23,sK24),relation_rng(sK19(sK23,sK24)))
| ~ spl27_6
| ~ spl27_238 ),
inference(resolution,[],[f9953,f466]) ).
fof(f14712,plain,
( ! [X0] :
( in(sK4(sK19(sK23,sK24),X0),relation_dom(sK19(sK23,sK24)))
| ~ in(X0,relation_rng(sK19(sK23,sK24)))
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_64 ),
inference(resolution,[],[f2028,f261]) ).
fof(f14714,plain,
( ! [X0] :
( in(sK4(sK19(sK23,sK24),X0),relation_dom(sK19(sK23,sK24)))
| ~ in(X0,relation_rng(sK19(sK23,sK24))) )
| ~ spl27_64
| ~ spl27_72 ),
inference(forward_subsumption_resolution,[],[f14712,f2313]) ).
fof(f14719,plain,
( ! [X0] :
( in(sK4(sK19(sK23,sK24),X0),sK24)
| ~ in(X0,relation_rng(sK19(sK23,sK24))) )
| ~ spl27_24
| ~ spl27_64
| ~ spl27_72 ),
inference(forward_demodulation,[],[f14714,f887]) ).
fof(f14827,plain,
( ! [X0] :
( finite(relation_image(sK19(sK23,sK24),X0))
| ~ finite(X0)
| ~ relation(sK19(sK23,sK24)) )
| ~ spl27_72 ),
inference(resolution,[],[f2313,f248]) ).
fof(f14890,plain,
( ~ finite(complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_86
| ~ spl27_89
| spl27_90 ),
inference(forward_subsumption_resolution,[],[f3478,f3517]) ).
fof(f14892,plain,
( $false
| ~ spl27_1
| ~ spl27_86
| ~ spl27_89
| spl27_90 ),
inference(forward_subsumption_resolution,[],[f14890,f293]) ).
fof(f14893,plain,
( ~ spl27_1
| ~ spl27_86
| ~ spl27_89
| spl27_90 ),
inference(avatar_contradiction_clause,[],[f14892]) ).
fof(f14930,plain,
( ~ in(sK2(sK13(sK23,sK24),sK24),sK24)
| finite(sK24)
| ~ spl27_282
| ~ spl27_291 ),
inference(resolution,[],[f12386,f12119]) ).
fof(f14942,plain,
( finite(sK24)
| ~ spl27_282
| ~ spl27_291 ),
inference(forward_subsumption_resolution,[],[f14930,f12386]) ).
fof(f14943,plain,
( $false
| spl27_2
| ~ spl27_282
| ~ spl27_291 ),
inference(forward_subsumption_resolution,[],[f14942,f298]) ).
fof(f14944,plain,
( spl27_2
| ~ spl27_282
| ~ spl27_291 ),
inference(avatar_contradiction_clause,[],[f14943]) ).
fof(f15292,definition,
( spl27_336
<=> element(sK4(sK19(sK23,sK24),sK14(sK23,sK24)),powerset(the_carrier(sK23))) ),
introduced(definition,[new_symbols(definition,[spl27_336])],[avatar_definition]) ).
fof(f15294,plain,
( ~ element(sK4(sK19(sK23,sK24),sK14(sK23,sK24)),powerset(the_carrier(sK23)))
| spl27_336 ),
inference(avatar_component_clause,[],[f15292]) ).
fof(f15295,plain,
( ~ spl27_336
| spl27_11
| ~ spl27_220 ),
inference(avatar_split_clause,[],[f14296,f7378,f557,f15292]) ).
fof(f15296,plain,
( ~ in(sK4(sK19(sK23,sK24),sK14(sK23,sK24)),sK24)
| ~ spl27_32
| spl27_336 ),
inference(resolution,[],[f15294,f1059]) ).
fof(f15300,plain,
( $false
| ~ spl27_32
| ~ spl27_221
| spl27_336 ),
inference(forward_subsumption_resolution,[],[f15296,f7395]) ).
fof(f15301,plain,
( ~ spl27_32
| ~ spl27_221
| spl27_336 ),
inference(avatar_contradiction_clause,[],[f15300]) ).
fof(f15305,plain,
( $false
| ~ spl27_56
| spl27_220
| ~ spl27_223 ),
inference(forward_subsumption_resolution,[],[f9285,f7404]) ).
fof(f15306,plain,
( ~ spl27_56
| spl27_220
| ~ spl27_223 ),
inference(avatar_contradiction_clause,[],[f15305]) ).
fof(f15347,plain,
( sP0(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_6
| spl27_39 ),
inference(forward_subsumption_resolution,[],[f14141,f465]) ).
fof(f15361,plain,
( ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_5
| spl27_6
| spl27_39 ),
inference(forward_subsumption_resolution,[],[f15347,f461]) ).
fof(f15371,plain,
( ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ spl27_3
| spl27_5
| spl27_6
| spl27_39 ),
inference(forward_subsumption_resolution,[],[f15361,f310]) ).
fof(f15380,plain,
( $false
| ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_6
| spl27_39 ),
inference(forward_subsumption_resolution,[],[f15371,f351]) ).
fof(f15381,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_6
| spl27_39 ),
inference(avatar_contradiction_clause,[],[f15380]) ).
fof(f15394,plain,
( relation_rng(sK13(sK23,sK24)) = relation_image(sK13(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_7
| ~ spl27_328 ),
inference(forward_demodulation,[],[f14122,f470]) ).
fof(f15447,plain,
( $false
| ~ spl27_6
| spl27_223
| ~ spl27_238 ),
inference(forward_subsumption_resolution,[],[f14689,f7403]) ).
fof(f15448,plain,
( ~ spl27_6
| spl27_223
| ~ spl27_238 ),
inference(avatar_contradiction_clause,[],[f15447]) ).
fof(f15682,plain,
( sK24 = relation_image(sK13(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_86
| ~ spl27_284 ),
inference(forward_demodulation,[],[f3378,f12187]) ).
fof(f15811,definition,
( spl27_337
<=> sK24 = relation_image(sK13(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24)) ),
introduced(definition,[new_symbols(definition,[spl27_337])],[avatar_definition]) ).
fof(f15813,plain,
( sK24 = relation_image(sK13(sK23,sK24),complements_of_subsets(the_carrier(sK23),sK24))
| ~ spl27_337 ),
inference(avatar_component_clause,[],[f15811]) ).
fof(f15814,plain,
( spl27_337
| ~ spl27_86
| ~ spl27_284 ),
inference(avatar_split_clause,[],[f15682,f12185,f3376,f15811]) ).
fof(f15818,plain,
( finite(sK24)
| ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24))
| ~ spl27_231
| ~ spl27_337 ),
inference(superposition,[],[f9708,f15813]) ).
fof(f15822,plain,
( in(sK4(sK19(sK23,sK24),sK14(sK23,sK24)),relation_dom(sK19(sK23,sK24)))
| ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24))
| ~ spl27_223 ),
inference(resolution,[],[f7404,f261]) ).
fof(f15839,plain,
( in(sK4(sK19(sK23,sK24),sK14(sK23,sK24)),relation_dom(sK19(sK23,sK24)))
| ~ function(sK19(sK23,sK24))
| ~ spl27_64
| ~ spl27_223 ),
inference(forward_subsumption_resolution,[],[f15822,f2028]) ).
fof(f15844,plain,
( in(sK4(sK19(sK23,sK24),sK14(sK23,sK24)),relation_dom(sK19(sK23,sK24)))
| ~ spl27_64
| ~ spl27_72
| ~ spl27_223 ),
inference(forward_subsumption_resolution,[],[f15839,f2313]) ).
fof(f15848,plain,
( in(sK4(sK19(sK23,sK24),sK14(sK23,sK24)),sK24)
| ~ spl27_24
| ~ spl27_64
| ~ spl27_72
| ~ spl27_223 ),
inference(forward_demodulation,[],[f15844,f887]) ).
fof(f15849,plain,
( $false
| ~ spl27_24
| ~ spl27_64
| ~ spl27_72
| spl27_221
| ~ spl27_223 ),
inference(forward_subsumption_resolution,[],[f15848,f7394]) ).
fof(f15850,plain,
( ~ spl27_24
| ~ spl27_64
| ~ spl27_72
| spl27_221
| ~ spl27_223 ),
inference(avatar_contradiction_clause,[],[f15849]) ).
fof(f15851,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),sK4(sK19(sK23,sK24),X0)) = X0
| ~ in(X0,relation_rng(sK19(sK23,sK24)))
| ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_43
| ~ spl27_51 ),
inference(forward_subsumption_resolution,[],[f1415,f1516]) ).
fof(f15855,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),sK4(sK19(sK23,sK24),X0)) = X0
| ~ in(X0,relation_rng(sK19(sK23,sK24)))
| ~ function(sK19(sK23,sK24)) )
| ~ spl27_43
| ~ spl27_51
| ~ spl27_64 ),
inference(forward_subsumption_resolution,[],[f15851,f2028]) ).
fof(f15857,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),sK4(sK19(sK23,sK24),X0)) = X0
| ~ in(X0,relation_rng(sK19(sK23,sK24))) )
| ~ spl27_43
| ~ spl27_51
| ~ spl27_64
| ~ spl27_72 ),
inference(forward_subsumption_resolution,[],[f15855,f2313]) ).
fof(f15859,plain,
( spl27_56
| ~ spl27_43
| ~ spl27_51
| ~ spl27_64
| ~ spl27_72 ),
inference(avatar_split_clause,[],[f15857,f2311,f2026,f1515,f1407,f1850]) ).
fof(f15879,plain,
( spl27_51
| ~ spl27_24
| ~ spl27_64
| ~ spl27_72 ),
inference(avatar_split_clause,[],[f14719,f2311,f2026,f885,f1515]) ).
fof(f15886,plain,
( sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| sP1(sK24,sK23)
| ~ spl27_3
| ~ spl27_4
| spl27_64 ),
inference(forward_subsumption_resolution,[],[f431,f2027]) ).
fof(f15890,plain,
( sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| sP1(sK24,sK23)
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ spl27_27
| spl27_64 ),
inference(forward_subsumption_resolution,[],[f13628,f2027]) ).
fof(f15892,plain,
( sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| sP1(sK24,sK23)
| ~ spl27_3
| ~ spl27_4
| ~ spl27_27
| spl27_64 ),
inference(forward_subsumption_resolution,[],[f15886,f993]) ).
fof(f15896,plain,
( sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ one_sorted_str(sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_22
| ~ spl27_27
| spl27_64 ),
inference(forward_subsumption_resolution,[],[f15890,f878]) ).
fof(f15898,plain,
( sK21(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_27
| spl27_64 ),
inference(forward_subsumption_resolution,[],[f15892,f878]) ).
fof(f15902,plain,
( sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| ~ spl27_3
| spl27_22
| ~ spl27_27
| spl27_64 ),
inference(forward_subsumption_resolution,[],[f15896,f310]) ).
fof(f15906,plain,
( sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_27
| spl27_64 ),
inference(forward_subsumption_resolution,[],[f15902,f351]) ).
fof(f15910,plain,
( sK21(sK23,sK24) = sK22(sK23,sK24)
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_27
| spl27_64 ),
inference(forward_demodulation,[],[f15906,f15898]) ).
fof(f15913,plain,
( $false
| ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_23
| ~ spl27_27
| spl27_64 ),
inference(forward_subsumption_resolution,[],[f15910,f883]) ).
fof(f15914,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_23
| ~ spl27_27
| spl27_64 ),
inference(avatar_contradiction_clause,[],[f15913]) ).
fof(f16003,plain,
( $false
| spl27_1
| ~ spl27_118
| ~ spl27_209 ),
inference(forward_subsumption_resolution,[],[f13212,f294]) ).
fof(f16004,plain,
( spl27_1
| ~ spl27_118
| ~ spl27_209 ),
inference(avatar_contradiction_clause,[],[f16003]) ).
fof(f16021,plain,
( ! [X0] :
( in(sK2(sK19(sK23,sK24),X0),complements_of_subsets(the_carrier(sK23),sK24))
| finite(X0)
| in(sK2(sK19(sK23,sK24),X0),X0) )
| ~ spl27_18
| ~ spl27_134
| ~ spl27_140 ),
inference(forward_subsumption_resolution,[],[f8121,f5157]) ).
fof(f16501,plain,
( ~ spl27_142
| spl27_1
| ~ spl27_54
| ~ spl27_151
| ~ spl27_227 ),
inference(avatar_split_clause,[],[f9542,f9529,f5491,f1654,f292,f5377]) ).
fof(f16502,plain,
( spl27_45
| ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_6 ),
inference(avatar_split_clause,[],[f2347,f464,f460,f349,f308,f1467]) ).
fof(f16655,plain,
( spl27_141
| ~ spl27_18
| ~ spl27_134
| ~ spl27_140 ),
inference(avatar_split_clause,[],[f16021,f5323,f5156,f733,f5349]) ).
fof(f16656,plain,
( ~ relation(sK19(sK23,sK24))
| ~ function(sK19(sK23,sK24))
| ~ spl27_33
| spl27_118
| ~ spl27_120 ),
inference(forward_subsumption_resolution,[],[f4600,f4562]) ).
fof(f16659,plain,
( ! [X0] :
( finite(relation_image(sK19(sK23,sK24),X0))
| ~ finite(X0) )
| ~ spl27_64
| ~ spl27_72 ),
inference(forward_subsumption_resolution,[],[f14827,f2028]) ).
fof(f16660,plain,
( ~ function(sK19(sK23,sK24))
| ~ spl27_33
| ~ spl27_64
| spl27_118
| ~ spl27_120 ),
inference(forward_subsumption_resolution,[],[f16656,f2028]) ).
fof(f16664,plain,
( $false
| ~ spl27_33
| ~ spl27_64
| ~ spl27_72
| spl27_118
| ~ spl27_120 ),
inference(forward_subsumption_resolution,[],[f16660,f2313]) ).
fof(f16665,plain,
( ~ spl27_33
| ~ spl27_64
| ~ spl27_72
| spl27_118
| ~ spl27_120 ),
inference(avatar_contradiction_clause,[],[f16664]) ).
fof(f16669,plain,
( ~ relation(sK19(sK23,sK24))
| ~ spl27_24
| spl27_33 ),
inference(forward_subsumption_resolution,[],[f1373,f1148]) ).
fof(f16670,plain,
( $false
| ~ spl27_24
| spl27_33
| ~ spl27_64 ),
inference(forward_subsumption_resolution,[],[f16669,f2028]) ).
fof(f16671,plain,
( ~ spl27_24
| spl27_33
| ~ spl27_64 ),
inference(avatar_contradiction_clause,[],[f16670]) ).
fof(f16720,plain,
( ~ relation(sK13(sK23,sK24))
| ~ function(sK13(sK23,sK24))
| spl27_2
| ~ spl27_231
| ~ spl27_337 ),
inference(forward_subsumption_resolution,[],[f15818,f298]) ).
fof(f16736,plain,
( ~ function(sK13(sK23,sK24))
| spl27_2
| ~ spl27_39
| ~ spl27_231
| ~ spl27_337 ),
inference(forward_subsumption_resolution,[],[f16720,f1315]) ).
fof(f16746,plain,
( $false
| spl27_2
| ~ spl27_39
| ~ spl27_45
| ~ spl27_231
| ~ spl27_337 ),
inference(forward_subsumption_resolution,[],[f16736,f1469]) ).
fof(f16747,plain,
( spl27_2
| ~ spl27_39
| ~ spl27_45
| ~ spl27_231
| ~ spl27_337 ),
inference(avatar_contradiction_clause,[],[f16746]) ).
fof(f16756,plain,
( spl27_86
| ~ spl27_7
| ~ spl27_328 ),
inference(avatar_split_clause,[],[f15394,f14120,f468,f3376]) ).
fof(f16785,plain,
( spl27_65
| ~ spl27_64
| ~ spl27_72 ),
inference(avatar_split_clause,[],[f16659,f2311,f2026,f2051]) ).
fof(f17091,plain,
( spl27_282
| ~ spl27_112
| ~ spl27_309 ),
inference(avatar_split_clause,[],[f12892,f12874,f4376,f12118]) ).
fof(f17099,plain,
( sP1(sK24,sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_24
| ~ spl27_27
| ~ spl27_214 ),
inference(forward_subsumption_resolution,[],[f13626,f886]) ).
fof(f17137,plain,
( ~ element(sK24,powerset(powerset(the_carrier(sK23))))
| spl27_22
| spl27_24
| ~ spl27_27
| ~ spl27_214 ),
inference(forward_subsumption_resolution,[],[f17099,f878]) ).
fof(f17140,plain,
( $false
| ~ spl27_4
| spl27_22
| spl27_24
| ~ spl27_27
| ~ spl27_214 ),
inference(forward_subsumption_resolution,[],[f17137,f351]) ).
fof(f17141,plain,
( ~ spl27_4
| spl27_22
| spl27_24
| ~ spl27_27
| ~ spl27_214 ),
inference(avatar_contradiction_clause,[],[f17140]) ).
fof(f17153,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24)
| sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24))
| sP1(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4
| ~ spl27_27 ),
inference(forward_subsumption_resolution,[],[f455,f993]) ).
fof(f17165,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24)
| sK22(sK23,sK24) = subset_complement(the_carrier(sK23),sK20(sK23,sK24)) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_27 ),
inference(forward_subsumption_resolution,[],[f17153,f878]) ).
fof(f17176,plain,
( ! [X0] :
( sK21(sK23,sK24) = sK22(sK23,sK24)
| subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_27
| ~ spl27_28 ),
inference(forward_demodulation,[],[f17165,f998]) ).
fof(f17187,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_23
| ~ spl27_27
| ~ spl27_28 ),
inference(forward_subsumption_resolution,[],[f17176,f883]) ).
fof(f17326,plain,
( spl27_43
| ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_23
| ~ spl27_27
| ~ spl27_28 ),
inference(avatar_split_clause,[],[f17187,f996,f992,f881,f877,f349,f308,f1407]) ).
fof(f17327,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24)
| ~ element(sK20(sK23,sK24),powerset(the_carrier(sK23)))
| sP1(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4
| spl27_28 ),
inference(forward_subsumption_resolution,[],[f456,f997]) ).
fof(f17341,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24)
| sP1(sK24,sK23) )
| ~ spl27_3
| ~ spl27_4
| ~ spl27_27
| spl27_28 ),
inference(forward_subsumption_resolution,[],[f17327,f993]) ).
fof(f17384,plain,
( ! [X0] :
( subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ in(X0,sK24) )
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_27
| spl27_28 ),
inference(forward_subsumption_resolution,[],[f17341,f878]) ).
fof(f17465,plain,
( spl27_43
| ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_27
| spl27_28 ),
inference(avatar_split_clause,[],[f17384,f996,f992,f877,f349,f308,f1407]) ).
fof(f17467,plain,
( ! [X0] :
( ~ in(X0,sK24)
| subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| sP1(sK24,sK23)
| ~ element(sK24,powerset(powerset(the_carrier(sK23)))) )
| ~ spl27_23
| ~ spl27_153 ),
inference(trivial_inequality_removal,[],[f14641]) ).
fof(f17468,plain,
( ! [X0] :
( ~ in(X0,sK24)
| subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0)
| ~ element(sK24,powerset(powerset(the_carrier(sK23)))) )
| spl27_22
| ~ spl27_23
| ~ spl27_153 ),
inference(forward_subsumption_resolution,[],[f17467,f878]) ).
fof(f17484,plain,
( ! [X0] :
( ~ in(X0,sK24)
| subset_complement(the_carrier(sK23),X0) = apply(sK19(sK23,sK24),X0) )
| ~ spl27_4
| spl27_22
| ~ spl27_23
| ~ spl27_153 ),
inference(forward_subsumption_resolution,[],[f17468,f351]) ).
fof(f17564,plain,
( spl27_43
| ~ spl27_4
| spl27_22
| ~ spl27_23
| ~ spl27_153 ),
inference(avatar_split_clause,[],[f17484,f5516,f881,f877,f349,f1407]) ).
cnf(s1,plain,
( ~ spl27_1
| ~ spl27_2 ),
inference(sat_conversion,[],[f299]) ).
cnf(s2,plain,
spl27_3,
inference(sat_conversion,[],[f311]) ).
cnf(s3,plain,
spl27_4,
inference(sat_conversion,[],[f352]) ).
cnf(s4,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_6
| spl27_7 ),
inference(sat_conversion,[],[f471]) ).
cnf(s6,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_7
| ~ spl27_9 ),
inference(sat_conversion,[],[f551]) ).
cnf(s7,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| ~ spl27_9
| spl27_10 ),
inference(sat_conversion,[],[f555]) ).
cnf(s10,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_7
| ~ spl27_11
| spl27_14 ),
inference(sat_conversion,[],[f577]) ).
cnf(s11,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_7
| ~ spl27_11
| spl27_15 ),
inference(sat_conversion,[],[f582]) ).
cnf(s14,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_10
| ~ spl27_11
| spl27_14 ),
inference(sat_conversion,[],[f585]) ).
cnf(s15,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_10
| ~ spl27_11
| spl27_15 ),
inference(sat_conversion,[],[f586]) ).
cnf(s16,plain,
( ~ spl27_4
| spl27_16 ),
inference(sat_conversion,[],[f591]) ).
cnf(s18,plain,
( ~ spl27_4
| ~ spl27_16
| spl27_18 ),
inference(sat_conversion,[],[f735]) ).
cnf(s21,plain,
( ~ spl27_4
| spl27_21 ),
inference(sat_conversion,[],[f844]) ).
cnf(s28,plain,
( ~ spl27_22
| spl27_31 ),
inference(sat_conversion,[],[f1021]) ).
cnf(s29,plain,
( ~ spl27_4
| spl27_32 ),
inference(sat_conversion,[],[f1060]) ).
cnf(s30,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| spl27_33 ),
inference(sat_conversion,[],[f1150]) ).
cnf(s39,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| ~ spl27_9
| spl27_39 ),
inference(sat_conversion,[],[f1316]) ).
cnf(s42,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_24
| spl27_27
| ~ spl27_32 ),
inference(sat_conversion,[],[f1331]) ).
cnf(s43,plain,
( spl27_27
| ~ spl27_30
| ~ spl27_32 ),
inference(sat_conversion,[],[f1352]) ).
cnf(s45,plain,
( ~ spl27_22
| ~ spl27_31
| spl27_42 ),
inference(sat_conversion,[],[f1366]) ).
cnf(s46,plain,
~ spl27_42,
inference(sat_conversion,[],[f1368]) ).
cnf(s47,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_30
| spl27_43 ),
inference(sat_conversion,[],[f1409]) ).
cnf(s48,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| spl27_44 ),
inference(sat_conversion,[],[f1440]) ).
cnf(s49,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| ~ spl27_11
| spl27_14
| spl27_39 ),
inference(sat_conversion,[],[f1465]) ).
cnf(s50,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| ~ spl27_9
| spl27_45 ),
inference(sat_conversion,[],[f1470]) ).
cnf(s51,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| ~ spl27_11
| spl27_15
| spl27_39 ),
inference(sat_conversion,[],[f1471]) ).
cnf(s53,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| ~ spl27_11
| spl27_14
| spl27_45 ),
inference(sat_conversion,[],[f1495]) ).
cnf(s54,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| ~ spl27_11
| spl27_15
| spl27_45 ),
inference(sat_conversion,[],[f1496]) ).
cnf(s55,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43
| spl27_47 ),
inference(sat_conversion,[],[f1500]) ).
cnf(s56,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43
| spl27_48 ),
inference(sat_conversion,[],[f1504]) ).
cnf(s63,plain,
( ~ spl27_4
| spl27_54 ),
inference(sat_conversion,[],[f1657]) ).
cnf(s65,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_24
| spl27_27
| ~ spl27_32
| ~ spl27_43
| spl27_56 ),
inference(sat_conversion,[],[f1852]) ).
cnf(s68,plain,
( ~ spl27_18
| ~ spl27_44
| ~ spl27_47
| spl27_59 ),
inference(sat_conversion,[],[f1931]) ).
cnf(s73,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_27
| ~ spl27_32
| spl27_64 ),
inference(sat_conversion,[],[f2029]) ).
cnf(s79,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_27
| ~ spl27_32
| spl27_72 ),
inference(sat_conversion,[],[f2314]) ).
cnf(s86,plain,
( ~ spl27_5
| spl27_76 ),
inference(sat_conversion,[],[f2983]) ).
cnf(s87,plain,
( ~ spl27_5
| ~ spl27_76
| spl27_77 ),
inference(sat_conversion,[],[f2988]) ).
cnf(s88,plain,
~ spl27_77,
inference(sat_conversion,[],[f2990]) ).
cnf(s89,plain,
( spl27_9
| ~ spl27_14
| ~ spl27_15 ),
inference(sat_conversion,[],[f3013]) ).
cnf(s92,plain,
( ~ spl27_10
| ~ spl27_54
| spl27_81 ),
inference(sat_conversion,[],[f3236]) ).
cnf(s97,plain,
( ~ spl27_7
| ~ spl27_39
| spl27_86 ),
inference(sat_conversion,[],[f3379]) ).
cnf(s106,plain,
( ~ spl27_39
| ~ spl27_45
| spl27_89 ),
inference(sat_conversion,[],[f3476]) ).
cnf(s107,plain,
( ~ spl27_1
| ~ spl27_39
| ~ spl27_45
| ~ spl27_86
| spl27_90 ),
inference(sat_conversion,[],[f3519]) ).
cnf(s109,plain,
( ~ spl27_39
| ~ spl27_45
| spl27_92 ),
inference(sat_conversion,[],[f3573]) ).
cnf(s112,plain,
( ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| ~ spl27_81
| spl27_95 ),
inference(sat_conversion,[],[f3651]) ).
cnf(s113,plain,
( ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| spl27_96 ),
inference(sat_conversion,[],[f3793]) ).
cnf(s123,plain,
( ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| ~ spl27_90
| spl27_106 ),
inference(sat_conversion,[],[f4127]) ).
cnf(s125,plain,
( ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| ~ spl27_90
| spl27_108 ),
inference(sat_conversion,[],[f4179]) ).
cnf(s129,plain,
( spl27_1
| spl27_2 ),
inference(sat_conversion,[],[f4278]) ).
cnf(s133,plain,
( ~ spl27_92
| ~ spl27_96
| ~ spl27_108
| spl27_111 ),
inference(sat_conversion,[],[f4373]) ).
cnf(s134,plain,
( ~ spl27_111
| spl27_112 ),
inference(sat_conversion,[],[f4378]) ).
cnf(s144,plain,
( spl27_1
| ~ spl27_33
| ~ spl27_65
| spl27_118 ),
inference(sat_conversion,[],[f4564]) ).
cnf(s146,plain,
( ~ spl27_2
| spl27_120 ),
inference(sat_conversion,[],[f4598]) ).
cnf(s162,plain,
( ~ spl27_24
| ~ spl27_64
| ~ spl27_72
| ~ spl27_118
| spl27_134 ),
inference(sat_conversion,[],[f5158]) ).
cnf(s163,plain,
( ~ spl27_24
| ~ spl27_64
| ~ spl27_72
| ~ spl27_118
| spl27_135 ),
inference(sat_conversion,[],[f5172]) ).
cnf(s166,plain,
( ~ spl27_43
| ~ spl27_135
| spl27_138 ),
inference(sat_conversion,[],[f5223]) ).
cnf(s167,plain,
( ~ spl27_64
| ~ spl27_72
| ~ spl27_118
| spl27_139 ),
inference(sat_conversion,[],[f5285]) ).
cnf(s168,plain,
( ~ spl27_43
| ~ spl27_134
| ~ spl27_139
| spl27_140 ),
inference(sat_conversion,[],[f5325]) ).
cnf(s170,plain,
( spl27_1
| ~ spl27_141
| spl27_142 ),
inference(sat_conversion,[],[f5380]) ).
cnf(s178,plain,
( ~ spl27_21
| ~ spl27_142
| spl27_151 ),
inference(sat_conversion,[],[f5494]) ).
cnf(s180,plain,
( ~ spl27_3
| spl27_153 ),
inference(sat_conversion,[],[f5518]) ).
cnf(s192,plain,
( ~ spl27_138
| spl27_164 ),
inference(sat_conversion,[],[f5779]) ).
cnf(s200,plain,
( ~ spl27_21
| ~ spl27_106
| spl27_172 ),
inference(sat_conversion,[],[f5899]) ).
cnf(s236,plain,
( ~ spl27_59
| spl27_142
| spl27_209 ),
inference(sat_conversion,[],[f7036]) ).
cnf(s240,plain,
( ~ spl27_3
| spl27_213 ),
inference(sat_conversion,[],[f7187]) ).
cnf(s241,plain,
( ~ spl27_3
| ~ spl27_213
| spl27_214 ),
inference(sat_conversion,[],[f7271]) ).
cnf(s273,plain,
( ~ spl27_164
| spl27_227 ),
inference(sat_conversion,[],[f9531]) ).
cnf(s280,plain,
( ~ spl27_1
| spl27_231 ),
inference(sat_conversion,[],[f9709]) ).
cnf(s285,plain,
( ~ spl27_48
| spl27_237 ),
inference(sat_conversion,[],[f9871]) ).
cnf(s286,plain,
( ~ spl27_4
| ~ spl27_237
| spl27_238 ),
inference(sat_conversion,[],[f9954]) ).
cnf(s347,plain,
( spl27_2
| ~ spl27_7
| ~ spl27_39
| ~ spl27_45
| ~ spl27_282
| spl27_284
| spl27_285 ),
inference(sat_conversion,[],[f12192]) ).
cnf(s350,plain,
( spl27_2
| ~ spl27_39
| ~ spl27_45
| ~ spl27_282
| spl27_284
| spl27_289 ),
inference(sat_conversion,[],[f12247]) ).
cnf(s372,plain,
( ~ spl27_95
| spl27_308 ),
inference(sat_conversion,[],[f12775]) ).
cnf(s373,plain,
( ~ spl27_18
| ~ spl27_32
| ~ spl27_308
| spl27_309 ),
inference(sat_conversion,[],[f12876]) ).
cnf(s391,plain,
( spl27_2
| ~ spl27_172
| spl27_291
| ~ spl27_292 ),
inference(sat_conversion,[],[f13384]) ).
cnf(s397,plain,
( ~ spl27_81
| ~ spl27_285
| ~ spl27_289
| spl27_292 ),
inference(sat_conversion,[],[f13454]) ).
cnf(s412,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_6
| ~ spl27_54
| spl27_81 ),
inference(sat_conversion,[],[f13670]) ).
cnf(s432,plain,
( ~ spl27_39
| spl27_328 ),
inference(sat_conversion,[],[f14123]) ).
cnf(s442,plain,
( ~ spl27_24
| ~ spl27_43
| spl27_48
| ~ spl27_64
| ~ spl27_72 ),
inference(sat_conversion,[],[f14351]) ).
cnf(s448,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_23
| ~ spl27_27
| spl27_72 ),
inference(sat_conversion,[],[f14424]) ).
cnf(s452,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_23
| spl27_72 ),
inference(sat_conversion,[],[f14463]) ).
cnf(s454,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_23
| spl27_64 ),
inference(sat_conversion,[],[f14507]) ).
cnf(s459,plain,
( ~ spl27_1
| ~ spl27_86
| ~ spl27_89
| spl27_90 ),
inference(sat_conversion,[],[f14893]) ).
cnf(s462,plain,
( spl27_2
| ~ spl27_282
| ~ spl27_291 ),
inference(sat_conversion,[],[f14944]) ).
cnf(s470,plain,
( spl27_11
| ~ spl27_220
| ~ spl27_336 ),
inference(sat_conversion,[],[f15295]) ).
cnf(s471,plain,
( ~ spl27_32
| ~ spl27_221
| spl27_336 ),
inference(sat_conversion,[],[f15301]) ).
cnf(s473,plain,
( ~ spl27_56
| spl27_220
| ~ spl27_223 ),
inference(sat_conversion,[],[f15306]) ).
cnf(s481,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_6
| spl27_39 ),
inference(sat_conversion,[],[f15381]) ).
cnf(s492,plain,
( ~ spl27_6
| spl27_223
| ~ spl27_238 ),
inference(sat_conversion,[],[f15448]) ).
cnf(s495,plain,
( ~ spl27_86
| ~ spl27_284
| spl27_337 ),
inference(sat_conversion,[],[f15814]) ).
cnf(s496,plain,
( ~ spl27_24
| ~ spl27_64
| ~ spl27_72
| spl27_221
| ~ spl27_223 ),
inference(sat_conversion,[],[f15850]) ).
cnf(s497,plain,
( ~ spl27_43
| ~ spl27_51
| spl27_56
| ~ spl27_64
| ~ spl27_72 ),
inference(sat_conversion,[],[f15859]) ).
cnf(s498,plain,
( ~ spl27_24
| spl27_51
| ~ spl27_64
| ~ spl27_72 ),
inference(sat_conversion,[],[f15879]) ).
cnf(s504,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_23
| ~ spl27_27
| spl27_64 ),
inference(sat_conversion,[],[f15914]) ).
cnf(s506,plain,
( spl27_1
| ~ spl27_118
| ~ spl27_209 ),
inference(sat_conversion,[],[f16004]) ).
cnf(s508,plain,
( spl27_1
| ~ spl27_54
| ~ spl27_142
| ~ spl27_151
| ~ spl27_227 ),
inference(sat_conversion,[],[f16501]) ).
cnf(s509,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_5
| spl27_6
| spl27_45 ),
inference(sat_conversion,[],[f16502]) ).
cnf(s513,plain,
( ~ spl27_18
| ~ spl27_134
| ~ spl27_140
| spl27_141 ),
inference(sat_conversion,[],[f16655]) ).
cnf(s515,plain,
( ~ spl27_33
| ~ spl27_64
| ~ spl27_72
| spl27_118
| ~ spl27_120 ),
inference(sat_conversion,[],[f16665]) ).
cnf(s517,plain,
( ~ spl27_24
| spl27_33
| ~ spl27_64 ),
inference(sat_conversion,[],[f16671]) ).
cnf(s524,plain,
( spl27_2
| ~ spl27_39
| ~ spl27_45
| ~ spl27_231
| ~ spl27_337 ),
inference(sat_conversion,[],[f16747]) ).
cnf(s526,plain,
( ~ spl27_7
| spl27_86
| ~ spl27_328 ),
inference(sat_conversion,[],[f16756]) ).
cnf(s528,plain,
( ~ spl27_64
| spl27_65
| ~ spl27_72 ),
inference(sat_conversion,[],[f16785]) ).
cnf(s533,plain,
( ~ spl27_112
| spl27_282
| ~ spl27_309 ),
inference(sat_conversion,[],[f17091]) ).
cnf(s535,plain,
( ~ spl27_4
| spl27_22
| spl27_24
| ~ spl27_27
| ~ spl27_214 ),
inference(sat_conversion,[],[f17141]) ).
cnf(s538,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| spl27_23
| ~ spl27_27
| ~ spl27_28
| spl27_43 ),
inference(sat_conversion,[],[f17326]) ).
cnf(s541,plain,
( ~ spl27_3
| ~ spl27_4
| spl27_22
| ~ spl27_27
| spl27_28
| spl27_43 ),
inference(sat_conversion,[],[f17465]) ).
cnf(s542,plain,
( ~ spl27_4
| spl27_22
| ~ spl27_23
| spl27_43
| ~ spl27_153 ),
inference(sat_conversion,[],[f17564]) ).
cnf(s544,plain,
( ~ spl27_5
| ~ spl27_76 ),
inference(rat,[],[s87,s88]) ).
cnf(s545,plain,
( ~ spl27_22
| ~ spl27_31 ),
inference(rat,[],[s45,s46]) ).
cnf(s551,plain,
spl27_54,
inference(rat,[],[s63,s3]) ).
cnf(s552,plain,
spl27_32,
inference(rat,[],[s29,s3]) ).
cnf(s554,plain,
spl27_21,
inference(rat,[],[s21,s3]) ).
cnf(s555,plain,
spl27_16,
inference(rat,[],[s16,s3]) ).
cnf(s557,plain,
spl27_18,
inference(rat,[],[s18,s3,s555]) ).
cnf(s567,plain,
spl27_213,
inference(rat,[],[s240,s2]) ).
cnf(s574,plain,
spl27_153,
inference(rat,[],[s180,s2]) ).
cnf(s579,plain,
spl27_214,
inference(rat,[],[s241,s2,s567]) ).
cnf(s587,plain,
( spl27_24
| spl27_22 ),
inference(rat,[],[s42,s535,s579,s552,s2,s3]) ).
cnf(s588,plain,
( spl27_27
| spl27_22
| spl27_1 ),
inference(rat,[],[s508,s178,s273,s236,s192,s68,s166,s506,s55,s163,s515,s47,s30,s48,s73,s79,s43,s146,s129,s587,s551,s554,s557,s3,s2,s552]) ).
cnf(s589,plain,
( ~ spl27_43
| ~ spl27_134
| ~ spl27_135
| ~ spl27_139
| spl27_1 ),
inference(rat,[],[s508,s178,s273,s170,s192,s513,s166,s168,s551,s554,s557]) ).
cnf(s590,plain,
( spl27_43
| spl27_23
| spl27_22
| ~ spl27_27 ),
inference(rat,[],[s541,s538,s2,s3]) ).
cnf(s591,plain,
( spl27_23
| spl27_22
| spl27_1 ),
inference(rat,[],[s590,s589,s162,s163,s167,s144,s517,s528,s448,s504,s587,s588,s3,s2]) ).
cnf(s592,plain,
( spl27_22
| spl27_1 ),
inference(rat,[],[s589,s162,s163,s167,s144,s517,s528,s452,s454,s542,s591,s587,s3,s2,s574]) ).
cnf(s593,plain,
~ spl27_22,
inference(rat,[],[s28,s545]) ).
cnf(s594,plain,
spl27_24,
inference(rat,[],[s587,s593]) ).
cnf(s595,plain,
spl27_1,
inference(rat,[],[s592,s593]) ).
cnf(s596,plain,
spl27_231,
inference(rat,[],[s280,s595]) ).
cnf(s600,plain,
~ spl27_2,
inference(rat,[],[s1,s595]) ).
cnf(s604,plain,
( spl27_6
| spl27_5 ),
inference(rat,[],[s397,s391,s347,s350,s462,s533,s134,s200,s133,s373,s123,s125,s372,s459,s495,s112,s113,s526,s106,s109,s432,s524,s4,s412,s481,s509,s551,s2,s3,s596,s595,s557,s552,s554,s600]) ).
cnf(s605,plain,
( ~ spl27_81
| ~ spl27_45
| ~ spl27_39
| ~ spl27_7 ),
inference(rat,[],[s397,s391,s347,s350,s462,s533,s373,s372,s112,s495,s524,s200,s123,s134,s133,s125,s107,s97,s109,s113,s600,s552,s557,s595,s554,s596]) ).
cnf(s606,plain,
( spl27_10
| ~ spl27_11
| spl27_5 ),
inference(rat,[],[s89,s14,s15,s7,s3,s2]) ).
cnf(s607,plain,
( spl27_45
| ~ spl27_11
| spl27_5 ),
inference(rat,[],[s89,s53,s54,s50,s3,s2]) ).
cnf(s608,plain,
( spl27_39
| ~ spl27_11
| spl27_5 ),
inference(rat,[],[s89,s49,s51,s39,s3,s2]) ).
cnf(s609,plain,
( spl27_7
| spl27_5
| ~ spl27_11 ),
inference(rat,[],[s89,s6,s10,s11,s2,s3]) ).
cnf(s610,plain,
( ~ spl27_11
| spl27_5 ),
inference(rat,[],[s609,s605,s608,s607,s92,s606,s551]) ).
cnf(s611,plain,
( spl27_5
| ~ spl27_238
| ~ spl27_56
| ~ spl27_72
| ~ spl27_64 ),
inference(rat,[],[s610,s470,s471,s473,s496,s492,s604,s552,s594]) ).
cnf(s612,plain,
~ spl27_5,
inference(rat,[],[s86,s544]) ).
cnf(s622,plain,
( spl27_23
| ~ spl27_27
| ~ spl27_43 ),
inference(rat,[],[s286,s611,s285,s497,s442,s498,s448,s504,s3,s612,s594,s2,s593]) ).
cnf(s623,plain,
( ~ spl27_23
| ~ spl27_43 ),
inference(rat,[],[s286,s611,s285,s497,s442,s498,s452,s454,s3,s612,s594,s2,s593]) ).
cnf(s624,plain,
( spl27_23
| ~ spl27_43 ),
inference(rat,[],[s286,s285,s611,s56,s65,s73,s79,s622,s594,s552,s593,s2,s612,s3]) ).
cnf(s625,plain,
~ spl27_43,
inference(rat,[],[s624,s623]) ).
cnf(s626,plain,
~ spl27_23,
inference(rat,[],[s542,s574,s593,s3,s625]) ).
cnf(s627,plain,
spl27_30,
inference(rat,[],[s47,s593,s2,s3,s625]) ).
cnf(s628,plain,
~ spl27_27,
inference(rat,[],[s590,s625,s593,s626]) ).
cnf(s631,plain,
$false,
inference(rat,[],[s43,s552,s627,s628]) ).
fof(f17565,plain,
$false,
inference(avatar_sat_refutation,[],[s631]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU335+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 % Computer : n017.cluster.edu
% 0.10/0.42 % Model : x86_64 x86_64
% 0.10/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.42 % Memory : 8046.5625MB
% 0.10/0.42 % OS : Linux 6.8.0-71-generic
% 0.10/0.42 % CPULimit : 300
% 0.10/0.42 % WCLimit : 300
% 0.10/0.42 % DateTime : Mon Sep 28 04:42:40 UTC 2026
% 0.10/0.43 % CPUTime :
% 0.10/0.43 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.46 Running first-order theorem proving
% 0.16/0.46 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.86/2.44 % (3209309)Detected formulas, will run a generic FOF schedule.
% 10.86/2.44 % (3209320)dis-21_1_sil=8000:lcm=predicate:random_seed=1177018186:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 10.86/2.44 % (3209320)Instruction limit reached!
% 10.86/2.44 % (3209320)------------------------------
% 10.86/2.44 % (3209320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.86/2.44 % (3209320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.86/2.44 % (3209320)CaDiCaL version: 2.1.3
% 10.86/2.44 % (3209320)Termination reason: Instruction limit
% 10.86/2.44 % (3209320)Termination phase: Saturation
% 10.86/2.44 % (3209320)Time elapsed: 0.036 s
% 10.86/2.44 % (3209320)Peak memory usage: 89 MB
% 10.86/2.44 % (3209320)Instructions burned: 133 (million)
% 10.86/2.44 % (3209319)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1923041356:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.86/2.44 % (3209315)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3400691948:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.86/2.44 % (3209316)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1522881762:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.86/2.44 % (3209317)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1443005433:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.86/2.44 % (3209318)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=598863279:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.86/2.44 % (3209314)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3593278403:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.86/2.44 % (3209317)Refutation not found, incomplete strategy
% 10.86/2.44 % (3209317)------------------------------
% 10.86/2.44 % (3209317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.86/2.44 % (3209317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.86/2.44 % (3209317)CaDiCaL version: 2.1.3
% 10.86/2.44 % (3209317)Termination reason: Refutation not found, incomplete strategy
% 10.86/2.44 % (3209317)Time elapsed: 0.004 s
% 10.86/2.44 % (3209317)Peak memory usage: 88 MB
% 10.86/2.44 % (3209317)Instructions burned: 4 (million)
% 10.86/2.44 % (3209318)Instruction limit reached!
% 10.86/2.44 % (3209318)------------------------------
% 10.86/2.44 % (3209318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.86/2.44 % (3209318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.86/2.44 % (3209318)CaDiCaL version: 2.1.3
% 10.86/2.44 % (3209318)Termination reason: Instruction limit
% 10.86/2.44 % (3209318)Termination phase: Saturation
% 10.86/2.44 % (3209318)Time elapsed: 0.077 s
% 10.86/2.44 % (3209318)Peak memory usage: 89 MB
% 10.86/2.44 % (3209318)Instructions burned: 121 (million)
% 10.86/2.44 % (3209328)lrs+10_1_sil=8000:sp=occurrence:random_seed=1330477278:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 10.86/2.44 % (3209319)Instruction limit reached!
% 10.86/2.44 % (3209319)------------------------------
% 10.86/2.44 % (3209319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.86/2.44 % (3209319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.86/2.44 % (3209319)CaDiCaL version: 2.1.3
% 10.86/2.44 % (3209319)Termination reason: Instruction limit
% 10.86/2.44 % (3209319)Termination phase: Saturation
% 10.86/2.44 % (3209319)Time elapsed: 0.099 s
% 10.86/2.44 % (3209319)Peak memory usage: 89 MB
% 10.86/2.44 % (3209319)Instructions burned: 140 (million)
% 10.86/2.44 % (3209328)Instruction limit reached!
% 10.86/2.44 % (3209328)------------------------------
% 10.86/2.44 % (3209328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.86/2.44 % (3209328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.86/2.44 % (3209328)CaDiCaL version: 2.1.3
% 10.86/2.44 % (3209328)Termination reason: Instruction limit
% 10.86/2.44 % (3209328)Termination phase: Saturation
% 10.86/2.44 % (3209328)Time elapsed: 0.094 s
% 10.86/2.44 % (3209328)Peak memory usage: 92 MB
% 10.86/2.44 % (3209328)Instructions burned: 285 (million)
% 19.25/3.65 % (3209329)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3108600069:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 19.25/3.65 % (3209331)lrs+1011_1_sil=32000:sp=occurrence:random_seed=97713756:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 19.25/3.65 % (3209317)------------------------------
% 19.25/3.65 % (3209317)------------------------------
% 19.25/3.65 % (3209332)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=4214673553:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 19.25/3.65 % (3209329)Instruction limit reached!
% 19.25/3.65 % (3209329)------------------------------
% 19.25/3.65 % (3209329)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.25/3.65 % (3209329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.25/3.65 % (3209329)CaDiCaL version: 2.1.3
% 19.25/3.65 % (3209329)Termination reason: Instruction limit
% 19.25/3.65 % (3209329)Termination phase: Saturation
% 19.25/3.65 % (3209329)Time elapsed: 0.062 s
% 19.25/3.65 % (3209329)Peak memory usage: 89 MB
% 19.25/3.65 % (3209329)Instructions burned: 160 (million)
% 19.25/3.65 % (3209332)Instruction limit reached!
% 19.25/3.65 % (3209332)------------------------------
% 19.25/3.65 % (3209332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.25/3.65 % (3209332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.25/3.65 % (3209332)CaDiCaL version: 2.1.3
% 19.25/3.65 % (3209332)Termination reason: Instruction limit
% 19.25/3.65 % (3209332)Termination phase: Saturation
% 19.25/3.65 % (3209332)Time elapsed: 0.078 s
% 19.25/3.65 % (3209332)Peak memory usage: 90 MB
% 19.25/3.65 % (3209332)Instructions burned: 249 (million)
% 19.25/3.65 % (3209335)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3169169834:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 19.25/3.65 % (3209337)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=475120596:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 19.25/3.65 % (3209335)Refutation not found, incomplete strategy
% 19.25/3.65 % (3209335)------------------------------
% 19.25/3.65 % (3209335)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.25/3.65 % (3209335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.25/3.65 % (3209335)CaDiCaL version: 2.1.3
% 19.25/3.65 % (3209335)Termination reason: Refutation not found, incomplete strategy
% 19.25/3.65 % (3209335)Time elapsed: 0.014 s
% 19.25/3.65 % (3209335)Peak memory usage: 89 MB
% 19.25/3.65 % (3209335)Instructions burned: 21 (million)
% 19.25/3.65 % (3209338)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=449805979:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 19.25/3.65 % (3209338)Instruction limit reached!
% 19.25/3.65 % (3209338)------------------------------
% 19.25/3.65 % (3209338)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.25/3.65 % (3209338)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.25/3.65 % (3209338)CaDiCaL version: 2.1.3
% 19.25/3.65 % (3209338)Termination reason: Instruction limit
% 19.25/3.65 % (3209338)Termination phase: Saturation
% 19.25/3.65 % (3209338)Time elapsed: 0.042 s
% 19.25/3.65 % (3209338)Peak memory usage: 90 MB
% 19.25/3.65 % (3209338)Instructions burned: 113 (million)
% 19.25/3.65 % (3209331)Instruction limit reached!
% 19.25/3.65 % (3209331)------------------------------
% 19.25/3.65 % (3209331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 19.25/3.65 % (3209331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 19.25/3.65 % (3209331)CaDiCaL version: 2.1.3
% 19.25/3.65 % (3209331)Termination reason: Instruction limit
% 19.25/3.65 % (3209331)Termination phase: Saturation
% 19.25/3.65 % (3209331)Time elapsed: 0.237 s
% 19.25/3.65 % (3209331)Peak memory usage: 92 MB
% 19.25/3.65 % (3209331)Instructions burned: 326 (million)
% 19.25/3.65 % (3209342)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=503452458:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 19.25/3.65 % (3209343)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2265672594:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 19.25/3.65 % (3209335)------------------------------
% 19.25/3.65 % (3209335)------------------------------
% 19.25/3.65 % (3209342)Instruction limit reached!
% 16.94/3.72 % (3209342)------------------------------
% 16.94/3.72 % (3209342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.94/3.72 % (3209342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/3.72 % (3209342)CaDiCaL version: 2.1.3
% 16.94/3.72 % (3209342)Termination reason: Instruction limit
% 16.94/3.72 % (3209342)Termination phase: Saturation
% 16.94/3.72 % (3209342)Time elapsed: 0.065 s
% 16.94/3.72 % (3209342)Peak memory usage: 88 MB
% 16.94/3.72 % (3209342)Instructions burned: 128 (million)
% 16.94/3.72 % (3209343)Instruction limit reached!
% 16.94/3.72 % (3209343)------------------------------
% 16.94/3.72 % (3209343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.94/3.72 % (3209343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/3.72 % (3209343)CaDiCaL version: 2.1.3
% 16.94/3.72 % (3209343)Termination reason: Instruction limit
% 16.94/3.72 % (3209343)Termination phase: Saturation
% 16.94/3.72 % (3209343)Time elapsed: 0.054 s
% 16.94/3.72 % (3209343)Peak memory usage: 89 MB
% 16.94/3.72 % (3209343)Instructions burned: 115 (million)
% 16.94/3.72 % (3209346)lrs+10_1_sil=8000:sp=occurrence:random_seed=46142478:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 16.94/3.72 % (3209348)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2392450386:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 16.94/3.72 % (3209347)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2271558373:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 16.94/3.72 % (3209347)Refutation not found, incomplete strategy
% 16.94/3.72 % (3209347)------------------------------
% 16.94/3.72 % (3209347)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.94/3.72 % (3209347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/3.72 % (3209347)CaDiCaL version: 2.1.3
% 16.94/3.72 % (3209347)Termination reason: Refutation not found, incomplete strategy
% 16.94/3.72 % (3209347)Time elapsed: 0.006 s
% 16.94/3.72 % (3209347)Peak memory usage: 88 MB
% 16.94/3.72 % (3209347)Instructions burned: 7 (million)
% 16.94/3.72 % (3209347)------------------------------
% 16.94/3.72 % (3209347)------------------------------
% 16.94/3.72 % (3209352)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=3190480225:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2988 on theBenchmark for (2988ds/134Mi)
% 16.94/3.72 % (3209352)Instruction limit reached!
% 16.94/3.72 % (3209352)------------------------------
% 16.94/3.72 % (3209352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.94/3.72 % (3209352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/3.72 % (3209352)CaDiCaL version: 2.1.3
% 16.94/3.72 % (3209352)Termination reason: Instruction limit
% 16.94/3.72 % (3209352)Termination phase: Saturation
% 16.94/3.72 % (3209352)Time elapsed: 0.074 s
% 16.94/3.72 % (3209352)Peak memory usage: 90 MB
% 16.94/3.72 % (3209352)Instructions burned: 134 (million)
% 16.94/3.72 % (3209346)Instruction limit reached!
% 16.94/3.72 % (3209346)------------------------------
% 16.94/3.72 % (3209346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.94/3.72 % (3209346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/3.72 % (3209346)CaDiCaL version: 2.1.3
% 16.94/3.72 % (3209346)Termination reason: Instruction limit
% 16.94/3.72 % (3209346)Termination phase: Saturation
% 16.94/3.72 % (3209346)Time elapsed: 0.497 s
% 16.94/3.72 % (3209346)Peak memory usage: 96 MB
% 16.94/3.72 % (3209346)Instructions burned: 907 (million)
% 16.94/3.72 % (3209354)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=2970630066:st=8:i=592:sd=3:ep=RST:ss=axioms_2986 on theBenchmark for (2986ds/592Mi)
% 16.94/3.72 % (3209354)Refutation not found, incomplete strategy
% 16.94/3.72 % (3209354)------------------------------
% 16.94/3.72 % (3209354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.94/3.72 % (3209354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/3.72 % (3209354)CaDiCaL version: 2.1.3
% 16.94/3.72 % (3209354)Termination reason: Refutation not found, incomplete strategy
% 16.94/3.72 % (3209354)Time elapsed: 0.008 s
% 16.94/3.72 % (3209354)Peak memory usage: 89 MB
% 16.94/3.72 % (3209354)Instructions burned: 10 (million)
% 16.94/3.72 % (3209355)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=3213619513:st=3:i=13193:sd=3:ss=axioms_2985 on theBenchmark for (2985ds/13193Mi)
% 16.94/3.72 % (3209354)------------------------------
% 16.94/3.72 % (3209354)------------------------------
% 16.94/3.72 % (3209358)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=4126582852:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2982 on theBenchmark for (2982ds/125Mi)
% 16.94/3.72 % (3209358)Instruction limit reached!
% 16.94/3.72 % (3209358)------------------------------
% 16.94/3.72 % (3209358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.94/3.72 % (3209358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/3.72 % (3209358)CaDiCaL version: 2.1.3
% 16.94/3.72 % (3209358)Termination reason: Instruction limit
% 16.94/3.72 % (3209358)Termination phase: Saturation
% 16.94/3.72 % (3209358)Time elapsed: 0.072 s
% 16.94/3.72 % (3209358)Peak memory usage: 90 MB
% 16.94/3.72 % (3209358)Instructions burned: 126 (million)
% 16.94/3.72 % (3209337)Instruction limit reached!
% 16.94/3.72 % (3209337)------------------------------
% 16.94/3.72 % (3209337)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.94/3.72 % (3209337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/3.72 % (3209337)CaDiCaL version: 2.1.3
% 16.94/3.72 % (3209337)Termination reason: Instruction limit
% 16.94/3.72 % (3209337)Termination phase: Saturation
% 16.94/3.72 % (3209337)Time elapsed: 1.572 s
% 16.94/3.72 % (3209337)Peak memory usage: 142 MB
% 16.94/3.72 % (3209337)Instructions burned: 2351 (million)
% 16.94/3.72 % (3209360)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=941337023:i=134:gtgl=5:slsql=off:gtg=exists_sym_2980 on theBenchmark for (2980ds/134Mi)
% 16.94/3.72 % (3209360)Instruction limit reached!
% 16.94/3.72 % (3209360)------------------------------
% 16.94/3.72 % (3209360)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.94/3.72 % (3209360)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/3.72 % (3209360)CaDiCaL version: 2.1.3
% 16.94/3.72 % (3209360)Termination reason: Instruction limit
% 16.94/3.72 % (3209360)Termination phase: Saturation
% 16.94/3.72 % (3209360)Time elapsed: 0.087 s
% 16.94/3.72 % (3209360)Peak memory usage: 90 MB
% 16.94/3.72 % (3209360)Instructions burned: 135 (million)
% 16.94/3.72 % (3209362)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=996381861:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2978 on theBenchmark for (2978ds/141Mi)
% 16.94/3.72 % (3209362)Refutation not found, incomplete strategy
% 16.94/3.72 % (3209362)------------------------------
% 16.94/3.72 % (3209362)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.94/3.72 % (3209362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/3.72 % (3209362)CaDiCaL version: 2.1.3
% 16.94/3.72 % (3209362)Termination reason: Refutation not found, incomplete strategy
% 16.94/3.72 % (3209362)Time elapsed: 0.006 s
% 16.94/3.72 % (3209362)Peak memory usage: 88 MB
% 16.94/3.72 % (3209362)Instructions burned: 10 (million)
% 16.94/3.72 % (3209363)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=1079833413:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2977 on theBenchmark for (2977ds/431Mi)
% 16.94/3.72 % (3209362)------------------------------
% 16.94/3.72 % (3209362)------------------------------
% 16.94/3.72 % (3209316)First to succeed.
% 16.94/3.72 % (3209316)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3209309"
% 16.94/3.72 % (3209363)Instruction limit reached!
% 16.94/3.72 % (3209363)------------------------------
% 16.94/3.72 % (3209363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 16.94/3.72 % (3209363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.94/3.72 % (3209363)CaDiCaL version: 2.1.3
% 16.94/3.72 % (3209363)Termination reason: Instruction limit
% 16.94/3.72 % (3209363)Termination phase: Saturation
% 16.94/3.72 % (3209363)Time elapsed: 0.262 s
% 16.94/3.72 % (3209363)Peak memory usage: 91 MB
% 16.94/3.72 % (3209363)Instructions burned: 432 (million)
% 16.94/3.72 % (3209366)lrs+1010_1_ncem=casc2026/models/loop6.pt:sil=64000:tgt=full:npcc=on:prc=on:urr=ec_only:bsr=on:fd=preordered:gs=on:sac=on:newcnf=on:random_seed=98613870:i=6060:aac=none:ins=25_2975 on theBenchmark for (2975ds/6060Mi)
% 16.94/3.72 % (3209367)lrs+10_16_anc=all:slsqr=32,1:sil=8000:avsql=on:sp=unary_frequency:lcm=predicate:urr=full:rp=on:br=off:slsqc=4:flr=on:sac=on:slsq=on:avsqc=1:random_seed=1992531993:avsq=on:s2a=on:i=150:kws=precedence:nicw=on:gsp=on:rawr=on_2973 on theBenchmark for (2973ds/150Mi)
% 16.94/3.72 % (3209316)Refutation found. Thanks to Tanya!
% 16.94/3.72 % SZS status Theorem for theBenchmark
% 16.94/3.72 % SZS output start Proof for theBenchmark
% See solution above
% 20.58/3.91 % (3209316)------------------------------
% 20.58/3.91 % (3209316)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 20.58/3.91 % (3209316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 20.58/3.91 % (3209316)CaDiCaL version: 2.1.3
% 20.58/3.91 % (3209316)Termination reason: Refutation
% 20.58/3.91 % (3209316)Time elapsed: 2.403 s
% 20.58/3.91 % (3209316)Peak memory usage: 147 MB
% 20.58/3.91 % (3209316)Instructions burned: 3604 (million)
% 20.58/3.91 % (3209316)------------------------------
% 20.58/3.91 % (3209316)------------------------------
% 20.58/3.91 % (3209309)Success in time 2.815 s
% 20.58/3.91 % Vampire exiting
%------------------------------------------------------------------------------