%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU301+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 12:48:14 PM UTC 2026
% Result : Theorem 4.68s 1.68s
% Output : Refutation 6.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 45
% Syntax : Number of formulae : 373 ( 34 unt; 35 def)
% Number of atoms : 2018 ( 343 equ)
% Maximal formula atoms : 49 ( 5 avg)
% Number of connectives : 2798 (1153 ~;1224 |; 275 &)
% ( 31 <=>; 115 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 44 ( 42 usr; 33 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 5 con; 0-2 aty)
% Number of variables : 481 ( 0 sgn 407 !; 74 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ( in(empty_set,omega)
=> ! [X0] :
( element(X0,powerset(powerset(empty_set)))
=> ~ ( X0 != empty_set
& ! [X1] :
~ ( in(X1,X0)
& ! [X2] :
( ( in(X2,X0)
& subset(X1,X2) )
=> X2 = X1 ) ) ) ) )
& ! [X3] :
( ordinal(X3)
=> ( ( in(X3,omega)
=> ! [X4] :
( element(X4,powerset(powerset(X3)))
=> ~ ( X4 != empty_set
& ! [X5] :
~ ( in(X5,X4)
& ! [X6] :
( ( in(X6,X4)
& subset(X5,X6) )
=> X6 = X5 ) ) ) ) )
=> ( in(succ(X3),omega)
=> ! [X7] :
( element(X7,powerset(powerset(succ(X3))))
=> ~ ( X7 != empty_set
& ! [X8] :
~ ( in(X8,X7)
& ! [X9] :
( ( in(X9,X7)
& subset(X8,X9) )
=> X9 = X8 ) ) ) ) ) ) )
& ! [X3] :
( ordinal(X3)
=> ( ( being_limit_ordinal(X3)
& ! [X10] :
( ordinal(X10)
=> ( in(X10,X3)
=> ( in(X10,omega)
=> ! [X11] :
( element(X11,powerset(powerset(X10)))
=> ~ ( X11 != empty_set
& ! [X12] :
~ ( in(X12,X11)
& ! [X13] :
( ( in(X13,X11)
& subset(X12,X13) )
=> X13 = X12 ) ) ) ) ) ) ) )
=> ( X3 = empty_set
| ( in(X3,omega)
=> ! [X14] :
( element(X14,powerset(powerset(X3)))
=> ~ ( X14 != empty_set
& ! [X15] :
~ ( in(X15,X14)
& ! [X16] :
( ( in(X16,X14)
& subset(X15,X16) )
=> X16 = X15 ) ) ) ) ) ) ) ) )
=> ! [X3] :
( ordinal(X3)
=> ( in(X3,omega)
=> ! [X17] :
( element(X17,powerset(powerset(X3)))
=> ~ ( X17 != empty_set
& ! [X18] :
~ ( in(X18,X17)
& ! [X19] :
( ( in(X19,X17)
& subset(X18,X19) )
=> X19 = X18 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_ordinal2__e18_27__finset_1) ).
fof(f2,negated_conjecture,
~ ( ( ( in(empty_set,omega)
=> ! [X0] :
( element(X0,powerset(powerset(empty_set)))
=> ~ ( X0 != empty_set
& ! [X1] :
~ ( in(X1,X0)
& ! [X2] :
( ( in(X2,X0)
& subset(X1,X2) )
=> X2 = X1 ) ) ) ) )
& ! [X3] :
( ordinal(X3)
=> ( ( in(X3,omega)
=> ! [X4] :
( element(X4,powerset(powerset(X3)))
=> ~ ( X4 != empty_set
& ! [X5] :
~ ( in(X5,X4)
& ! [X6] :
( ( in(X6,X4)
& subset(X5,X6) )
=> X6 = X5 ) ) ) ) )
=> ( in(succ(X3),omega)
=> ! [X7] :
( element(X7,powerset(powerset(succ(X3))))
=> ~ ( X7 != empty_set
& ! [X8] :
~ ( in(X8,X7)
& ! [X9] :
( ( in(X9,X7)
& subset(X8,X9) )
=> X9 = X8 ) ) ) ) ) ) )
& ! [X3] :
( ordinal(X3)
=> ( ( being_limit_ordinal(X3)
& ! [X10] :
( ordinal(X10)
=> ( in(X10,X3)
=> ( in(X10,omega)
=> ! [X11] :
( element(X11,powerset(powerset(X10)))
=> ~ ( X11 != empty_set
& ! [X12] :
~ ( in(X12,X11)
& ! [X13] :
( ( in(X13,X11)
& subset(X12,X13) )
=> X13 = X12 ) ) ) ) ) ) ) )
=> ( X3 = empty_set
| ( in(X3,omega)
=> ! [X14] :
( element(X14,powerset(powerset(X3)))
=> ~ ( X14 != empty_set
& ! [X15] :
~ ( in(X15,X14)
& ! [X16] :
( ( in(X16,X14)
& subset(X15,X16) )
=> X16 = X15 ) ) ) ) ) ) ) ) )
=> ! [X3] :
( ordinal(X3)
=> ( in(X3,omega)
=> ! [X17] :
( element(X17,powerset(powerset(X3)))
=> ~ ( X17 != empty_set
& ! [X18] :
~ ( in(X18,X17)
& ! [X19] :
( ( in(X19,X17)
& subset(X18,X19) )
=> X19 = X18 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f39,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f47,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f49,axiom,
( ! [X0] :
( ordinal(X0)
=> ( ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
=> ( in(X1,omega)
=> ! [X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
( ( in(X4,X2)
& subset(X3,X4) )
=> X4 = X3 ) ) ) ) ) ) )
=> ( in(X0,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X0)))
=> ~ ( X5 != empty_set
& ! [X6] :
~ ( in(X6,X5)
& ! [X7] :
( ( in(X7,X5)
& subset(X6,X7) )
=> X7 = X6 ) ) ) ) ) ) )
=> ! [X0] :
( ordinal(X0)
=> ( in(X0,omega)
=> ! [X8] :
( element(X8,powerset(powerset(X0)))
=> ~ ( X8 != empty_set
& ! [X9] :
~ ( in(X9,X8)
& ! [X10] :
( ( in(X10,X8)
& subset(X9,X10) )
=> X10 = X9 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s2_ordinal1__e18_27__finset_1__1) ).
fof(f51,axiom,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_ordinal1) ).
fof(f59,axiom,
! [X0] : in(X0,succ(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_ordinal1) ).
fof(f61,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f62,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f63,axiom,
! [X0] :
( ordinal(X0)
=> ( ~ ( ~ being_limit_ordinal(X0)
& ! [X1] :
( ordinal(X1)
=> X0 != succ(X1) ) )
& ~ ( ? [X1] :
( ordinal(X1)
& X0 = succ(X1) )
& being_limit_ordinal(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_ordinal1) ).
fof(f64,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f67,plain,
~ ( ( ( in(empty_set,omega)
=> ! [X0] :
( element(X0,powerset(powerset(empty_set)))
=> ~ ( X0 != empty_set
& ! [X1] :
~ ( in(X1,X0)
& ! [X2] :
( ( in(X2,X0)
& subset(X1,X2) )
=> X2 = X1 ) ) ) ) )
& ! [X3] :
( ordinal(X3)
=> ( ( in(X3,omega)
=> ! [X4] :
( element(X4,powerset(powerset(X3)))
=> ~ ( X4 != empty_set
& ! [X5] :
~ ( in(X5,X4)
& ! [X6] :
( ( in(X6,X4)
& subset(X5,X6) )
=> X6 = X5 ) ) ) ) )
=> ( in(succ(X3),omega)
=> ! [X7] :
( element(X7,powerset(powerset(succ(X3))))
=> ~ ( X7 != empty_set
& ! [X8] :
~ ( in(X8,X7)
& ! [X9] :
( ( in(X9,X7)
& subset(X8,X9) )
=> X9 = X8 ) ) ) ) ) ) )
& ! [X10] :
( ordinal(X10)
=> ( ( being_limit_ordinal(X10)
& ! [X11] :
( ordinal(X11)
=> ( in(X11,X10)
=> ( in(X11,omega)
=> ! [X12] :
( element(X12,powerset(powerset(X11)))
=> ~ ( empty_set != X12
& ! [X13] :
~ ( in(X13,X12)
& ! [X14] :
( ( in(X14,X12)
& subset(X13,X14) )
=> X13 = X14 ) ) ) ) ) ) ) )
=> ( empty_set = X10
| ( in(X10,omega)
=> ! [X15] :
( element(X15,powerset(powerset(X10)))
=> ~ ( empty_set != X15
& ! [X16] :
~ ( in(X16,X15)
& ! [X17] :
( ( in(X17,X15)
& subset(X16,X17) )
=> X16 = X17 ) ) ) ) ) ) ) ) )
=> ! [X18] :
( ordinal(X18)
=> ( in(X18,omega)
=> ! [X19] :
( element(X19,powerset(powerset(X18)))
=> ~ ( empty_set != X19
& ! [X20] :
~ ( in(X20,X19)
& ! [X21] :
( ( in(X21,X19)
& subset(X20,X21) )
=> X20 = X21 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
fof(f68,plain,
! [X0] :
( ordinal(X0)
=> ( ~ ( ~ being_limit_ordinal(X0)
& ! [X1] :
( ordinal(X1)
=> X0 != succ(X1) ) )
& ~ ( ? [X2] :
( ordinal(X2)
& succ(X2) = X0 )
& being_limit_ordinal(X0) ) ) ),
inference(rectify,[],[f63]) ).
fof(f70,plain,
( ! [X0] :
( ordinal(X0)
=> ( ! [X1] :
( ordinal(X1)
=> ( in(X1,X0)
=> ( in(X1,omega)
=> ! [X2] :
( element(X2,powerset(powerset(X1)))
=> ~ ( X2 != empty_set
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
( ( in(X4,X2)
& subset(X3,X4) )
=> X4 = X3 ) ) ) ) ) ) )
=> ( in(X0,omega)
=> ! [X5] :
( element(X5,powerset(powerset(X0)))
=> ~ ( X5 != empty_set
& ! [X6] :
~ ( in(X6,X5)
& ! [X7] :
( ( in(X7,X5)
& subset(X6,X7) )
=> X7 = X6 ) ) ) ) ) ) )
=> ! [X8] :
( ordinal(X8)
=> ( in(X8,omega)
=> ! [X9] :
( element(X9,powerset(powerset(X8)))
=> ~ ( empty_set != X9
& ! [X10] :
~ ( in(X10,X9)
& ! [X11] :
( ( in(X11,X9)
& subset(X10,X11) )
=> X10 = X11 ) ) ) ) ) ) ),
inference(rectify,[],[f49]) ).
fof(f80,plain,
empty(empty_set),
inference(pure_predicate_removal,[],[f39]) ).
fof(f85,plain,
( ? [X18] :
( ? [X19] :
( empty_set != X19
& ! [X20] :
( ~ in(X20,X19)
| ? [X21] :
( X20 != X21
& in(X21,X19)
& subset(X20,X21) ) )
& element(X19,powerset(powerset(X18))) )
& in(X18,omega)
& ordinal(X18) )
& ( ! [X0] :
( empty_set = X0
| ? [X1] :
( in(X1,X0)
& ! [X2] :
( X2 = X1
| ~ in(X2,X0)
| ~ subset(X1,X2) ) )
| ~ element(X0,powerset(powerset(empty_set))) )
| ~ in(empty_set,omega) )
& ! [X3] :
( ! [X7] :
( empty_set = X7
| ? [X8] :
( in(X8,X7)
& ! [X9] :
( X9 = X8
| ~ in(X9,X7)
| ~ subset(X8,X9) ) )
| ~ element(X7,powerset(powerset(succ(X3)))) )
| ~ in(succ(X3),omega)
| ( ? [X4] :
( X4 != empty_set
& ! [X5] :
( ~ in(X5,X4)
| ? [X6] :
( X5 != X6
& in(X6,X4)
& subset(X5,X6) ) )
& element(X4,powerset(powerset(X3))) )
& in(X3,omega) )
| ~ ordinal(X3) )
& ! [X10] :
( empty_set = X10
| ! [X15] :
( empty_set = X15
| ? [X16] :
( in(X16,X15)
& ! [X17] :
( X16 = X17
| ~ in(X17,X15)
| ~ subset(X16,X17) ) )
| ~ element(X15,powerset(powerset(X10))) )
| ~ in(X10,omega)
| ~ being_limit_ordinal(X10)
| ? [X11] :
( ? [X12] :
( empty_set != X12
& ! [X13] :
( ~ in(X13,X12)
| ? [X14] :
( X13 != X14
& in(X14,X12)
& subset(X13,X14) ) )
& element(X12,powerset(powerset(X11))) )
& in(X11,omega)
& in(X11,X10)
& ordinal(X11) )
| ~ ordinal(X10) ) ),
inference(ennf_transformation,[],[f67]) ).
fof(f86,plain,
( ? [X18] :
( ? [X19] :
( empty_set != X19
& ! [X20] :
( ~ in(X20,X19)
| ? [X21] :
( X20 != X21
& in(X21,X19)
& subset(X20,X21) ) )
& element(X19,powerset(powerset(X18))) )
& in(X18,omega)
& ordinal(X18) )
& ( ! [X0] :
( empty_set = X0
| ? [X1] :
( in(X1,X0)
& ! [X2] :
( X2 = X1
| ~ in(X2,X0)
| ~ subset(X1,X2) ) )
| ~ element(X0,powerset(powerset(empty_set))) )
| ~ in(empty_set,omega) )
& ! [X3] :
( ! [X7] :
( empty_set = X7
| ? [X8] :
( in(X8,X7)
& ! [X9] :
( X9 = X8
| ~ in(X9,X7)
| ~ subset(X8,X9) ) )
| ~ element(X7,powerset(powerset(succ(X3)))) )
| ~ in(succ(X3),omega)
| ( ? [X4] :
( X4 != empty_set
& ! [X5] :
( ~ in(X5,X4)
| ? [X6] :
( X5 != X6
& in(X6,X4)
& subset(X5,X6) ) )
& element(X4,powerset(powerset(X3))) )
& in(X3,omega) )
| ~ ordinal(X3) )
& ! [X10] :
( empty_set = X10
| ! [X15] :
( empty_set = X15
| ? [X16] :
( in(X16,X15)
& ! [X17] :
( X16 = X17
| ~ in(X17,X15)
| ~ subset(X16,X17) ) )
| ~ element(X15,powerset(powerset(X10))) )
| ~ in(X10,omega)
| ~ being_limit_ordinal(X10)
| ? [X11] :
( ? [X12] :
( empty_set != X12
& ! [X13] :
( ~ in(X13,X12)
| ? [X14] :
( X13 != X14
& in(X14,X12)
& subset(X13,X14) ) )
& element(X12,powerset(powerset(X11))) )
& in(X11,omega)
& in(X11,X10)
& ordinal(X11) )
| ~ ordinal(X10) ) ),
inference(flattening,[],[f85]) ).
fof(f88,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f89,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ? [X1] :
( succ(X1) = X0
& ordinal(X1) ) )
& ( ! [X2] :
( ~ ordinal(X2)
| succ(X2) != X0 )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f90,plain,
( ! [X8] :
( ! [X9] :
( empty_set = X9
| ? [X10] :
( in(X10,X9)
& ! [X11] :
( X10 = X11
| ~ in(X11,X9)
| ~ subset(X10,X11) ) )
| ~ element(X9,powerset(powerset(X8))) )
| ~ in(X8,omega)
| ~ ordinal(X8) )
| ? [X0] :
( ? [X5] :
( X5 != empty_set
& ! [X6] :
( ~ in(X6,X5)
| ? [X7] :
( X6 != X7
& in(X7,X5)
& subset(X6,X7) ) )
& element(X5,powerset(powerset(X0))) )
& in(X0,omega)
& ! [X1] :
( ! [X2] :
( empty_set = X2
| ? [X3] :
( in(X3,X2)
& ! [X4] :
( X4 = X3
| ~ in(X4,X2)
| ~ subset(X3,X4) ) )
| ~ element(X2,powerset(powerset(X1))) )
| ~ in(X1,omega)
| ~ in(X1,X0)
| ~ ordinal(X1) )
& ordinal(X0) ) ),
inference(ennf_transformation,[],[f70]) ).
fof(f91,plain,
( ! [X8] :
( ! [X9] :
( empty_set = X9
| ? [X10] :
( in(X10,X9)
& ! [X11] :
( X10 = X11
| ~ in(X11,X9)
| ~ subset(X10,X11) ) )
| ~ element(X9,powerset(powerset(X8))) )
| ~ in(X8,omega)
| ~ ordinal(X8) )
| ? [X0] :
( ? [X5] :
( X5 != empty_set
& ! [X6] :
( ~ in(X6,X5)
| ? [X7] :
( X6 != X7
& in(X7,X5)
& subset(X6,X7) ) )
& element(X5,powerset(powerset(X0))) )
& in(X0,omega)
& ! [X1] :
( ! [X2] :
( empty_set = X2
| ? [X3] :
( in(X3,X2)
& ! [X4] :
( X4 = X3
| ~ in(X4,X2)
| ~ subset(X3,X4) ) )
| ~ element(X2,powerset(powerset(X1))) )
| ~ in(X1,omega)
| ~ in(X1,X0)
| ~ ordinal(X1) )
& ordinal(X0) ) ),
inference(flattening,[],[f90]) ).
fof(f93,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f94,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f61]) ).
fof(f111,definition,
! [X10] :
( ? [X11] :
( ? [X12] :
( empty_set != X12
& ! [X13] :
( ~ in(X13,X12)
| ? [X14] :
( X13 != X14
& in(X14,X12)
& subset(X13,X14) ) )
& element(X12,powerset(powerset(X11))) )
& in(X11,omega)
& in(X11,X10)
& ordinal(X11) )
| ~ sP0(X10) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f112,definition,
! [X3] :
( ( ? [X4] :
( X4 != empty_set
& ! [X5] :
( ~ in(X5,X4)
| ? [X6] :
( X5 != X6
& in(X6,X4)
& subset(X5,X6) ) )
& element(X4,powerset(powerset(X3))) )
& in(X3,omega) )
| ~ sP1(X3) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f113,plain,
( ? [X18] :
( ? [X19] :
( empty_set != X19
& ! [X20] :
( ~ in(X20,X19)
| ? [X21] :
( X20 != X21
& in(X21,X19)
& subset(X20,X21) ) )
& element(X19,powerset(powerset(X18))) )
& in(X18,omega)
& ordinal(X18) )
& ( ! [X0] :
( empty_set = X0
| ? [X1] :
( in(X1,X0)
& ! [X2] :
( X2 = X1
| ~ in(X2,X0)
| ~ subset(X1,X2) ) )
| ~ element(X0,powerset(powerset(empty_set))) )
| ~ in(empty_set,omega) )
& ! [X3] :
( ! [X7] :
( empty_set = X7
| ? [X8] :
( in(X8,X7)
& ! [X9] :
( X9 = X8
| ~ in(X9,X7)
| ~ subset(X8,X9) ) )
| ~ element(X7,powerset(powerset(succ(X3)))) )
| ~ in(succ(X3),omega)
| sP1(X3)
| ~ ordinal(X3) )
& ! [X10] :
( empty_set = X10
| ! [X15] :
( empty_set = X15
| ? [X16] :
( in(X16,X15)
& ! [X17] :
( X16 = X17
| ~ in(X17,X15)
| ~ subset(X16,X17) ) )
| ~ element(X15,powerset(powerset(X10))) )
| ~ in(X10,omega)
| ~ being_limit_ordinal(X10)
| sP0(X10)
| ~ ordinal(X10) ) ),
inference(definition_folding,[],[f86,f112,f111]) ).
fof(f114,definition,
! [X0] :
( ? [X5] :
( X5 != empty_set
& ! [X6] :
( ~ in(X6,X5)
| ? [X7] :
( X6 != X7
& in(X7,X5)
& subset(X6,X7) ) )
& element(X5,powerset(powerset(X0))) )
| ~ sP2(X0) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f115,definition,
( ? [X0] :
( sP2(X0)
& in(X0,omega)
& ! [X1] :
( ! [X2] :
( empty_set = X2
| ? [X3] :
( in(X3,X2)
& ! [X4] :
( X4 = X3
| ~ in(X4,X2)
| ~ subset(X3,X4) ) )
| ~ element(X2,powerset(powerset(X1))) )
| ~ in(X1,omega)
| ~ in(X1,X0)
| ~ ordinal(X1) )
& ordinal(X0) )
| ~ sP3 ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f116,plain,
( ! [X8] :
( ! [X9] :
( empty_set = X9
| ? [X10] :
( in(X10,X9)
& ! [X11] :
( X10 = X11
| ~ in(X11,X9)
| ~ subset(X10,X11) ) )
| ~ element(X9,powerset(powerset(X8))) )
| ~ in(X8,omega)
| ~ ordinal(X8) )
| sP3 ),
inference(definition_folding,[],[f91,f115,f114]) ).
fof(f117,plain,
! [X3] :
( ( ? [X4] :
( X4 != empty_set
& ! [X5] :
( ~ in(X5,X4)
| ? [X6] :
( X5 != X6
& in(X6,X4)
& subset(X5,X6) ) )
& element(X4,powerset(powerset(X3))) )
& in(X3,omega) )
| ~ sP1(X3) ),
inference(nnf_transformation,[],[f112]) ).
fof(f118,plain,
! [X0] :
( ( ? [X1] :
( empty_set != X1
& ! [X2] :
( ~ in(X2,X1)
| ? [X3] :
( X2 != X3
& in(X3,X1)
& subset(X2,X3) ) )
& element(X1,powerset(powerset(X0))) )
& in(X0,omega) )
| ~ sP1(X0) ),
inference(rectify,[],[f117]) ).
fof(f119,plain,
! [X0] :
( ( empty_set != sK4(X0)
& ! [X2] :
( ~ in(X2,sK4(X0))
| ( sK5(X0,X2) != X2
& in(sK5(X0,X2),sK4(X0))
& subset(X2,sK5(X0,X2)) ) )
& element(sK4(X0),powerset(powerset(X0)))
& in(X0,omega) )
| ~ sP1(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X1,sK4(X0)),skolemize(X3,sK5(X0,X2))],[f118]) ).
fof(f120,plain,
! [X10] :
( ? [X11] :
( ? [X12] :
( empty_set != X12
& ! [X13] :
( ~ in(X13,X12)
| ? [X14] :
( X13 != X14
& in(X14,X12)
& subset(X13,X14) ) )
& element(X12,powerset(powerset(X11))) )
& in(X11,omega)
& in(X11,X10)
& ordinal(X11) )
| ~ sP0(X10) ),
inference(nnf_transformation,[],[f111]) ).
fof(f121,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ! [X3] :
( ~ in(X3,X2)
| ? [X4] :
( X3 != X4
& in(X4,X2)
& subset(X3,X4) ) )
& element(X2,powerset(powerset(X1))) )
& in(X1,omega)
& in(X1,X0)
& ordinal(X1) )
| ~ sP0(X0) ),
inference(rectify,[],[f120]) ).
fof(f122,plain,
! [X0] :
( ( empty_set != sK7(X0)
& ! [X3] :
( ~ in(X3,sK7(X0))
| ( sK8(X0,X3) != X3
& in(sK8(X0,X3),sK7(X0))
& subset(X3,sK8(X0,X3)) ) )
& element(sK7(X0),powerset(powerset(sK6(X0))))
& in(sK6(X0),omega)
& in(sK6(X0),X0)
& ordinal(sK6(X0)) )
| ~ sP0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X1,sK6(X0)),skolemize(X2,sK7(X0)),skolemize(X4,sK8(X0,X3))],[f121]) ).
fof(f123,plain,
( ? [X0] :
( ? [X1] :
( empty_set != X1
& ! [X2] :
( ~ in(X2,X1)
| ? [X3] :
( X2 != X3
& in(X3,X1)
& subset(X2,X3) ) )
& element(X1,powerset(powerset(X0))) )
& in(X0,omega)
& ordinal(X0) )
& ( ! [X4] :
( empty_set = X4
| ? [X5] :
( in(X5,X4)
& ! [X6] :
( X5 = X6
| ~ in(X6,X4)
| ~ subset(X5,X6) ) )
| ~ element(X4,powerset(powerset(empty_set))) )
| ~ in(empty_set,omega) )
& ! [X7] :
( ! [X8] :
( empty_set = X8
| ? [X9] :
( in(X9,X8)
& ! [X10] :
( X9 = X10
| ~ in(X10,X8)
| ~ subset(X9,X10) ) )
| ~ element(X8,powerset(powerset(succ(X7)))) )
| ~ in(succ(X7),omega)
| sP1(X7)
| ~ ordinal(X7) )
& ! [X11] :
( empty_set = X11
| ! [X12] :
( empty_set = X12
| ? [X13] :
( in(X13,X12)
& ! [X14] :
( X13 = X14
| ~ in(X14,X12)
| ~ subset(X13,X14) ) )
| ~ element(X12,powerset(powerset(X11))) )
| ~ in(X11,omega)
| ~ being_limit_ordinal(X11)
| sP0(X11)
| ~ ordinal(X11) ) ),
inference(rectify,[],[f113]) ).
fof(f124,plain,
( empty_set != sK10
& ! [X2] :
( ~ in(X2,sK10)
| ( sK11(X2) != X2
& in(sK11(X2),sK10)
& subset(X2,sK11(X2)) ) )
& element(sK10,powerset(powerset(sK9)))
& in(sK9,omega)
& ordinal(sK9)
& ( ! [X4] :
( empty_set = X4
| ( in(sK12(X4),X4)
& ! [X6] :
( sK12(X4) = X6
| ~ in(X6,X4)
| ~ subset(sK12(X4),X6) ) )
| ~ element(X4,powerset(powerset(empty_set))) )
| ~ in(empty_set,omega) )
& ! [X7] :
( ! [X8] :
( empty_set = X8
| ( in(sK13(X8),X8)
& ! [X10] :
( sK13(X8) = X10
| ~ in(X10,X8)
| ~ subset(sK13(X8),X10) ) )
| ~ element(X8,powerset(powerset(succ(X7)))) )
| ~ in(succ(X7),omega)
| sP1(X7)
| ~ ordinal(X7) )
& ! [X11] :
( empty_set = X11
| ! [X12] :
( empty_set = X12
| ( in(sK14(X12),X12)
& ! [X14] :
( sK14(X12) = X14
| ~ in(X14,X12)
| ~ subset(sK14(X12),X14) ) )
| ~ element(X12,powerset(powerset(X11))) )
| ~ in(X11,omega)
| ~ being_limit_ordinal(X11)
| sP0(X11)
| ~ ordinal(X11) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13,sK14]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X3,sK11(X2)),skolemize(X5,sK12(X4)),skolemize(X9,sK13(X8)),skolemize(X13,sK14(X12))],[f123]) ).
fof(f125,plain,
! [X0] :
( ( ( being_limit_ordinal(X0)
| ( succ(sK15(X0)) = X0
& ordinal(sK15(X0)) ) )
& ( ! [X2] :
( ~ ordinal(X2)
| succ(X2) != X0 )
| ~ being_limit_ordinal(X0) ) )
| ~ ordinal(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(X1,sK15(X0))],[f89]) ).
fof(f126,plain,
( ? [X0] :
( sP2(X0)
& in(X0,omega)
& ! [X1] :
( ! [X2] :
( empty_set = X2
| ? [X3] :
( in(X3,X2)
& ! [X4] :
( X4 = X3
| ~ in(X4,X2)
| ~ subset(X3,X4) ) )
| ~ element(X2,powerset(powerset(X1))) )
| ~ in(X1,omega)
| ~ in(X1,X0)
| ~ ordinal(X1) )
& ordinal(X0) )
| ~ sP3 ),
inference(nnf_transformation,[],[f115]) ).
fof(f127,plain,
( ( sP2(sK16)
& in(sK16,omega)
& ! [X1] :
( ! [X2] :
( empty_set = X2
| ( in(sK17(X2),X2)
& ! [X4] :
( sK17(X2) = X4
| ~ in(X4,X2)
| ~ subset(sK17(X2),X4) ) )
| ~ element(X2,powerset(powerset(X1))) )
| ~ in(X1,omega)
| ~ in(X1,sK16)
| ~ ordinal(X1) )
& ordinal(sK16) )
| ~ sP3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X0,sK16),skolemize(X3,sK17(X2))],[f126]) ).
fof(f128,plain,
! [X0] :
( ? [X5] :
( X5 != empty_set
& ! [X6] :
( ~ in(X6,X5)
| ? [X7] :
( X6 != X7
& in(X7,X5)
& subset(X6,X7) ) )
& element(X5,powerset(powerset(X0))) )
| ~ sP2(X0) ),
inference(nnf_transformation,[],[f114]) ).
fof(f129,plain,
! [X0] :
( ? [X1] :
( empty_set != X1
& ! [X2] :
( ~ in(X2,X1)
| ? [X3] :
( X2 != X3
& in(X3,X1)
& subset(X2,X3) ) )
& element(X1,powerset(powerset(X0))) )
| ~ sP2(X0) ),
inference(rectify,[],[f128]) ).
fof(f130,plain,
! [X0] :
( ( empty_set != sK18(X0)
& ! [X2] :
( ~ in(X2,sK18(X0))
| ( sK19(X0,X2) != X2
& in(sK19(X0,X2),sK18(X0))
& subset(X2,sK19(X0,X2)) ) )
& element(sK18(X0),powerset(powerset(X0))) )
| ~ sP2(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19]),skolemize(X1,sK18(X0)),skolemize(X3,sK19(X0,X2))],[f129]) ).
fof(f131,plain,
( ! [X0] :
( ! [X1] :
( empty_set = X1
| ? [X2] :
( in(X2,X1)
& ! [X3] :
( X2 = X3
| ~ in(X3,X1)
| ~ subset(X2,X3) ) )
| ~ element(X1,powerset(powerset(X0))) )
| ~ in(X0,omega)
| ~ ordinal(X0) )
| sP3 ),
inference(rectify,[],[f116]) ).
fof(f132,plain,
( ! [X0] :
( ! [X1] :
( empty_set = X1
| ( in(sK20(X1),X1)
& ! [X3] :
( sK20(X1) = X3
| ~ in(X3,X1)
| ~ subset(sK20(X1),X3) ) )
| ~ element(X1,powerset(powerset(X0))) )
| ~ in(X0,omega)
| ~ ordinal(X0) )
| sP3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(X2,sK20(X1))],[f131]) ).
fof(f143,plain,
! [X0] :
( ~ sP1(X0)
| in(X0,omega) ),
inference(cnf_transformation,[],[f119]) ).
fof(f144,plain,
! [X0] :
( element(sK4(X0),powerset(powerset(X0)))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f145,plain,
! [X2,X0] :
( ~ sP1(X0)
| subset(X2,sK5(X0,X2))
| ~ in(X2,sK4(X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f146,plain,
! [X2,X0] :
( ~ sP1(X0)
| in(sK5(X0,X2),sK4(X0))
| ~ in(X2,sK4(X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f147,plain,
! [X2,X0] :
( ~ sP1(X0)
| sK5(X0,X2) != X2
| ~ in(X2,sK4(X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f148,plain,
! [X0] :
( empty_set != sK4(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f149,plain,
! [X0] :
( ordinal(sK6(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f150,plain,
! [X0] :
( in(sK6(X0),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f151,plain,
! [X0] :
( in(sK6(X0),omega)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f152,plain,
! [X0] :
( element(sK7(X0),powerset(powerset(sK6(X0))))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f153,plain,
! [X3,X0] :
( subset(X3,sK8(X0,X3))
| ~ in(X3,sK7(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f154,plain,
! [X3,X0] :
( ~ in(X3,sK7(X0))
| in(sK8(X0,X3),sK7(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f155,plain,
! [X3,X0] :
( sK8(X0,X3) != X3
| ~ in(X3,sK7(X0))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f156,plain,
! [X0] :
( empty_set != sK7(X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f157,plain,
! [X11,X14,X12] :
( sP0(X11)
| empty_set = X12
| sK14(X12) = X14
| ~ in(X14,X12)
| ~ subset(sK14(X12),X14)
| ~ element(X12,powerset(powerset(X11)))
| ~ in(X11,omega)
| ~ being_limit_ordinal(X11)
| empty_set = X11
| ~ ordinal(X11) ),
inference(cnf_transformation,[],[f124]) ).
fof(f158,plain,
! [X11,X12] :
( sP0(X11)
| empty_set = X12
| in(sK14(X12),X12)
| ~ element(X12,powerset(powerset(X11)))
| ~ in(X11,omega)
| ~ being_limit_ordinal(X11)
| empty_set = X11
| ~ ordinal(X11) ),
inference(cnf_transformation,[],[f124]) ).
fof(f159,plain,
! [X10,X8,X7] :
( empty_set = X8
| sK13(X8) = X10
| ~ in(X10,X8)
| ~ subset(sK13(X8),X10)
| ~ element(X8,powerset(powerset(succ(X7))))
| ~ in(succ(X7),omega)
| sP1(X7)
| ~ ordinal(X7) ),
inference(cnf_transformation,[],[f124]) ).
fof(f160,plain,
! [X8,X7] :
( empty_set = X8
| in(sK13(X8),X8)
| ~ element(X8,powerset(powerset(succ(X7))))
| ~ in(succ(X7),omega)
| sP1(X7)
| ~ ordinal(X7) ),
inference(cnf_transformation,[],[f124]) ).
fof(f161,plain,
! [X6,X4] :
( empty_set = X4
| sK12(X4) = X6
| ~ in(X6,X4)
| ~ subset(sK12(X4),X6)
| ~ element(X4,powerset(powerset(empty_set)))
| ~ in(empty_set,omega) ),
inference(cnf_transformation,[],[f124]) ).
fof(f162,plain,
! [X4] :
( empty_set = X4
| in(sK12(X4),X4)
| ~ element(X4,powerset(powerset(empty_set)))
| ~ in(empty_set,omega) ),
inference(cnf_transformation,[],[f124]) ).
fof(f163,plain,
ordinal(sK9),
inference(cnf_transformation,[],[f124]) ).
fof(f164,plain,
in(sK9,omega),
inference(cnf_transformation,[],[f124]) ).
fof(f165,plain,
element(sK10,powerset(powerset(sK9))),
inference(cnf_transformation,[],[f124]) ).
fof(f166,plain,
! [X2] :
( subset(X2,sK11(X2))
| ~ in(X2,sK10) ),
inference(cnf_transformation,[],[f124]) ).
fof(f167,plain,
! [X2] :
( in(sK11(X2),sK10)
| ~ in(X2,sK10) ),
inference(cnf_transformation,[],[f124]) ).
fof(f168,plain,
! [X2] :
( sK11(X2) != X2
| ~ in(X2,sK10) ),
inference(cnf_transformation,[],[f124]) ).
fof(f169,plain,
empty_set != sK10,
inference(cnf_transformation,[],[f124]) ).
fof(f171,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f88]) ).
fof(f173,plain,
! [X0] :
( ordinal(sK15(X0))
| being_limit_ordinal(X0)
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f174,plain,
! [X0] :
( being_limit_ordinal(X0)
| succ(sK15(X0)) = X0
| ~ ordinal(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f177,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[],[f51]) ).
fof(f179,plain,
( ordinal(sK16)
| ~ sP3 ),
inference(cnf_transformation,[],[f127]) ).
fof(f180,plain,
! [X2,X1,X4] :
( empty_set = X2
| sK17(X2) = X4
| ~ in(X4,X2)
| ~ subset(sK17(X2),X4)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ in(X1,sK16)
| ~ ordinal(X1)
| ~ sP3 ),
inference(cnf_transformation,[],[f127]) ).
fof(f181,plain,
! [X2,X1] :
( empty_set = X2
| in(sK17(X2),X2)
| ~ element(X2,powerset(powerset(X1)))
| ~ in(X1,omega)
| ~ in(X1,sK16)
| ~ ordinal(X1)
| ~ sP3 ),
inference(cnf_transformation,[],[f127]) ).
fof(f182,plain,
( in(sK16,omega)
| ~ sP3 ),
inference(cnf_transformation,[],[f127]) ).
fof(f183,plain,
( sP2(sK16)
| ~ sP3 ),
inference(cnf_transformation,[],[f127]) ).
fof(f184,plain,
! [X0] :
( element(sK18(X0),powerset(powerset(X0)))
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f185,plain,
! [X2,X0] :
( ~ sP2(X0)
| subset(X2,sK19(X0,X2))
| ~ in(X2,sK18(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f186,plain,
! [X2,X0] :
( ~ sP2(X0)
| in(sK19(X0,X2),sK18(X0))
| ~ in(X2,sK18(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f187,plain,
! [X2,X0] :
( ~ sP2(X0)
| sK19(X0,X2) != X2
| ~ in(X2,sK18(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f188,plain,
! [X0] :
( empty_set != sK18(X0)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f189,plain,
! [X3,X0,X1] :
( empty_set = X1
| sK20(X1) = X3
| ~ in(X3,X1)
| ~ subset(sK20(X1),X3)
| ~ element(X1,powerset(powerset(X0)))
| ~ in(X0,omega)
| ~ ordinal(X0)
| sP3 ),
inference(cnf_transformation,[],[f132]) ).
fof(f190,plain,
! [X0,X1] :
( empty_set = X1
| in(sK20(X1),X1)
| ~ element(X1,powerset(powerset(X0)))
| ~ in(X0,omega)
| ~ ordinal(X0)
| sP3 ),
inference(cnf_transformation,[],[f132]) ).
fof(f197,plain,
empty(empty_set),
inference(cnf_transformation,[],[f80]) ).
fof(f199,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f200,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f201,plain,
! [X0] : in(X0,succ(X0)),
inference(cnf_transformation,[],[f59]) ).
fof(f230,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f47]) ).
fof(f272,plain,
! [X8,X7] :
( ~ in(set_union2(X7,singleton(X7)),omega)
| in(sK13(X8),X8)
| ~ element(X8,powerset(powerset(set_union2(X7,singleton(X7)))))
| empty_set = X8
| sP1(X7)
| ~ ordinal(X7) ),
inference(definition_unfolding,[],[f160,f177,f177]) ).
fof(f273,plain,
! [X10,X8,X7] :
( ~ in(set_union2(X7,singleton(X7)),omega)
| sK13(X8) = X10
| ~ in(X10,X8)
| ~ subset(sK13(X8),X10)
| ~ element(X8,powerset(powerset(set_union2(X7,singleton(X7)))))
| empty_set = X8
| sP1(X7)
| ~ ordinal(X7) ),
inference(definition_unfolding,[],[f159,f177,f177]) ).
fof(f274,plain,
! [X0] :
( being_limit_ordinal(X0)
| set_union2(sK15(X0),singleton(sK15(X0))) = X0
| ~ ordinal(X0) ),
inference(definition_unfolding,[],[f174,f177]) ).
fof(f276,plain,
! [X0] : in(X0,set_union2(X0,singleton(X0))),
inference(definition_unfolding,[],[f201,f177]) ).
fof(f289,definition,
( spl31_1
<=> sP3 ),
introduced(definition,[new_symbols(definition,[spl31_1])],[avatar_definition]) ).
fof(f293,definition,
( spl31_2
<=> ! [X0,X1,X3] :
( empty_set = X1
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| ~ subset(sK20(X1),X3)
| ~ in(X3,X1)
| sK20(X1) = X3 ) ),
introduced(definition,[new_symbols(definition,[spl31_2])],[avatar_definition]) ).
fof(f294,plain,
( ! [X3,X0,X1] :
( ~ subset(sK20(X1),X3)
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| ~ in(X3,X1)
| sK20(X1) = X3 )
| ~ spl31_2 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f295,plain,
( spl31_1
| spl31_2 ),
inference(avatar_split_clause,[],[f189,f293,f289]) ).
fof(f297,definition,
( spl31_3
<=> ! [X0,X1] :
( empty_set = X1
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| in(sK20(X1),X1) ) ),
introduced(definition,[new_symbols(definition,[spl31_3])],[avatar_definition]) ).
fof(f298,plain,
( ! [X0,X1] :
( in(sK20(X1),X1)
| ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| empty_set = X1 )
| ~ spl31_3 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f299,plain,
( spl31_1
| spl31_3 ),
inference(avatar_split_clause,[],[f190,f297,f289]) ).
fof(f301,definition,
( spl31_4
<=> ordinal(sK16) ),
introduced(definition,[new_symbols(definition,[spl31_4])],[avatar_definition]) ).
fof(f303,plain,
( ordinal(sK16)
| ~ spl31_4 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f304,plain,
( ~ spl31_1
| spl31_4 ),
inference(avatar_split_clause,[],[f179,f301,f289]) ).
fof(f306,definition,
( spl31_5
<=> ! [X2,X1,X4] :
( empty_set = X2
| ~ ordinal(X1)
| ~ in(X1,sK16)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(sK17(X2),X4)
| ~ in(X4,X2)
| sK17(X2) = X4 ) ),
introduced(definition,[new_symbols(definition,[spl31_5])],[avatar_definition]) ).
fof(f307,plain,
( ! [X2,X1,X4] :
( ~ in(X1,sK16)
| ~ ordinal(X1)
| empty_set = X2
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| ~ subset(sK17(X2),X4)
| ~ in(X4,X2)
| sK17(X2) = X4 )
| ~ spl31_5 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f308,plain,
( ~ spl31_1
| spl31_5 ),
inference(avatar_split_clause,[],[f180,f306,f289]) ).
fof(f310,definition,
( spl31_6
<=> ! [X2,X1] :
( empty_set = X2
| ~ ordinal(X1)
| ~ in(X1,sK16)
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| in(sK17(X2),X2) ) ),
introduced(definition,[new_symbols(definition,[spl31_6])],[avatar_definition]) ).
fof(f311,plain,
( ! [X2,X1] :
( ~ in(X1,sK16)
| ~ ordinal(X1)
| empty_set = X2
| ~ in(X1,omega)
| ~ element(X2,powerset(powerset(X1)))
| in(sK17(X2),X2) )
| ~ spl31_6 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f312,plain,
( ~ spl31_1
| spl31_6 ),
inference(avatar_split_clause,[],[f181,f310,f289]) ).
fof(f314,definition,
( spl31_7
<=> in(sK16,omega) ),
introduced(definition,[new_symbols(definition,[spl31_7])],[avatar_definition]) ).
fof(f316,plain,
( in(sK16,omega)
| ~ spl31_7 ),
inference(avatar_component_clause,[],[f314]) ).
fof(f317,plain,
( ~ spl31_1
| spl31_7 ),
inference(avatar_split_clause,[],[f182,f314,f289]) ).
fof(f319,definition,
( spl31_8
<=> sP2(sK16) ),
introduced(definition,[new_symbols(definition,[spl31_8])],[avatar_definition]) ).
fof(f321,plain,
( sP2(sK16)
| ~ spl31_8 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f322,plain,
( ~ spl31_1
| spl31_8 ),
inference(avatar_split_clause,[],[f183,f319,f289]) ).
fof(f325,definition,
( spl31_9
<=> in(empty_set,omega) ),
introduced(definition,[new_symbols(definition,[spl31_9])],[avatar_definition]) ).
fof(f327,plain,
( ~ in(empty_set,omega)
| spl31_9 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f329,definition,
( spl31_10
<=> ! [X6,X4] :
( empty_set = X4
| ~ element(X4,powerset(powerset(empty_set)))
| ~ subset(sK12(X4),X6)
| ~ in(X6,X4)
| sK12(X4) = X6 ) ),
introduced(definition,[new_symbols(definition,[spl31_10])],[avatar_definition]) ).
fof(f330,plain,
( ! [X6,X4] :
( ~ subset(sK12(X4),X6)
| ~ element(X4,powerset(powerset(empty_set)))
| empty_set = X4
| ~ in(X6,X4)
| sK12(X4) = X6 )
| ~ spl31_10 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f331,plain,
( ~ spl31_9
| spl31_10 ),
inference(avatar_split_clause,[],[f161,f329,f325]) ).
fof(f333,definition,
( spl31_11
<=> ! [X4] :
( empty_set = X4
| ~ element(X4,powerset(powerset(empty_set)))
| in(sK12(X4),X4) ) ),
introduced(definition,[new_symbols(definition,[spl31_11])],[avatar_definition]) ).
fof(f334,plain,
( ! [X4] :
( in(sK12(X4),X4)
| ~ element(X4,powerset(powerset(empty_set)))
| empty_set = X4 )
| ~ spl31_11 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f335,plain,
( ~ spl31_9
| spl31_11 ),
inference(avatar_split_clause,[],[f162,f333,f325]) ).
fof(f414,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty_set = X1 ),
inference(resolution,[],[f199,f171]) ).
fof(f540,plain,
( ! [X0,X1] :
( ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| ~ in(sK11(sK20(X1)),X1)
| sK20(X1) = sK11(sK20(X1))
| ~ in(sK20(X1),sK10) )
| ~ spl31_2 ),
inference(resolution,[],[f294,f166]) ).
fof(f544,plain,
( ! [X0,X1] :
( ~ in(sK20(X1),sK10)
| ~ in(X0,omega)
| ~ element(X1,powerset(powerset(X0)))
| empty_set = X1
| ~ in(sK11(sK20(X1)),X1)
| ~ ordinal(X0) )
| ~ spl31_2 ),
inference(forward_subsumption_resolution,[],[f540,f168]) ).
fof(f545,plain,
( ! [X0,X1] :
( ~ in(X0,omega)
| ~ element(sK10,powerset(powerset(X0)))
| empty_set = sK10
| ~ in(sK11(sK20(sK10)),sK10)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(sK10,powerset(powerset(X1)))
| empty_set = sK10 )
| ~ spl31_2
| ~ spl31_3 ),
inference(resolution,[],[f544,f298]) ).
fof(f546,plain,
( ! [X0,X1] :
( ~ in(X0,omega)
| ~ element(sK10,powerset(powerset(X0)))
| empty_set = sK10
| ~ in(sK11(sK20(sK10)),sK10)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(sK10,powerset(powerset(X1))) )
| ~ spl31_2
| ~ spl31_3 ),
inference(duplicate_literal_removal,[],[f545]) ).
fof(f547,plain,
( ! [X0,X1] :
( ~ in(X0,omega)
| ~ element(sK10,powerset(powerset(X0)))
| ~ in(sK11(sK20(sK10)),sK10)
| ~ ordinal(X0)
| ~ ordinal(X1)
| ~ in(X1,omega)
| ~ element(sK10,powerset(powerset(X1))) )
| ~ spl31_2
| ~ spl31_3 ),
inference(forward_subsumption_resolution,[],[f546,f169]) ).
fof(f549,definition,
( spl31_26
<=> ! [X1] :
( ~ ordinal(X1)
| ~ element(sK10,powerset(powerset(X1)))
| ~ in(X1,omega) ) ),
introduced(definition,[new_symbols(definition,[spl31_26])],[avatar_definition]) ).
fof(f550,plain,
( ! [X1] :
( ~ element(sK10,powerset(powerset(X1)))
| ~ ordinal(X1)
| ~ in(X1,omega) )
| ~ spl31_26 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f552,definition,
( spl31_27
<=> in(sK11(sK20(sK10)),sK10) ),
introduced(definition,[new_symbols(definition,[spl31_27])],[avatar_definition]) ).
fof(f554,plain,
( ~ in(sK11(sK20(sK10)),sK10)
| spl31_27 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f555,plain,
( spl31_26
| ~ spl31_27
| spl31_26
| ~ spl31_2
| ~ spl31_3 ),
inference(avatar_split_clause,[],[f547,f297,f293,f549,f552,f549]) ).
fof(f556,plain,
( ~ in(sK20(sK10),sK10)
| spl31_27 ),
inference(resolution,[],[f554,f167]) ).
fof(f559,plain,
( ! [X0] :
( ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(sK10,powerset(powerset(X0)))
| empty_set = sK10 )
| ~ spl31_3
| spl31_27 ),
inference(resolution,[],[f556,f298]) ).
fof(f560,plain,
( ! [X0] :
( ~ ordinal(X0)
| ~ in(X0,omega)
| ~ element(sK10,powerset(powerset(X0))) )
| ~ spl31_3
| spl31_27 ),
inference(forward_subsumption_resolution,[],[f559,f169]) ).
fof(f561,plain,
( spl31_26
| ~ spl31_3
| spl31_27 ),
inference(avatar_split_clause,[],[f560,f552,f297,f549]) ).
fof(f564,plain,
( ~ ordinal(sK9)
| ~ in(sK9,omega)
| ~ spl31_26 ),
inference(resolution,[],[f550,f165]) ).
fof(f566,plain,
( ~ in(sK9,omega)
| ~ spl31_26 ),
inference(forward_subsumption_resolution,[],[f564,f163]) ).
fof(f567,plain,
( $false
| ~ spl31_26 ),
inference(forward_subsumption_resolution,[],[f566,f164]) ).
fof(f568,plain,
~ spl31_26,
inference(avatar_contradiction_clause,[],[f567]) ).
fof(f569,plain,
( ! [X0] :
( ~ in(X0,sK18(sK16))
| in(sK19(sK16,X0),sK18(sK16)) )
| ~ spl31_8 ),
inference(resolution,[],[f321,f186]) ).
fof(f570,plain,
( ! [X0] :
( sK19(sK16,X0) != X0
| ~ in(X0,sK18(sK16)) )
| ~ spl31_8 ),
inference(resolution,[],[f321,f187]) ).
fof(f571,plain,
( ! [X0] :
( subset(X0,sK19(sK16,X0))
| ~ in(X0,sK18(sK16)) )
| ~ spl31_8 ),
inference(resolution,[],[f321,f185]) ).
fof(f574,plain,
( ! [X0] :
( ~ ordinal(sK6(sK16))
| empty_set = X0
| ~ in(sK6(sK16),omega)
| ~ element(X0,powerset(powerset(sK6(sK16))))
| in(sK17(X0),X0)
| ~ sP0(sK16) )
| ~ spl31_6 ),
inference(resolution,[],[f311,f150]) ).
fof(f575,plain,
( ! [X0] :
( empty_set = X0
| ~ in(sK6(sK16),omega)
| ~ element(X0,powerset(powerset(sK6(sK16))))
| in(sK17(X0),X0)
| ~ sP0(sK16) )
| ~ spl31_6 ),
inference(forward_subsumption_resolution,[],[f574,f149]) ).
fof(f576,plain,
( ! [X0] :
( empty_set = X0
| ~ element(X0,powerset(powerset(sK6(sK16))))
| in(sK17(X0),X0)
| ~ sP0(sK16) )
| ~ spl31_6 ),
inference(forward_subsumption_resolution,[],[f575,f151]) ).
fof(f578,definition,
( spl31_28
<=> sP0(sK16) ),
introduced(definition,[new_symbols(definition,[spl31_28])],[avatar_definition]) ).
fof(f579,plain,
( sP0(sK16)
| ~ spl31_28 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f580,plain,
( ~ sP0(sK16)
| spl31_28 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f582,definition,
( spl31_29
<=> ! [X0] :
( empty_set = X0
| in(sK17(X0),X0)
| ~ element(X0,powerset(powerset(sK6(sK16)))) ) ),
introduced(definition,[new_symbols(definition,[spl31_29])],[avatar_definition]) ).
fof(f583,plain,
( ! [X0] :
( in(sK17(X0),X0)
| empty_set = X0
| ~ element(X0,powerset(powerset(sK6(sK16)))) )
| ~ spl31_29 ),
inference(avatar_component_clause,[],[f582]) ).
fof(f584,plain,
( ~ spl31_28
| spl31_29
| ~ spl31_6 ),
inference(avatar_split_clause,[],[f576,f310,f582,f578]) ).
fof(f585,plain,
( ! [X0,X1] :
( empty_set = X0
| sK14(X0) = X1
| ~ in(X1,X0)
| ~ subset(sK14(X0),X1)
| ~ element(X0,powerset(powerset(sK16)))
| ~ in(sK16,omega)
| ~ being_limit_ordinal(sK16)
| empty_set = sK16
| ~ ordinal(sK16) )
| spl31_28 ),
inference(resolution,[],[f580,f157]) ).
fof(f586,plain,
( ! [X0] :
( empty_set = X0
| in(sK14(X0),X0)
| ~ element(X0,powerset(powerset(sK16)))
| ~ in(sK16,omega)
| ~ being_limit_ordinal(sK16)
| empty_set = sK16
| ~ ordinal(sK16) )
| spl31_28 ),
inference(resolution,[],[f580,f158]) ).
fof(f587,plain,
( ! [X0] :
( empty_set = X0
| in(sK14(X0),X0)
| ~ element(X0,powerset(powerset(sK16)))
| ~ being_limit_ordinal(sK16)
| empty_set = sK16
| ~ ordinal(sK16) )
| ~ spl31_7
| spl31_28 ),
inference(forward_subsumption_resolution,[],[f586,f316]) ).
fof(f588,plain,
( ! [X0,X1] :
( empty_set = X0
| sK14(X0) = X1
| ~ in(X1,X0)
| ~ subset(sK14(X0),X1)
| ~ element(X0,powerset(powerset(sK16)))
| ~ being_limit_ordinal(sK16)
| empty_set = sK16
| ~ ordinal(sK16) )
| ~ spl31_7
| spl31_28 ),
inference(forward_subsumption_resolution,[],[f585,f316]) ).
fof(f589,plain,
( ! [X0] :
( empty_set = X0
| in(sK14(X0),X0)
| ~ element(X0,powerset(powerset(sK16)))
| ~ being_limit_ordinal(sK16)
| empty_set = sK16 )
| ~ spl31_4
| ~ spl31_7
| spl31_28 ),
inference(forward_subsumption_resolution,[],[f587,f303]) ).
fof(f590,plain,
( ! [X0,X1] :
( empty_set = X0
| sK14(X0) = X1
| ~ in(X1,X0)
| ~ subset(sK14(X0),X1)
| ~ element(X0,powerset(powerset(sK16)))
| ~ being_limit_ordinal(sK16)
| empty_set = sK16 )
| ~ spl31_4
| ~ spl31_7
| spl31_28 ),
inference(forward_subsumption_resolution,[],[f588,f303]) ).
fof(f592,definition,
( spl31_30
<=> empty_set = sK16 ),
introduced(definition,[new_symbols(definition,[spl31_30])],[avatar_definition]) ).
fof(f594,plain,
( empty_set = sK16
| ~ spl31_30 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f596,definition,
( spl31_31
<=> being_limit_ordinal(sK16) ),
introduced(definition,[new_symbols(definition,[spl31_31])],[avatar_definition]) ).
fof(f598,plain,
( ~ being_limit_ordinal(sK16)
| spl31_31 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f600,definition,
( spl31_32
<=> ! [X0] :
( empty_set = X0
| ~ element(X0,powerset(powerset(sK16)))
| in(sK14(X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl31_32])],[avatar_definition]) ).
fof(f601,plain,
( ! [X0] :
( in(sK14(X0),X0)
| ~ element(X0,powerset(powerset(sK16)))
| empty_set = X0 )
| ~ spl31_32 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f602,plain,
( spl31_30
| ~ spl31_31
| spl31_32
| ~ spl31_4
| ~ spl31_7
| spl31_28 ),
inference(avatar_split_clause,[],[f589,f578,f314,f301,f600,f596,f592]) ).
fof(f604,definition,
( spl31_33
<=> ! [X0,X1] :
( empty_set = X0
| ~ element(X0,powerset(powerset(sK16)))
| ~ subset(sK14(X0),X1)
| ~ in(X1,X0)
| sK14(X0) = X1 ) ),
introduced(definition,[new_symbols(definition,[spl31_33])],[avatar_definition]) ).
fof(f605,plain,
( ! [X0,X1] :
( ~ subset(sK14(X0),X1)
| ~ element(X0,powerset(powerset(sK16)))
| empty_set = X0
| ~ in(X1,X0)
| sK14(X0) = X1 )
| ~ spl31_33 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f606,plain,
( spl31_30
| ~ spl31_31
| spl31_33
| ~ spl31_4
| ~ spl31_7
| spl31_28 ),
inference(avatar_split_clause,[],[f590,f578,f314,f301,f604,f596,f592]) ).
fof(f607,plain,
( ! [X0,X1] :
( ~ ordinal(sK6(sK16))
| empty_set = X0
| ~ in(sK6(sK16),omega)
| ~ element(X0,powerset(powerset(sK6(sK16))))
| ~ subset(sK17(X0),X1)
| ~ in(X1,X0)
| sK17(X0) = X1
| ~ sP0(sK16) )
| ~ spl31_5 ),
inference(resolution,[],[f307,f150]) ).
fof(f608,plain,
( sK16 = set_union2(sK15(sK16),singleton(sK15(sK16)))
| ~ ordinal(sK16)
| spl31_31 ),
inference(resolution,[],[f598,f274]) ).
fof(f609,plain,
( sK16 = set_union2(sK15(sK16),singleton(sK15(sK16)))
| ~ spl31_4
| spl31_31 ),
inference(forward_subsumption_resolution,[],[f608,f303]) ).
fof(f610,plain,
( ! [X0] :
( ~ in(sK16,omega)
| in(sK13(X0),X0)
| ~ element(X0,powerset(powerset(sK16)))
| empty_set = X0
| sP1(sK15(sK16))
| ~ ordinal(sK15(sK16)) )
| ~ spl31_4
| spl31_31 ),
inference(superposition,[],[f272,f609]) ).
fof(f611,plain,
( ! [X0,X1] :
( ~ in(sK16,omega)
| sK13(X0) = X1
| ~ in(X1,X0)
| ~ subset(sK13(X0),X1)
| ~ element(X0,powerset(powerset(sK16)))
| empty_set = X0
| sP1(sK15(sK16))
| ~ ordinal(sK15(sK16)) )
| ~ spl31_4
| spl31_31 ),
inference(superposition,[],[f273,f609]) ).
fof(f629,definition,
( spl31_35
<=> ordinal(sK15(sK16)) ),
introduced(definition,[new_symbols(definition,[spl31_35])],[avatar_definition]) ).
fof(f630,plain,
( ordinal(sK15(sK16))
| ~ spl31_35 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f631,plain,
( ~ ordinal(sK15(sK16))
| spl31_35 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f655,plain,
( ! [X0,X1] :
( sK13(X0) = X1
| ~ in(X1,X0)
| ~ subset(sK13(X0),X1)
| ~ element(X0,powerset(powerset(sK16)))
| empty_set = X0
| sP1(sK15(sK16))
| ~ ordinal(sK15(sK16)) )
| ~ spl31_4
| ~ spl31_7
| spl31_31 ),
inference(forward_subsumption_resolution,[],[f611,f316]) ).
fof(f656,plain,
( ! [X0] :
( in(sK13(X0),X0)
| ~ element(X0,powerset(powerset(sK16)))
| empty_set = X0
| sP1(sK15(sK16))
| ~ ordinal(sK15(sK16)) )
| ~ spl31_4
| ~ spl31_7
| spl31_31 ),
inference(forward_subsumption_resolution,[],[f610,f316]) ).
fof(f658,definition,
( spl31_40
<=> sP1(sK15(sK16)) ),
introduced(definition,[new_symbols(definition,[spl31_40])],[avatar_definition]) ).
fof(f660,plain,
( sP1(sK15(sK16))
| ~ spl31_40 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f662,definition,
( spl31_41
<=> ! [X0,X1] :
( sK13(X0) = X1
| empty_set = X0
| ~ element(X0,powerset(powerset(sK16)))
| ~ subset(sK13(X0),X1)
| ~ in(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl31_41])],[avatar_definition]) ).
fof(f663,plain,
( ! [X0,X1] :
( ~ subset(sK13(X0),X1)
| empty_set = X0
| ~ element(X0,powerset(powerset(sK16)))
| sK13(X0) = X1
| ~ in(X1,X0) )
| ~ spl31_41 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f664,plain,
( ~ spl31_35
| spl31_40
| spl31_41
| ~ spl31_4
| ~ spl31_7
| spl31_31 ),
inference(avatar_split_clause,[],[f655,f596,f314,f301,f662,f658,f629]) ).
fof(f666,definition,
( spl31_42
<=> ! [X0] :
( in(sK13(X0),X0)
| empty_set = X0
| ~ element(X0,powerset(powerset(sK16))) ) ),
introduced(definition,[new_symbols(definition,[spl31_42])],[avatar_definition]) ).
fof(f667,plain,
( ! [X0] :
( ~ element(X0,powerset(powerset(sK16)))
| empty_set = X0
| in(sK13(X0),X0) )
| ~ spl31_42 ),
inference(avatar_component_clause,[],[f666]) ).
fof(f668,plain,
( ~ spl31_35
| spl31_40
| spl31_42
| ~ spl31_4
| ~ spl31_7
| spl31_31 ),
inference(avatar_split_clause,[],[f656,f596,f314,f301,f666,f658,f629]) ).
fof(f672,plain,
( being_limit_ordinal(sK16)
| ~ ordinal(sK16)
| spl31_35 ),
inference(resolution,[],[f631,f173]) ).
fof(f686,plain,
( ~ ordinal(sK16)
| spl31_31
| spl31_35 ),
inference(forward_subsumption_resolution,[],[f672,f598]) ).
fof(f687,plain,
( $false
| ~ spl31_4
| spl31_31
| spl31_35 ),
inference(forward_subsumption_resolution,[],[f686,f303]) ).
fof(f688,plain,
( ~ spl31_4
| spl31_31
| spl31_35 ),
inference(avatar_contradiction_clause,[],[f687]) ).
fof(f753,plain,
( ~ element(sK18(sK16),powerset(powerset(sK16)))
| empty_set = sK18(sK16)
| in(sK19(sK16,sK14(sK18(sK16))),sK18(sK16))
| ~ spl31_8
| ~ spl31_32 ),
inference(resolution,[],[f601,f569]) ).
fof(f755,definition,
( spl31_47
<=> in(sK19(sK16,sK14(sK18(sK16))),sK18(sK16)) ),
introduced(definition,[new_symbols(definition,[spl31_47])],[avatar_definition]) ).
fof(f757,plain,
( in(sK19(sK16,sK14(sK18(sK16))),sK18(sK16))
| ~ spl31_47 ),
inference(avatar_component_clause,[],[f755]) ).
fof(f759,definition,
( spl31_48
<=> empty_set = sK18(sK16) ),
introduced(definition,[new_symbols(definition,[spl31_48])],[avatar_definition]) ).
fof(f760,plain,
( empty_set != sK18(sK16)
| spl31_48 ),
inference(avatar_component_clause,[],[f759]) ).
fof(f761,plain,
( empty_set = sK18(sK16)
| ~ spl31_48 ),
inference(avatar_component_clause,[],[f759]) ).
fof(f763,definition,
( spl31_49
<=> element(sK18(sK16),powerset(powerset(sK16))) ),
introduced(definition,[new_symbols(definition,[spl31_49])],[avatar_definition]) ).
fof(f764,plain,
( element(sK18(sK16),powerset(powerset(sK16)))
| ~ spl31_49 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f765,plain,
( ~ element(sK18(sK16),powerset(powerset(sK16)))
| spl31_49 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f766,plain,
( spl31_47
| spl31_48
| ~ spl31_49
| ~ spl31_8
| ~ spl31_32 ),
inference(avatar_split_clause,[],[f753,f600,f319,f763,f759,f755]) ).
fof(f878,plain,
( ! [X0] :
( ~ element(X0,powerset(powerset(sK16)))
| empty_set = X0
| ~ in(sK19(sK16,sK14(X0)),X0)
| sK14(X0) = sK19(sK16,sK14(X0))
| ~ in(sK14(X0),sK18(sK16)) )
| ~ spl31_8
| ~ spl31_33 ),
inference(resolution,[],[f605,f571]) ).
fof(f879,plain,
( ! [X0] :
( ~ in(sK14(X0),sK18(sK16))
| empty_set = X0
| ~ in(sK19(sK16,sK14(X0)),X0)
| ~ element(X0,powerset(powerset(sK16))) )
| ~ spl31_8
| ~ spl31_33 ),
inference(forward_subsumption_resolution,[],[f878,f570]) ).
fof(f943,plain,
( ~ sP2(sK16)
| spl31_49 ),
inference(resolution,[],[f765,f184]) ).
fof(f945,plain,
( $false
| ~ spl31_8
| spl31_49 ),
inference(forward_subsumption_resolution,[],[f943,f321]) ).
fof(f946,plain,
( ~ spl31_8
| spl31_49 ),
inference(avatar_contradiction_clause,[],[f945]) ).
fof(f947,plain,
( ! [X0,X1] :
( empty_set = X0
| ~ in(sK6(sK16),omega)
| ~ element(X0,powerset(powerset(sK6(sK16))))
| ~ subset(sK17(X0),X1)
| ~ in(X1,X0)
| sK17(X0) = X1
| ~ sP0(sK16) )
| ~ spl31_5 ),
inference(forward_subsumption_resolution,[],[f607,f149]) ).
fof(f948,plain,
( ! [X0,X1] :
( empty_set = X0
| ~ element(X0,powerset(powerset(sK6(sK16))))
| ~ subset(sK17(X0),X1)
| ~ in(X1,X0)
| sK17(X0) = X1
| ~ sP0(sK16) )
| ~ spl31_5 ),
inference(forward_subsumption_resolution,[],[f947,f151]) ).
fof(f949,plain,
( ! [X0,X1] :
( ~ subset(sK17(X0),X1)
| ~ element(X0,powerset(powerset(sK6(sK16))))
| empty_set = X0
| ~ in(X1,X0)
| sK17(X0) = X1 )
| ~ spl31_5
| ~ spl31_28 ),
inference(forward_subsumption_resolution,[],[f948,f579]) ).
fof(f951,plain,
( in(sK18(sK16),powerset(powerset(sK16)))
| empty_set = powerset(powerset(sK16))
| ~ spl31_49 ),
inference(resolution,[],[f764,f414]) ).
fof(f953,definition,
( spl31_78
<=> empty_set = powerset(powerset(sK16)) ),
introduced(definition,[new_symbols(definition,[spl31_78])],[avatar_definition]) ).
fof(f955,plain,
( empty_set = powerset(powerset(sK16))
| ~ spl31_78 ),
inference(avatar_component_clause,[],[f953]) ).
fof(f957,definition,
( spl31_79
<=> in(sK18(sK16),powerset(powerset(sK16))) ),
introduced(definition,[new_symbols(definition,[spl31_79])],[avatar_definition]) ).
fof(f959,plain,
( in(sK18(sK16),powerset(powerset(sK16)))
| ~ spl31_79 ),
inference(avatar_component_clause,[],[f957]) ).
fof(f960,plain,
( spl31_78
| spl31_79
| ~ spl31_49 ),
inference(avatar_split_clause,[],[f951,f763,f957,f953]) ).
fof(f963,plain,
( ! [X0] :
( empty_set = sK7(X0)
| ~ element(sK7(X0),powerset(powerset(sK6(sK16))))
| in(sK8(X0,sK17(sK7(X0))),sK7(X0))
| ~ sP0(X0) )
| ~ spl31_29 ),
inference(resolution,[],[f583,f154]) ).
fof(f996,plain,
( ! [X0] :
( ~ element(sK7(X0),powerset(powerset(sK6(sK16))))
| in(sK8(X0,sK17(sK7(X0))),sK7(X0))
| ~ sP0(X0) )
| ~ spl31_29 ),
inference(forward_subsumption_resolution,[],[f963,f156]) ).
fof(f1006,plain,
( ~ empty(empty_set)
| ~ spl31_78 ),
inference(superposition,[],[f230,f955]) ).
fof(f1012,plain,
( $false
| ~ spl31_78 ),
inference(forward_subsumption_resolution,[],[f1006,f197]) ).
fof(f1013,plain,
~ spl31_78,
inference(avatar_contradiction_clause,[],[f1012]) ).
fof(f1047,plain,
( ! [X0,X1] :
( ~ element(X0,powerset(powerset(sK6(sK16))))
| empty_set = X0
| ~ in(sK8(X1,sK17(X0)),X0)
| sK17(X0) = sK8(X1,sK17(X0))
| ~ in(sK17(X0),sK7(X1))
| ~ sP0(X1) )
| ~ spl31_5
| ~ spl31_28 ),
inference(resolution,[],[f949,f153]) ).
fof(f1052,plain,
( ! [X0,X1] :
( ~ in(sK17(X0),sK7(X1))
| empty_set = X0
| ~ in(sK8(X1,sK17(X0)),X0)
| ~ element(X0,powerset(powerset(sK6(sK16))))
| ~ sP0(X1) )
| ~ spl31_5
| ~ spl31_28 ),
inference(forward_subsumption_resolution,[],[f1047,f155]) ).
fof(f1640,plain,
( ! [X0] :
( empty_set = sK7(X0)
| ~ in(sK8(X0,sK17(sK7(X0))),sK7(X0))
| ~ element(sK7(X0),powerset(powerset(sK6(sK16))))
| ~ sP0(X0)
| empty_set = sK7(X0)
| ~ element(sK7(X0),powerset(powerset(sK6(sK16)))) )
| ~ spl31_5
| ~ spl31_28
| ~ spl31_29 ),
inference(resolution,[],[f1052,f583]) ).
fof(f1641,plain,
( ! [X0] :
( empty_set = sK7(X0)
| ~ in(sK8(X0,sK17(sK7(X0))),sK7(X0))
| ~ element(sK7(X0),powerset(powerset(sK6(sK16))))
| ~ sP0(X0) )
| ~ spl31_5
| ~ spl31_28
| ~ spl31_29 ),
inference(duplicate_literal_removal,[],[f1640]) ).
fof(f1642,plain,
( ! [X0] :
( ~ in(sK8(X0,sK17(sK7(X0))),sK7(X0))
| ~ element(sK7(X0),powerset(powerset(sK6(sK16))))
| ~ sP0(X0) )
| ~ spl31_5
| ~ spl31_28
| ~ spl31_29 ),
inference(forward_subsumption_resolution,[],[f1641,f156]) ).
fof(f1643,plain,
( ! [X0] :
( ~ element(sK7(X0),powerset(powerset(sK6(sK16))))
| ~ sP0(X0) )
| ~ spl31_5
| ~ spl31_28
| ~ spl31_29 ),
inference(forward_subsumption_resolution,[],[f1642,f996]) ).
fof(f2325,plain,
( ~ sP0(sK16)
| ~ sP0(sK16)
| ~ spl31_5
| ~ spl31_28
| ~ spl31_29 ),
inference(resolution,[],[f1643,f152]) ).
fof(f2327,plain,
( ~ sP0(sK16)
| ~ spl31_5
| ~ spl31_28
| ~ spl31_29 ),
inference(duplicate_literal_removal,[],[f2325]) ).
fof(f2328,plain,
( $false
| ~ spl31_5
| ~ spl31_28
| ~ spl31_29 ),
inference(forward_subsumption_resolution,[],[f2327,f579]) ).
fof(f2329,plain,
( ~ spl31_5
| ~ spl31_28
| ~ spl31_29 ),
inference(avatar_contradiction_clause,[],[f2328]) ).
fof(f2346,plain,
( ~ element(sK18(sK16),powerset(powerset(sK16)))
| empty_set = sK18(sK16)
| empty_set = sK18(sK16)
| ~ in(sK19(sK16,sK14(sK18(sK16))),sK18(sK16))
| ~ element(sK18(sK16),powerset(powerset(sK16)))
| ~ spl31_8
| ~ spl31_32
| ~ spl31_33 ),
inference(resolution,[],[f601,f879]) ).
fof(f2348,plain,
( ~ element(sK18(sK16),powerset(powerset(sK16)))
| empty_set = sK18(sK16)
| ~ in(sK19(sK16,sK14(sK18(sK16))),sK18(sK16))
| ~ spl31_8
| ~ spl31_32
| ~ spl31_33 ),
inference(duplicate_literal_removal,[],[f2346]) ).
fof(f2351,plain,
( empty_set = sK18(sK16)
| ~ in(sK19(sK16,sK14(sK18(sK16))),sK18(sK16))
| ~ spl31_8
| ~ spl31_32
| ~ spl31_33
| ~ spl31_49 ),
inference(forward_subsumption_resolution,[],[f2348,f764]) ).
fof(f2355,plain,
( empty_set = sK18(sK16)
| ~ spl31_8
| ~ spl31_32
| ~ spl31_33
| ~ spl31_47
| ~ spl31_49 ),
inference(forward_subsumption_resolution,[],[f2351,f757]) ).
fof(f2366,plain,
( spl31_48
| ~ spl31_8
| ~ spl31_32
| ~ spl31_33
| ~ spl31_47
| ~ spl31_49 ),
inference(avatar_split_clause,[],[f2355,f763,f755,f604,f600,f319,f759]) ).
fof(f2400,plain,
( empty_set != empty_set
| ~ sP2(sK16)
| ~ spl31_48 ),
inference(superposition,[],[f188,f761]) ).
fof(f2401,plain,
( ~ sP2(sK16)
| ~ spl31_48 ),
inference(trivial_inequality_removal,[],[f2400]) ).
fof(f2402,plain,
( $false
| ~ spl31_8
| ~ spl31_48 ),
inference(forward_subsumption_resolution,[],[f2401,f321]) ).
fof(f2403,plain,
( ~ spl31_8
| ~ spl31_48 ),
inference(avatar_contradiction_clause,[],[f2402]) ).
fof(f2428,plain,
( empty_set != sK18(empty_set)
| ~ spl31_30
| spl31_48 ),
inference(forward_demodulation,[],[f760,f594]) ).
fof(f2432,plain,
( in(empty_set,omega)
| ~ spl31_7
| ~ spl31_30 ),
inference(superposition,[],[f316,f594]) ).
fof(f2449,plain,
( element(sK18(empty_set),powerset(powerset(empty_set)))
| ~ spl31_30
| ~ spl31_49 ),
inference(superposition,[],[f764,f594]) ).
fof(f2520,plain,
( $false
| ~ spl31_7
| spl31_9
| ~ spl31_30 ),
inference(forward_subsumption_resolution,[],[f2432,f327]) ).
fof(f2521,plain,
( ~ spl31_7
| spl31_9
| ~ spl31_30 ),
inference(avatar_contradiction_clause,[],[f2520]) ).
fof(f2534,plain,
( ~ element(sK18(sK16),powerset(powerset(empty_set)))
| empty_set = sK18(sK16)
| in(sK19(sK16,sK12(sK18(sK16))),sK18(sK16))
| ~ spl31_8
| ~ spl31_11 ),
inference(resolution,[],[f334,f569]) ).
fof(f2535,plain,
( ~ element(sK18(empty_set),powerset(powerset(empty_set)))
| empty_set = sK18(sK16)
| in(sK19(sK16,sK12(sK18(sK16))),sK18(sK16))
| ~ spl31_8
| ~ spl31_11
| ~ spl31_30 ),
inference(forward_demodulation,[],[f2534,f594]) ).
fof(f2537,plain,
( empty_set = sK18(sK16)
| in(sK19(sK16,sK12(sK18(sK16))),sK18(sK16))
| ~ spl31_8
| ~ spl31_11
| ~ spl31_30
| ~ spl31_49 ),
inference(forward_subsumption_resolution,[],[f2535,f2449]) ).
fof(f2538,plain,
( empty_set = sK18(empty_set)
| in(sK19(sK16,sK12(sK18(sK16))),sK18(sK16))
| ~ spl31_8
| ~ spl31_11
| ~ spl31_30
| ~ spl31_49 ),
inference(forward_demodulation,[],[f2537,f594]) ).
fof(f2539,plain,
( in(sK19(sK16,sK12(sK18(sK16))),sK18(sK16))
| ~ spl31_8
| ~ spl31_11
| ~ spl31_30
| spl31_48
| ~ spl31_49 ),
inference(forward_subsumption_resolution,[],[f2538,f2428]) ).
fof(f2540,plain,
( in(sK19(empty_set,sK12(sK18(empty_set))),sK18(empty_set))
| ~ spl31_8
| ~ spl31_11
| ~ spl31_30
| spl31_48
| ~ spl31_49 ),
inference(forward_demodulation,[],[f2539,f594]) ).
fof(f2546,plain,
( ! [X0] :
( ~ element(X0,powerset(powerset(empty_set)))
| empty_set = X0
| ~ in(sK19(sK16,sK12(X0)),X0)
| sK12(X0) = sK19(sK16,sK12(X0))
| ~ in(sK12(X0),sK18(sK16)) )
| ~ spl31_8
| ~ spl31_10 ),
inference(resolution,[],[f330,f571]) ).
fof(f2547,plain,
( ! [X0] :
( ~ in(sK12(X0),sK18(sK16))
| empty_set = X0
| ~ in(sK19(sK16,sK12(X0)),X0)
| ~ element(X0,powerset(powerset(empty_set))) )
| ~ spl31_8
| ~ spl31_10 ),
inference(forward_subsumption_resolution,[],[f2546,f570]) ).
fof(f2550,plain,
( ! [X0] :
( ~ in(sK19(empty_set,sK12(X0)),X0)
| ~ element(X0,powerset(powerset(empty_set)))
| empty_set = X0
| ~ in(sK12(X0),sK18(sK16)) )
| ~ spl31_8
| ~ spl31_10
| ~ spl31_30 ),
inference(forward_demodulation,[],[f2547,f594]) ).
fof(f2551,plain,
( ! [X0] :
( ~ in(sK12(X0),sK18(empty_set))
| ~ in(sK19(empty_set,sK12(X0)),X0)
| ~ element(X0,powerset(powerset(empty_set)))
| empty_set = X0 )
| ~ spl31_8
| ~ spl31_10
| ~ spl31_30 ),
inference(forward_demodulation,[],[f2550,f594]) ).
fof(f2585,plain,
( ! [X0] :
( in(sK5(sK15(sK16),X0),sK4(sK15(sK16)))
| ~ in(X0,sK4(sK15(sK16))) )
| ~ spl31_40 ),
inference(resolution,[],[f660,f146]) ).
fof(f2586,plain,
( ! [X0] :
( sK5(sK15(sK16),X0) != X0
| ~ in(X0,sK4(sK15(sK16))) )
| ~ spl31_40 ),
inference(resolution,[],[f660,f147]) ).
fof(f2587,plain,
( ! [X0] :
( subset(X0,sK5(sK15(sK16),X0))
| ~ in(X0,sK4(sK15(sK16))) )
| ~ spl31_40 ),
inference(resolution,[],[f660,f145]) ).
fof(f2588,plain,
( in(sK15(sK16),omega)
| ~ spl31_40 ),
inference(resolution,[],[f660,f143]) ).
fof(f2623,plain,
( ~ in(sK19(empty_set,sK12(sK18(empty_set))),sK18(empty_set))
| ~ element(sK18(empty_set),powerset(powerset(empty_set)))
| empty_set = sK18(empty_set)
| ~ element(sK18(empty_set),powerset(powerset(empty_set)))
| empty_set = sK18(empty_set)
| ~ spl31_8
| ~ spl31_10
| ~ spl31_11
| ~ spl31_30 ),
inference(resolution,[],[f2551,f334]) ).
fof(f2624,plain,
( ~ in(sK19(empty_set,sK12(sK18(empty_set))),sK18(empty_set))
| ~ element(sK18(empty_set),powerset(powerset(empty_set)))
| empty_set = sK18(empty_set)
| ~ spl31_8
| ~ spl31_10
| ~ spl31_11
| ~ spl31_30 ),
inference(duplicate_literal_removal,[],[f2623]) ).
fof(f2625,plain,
( ~ element(sK18(empty_set),powerset(powerset(empty_set)))
| empty_set = sK18(empty_set)
| ~ spl31_8
| ~ spl31_10
| ~ spl31_11
| ~ spl31_30
| spl31_48
| ~ spl31_49 ),
inference(forward_subsumption_resolution,[],[f2624,f2540]) ).
fof(f2626,plain,
( empty_set = sK18(empty_set)
| ~ spl31_8
| ~ spl31_10
| ~ spl31_11
| ~ spl31_30
| spl31_48
| ~ spl31_49 ),
inference(forward_subsumption_resolution,[],[f2625,f2449]) ).
fof(f2627,plain,
( $false
| ~ spl31_8
| ~ spl31_10
| ~ spl31_11
| ~ spl31_30
| spl31_48
| ~ spl31_49 ),
inference(forward_subsumption_resolution,[],[f2626,f2428]) ).
fof(f2628,plain,
( ~ spl31_8
| ~ spl31_10
| ~ spl31_11
| ~ spl31_30
| spl31_48
| ~ spl31_49 ),
inference(avatar_contradiction_clause,[],[f2627]) ).
fof(f2671,plain,
( sK16 = set_union2(sK15(sK16),singleton(sK15(sK16)))
| ~ ordinal(sK16)
| spl31_31 ),
inference(resolution,[],[f598,f274]) ).
fof(f2672,plain,
( sK16 = set_union2(sK15(sK16),singleton(sK15(sK16)))
| ~ spl31_4
| spl31_31 ),
inference(forward_subsumption_resolution,[],[f2671,f303]) ).
fof(f2787,plain,
( in(sK15(sK16),sK16)
| ~ spl31_4
| spl31_31 ),
inference(superposition,[],[f276,f2672]) ).
fof(f2804,plain,
( ! [X0,X1] :
( ~ ordinal(sK15(sK16))
| empty_set = X0
| ~ in(sK15(sK16),omega)
| ~ element(X0,powerset(powerset(sK15(sK16))))
| ~ subset(sK17(X0),X1)
| ~ in(X1,X0)
| sK17(X0) = X1 )
| ~ spl31_4
| ~ spl31_5
| spl31_31 ),
inference(resolution,[],[f2787,f307]) ).
fof(f2805,plain,
( ! [X0] :
( ~ ordinal(sK15(sK16))
| empty_set = X0
| ~ in(sK15(sK16),omega)
| ~ element(X0,powerset(powerset(sK15(sK16))))
| in(sK17(X0),X0) )
| ~ spl31_4
| ~ spl31_6
| spl31_31 ),
inference(resolution,[],[f2787,f311]) ).
fof(f2808,plain,
( ! [X0] :
( empty_set = X0
| ~ in(sK15(sK16),omega)
| ~ element(X0,powerset(powerset(sK15(sK16))))
| in(sK17(X0),X0) )
| ~ spl31_4
| ~ spl31_6
| spl31_31
| ~ spl31_35 ),
inference(forward_subsumption_resolution,[],[f2805,f630]) ).
fof(f2809,plain,
( ! [X0,X1] :
( empty_set = X0
| ~ in(sK15(sK16),omega)
| ~ element(X0,powerset(powerset(sK15(sK16))))
| ~ subset(sK17(X0),X1)
| ~ in(X1,X0)
| sK17(X0) = X1 )
| ~ spl31_4
| ~ spl31_5
| spl31_31
| ~ spl31_35 ),
inference(forward_subsumption_resolution,[],[f2804,f630]) ).
fof(f2810,plain,
( ! [X0] :
( in(sK17(X0),X0)
| ~ element(X0,powerset(powerset(sK15(sK16))))
| empty_set = X0 )
| ~ spl31_4
| ~ spl31_6
| spl31_31
| ~ spl31_35
| ~ spl31_40 ),
inference(forward_subsumption_resolution,[],[f2808,f2588]) ).
fof(f2811,plain,
( ! [X0,X1] :
( ~ subset(sK17(X0),X1)
| ~ element(X0,powerset(powerset(sK15(sK16))))
| empty_set = X0
| ~ in(X1,X0)
| sK17(X0) = X1 )
| ~ spl31_4
| ~ spl31_5
| spl31_31
| ~ spl31_35
| ~ spl31_40 ),
inference(forward_subsumption_resolution,[],[f2809,f2588]) ).
fof(f4674,plain,
( ! [X0] :
( ~ element(X0,powerset(powerset(sK15(sK16))))
| empty_set = X0
| ~ in(sK5(sK15(sK16),sK17(X0)),X0)
| sK17(X0) = sK5(sK15(sK16),sK17(X0))
| ~ in(sK17(X0),sK4(sK15(sK16))) )
| ~ spl31_4
| ~ spl31_5
| spl31_31
| ~ spl31_35
| ~ spl31_40 ),
inference(resolution,[],[f2811,f2587]) ).
fof(f4681,plain,
( ! [X0] :
( ~ in(sK17(X0),sK4(sK15(sK16)))
| empty_set = X0
| ~ in(sK5(sK15(sK16),sK17(X0)),X0)
| ~ element(X0,powerset(powerset(sK15(sK16)))) )
| ~ spl31_4
| ~ spl31_5
| spl31_31
| ~ spl31_35
| ~ spl31_40 ),
inference(forward_subsumption_resolution,[],[f4674,f2586]) ).
fof(f4921,definition,
( spl31_453
<=> empty_set = sK4(sK15(sK16)) ),
introduced(definition,[new_symbols(definition,[spl31_453])],[avatar_definition]) ).
fof(f4923,plain,
( empty_set = sK4(sK15(sK16))
| ~ spl31_453 ),
inference(avatar_component_clause,[],[f4921]) ).
fof(f5023,plain,
( empty_set = sK4(sK15(sK16))
| ~ in(sK5(sK15(sK16),sK17(sK4(sK15(sK16)))),sK4(sK15(sK16)))
| ~ element(sK4(sK15(sK16)),powerset(powerset(sK15(sK16))))
| ~ element(sK4(sK15(sK16)),powerset(powerset(sK15(sK16))))
| empty_set = sK4(sK15(sK16))
| ~ spl31_4
| ~ spl31_5
| ~ spl31_6
| spl31_31
| ~ spl31_35
| ~ spl31_40 ),
inference(resolution,[],[f4681,f2810]) ).
fof(f5026,plain,
( empty_set = sK4(sK15(sK16))
| ~ in(sK5(sK15(sK16),sK17(sK4(sK15(sK16)))),sK4(sK15(sK16)))
| ~ element(sK4(sK15(sK16)),powerset(powerset(sK15(sK16))))
| ~ spl31_4
| ~ spl31_5
| ~ spl31_6
| spl31_31
| ~ spl31_35
| ~ spl31_40 ),
inference(duplicate_literal_removal,[],[f5023]) ).
fof(f5032,definition,
( spl31_463
<=> element(sK4(sK15(sK16)),powerset(powerset(sK15(sK16)))) ),
introduced(definition,[new_symbols(definition,[spl31_463])],[avatar_definition]) ).
fof(f5033,plain,
( element(sK4(sK15(sK16)),powerset(powerset(sK15(sK16))))
| ~ spl31_463 ),
inference(avatar_component_clause,[],[f5032]) ).
fof(f5034,plain,
( ~ element(sK4(sK15(sK16)),powerset(powerset(sK15(sK16))))
| spl31_463 ),
inference(avatar_component_clause,[],[f5032]) ).
fof(f5036,definition,
( spl31_464
<=> in(sK5(sK15(sK16),sK17(sK4(sK15(sK16)))),sK4(sK15(sK16))) ),
introduced(definition,[new_symbols(definition,[spl31_464])],[avatar_definition]) ).
fof(f5038,plain,
( ~ in(sK5(sK15(sK16),sK17(sK4(sK15(sK16)))),sK4(sK15(sK16)))
| spl31_464 ),
inference(avatar_component_clause,[],[f5036]) ).
fof(f5040,plain,
( ~ spl31_463
| ~ spl31_464
| spl31_453
| ~ spl31_4
| ~ spl31_5
| ~ spl31_6
| spl31_31
| ~ spl31_35
| ~ spl31_40 ),
inference(avatar_split_clause,[],[f5026,f658,f629,f596,f310,f306,f301,f4921,f5036,f5032]) ).
fof(f5051,plain,
( ~ sP1(sK15(sK16))
| spl31_463 ),
inference(resolution,[],[f5034,f144]) ).
fof(f5055,plain,
( $false
| ~ spl31_40
| spl31_463 ),
inference(forward_subsumption_resolution,[],[f5051,f660]) ).
fof(f5056,plain,
( ~ spl31_40
| spl31_463 ),
inference(avatar_contradiction_clause,[],[f5055]) ).
fof(f5080,plain,
( ~ in(sK17(sK4(sK15(sK16))),sK4(sK15(sK16)))
| ~ spl31_40
| spl31_464 ),
inference(resolution,[],[f5038,f2585]) ).
fof(f5092,plain,
( ~ element(sK4(sK15(sK16)),powerset(powerset(sK15(sK16))))
| empty_set = sK4(sK15(sK16))
| ~ spl31_4
| ~ spl31_6
| spl31_31
| ~ spl31_35
| ~ spl31_40
| spl31_464 ),
inference(resolution,[],[f5080,f2810]) ).
fof(f5095,plain,
( empty_set = sK4(sK15(sK16))
| ~ spl31_4
| ~ spl31_6
| spl31_31
| ~ spl31_35
| ~ spl31_40
| ~ spl31_463
| spl31_464 ),
inference(forward_subsumption_resolution,[],[f5092,f5033]) ).
fof(f5096,plain,
( spl31_453
| ~ spl31_4
| ~ spl31_6
| spl31_31
| ~ spl31_35
| ~ spl31_40
| ~ spl31_463
| spl31_464 ),
inference(avatar_split_clause,[],[f5095,f5036,f5032,f658,f629,f596,f310,f301,f4921]) ).
fof(f5109,plain,
( ! [X0] :
( in(sK13(X0),X0)
| empty_set = X0
| ~ in(X0,powerset(powerset(sK16))) )
| ~ spl31_42 ),
inference(resolution,[],[f667,f200]) ).
fof(f5113,plain,
( empty_set = sK18(sK16)
| in(sK13(sK18(sK16)),sK18(sK16))
| ~ spl31_42
| ~ spl31_49 ),
inference(resolution,[],[f667,f764]) ).
fof(f5130,plain,
( in(sK13(sK18(sK16)),sK18(sK16))
| ~ spl31_42
| spl31_48
| ~ spl31_49 ),
inference(forward_subsumption_resolution,[],[f5113,f760]) ).
fof(f5159,plain,
( ! [X0] :
( empty_set = X0
| ~ element(X0,powerset(powerset(sK16)))
| sK13(X0) = sK19(sK16,sK13(X0))
| ~ in(sK19(sK16,sK13(X0)),X0)
| ~ in(sK13(X0),sK18(sK16)) )
| ~ spl31_8
| ~ spl31_41 ),
inference(resolution,[],[f663,f571]) ).
fof(f5160,plain,
( ! [X0] :
( ~ in(sK13(X0),sK18(sK16))
| ~ element(X0,powerset(powerset(sK16)))
| ~ in(sK19(sK16,sK13(X0)),X0)
| empty_set = X0 )
| ~ spl31_8
| ~ spl31_41 ),
inference(forward_subsumption_resolution,[],[f5159,f570]) ).
fof(f5203,plain,
( in(sK19(sK16,sK13(sK18(sK16))),sK18(sK16))
| ~ spl31_8
| ~ spl31_42
| spl31_48
| ~ spl31_49 ),
inference(resolution,[],[f5130,f569]) ).
fof(f5575,plain,
( ~ element(sK18(sK16),powerset(powerset(sK16)))
| ~ in(sK19(sK16,sK13(sK18(sK16))),sK18(sK16))
| empty_set = sK18(sK16)
| empty_set = sK18(sK16)
| ~ in(sK18(sK16),powerset(powerset(sK16)))
| ~ spl31_8
| ~ spl31_41
| ~ spl31_42 ),
inference(resolution,[],[f5160,f5109]) ).
fof(f5576,plain,
( ~ element(sK18(sK16),powerset(powerset(sK16)))
| ~ in(sK19(sK16,sK13(sK18(sK16))),sK18(sK16))
| empty_set = sK18(sK16)
| ~ in(sK18(sK16),powerset(powerset(sK16)))
| ~ spl31_8
| ~ spl31_41
| ~ spl31_42 ),
inference(duplicate_literal_removal,[],[f5575]) ).
fof(f5577,plain,
( ~ in(sK19(sK16,sK13(sK18(sK16))),sK18(sK16))
| empty_set = sK18(sK16)
| ~ in(sK18(sK16),powerset(powerset(sK16)))
| ~ spl31_8
| ~ spl31_41
| ~ spl31_42 ),
inference(forward_subsumption_resolution,[],[f5576,f200]) ).
fof(f5579,plain,
( empty_set = sK18(sK16)
| ~ in(sK18(sK16),powerset(powerset(sK16)))
| ~ spl31_8
| ~ spl31_41
| ~ spl31_42
| spl31_48
| ~ spl31_49 ),
inference(forward_subsumption_resolution,[],[f5577,f5203]) ).
fof(f5581,plain,
( ~ in(sK18(sK16),powerset(powerset(sK16)))
| ~ spl31_8
| ~ spl31_41
| ~ spl31_42
| spl31_48
| ~ spl31_49 ),
inference(forward_subsumption_resolution,[],[f5579,f760]) ).
fof(f5584,plain,
( $false
| ~ spl31_8
| ~ spl31_41
| ~ spl31_42
| spl31_48
| ~ spl31_49
| ~ spl31_79 ),
inference(forward_subsumption_resolution,[],[f5581,f959]) ).
fof(f5585,plain,
( ~ spl31_8
| ~ spl31_41
| ~ spl31_42
| spl31_48
| ~ spl31_49
| ~ spl31_79 ),
inference(avatar_contradiction_clause,[],[f5584]) ).
fof(f5633,plain,
( empty_set != empty_set
| ~ sP1(sK15(sK16))
| ~ spl31_453 ),
inference(superposition,[],[f148,f4923]) ).
fof(f5634,plain,
( ~ sP1(sK15(sK16))
| ~ spl31_453 ),
inference(trivial_inequality_removal,[],[f5633]) ).
fof(f5635,plain,
( $false
| ~ spl31_40
| ~ spl31_453 ),
inference(forward_subsumption_resolution,[],[f5634,f660]) ).
fof(f5636,plain,
( ~ spl31_40
| ~ spl31_453 ),
inference(avatar_contradiction_clause,[],[f5635]) ).
cnf(s1,plain,
( spl31_1
| spl31_2 ),
inference(sat_conversion,[],[f295]) ).
cnf(s2,plain,
( spl31_1
| spl31_3 ),
inference(sat_conversion,[],[f299]) ).
cnf(s3,plain,
( ~ spl31_1
| spl31_4 ),
inference(sat_conversion,[],[f304]) ).
cnf(s4,plain,
( ~ spl31_1
| spl31_5 ),
inference(sat_conversion,[],[f308]) ).
cnf(s5,plain,
( ~ spl31_1
| spl31_6 ),
inference(sat_conversion,[],[f312]) ).
cnf(s6,plain,
( ~ spl31_1
| spl31_7 ),
inference(sat_conversion,[],[f317]) ).
cnf(s7,plain,
( ~ spl31_1
| spl31_8 ),
inference(sat_conversion,[],[f322]) ).
cnf(s8,plain,
( ~ spl31_9
| spl31_10 ),
inference(sat_conversion,[],[f331]) ).
cnf(s9,plain,
( ~ spl31_9
| spl31_11 ),
inference(sat_conversion,[],[f335]) ).
cnf(s18,plain,
( spl31_26
| ~ spl31_3
| ~ spl31_2
| spl31_26
| ~ spl31_27 ),
inference(sat_conversion,[],[f555]) ).
cnf(s19,plain,
( ~ spl31_2
| ~ spl31_3
| spl31_26
| ~ spl31_27 ),
inference(rat,[],[s18]) ).
cnf(s20,plain,
( ~ spl31_3
| spl31_26
| spl31_27 ),
inference(sat_conversion,[],[f561]) ).
cnf(s21,plain,
~ spl31_26,
inference(sat_conversion,[],[f568]) ).
cnf(s22,plain,
( ~ spl31_6
| ~ spl31_28
| spl31_29 ),
inference(sat_conversion,[],[f584]) ).
cnf(s23,plain,
( ~ spl31_4
| ~ spl31_7
| spl31_28
| spl31_30
| ~ spl31_31
| spl31_32 ),
inference(sat_conversion,[],[f602]) ).
cnf(s24,plain,
( ~ spl31_4
| ~ spl31_7
| spl31_28
| spl31_30
| ~ spl31_31
| spl31_33 ),
inference(sat_conversion,[],[f606]) ).
cnf(s32,plain,
( ~ spl31_4
| ~ spl31_7
| spl31_31
| ~ spl31_35
| spl31_40
| spl31_41 ),
inference(sat_conversion,[],[f664]) ).
cnf(s33,plain,
( ~ spl31_4
| ~ spl31_7
| spl31_31
| ~ spl31_35
| spl31_40
| spl31_42 ),
inference(sat_conversion,[],[f668]) ).
cnf(s35,plain,
( ~ spl31_4
| spl31_31
| spl31_35 ),
inference(sat_conversion,[],[f688]) ).
cnf(s37,plain,
( ~ spl31_8
| ~ spl31_32
| spl31_47
| spl31_48
| ~ spl31_49 ),
inference(sat_conversion,[],[f766]) ).
cnf(s57,plain,
( ~ spl31_8
| spl31_49 ),
inference(sat_conversion,[],[f946]) ).
cnf(s58,plain,
( ~ spl31_49
| spl31_78
| spl31_79 ),
inference(sat_conversion,[],[f960]) ).
cnf(s62,plain,
~ spl31_78,
inference(sat_conversion,[],[f1013]) ).
cnf(s185,plain,
( ~ spl31_5
| ~ spl31_28
| ~ spl31_29 ),
inference(sat_conversion,[],[f2329]) ).
cnf(s189,plain,
( ~ spl31_8
| ~ spl31_32
| ~ spl31_33
| ~ spl31_47
| spl31_48
| ~ spl31_49 ),
inference(sat_conversion,[],[f2366]) ).
cnf(s190,plain,
( ~ spl31_8
| ~ spl31_48 ),
inference(sat_conversion,[],[f2403]) ).
cnf(s198,plain,
( ~ spl31_7
| spl31_9
| ~ spl31_30 ),
inference(sat_conversion,[],[f2521]) ).
cnf(s201,plain,
( ~ spl31_8
| ~ spl31_10
| ~ spl31_11
| ~ spl31_30
| spl31_48
| ~ spl31_49 ),
inference(sat_conversion,[],[f2628]) ).
cnf(s424,plain,
( ~ spl31_4
| ~ spl31_5
| ~ spl31_6
| spl31_31
| ~ spl31_35
| ~ spl31_40
| spl31_453
| ~ spl31_463
| ~ spl31_464 ),
inference(sat_conversion,[],[f5040]) ).
cnf(s426,plain,
( ~ spl31_40
| spl31_463 ),
inference(sat_conversion,[],[f5056]) ).
cnf(s433,plain,
( ~ spl31_4
| ~ spl31_6
| spl31_31
| ~ spl31_35
| ~ spl31_40
| spl31_453
| ~ spl31_463
| spl31_464 ),
inference(sat_conversion,[],[f5096]) ).
cnf(s480,plain,
( ~ spl31_8
| ~ spl31_41
| ~ spl31_42
| spl31_48
| ~ spl31_49
| ~ spl31_79 ),
inference(sat_conversion,[],[f5585]) ).
cnf(s486,plain,
( ~ spl31_40
| ~ spl31_453 ),
inference(sat_conversion,[],[f5636]) ).
cnf(s563,plain,
( ~ spl31_49
| spl31_79 ),
inference(rat,[],[s58,s62]) ).
cnf(s569,plain,
( ~ spl31_3
| spl31_27 ),
inference(rat,[],[s20,s21]) ).
cnf(s570,plain,
( ~ spl31_2
| ~ spl31_3
| ~ spl31_27 ),
inference(rat,[],[s19,s21]) ).
cnf(s572,plain,
spl31_1,
inference(rat,[],[s570,s569,s1,s2]) ).
cnf(s573,plain,
spl31_8,
inference(rat,[],[s7,s572]) ).
cnf(s574,plain,
spl31_7,
inference(rat,[],[s6,s572]) ).
cnf(s575,plain,
spl31_6,
inference(rat,[],[s5,s572]) ).
cnf(s576,plain,
spl31_5,
inference(rat,[],[s4,s572]) ).
cnf(s577,plain,
spl31_4,
inference(rat,[],[s3,s572]) ).
cnf(s578,plain,
~ spl31_48,
inference(rat,[],[s190,s573]) ).
cnf(s579,plain,
spl31_49,
inference(rat,[],[s57,s573]) ).
cnf(s583,plain,
spl31_79,
inference(rat,[],[s563,s579]) ).
cnf(s593,plain,
( spl31_40
| ~ spl31_35
| spl31_31 ),
inference(rat,[],[s480,s32,s33,s577,s574,s583,s579,s578,s573]) ).
cnf(s594,plain,
( spl31_453
| ~ spl31_40
| spl31_31
| ~ spl31_35
| ~ spl31_463 ),
inference(rat,[],[s424,s433,s577,s576,s575]) ).
cnf(s595,plain,
( ~ spl31_35
| spl31_31 ),
inference(rat,[],[s594,s426,s486,s593]) ).
cnf(s596,plain,
spl31_31,
inference(rat,[],[s595,s35,s577]) ).
cnf(s597,plain,
( ~ spl31_32
| ~ spl31_33 ),
inference(rat,[],[s37,s189,s579,s578,s573]) ).
cnf(s598,plain,
( spl31_30
| spl31_28 ),
inference(rat,[],[s597,s23,s24,s577,s574,s596]) ).
cnf(s599,plain,
~ spl31_28,
inference(rat,[],[s22,s185,s575,s576]) ).
cnf(s600,plain,
spl31_30,
inference(rat,[],[s598,s599]) ).
cnf(s602,plain,
spl31_9,
inference(rat,[],[s198,s574,s600]) ).
cnf(s603,plain,
spl31_11,
inference(rat,[],[s9,s602]) ).
cnf(s604,plain,
spl31_10,
inference(rat,[],[s8,s602]) ).
cnf(s605,plain,
$false,
inference(rat,[],[s201,s579,s578,s600,s573,s603,s604]) ).
fof(f5639,plain,
$false,
inference(avatar_sat_refutation,[],[s605]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU301+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 04:34:06 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.68/1.68 % (803375)Detected formulas, will run a generic FOF schedule.
% 4.68/1.68 % (803384)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3989841104:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.68/1.68 % (803384)Instruction limit reached!
% 4.68/1.68 % (803384)------------------------------
% 4.68/1.68 % (803384)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.68/1.68 % (803384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.68/1.68 % (803384)CaDiCaL version: 2.1.3
% 4.68/1.68 % (803384)Termination reason: Instruction limit
% 4.68/1.68 % (803384)Termination phase: Saturation
% 4.68/1.68 % (803384)Time elapsed: 0.041 s
% 4.68/1.68 % (803384)Peak memory usage: 89 MB
% 4.68/1.68 % (803384)Instructions burned: 122 (million)
% 4.68/1.68 % (803386)dis-21_1_sil=8000:lcm=predicate:random_seed=1716495817: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)
% 4.68/1.68 % (803383)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2706652831:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.68/1.68 % (803380)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=990967746:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.68/1.68 % (803382)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=2127064453:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.68/1.68 % (803381)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=1814781529:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.68/1.68 % (803385)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=365752366:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.68/1.68 % (803383)Instruction limit reached!
% 4.68/1.68 % (803383)------------------------------
% 4.68/1.68 % (803383)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.68/1.68 % (803383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.68/1.68 % (803383)CaDiCaL version: 2.1.3
% 4.68/1.68 % (803383)Termination reason: Instruction limit
% 4.68/1.68 % (803383)Termination phase: Saturation
% 4.68/1.68 % (803383)Time elapsed: 0.065 s
% 4.68/1.68 % (803383)Peak memory usage: 89 MB
% 4.68/1.68 % (803383)Instructions burned: 111 (million)
% 4.68/1.68 % (803385)Instruction limit reached!
% 4.68/1.68 % (803385)------------------------------
% 4.68/1.68 % (803385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.68/1.68 % (803385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.68/1.68 % (803385)CaDiCaL version: 2.1.3
% 4.68/1.68 % (803385)Termination reason: Instruction limit
% 4.68/1.68 % (803385)Termination phase: Saturation
% 4.68/1.68 % (803385)Time elapsed: 0.068 s
% 4.68/1.68 % (803385)Peak memory usage: 90 MB
% 4.68/1.68 % (803385)Instructions burned: 141 (million)
% 4.68/1.68 % (803386)Instruction limit reached!
% 4.68/1.68 % (803386)------------------------------
% 4.68/1.68 % (803386)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.68/1.68 % (803386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.68/1.68 % (803386)CaDiCaL version: 2.1.3
% 4.68/1.68 % (803386)Termination reason: Instruction limit
% 4.68/1.68 % (803386)Termination phase: Saturation
% 4.68/1.68 % (803386)Time elapsed: 0.070 s
% 4.68/1.68 % (803386)Peak memory usage: 89 MB
% 4.68/1.68 % (803386)Instructions burned: 130 (million)
% 4.68/1.68 % (803394)lrs+10_1_sil=8000:sp=occurrence:random_seed=3520256187:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.68/1.68 % (803394)Instruction limit reached!
% 4.68/1.68 % (803394)------------------------------
% 4.68/1.68 % (803394)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.68/1.68 % (803394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.68/1.68 % (803394)CaDiCaL version: 2.1.3
% 4.68/1.68 % (803394)Termination reason: Instruction limit
% 4.68/1.68 % (803394)Termination phase: Saturation
% 4.68/1.68 % (803394)Time elapsed: 0.090 s
% 4.68/1.68 % (803394)Peak memory usage: 94 MB
% 4.68/1.68 % (803394)Instructions burned: 287 (million)
% 4.68/1.68 % (803396)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3403104296:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.68/1.68 % (803397)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=3812421797:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.68/1.68 % (803395)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1799519135:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.68/1.68 % (803399)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1757776835:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.68/1.68 % (803395)Instruction limit reached!
% 4.68/1.68 % (803395)------------------------------
% 4.68/1.68 % (803395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.68/1.68 % (803395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.68/1.68 % (803395)CaDiCaL version: 2.1.3
% 4.68/1.68 % (803395)Termination reason: Instruction limit
% 4.68/1.68 % (803395)Termination phase: Saturation
% 4.68/1.68 % (803395)Time elapsed: 0.091 s
% 4.68/1.68 % (803395)Peak memory usage: 90 MB
% 4.68/1.68 % (803395)Instructions burned: 158 (million)
% 4.68/1.68 % (803399)Refutation not found, incomplete strategy
% 4.68/1.68 % (803399)------------------------------
% 4.68/1.68 % (803399)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.68/1.68 % (803399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.68/1.68 % (803399)CaDiCaL version: 2.1.3
% 4.68/1.68 % (803399)Termination reason: Refutation not found, incomplete strategy
% 4.68/1.68 % (803399)Time elapsed: 0.022 s
% 4.68/1.68 % (803399)Peak memory usage: 89 MB
% 4.68/1.68 % (803399)Instructions burned: 68 (million)
% 4.68/1.68 % (803396)First to succeed.
% 4.68/1.68 % (803397)Instruction limit reached!
% 4.68/1.68 % (803397)------------------------------
% 4.68/1.68 % (803397)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.68/1.68 % (803397)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.68/1.68 % (803397)CaDiCaL version: 2.1.3
% 4.68/1.68 % (803397)Termination reason: Instruction limit
% 4.68/1.68 % (803397)Termination phase: Saturation
% 4.68/1.68 % (803397)Time elapsed: 0.146 s
% 4.68/1.68 % (803397)Peak memory usage: 91 MB
% 4.68/1.68 % (803397)Instructions burned: 248 (million)
% 4.68/1.68 % (803396)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-803375"
% 4.68/1.68 % (803404)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1636826503:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.68/1.68 % (803399)------------------------------
% 4.68/1.68 % (803399)------------------------------
% 4.68/1.68 % (803405)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1461726236:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.68/1.68 % (803405)Instruction limit reached!
% 4.68/1.68 % (803405)------------------------------
% 4.68/1.68 % (803405)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.68/1.68 % (803405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.68/1.68 % (803405)CaDiCaL version: 2.1.3
% 4.68/1.68 % (803405)Termination reason: Instruction limit
% 4.68/1.68 % (803405)Termination phase: Saturation
% 4.68/1.68 % (803405)Time elapsed: 0.080 s
% 4.68/1.68 % (803405)Peak memory usage: 90 MB
% 4.68/1.68 % (803405)Instructions burned: 114 (million)
% 4.68/1.68 % (803407)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3777857650:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 4.68/1.68 % (803396)Refutation found. Thanks to Tanya!
% 4.68/1.68 % SZS status Theorem for theBenchmark
% 4.68/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 6.35/1.87 % (803396)------------------------------
% 6.35/1.87 % (803396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.35/1.87 % (803396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.35/1.87 % (803396)CaDiCaL version: 2.1.3
% 6.35/1.87 % (803396)Termination reason: Refutation
% 6.35/1.87 % (803396)Time elapsed: 0.150 s
% 6.35/1.87 % (803396)Peak memory usage: 93 MB
% 6.35/1.87 % (803396)Instructions burned: 228 (million)
% 6.35/1.87 % (803396)------------------------------
% 6.35/1.87 % (803396)------------------------------
% 6.35/1.87 % (803375)Success in time 0.816 s
% 6.35/1.87 % Vampire exiting
%------------------------------------------------------------------------------