%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU462^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 : Wed Sep 30 08:29:43 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 27
% Syntax : Number of formulae : 222 ( 56 unt; 0 typ; 23 def)
% Number of atoms : 1627 ( 348 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 2243 ( 219 ~; 397 |; 71 &;1344 @)
% ( 19 <=>; 81 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 242 ( 242 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 75 usr; 28 con; 0-4 aty)
% ( 112 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 317 ( 0 sgn 113 !; 12 ?; 317 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
subrel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_2,type,
inv: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_3,type,
idem: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_4,type,
infl: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_5,type,
mono: ( ( $i > $i > $o ) > $i > $i > $o ) > $o ).
thf(func_def_6,type,
refl: ( $i > $i > $o ) > $o ).
thf(func_def_7,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(func_def_8,type,
rc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_9,type,
symm: ( $i > $i > $o ) > $o ).
thf(func_def_10,type,
antisymm: ( $i > $i > $o ) > $o ).
thf(func_def_11,type,
asymm: ( $i > $i > $o ) > $o ).
thf(func_def_12,type,
sc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_13,type,
trans: ( $i > $i > $o ) > $o ).
thf(func_def_14,type,
tc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_15,type,
trc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
trsc: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_17,type,
po: ( $i > $i > $o ) > $o ).
thf(func_def_18,type,
so: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
total: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
term: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
ind: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
innf: ( $i > $i > $o ) > $i > $o ).
thf(func_def_23,type,
nfof: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_24,type,
norm: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
join: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
lconfl: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
sconfl: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
confl: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
cr: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vIMP: $o > $o > $o ).
thf(func_def_32,type,
vAND: $o > $o > $o ).
thf(func_def_33,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_38,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vOR: $o > $o > $o ).
thf(func_def_40,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_45,type,
sK1: $i > $i > $o ).
thf(func_def_46,type,
sK2: $i > $i > $o ).
thf(func_def_48,type,
sF4: $o ).
thf(func_def_49,type,
sF5: $o ).
thf(func_def_50,type,
sF6: $o ).
thf(func_def_51,type,
sF7: $o ).
thf(func_def_52,type,
sK8: $i > $i > $o ).
thf(func_def_53,type,
sK9: ( $i > $i > $o ) > $i ).
thf(func_def_54,type,
sK10: ( $i > $i > $o ) > $i ).
thf(func_def_55,type,
sK11: ( $i > $i > $o ) > $i ).
thf(func_def_56,type,
sK12: ( $i > $i > $o ) > $i ).
thf(func_def_57,type,
sK13: ( $i > $i > $o ) > $i ).
thf(f1,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X3: $i,X2: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
= subrel ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',subrel) ).
thf(f13,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $i,X2: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
= trans ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',transitive) ).
thf(f14,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ( ( trans @ X3 )
& ( subrel @ X0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) )
= tc ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',transitive_closure) ).
thf(f30,conjecture,
! [X2: $i,X0: $i > $i > $o,X1: $i,X3: $i > $i > $o] :
( ( ( subrel @ X0 @ X3 )
& ( tc @ X0 @ X1 @ X2 )
& ( trans @ X3 ) )
=> ( X3 @ X1 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitive_closure_is_transitive2) ).
thf(f31,negated_conjecture,
~ ! [X2: $i,X0: $i > $i > $o,X1: $i,X3: $i > $i > $o] :
( ( ( subrel @ X0 @ X3 )
& ( tc @ X0 @ X1 @ X2 )
& ( trans @ X3 ) )
=> ( X3 @ X1 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f45,plain,
( ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
! [X3: $i > $i > $o] :
( ( ( trans @ X3 )
& ( subrel @ X0 @ X3 ) )
=> ( X3 @ X1 @ X2 ) ) )
= tc ),
inference(rectify,[],[f14]) ).
thf(f46,plain,
( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( subrel @ Y0 @ Y3 )
& ( trans @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f56,plain,
~ ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i > $i > $o] :
( ( ( subrel @ X1 @ X3 )
& ( tc @ X1 @ X2 @ X0 )
& ( trans @ X3 ) )
=> ( X3 @ X2 @ X0 ) ),
inference(rectify,[],[f31]) ).
thf(f57,plain,
~ ! [X3: $i > $i > $o,X2: $i,X0: $i,X1: $i > $i > $o] :
( ( ( ( subrel @ X1 @ X3 )
= $true )
& ( ( tc @ X1 @ X2 @ X0 )
= $true )
& ( ( trans @ X3 )
= $true ) )
=> ( ( X3 @ X2 @ X0 )
= $true ) ),
inference(fool_elimination,[],[f56]) ).
thf(f65,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X3 @ X2 )
=> ( X1 @ X3 @ X2 ) ) )
= subrel ),
inference(rectify,[],[f1]) ).
thf(f66,plain,
( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f69,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X1 @ X2 ) ) )
= trans ),
inference(rectify,[],[f13]) ).
thf(f70,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f88,plain,
? [X3: $i > $i > $o,X2: $i,X0: $i,X1: $i > $i > $o] :
( ( ( X3 @ X2 @ X0 )
!= $true )
& ( ( subrel @ X1 @ X3 )
= $true )
& ( ( tc @ X1 @ X2 @ X0 )
= $true )
& ( ( trans @ X3 )
= $true ) ),
inference(ennf_transformation,[],[f57]) ).
thf(f89,plain,
? [X0: $i,X3: $i > $i > $o,X1: $i > $i > $o,X2: $i] :
( ( ( trans @ X3 )
= $true )
& ( ( X3 @ X2 @ X0 )
!= $true )
& ( ( tc @ X1 @ X2 @ X0 )
= $true )
& ( ( subrel @ X1 @ X3 )
= $true ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
? [X0: $i,X1: $i > $i > $o,X2: $i > $i > $o,X3: $i] :
( ( $true
= ( trans @ X1 ) )
& ( $true
!= ( X1 @ X3 @ X0 ) )
& ( $true
= ( tc @ X2 @ X3 @ X0 ) )
& ( $true
= ( subrel @ X2 @ X1 ) ) ),
inference(rectify,[],[f89]) ).
thf(f91,plain,
( ( ( trans @ sK1 )
= $true )
& ( $true
!= ( sK1 @ sK3 @ sK0 ) )
& ( $true
= ( tc @ sK2 @ sK3 @ sK0 ) )
& ( ( subrel @ sK2 @ sK1 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f90]) ).
thf(f92,plain,
( ( subrel @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[],[f91]) ).
thf(f93,plain,
( $true
= ( tc @ sK2 @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f94,plain,
( $true
!= ( sK1 @ sK3 @ sK0 ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f95,plain,
( ( trans @ sK1 )
= $true ),
inference(cnf_transformation,[],[f91]) ).
thf(f96,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f112,plain,
( subrel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f120,plain,
( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( subrel @ Y0 @ Y3 )
& ( trans @ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f129,plain,
( tc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( ^ [Y4: $i > $i > $o,Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
@ Y0
@ Y3 )
& ( ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
@ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ),
inference(definition_unfolding,[],[f120,f112,f96]) ).
thf(f142,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK1 ) ),
inference(definition_unfolding,[],[f95,f96]) ).
thf(f143,plain,
( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( ^ [Y4: $i > $i > $o,Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
@ Y0
@ Y3 )
& ( ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
@ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ sK2
@ sK3
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f93,f129]) ).
thf(f144,plain,
( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
@ sK2
@ sK1 )
= $true ),
inference(definition_unfolding,[],[f92,f112]) ).
thf(f145,definition,
( sF4
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f146,plain,
sF4 = $true,
inference(definition_folding,[],[f142,f145]) ).
thf(f147,definition,
( sF5
= ( sK1 @ sK3 @ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f148,plain,
( ( sK1 @ sK3 @ sK0 )
= sF5 ),
inference(reorient_equations,[],[f147]) ).
thf(f149,plain,
$true != sF5,
inference(definition_folding,[],[f94,f148]) ).
thf(f150,definition,
( sF6
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( ^ [Y4: $i > $i > $o,Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
@ Y0
@ Y3 )
& ( ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
@ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ sK2
@ sK3
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f151,plain,
( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( ^ [Y4: $i > $i > $o,Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
@ Y0
@ Y3 )
& ( ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
@ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ sK2
@ sK3
@ sK0 )
= sF6 ),
inference(reorient_equations,[],[f150]) ).
thf(f152,plain,
sF6 = $true,
inference(definition_folding,[],[f143,f151]) ).
thf(f153,definition,
( sF7
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
@ sK2
@ sK1 ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f154,plain,
( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
@ sK2
@ sK1 )
= sF7 ),
inference(reorient_equations,[],[f153]) ).
thf(f155,plain,
$true = sF7,
inference(definition_folding,[],[f144,f154]) ).
thf(f156,plain,
( ( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y3: $i > $i > $o] :
( ( ( ^ [Y4: $i > $i > $o,Y5: $i > $i > $o] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y6 @ Y7 ) ) ) )
@ Y0
@ Y3 )
& ( ^ [Y4: $i > $i > $o] :
( !! @ $i
@ ^ [Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( ( Y4 @ Y7 @ Y5 )
& ( Y4 @ Y5 @ Y6 ) )
=> ( Y4 @ Y7 @ Y6 ) ) ) ) )
@ Y3 ) )
=> ( Y3 @ Y1 @ Y2 ) ) )
@ sK2
@ sK3
@ sK0 )
= $true )
| ( $false = sF6 ) ),
inference(iff_proxy_clausification,[],[f151]) ).
thf(f178,plain,
( ( $false = sF6 )
| ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f179,plain,
! [X1: $i > $i > $o] :
( ( $false = sF6 )
| ( ( ^ [Y0: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( sK2 @ Y1 @ Y2 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
=> ( Y0 @ sK3 @ sK0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) ) )
=> ( X1 @ sK3 @ sK0 ) ) )
| ( $false = sF6 ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X1: $i > $i > $o] :
( ( $false = sF6 )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i > $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) ) )
= $false )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $false = sF6 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) ) )
| ( $false = sF6 )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) )
@ ( sK9 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) )
@ ( sK10 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( X1 @ Y0 @ Y1 ) ) )
@ ( sK9 @ X1 ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $false = sF6 ) ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ ( sK9 @ X1 ) @ Y0 )
=> ( X1 @ ( sK9 @ X1 ) @ Y0 ) ) ) )
| ( $false = sF6 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( X1 @ Y1 @ ( sK10 @ X1 ) )
& ( X1 @ ( sK10 @ X1 ) @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $false = sF6 )
| ( ( ^ [Y0: $i] :
( ( sK2 @ ( sK9 @ X1 ) @ Y0 )
=> ( X1 @ ( sK9 @ X1 ) @ Y0 ) )
@ ( sK11 @ X1 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( X1 @ Y1 @ ( sK10 @ X1 ) )
& ( X1 @ ( sK10 @ X1 ) @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( X1 @ Y1 @ ( sK10 @ X1 ) )
& ( X1 @ ( sK10 @ X1 ) @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) )
@ ( sK12 @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( sK2 @ ( sK9 @ X1 ) @ Y0 )
=> ( X1 @ ( sK9 @ X1 ) @ Y0 ) )
@ ( sK11 @ X1 ) )
= $false )
| ( $false = sF6 ) ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( X1 @ Y0 @ ( sK10 @ X1 ) )
& ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) ) )
=> ( X1 @ Y0 @ ( sK12 @ X1 ) ) ) ) )
| ( $false = sF6 )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $false
= ( ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
=> ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
=> ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( X1 @ Y0 @ ( sK10 @ X1 ) )
& ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) ) )
=> ( X1 @ Y0 @ ( sK12 @ X1 ) ) )
@ ( sK13 @ X1 ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $false = sF6 ) ),
inference(sigma_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( X1 @ Y0 @ ( sK10 @ X1 ) )
& ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) ) )
=> ( X1 @ Y0 @ ( sK12 @ X1 ) ) )
@ ( sK13 @ X1 ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
= $false )
| ( $false = sF6 ) ),
inference(imp_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $false = sF6 )
| ( $true
= ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( X1 @ Y0 @ ( sK10 @ X1 ) )
& ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) ) )
=> ( X1 @ Y0 @ ( sK12 @ X1 ) ) )
@ ( sK13 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f189]) ).
thf(f192,plain,
! [X1: $i > $i > $o] :
( ( $false = sF6 )
| ( $true
= ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) )
| ( $false
= ( ( ( X1 @ ( sK13 @ X1 ) @ ( sK10 @ X1 ) )
& ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) ) )
=> ( X1 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X1: $i > $i > $o] :
( ( $false = sF6 )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $true
= ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) )
| ( $false
= ( X1 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i > $i > $o] :
( ( $false = sF6 )
| ( $true
= ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( ( ( X1 @ ( sK13 @ X1 ) @ ( sK10 @ X1 ) )
& ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f195,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) )
| ( $false = sF6 )
| ( ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) )
= $true )
| ( $true
= ( X1 @ sK3 @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ ( sK13 @ X1 ) @ ( sK10 @ X1 ) ) )
| ( $true
= ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) )
| ( $false = sF6 )
| ( $true
= ( X1 @ sK3 @ sK0 ) ) ),
inference(and_proxy_clausification,[],[f194]) ).
thf(f197,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
= $false )
| ( $false = sF6 )
| ( $false
= ( ( ( X1 @ ( sK13 @ X1 ) @ ( sK10 @ X1 ) )
& ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) ) )
=> ( X1 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f198,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) ) )
| ( ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $false = sF6 ) ),
inference(imp_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X1: $i > $i > $o] :
( ( $false = sF6 )
| ( ( ( X1 @ ( sK13 @ X1 ) @ ( sK10 @ X1 ) )
& ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) ) )
= $true )
| ( ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK3 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f197]) ).
thf(f200,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) )
= $true )
| ( $false = sF6 )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i > $i > $o] :
( ( $false = sF6 )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $true
= ( X1 @ ( sK13 @ X1 ) @ ( sK10 @ X1 ) ) )
| ( ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f199]) ).
thf(f203,plain,
( ( sF4 = $false )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK1 ) ) ),
inference(iff_proxy_clausification,[],[f145]) ).
thf(f204,plain,
( ( sF4 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y0 )
& ( sK1 @ Y0 @ Y1 ) )
=> ( sK1 @ Y2 @ Y1 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( sF4 = $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y0 )
& ( sK1 @ Y0 @ Y1 ) )
=> ( sK1 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK1 @ Y1 @ X1 )
& ( sK1 @ X1 @ Y0 ) )
=> ( sK1 @ Y1 @ Y0 ) ) ) ) )
| ( sF4 = $false ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK1 @ Y1 @ X1 )
& ( sK1 @ X1 @ Y0 ) )
=> ( sK1 @ Y1 @ Y0 ) ) )
@ X2 )
= $true )
| ( sF4 = $false ) ),
inference(pi_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( sF4 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK1 @ Y0 @ X1 )
& ( sK1 @ X1 @ X2 ) )
=> ( sK1 @ Y0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF4 = $false )
| ( ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 @ X1 )
& ( sK1 @ X1 @ X2 ) )
=> ( sK1 @ Y0 @ X2 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF4 = $false )
| ( ( ( ( sK1 @ X3 @ X1 )
& ( sK1 @ X1 @ X2 ) )
=> ( sK1 @ X3 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK1 @ X3 @ X2 )
= $true )
| ( sF4 = $false )
| ( $false
= ( ( sK1 @ X3 @ X1 )
& ( sK1 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK1 @ X3 @ X1 ) )
| ( ( sK1 @ X1 @ X2 )
= $false )
| ( ( sK1 @ X3 @ X2 )
= $true )
| ( sF4 = $false ) ),
inference(and_proxy_clausification,[],[f211]) ).
thf(f224,plain,
( ( $false = sF7 )
| ( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y2 @ Y3 ) ) ) )
@ sK2
@ sK1 )
= $true ) ),
inference(iff_proxy_clausification,[],[f154]) ).
thf(f233,plain,
( ( $false = sF7 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK1 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f234,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y0 @ Y1 )
=> ( sK1 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( $false = sF7 ) ),
inference(pi_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X1: $i] :
( ( $false = sF7 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ X1 @ Y0 )
=> ( sK1 @ X1 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X1: $i] :
( ( $false = sF7 )
| ( ( ^ [Y0: $i] :
( ( sK2 @ X1 @ Y0 )
=> ( sK1 @ X1 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( sK2 @ X1 @ X2 )
=> ( sK1 @ X1 @ X2 ) ) )
| ( $false = sF7 ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 @ X2 )
= $true )
| ( $false
= ( sK2 @ X1 @ X2 ) )
| ( $false = sF7 ) ),
inference(imp_proxy_clausification,[],[f237]) ).
thf(f240,plain,
( ( $true = sF5 )
| ( $false
= ( sK1 @ sK3 @ sK0 ) ) ),
inference(iff_proxy_clausification,[],[f148]) ).
thf(f242,definition,
( spl19_1
<=> ( sF6 = $true ) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
thf(f244,plain,
( ( sF6 = $true )
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f242]) ).
thf(f259,definition,
( spl19_5
<=> ! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ ( sK13 @ X1 ) @ ( sK10 @ X1 ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $true
= ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_5])],[avatar_definition]) ).
thf(f260,plain,
( ! [X1: $i > $i > $o] :
( ( $true
= ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $true
= ( X1 @ ( sK13 @ X1 ) @ ( sK10 @ X1 ) ) ) )
| ~ spl19_5 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f262,definition,
( spl19_6
<=> ( $false = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl19_6])],[avatar_definition]) ).
thf(f264,plain,
( ( $false = sF6 )
| ~ spl19_6 ),
inference(avatar_component_clause,[],[f262]) ).
thf(f265,plain,
( spl19_5
| spl19_6 ),
inference(avatar_split_clause,[],[f196,f262,f259]) ).
thf(f267,definition,
( spl19_7
<=> ! [X1: $i > $i > $o] :
( ( $true
= ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl19_7])],[avatar_definition]) ).
thf(f268,plain,
( ! [X1: $i > $i > $o] :
( ( $true
= ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) )
= $true ) )
| ~ spl19_7 ),
inference(avatar_component_clause,[],[f267]) ).
thf(f269,plain,
( spl19_6
| spl19_7 ),
inference(avatar_split_clause,[],[f195,f267,f262]) ).
thf(f271,definition,
( spl19_8
<=> ! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( $false
= ( X1 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) ) )
| ( $true
= ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_8])],[avatar_definition]) ).
thf(f272,plain,
( ! [X1: $i > $i > $o] :
( ( $true
= ( sK2 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) ) )
| ( $false
= ( X1 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) ) )
| ~ spl19_8 ),
inference(avatar_component_clause,[],[f271]) ).
thf(f273,plain,
( spl19_8
| spl19_6 ),
inference(avatar_split_clause,[],[f193,f262,f271]) ).
thf(f275,definition,
( spl19_9
<=> ! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
= $false )
| ( $true
= ( X1 @ ( sK13 @ X1 ) @ ( sK10 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_9])],[avatar_definition]) ).
thf(f276,plain,
( ! [X1: $i > $i > $o] :
( ( $true
= ( X1 @ ( sK13 @ X1 ) @ ( sK10 @ X1 ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
= $false ) )
| ~ spl19_9 ),
inference(avatar_component_clause,[],[f275]) ).
thf(f277,plain,
( spl19_6
| spl19_9 ),
inference(avatar_split_clause,[],[f201,f275,f262]) ).
thf(f279,definition,
( spl19_10
<=> ! [X1: $i > $i > $o] :
( ( ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) )
= $true )
| ( ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK3 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_10])],[avatar_definition]) ).
thf(f280,plain,
( ! [X1: $i > $i > $o] :
( ( ( X1 @ ( sK10 @ X1 ) @ ( sK12 @ X1 ) )
= $true )
| ( ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK3 @ sK0 ) ) )
| ~ spl19_10 ),
inference(avatar_component_clause,[],[f279]) ).
thf(f281,plain,
( spl19_6
| spl19_10 ),
inference(avatar_split_clause,[],[f200,f279,f262]) ).
thf(f283,definition,
( spl19_11
<=> ! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) ) )
| ( $true
= ( X1 @ sK3 @ sK0 ) )
| ( ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl19_11])],[avatar_definition]) ).
thf(f284,plain,
( ! [X1: $i > $i > $o] :
( ( $false
= ( X1 @ ( sK13 @ X1 ) @ ( sK12 @ X1 ) ) )
| ( ( X1 @ ( sK9 @ X1 ) @ ( sK11 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK3 @ sK0 ) ) )
| ~ spl19_11 ),
inference(avatar_component_clause,[],[f283]) ).
thf(f285,plain,
( spl19_6
| spl19_11 ),
inference(avatar_split_clause,[],[f198,f283,f262]) ).
thf(f286,plain,
spl19_1,
inference(avatar_split_clause,[],[f152,f242]) ).
thf(f288,definition,
( spl19_12
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( sK1 @ X3 @ X1 ) )
| ( ( sK1 @ X3 @ X2 )
= $true )
| ( ( sK1 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl19_12])],[avatar_definition]) ).
thf(f289,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK1 @ X3 @ X1 ) )
| ( ( sK1 @ X3 @ X2 )
= $true )
| ( ( sK1 @ X1 @ X2 )
= $false ) )
| ~ spl19_12 ),
inference(avatar_component_clause,[],[f288]) ).
thf(f291,definition,
( spl19_13
<=> ( sF4 = $false ) ),
introduced(definition,[new_symbols(definition,[spl19_13])],[avatar_definition]) ).
thf(f293,plain,
( ( sF4 = $false )
| ~ spl19_13 ),
inference(avatar_component_clause,[],[f291]) ).
thf(f294,plain,
( spl19_12
| spl19_13 ),
inference(avatar_split_clause,[],[f212,f291,f288]) ).
thf(f300,definition,
( spl19_15
<=> ( sF4 = $true ) ),
introduced(definition,[new_symbols(definition,[spl19_15])],[avatar_definition]) ).
thf(f302,plain,
( ( sF4 = $true )
| ~ spl19_15 ),
inference(avatar_component_clause,[],[f300]) ).
thf(f314,plain,
spl19_15,
inference(avatar_split_clause,[],[f146,f300]) ).
thf(f316,definition,
( spl19_18
<=> ( $true = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl19_18])],[avatar_definition]) ).
thf(f318,plain,
( ( $true = sF7 )
| ~ spl19_18 ),
inference(avatar_component_clause,[],[f316]) ).
thf(f330,definition,
( spl19_21
<=> ( $false = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl19_21])],[avatar_definition]) ).
thf(f332,plain,
( ( $false = sF7 )
| ~ spl19_21 ),
inference(avatar_component_clause,[],[f330]) ).
thf(f334,definition,
( spl19_22
<=> ! [X2: $i,X1: $i] :
( ( ( sK1 @ X1 @ X2 )
= $true )
| ( $false
= ( sK2 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_22])],[avatar_definition]) ).
thf(f335,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( sK2 @ X1 @ X2 ) )
| ( ( sK1 @ X1 @ X2 )
= $true ) )
| ~ spl19_22 ),
inference(avatar_component_clause,[],[f334]) ).
thf(f336,plain,
( spl19_21
| spl19_22 ),
inference(avatar_split_clause,[],[f238,f334,f330]) ).
thf(f338,definition,
( spl19_23
<=> ( $false
= ( sK1 @ sK3 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl19_23])],[avatar_definition]) ).
thf(f340,plain,
( ( $false
= ( sK1 @ sK3 @ sK0 ) )
| ~ spl19_23 ),
inference(avatar_component_clause,[],[f338]) ).
thf(f342,definition,
( spl19_24
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl19_24])],[avatar_definition]) ).
thf(f345,plain,
( spl19_23
| spl19_24 ),
inference(avatar_split_clause,[],[f240,f342,f338]) ).
thf(f355,plain,
spl19_18,
inference(avatar_split_clause,[],[f155,f316]) ).
thf(f356,plain,
~ spl19_24,
inference(avatar_split_clause,[],[f149,f342]) ).
thf(f372,plain,
( ( $false = $true )
| ~ spl19_18
| ~ spl19_21 ),
inference(forward_demodulation,[],[f318,f332]) ).
thf(f373,plain,
( $false
| ~ spl19_18
| ~ spl19_21 ),
inference(trivial_inequality_removal,[],[f372]) ).
thf(f374,plain,
( ~ spl19_18
| ~ spl19_21 ),
inference(avatar_contradiction_clause,[],[f373]) ).
thf(f379,plain,
( ( $false = $true )
| ~ spl19_1
| ~ spl19_6 ),
inference(forward_demodulation,[],[f264,f244]) ).
thf(f380,plain,
( $false
| ~ spl19_1
| ~ spl19_6 ),
inference(trivial_inequality_removal,[],[f379]) ).
thf(f381,plain,
( ~ spl19_1
| ~ spl19_6 ),
inference(avatar_contradiction_clause,[],[f380]) ).
thf(f390,plain,
( ! [X0: $i > $i > $o] :
( ( $true
= ( X0 @ sK3 @ sK0 ) )
| ( $false
= ( X0 @ ( sK13 @ X0 ) @ ( sK12 @ X0 ) ) )
| ( ( sK1 @ ( sK9 @ X0 ) @ ( sK11 @ X0 ) )
= $true )
| ( $false = $true ) )
| ~ spl19_8
| ~ spl19_22 ),
inference(constrained_superposition,[],[f272,f335]) ).
thf(f392,plain,
( ! [X0: $i > $i > $o] :
( ( $false
= ( X0 @ ( sK13 @ X0 ) @ ( sK12 @ X0 ) ) )
| ( $true
= ( X0 @ sK3 @ sK0 ) )
| ( ( sK1 @ ( sK9 @ X0 ) @ ( sK11 @ X0 ) )
= $true ) )
| ~ spl19_8
| ~ spl19_22 ),
inference(trivial_inequality_removal,[],[f390]) ).
thf(f397,plain,
( ! [X0: $i > $i > $o] :
( ( ( X0 @ ( sK13 @ X0 ) @ ( sK10 @ X0 ) )
= $true )
| ( ( sK1 @ ( sK9 @ X0 ) @ ( sK11 @ X0 ) )
= $true )
| ( $false = $true )
| ( $true
= ( X0 @ sK3 @ sK0 ) ) )
| ~ spl19_5
| ~ spl19_22 ),
inference(constrained_superposition,[],[f335,f260]) ).
thf(f398,plain,
( ! [X0: $i > $i > $o] :
( ( ( sK1 @ ( sK9 @ X0 ) @ ( sK11 @ X0 ) )
= $true )
| ( $true
= ( X0 @ sK3 @ sK0 ) )
| ( ( X0 @ ( sK13 @ X0 ) @ ( sK10 @ X0 ) )
= $true ) )
| ~ spl19_5
| ~ spl19_22 ),
inference(trivial_inequality_removal,[],[f397]) ).
thf(f400,plain,
( ! [X0: $i > $i > $o] :
( ( $true
= ( X0 @ sK3 @ sK0 ) )
| ( $false = $true )
| ( ( sK1 @ ( sK9 @ X0 ) @ ( sK11 @ X0 ) )
= $true )
| ( $true
= ( X0 @ ( sK10 @ X0 ) @ ( sK12 @ X0 ) ) ) )
| ~ spl19_7
| ~ spl19_22 ),
inference(constrained_superposition,[],[f268,f335]) ).
thf(f402,plain,
( ! [X0: $i > $i > $o] :
( ( $true
= ( X0 @ ( sK10 @ X0 ) @ ( sK12 @ X0 ) ) )
| ( $true
= ( X0 @ sK3 @ sK0 ) )
| ( ( sK1 @ ( sK9 @ X0 ) @ ( sK11 @ X0 ) )
= $true ) )
| ~ spl19_7
| ~ spl19_22 ),
inference(trivial_inequality_removal,[],[f400]) ).
thf(f431,definition,
( spl19_30
<=> ! [X0: $i] :
( ( $true
= ( sK1 @ ( sK13 @ sK1 ) @ X0 ) )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_30])],[avatar_definition]) ).
thf(f432,plain,
( ! [X0: $i] :
( ( $true
= ( sK1 @ ( sK13 @ sK1 ) @ X0 ) )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ X0 ) ) )
| ~ spl19_30 ),
inference(avatar_component_clause,[],[f431]) ).
thf(f434,definition,
( spl19_31
<=> ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_31])],[avatar_definition]) ).
thf(f436,plain,
( ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ~ spl19_31 ),
inference(avatar_component_clause,[],[f434]) ).
thf(f439,plain,
( ( $false = $true )
| ~ spl19_13
| ~ spl19_15 ),
inference(forward_demodulation,[],[f293,f302]) ).
thf(f440,plain,
( $false
| ~ spl19_13
| ~ spl19_15 ),
inference(trivial_inequality_removal,[],[f439]) ).
thf(f441,plain,
( ~ spl19_13
| ~ spl19_15 ),
inference(avatar_contradiction_clause,[],[f440]) ).
thf(f445,plain,
( ! [X0: $i] :
( ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ( $true
= ( sK1 @ ( sK13 @ sK1 ) @ X0 ) )
| ( $false = $true )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ X0 ) )
| ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) ) )
| ~ spl19_9
| ~ spl19_12 ),
inference(constrained_superposition,[],[f276,f289]) ).
thf(f451,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ( $true
= ( sK1 @ ( sK13 @ sK1 ) @ X0 ) )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ X0 ) ) )
| ~ spl19_9
| ~ spl19_12 ),
inference(trivial_inequality_removal,[],[f445]) ).
thf(f454,plain,
( ! [X0: $i] :
( ( $true
= ( sK1 @ ( sK13 @ sK1 ) @ X0 ) )
| ( $false = $true )
| ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ X0 ) ) )
| ~ spl19_9
| ~ spl19_12
| ~ spl19_23 ),
inference(forward_demodulation,[],[f451,f340]) ).
thf(f455,plain,
( ! [X0: $i] :
( ( $true
= ( sK1 @ ( sK13 @ sK1 ) @ X0 ) )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ X0 ) )
| ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) ) )
| ~ spl19_9
| ~ spl19_12
| ~ spl19_23 ),
inference(trivial_inequality_removal,[],[f454]) ).
thf(f457,plain,
( spl19_31
| spl19_30
| ~ spl19_9
| ~ spl19_12
| ~ spl19_23 ),
inference(avatar_split_clause,[],[f455,f338,f288,f275,f431,f434]) ).
thf(f465,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ ( sK12 @ sK1 ) ) )
| ( $false = $true )
| ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ~ spl19_11
| ~ spl19_30 ),
inference(constrained_superposition,[],[f284,f432]) ).
thf(f469,plain,
( ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ ( sK12 @ sK1 ) ) )
| ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ~ spl19_11
| ~ spl19_30 ),
inference(trivial_inequality_removal,[],[f465]) ).
thf(f472,plain,
( ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ ( sK12 @ sK1 ) ) )
| ( $false = $true )
| ~ spl19_11
| ~ spl19_23
| ~ spl19_30 ),
inference(forward_demodulation,[],[f469,f340]) ).
thf(f473,plain,
( ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ ( sK12 @ sK1 ) ) )
| ~ spl19_11
| ~ spl19_23
| ~ spl19_30 ),
inference(trivial_inequality_removal,[],[f472]) ).
thf(f475,definition,
( spl19_32
<=> ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ ( sK12 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl19_32])],[avatar_definition]) ).
thf(f477,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ ( sK12 @ sK1 ) ) )
| ~ spl19_32 ),
inference(avatar_component_clause,[],[f475]) ).
thf(f479,plain,
( spl19_32
| spl19_31
| ~ spl19_11
| ~ spl19_23
| ~ spl19_30 ),
inference(avatar_split_clause,[],[f473,f431,f338,f283,f434,f475]) ).
thf(f539,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ ( sK12 @ sK1 ) ) )
| ( $false = $true )
| ( $true
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ~ spl19_8
| ~ spl19_22
| ~ spl19_30 ),
inference(constrained_superposition,[],[f392,f432]) ).
thf(f548,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ ( sK12 @ sK1 ) ) )
| ( $true
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ~ spl19_8
| ~ spl19_22
| ~ spl19_30 ),
inference(trivial_inequality_removal,[],[f539]) ).
thf(f557,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ ( sK12 @ sK1 ) ) )
| ( $false = $true )
| ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ~ spl19_8
| ~ spl19_22
| ~ spl19_30
| ~ spl19_31 ),
inference(forward_demodulation,[],[f548,f436]) ).
thf(f558,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ ( sK12 @ sK1 ) ) )
| ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ~ spl19_8
| ~ spl19_22
| ~ spl19_30
| ~ spl19_31 ),
inference(trivial_inequality_removal,[],[f557]) ).
thf(f569,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ ( sK12 @ sK1 ) ) )
| ( $false = $true )
| ~ spl19_8
| ~ spl19_22
| ~ spl19_23
| ~ spl19_30
| ~ spl19_31 ),
inference(forward_demodulation,[],[f558,f340]) ).
thf(f570,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ ( sK12 @ sK1 ) ) )
| ~ spl19_8
| ~ spl19_22
| ~ spl19_23
| ~ spl19_30
| ~ spl19_31 ),
inference(trivial_inequality_removal,[],[f569]) ).
thf(f575,plain,
( spl19_32
| ~ spl19_8
| ~ spl19_22
| ~ spl19_23
| ~ spl19_30
| ~ spl19_31 ),
inference(avatar_split_clause,[],[f570,f434,f431,f338,f334,f271,f475]) ).
thf(f588,plain,
( ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ( $false = $true )
| ( ( sK1 @ ( sK13 @ sK1 ) @ ( sK10 @ sK1 ) )
= $true )
| ~ spl19_5
| ~ spl19_22
| ~ spl19_31 ),
inference(constrained_superposition,[],[f398,f436]) ).
thf(f592,plain,
( ( ( sK1 @ ( sK13 @ sK1 ) @ ( sK10 @ sK1 ) )
= $true )
| ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ~ spl19_5
| ~ spl19_22
| ~ spl19_31 ),
inference(trivial_inequality_removal,[],[f588]) ).
thf(f596,plain,
( ( ( sK1 @ ( sK13 @ sK1 ) @ ( sK10 @ sK1 ) )
= $true )
| ( $false = $true )
| ~ spl19_5
| ~ spl19_22
| ~ spl19_23
| ~ spl19_31 ),
inference(forward_demodulation,[],[f592,f340]) ).
thf(f597,plain,
( ( ( sK1 @ ( sK13 @ sK1 ) @ ( sK10 @ sK1 ) )
= $true )
| ~ spl19_5
| ~ spl19_22
| ~ spl19_23
| ~ spl19_31 ),
inference(trivial_inequality_removal,[],[f596]) ).
thf(f600,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ X0 ) )
| ( $true
= ( sK1 @ ( sK13 @ sK1 ) @ X0 ) ) )
| ~ spl19_5
| ~ spl19_12
| ~ spl19_22
| ~ spl19_23
| ~ spl19_31 ),
inference(constrained_superposition,[],[f597,f289]) ).
thf(f602,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) @ X0 ) )
| ( $true
= ( sK1 @ ( sK13 @ sK1 ) @ X0 ) ) )
| ~ spl19_5
| ~ spl19_12
| ~ spl19_22
| ~ spl19_23
| ~ spl19_31 ),
inference(trivial_inequality_removal,[],[f600]) ).
thf(f604,plain,
( spl19_30
| ~ spl19_5
| ~ spl19_12
| ~ spl19_22
| ~ spl19_23
| ~ spl19_31 ),
inference(avatar_split_clause,[],[f602,f434,f338,f334,f288,f259,f431]) ).
thf(f614,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ~ spl19_10
| ~ spl19_32 ),
inference(constrained_superposition,[],[f477,f280]) ).
thf(f617,plain,
( ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ~ spl19_10
| ~ spl19_32 ),
inference(trivial_inequality_removal,[],[f614]) ).
thf(f620,plain,
( ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ( $false = $true )
| ~ spl19_10
| ~ spl19_23
| ~ spl19_32 ),
inference(forward_demodulation,[],[f617,f340]) ).
thf(f621,plain,
( ( $false
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ~ spl19_10
| ~ spl19_23
| ~ spl19_32 ),
inference(trivial_inequality_removal,[],[f620]) ).
thf(f624,plain,
( spl19_31
| ~ spl19_10
| ~ spl19_23
| ~ spl19_32 ),
inference(avatar_split_clause,[],[f621,f475,f338,f279,f434]) ).
thf(f717,plain,
( ( $false = $true )
| ( $true
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ~ spl19_7
| ~ spl19_22
| ~ spl19_32 ),
inference(constrained_superposition,[],[f402,f477]) ).
thf(f731,plain,
( ( $true
= ( sK1 @ ( sK9 @ sK1 ) @ ( sK11 @ sK1 ) ) )
| ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ~ spl19_7
| ~ spl19_22
| ~ spl19_32 ),
inference(trivial_inequality_removal,[],[f717]) ).
thf(f735,plain,
( ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ( $false = $true )
| ~ spl19_7
| ~ spl19_22
| ~ spl19_31
| ~ spl19_32 ),
inference(forward_demodulation,[],[f731,f436]) ).
thf(f736,plain,
( ( $true
= ( sK1 @ sK3 @ sK0 ) )
| ~ spl19_7
| ~ spl19_22
| ~ spl19_31
| ~ spl19_32 ),
inference(trivial_inequality_removal,[],[f735]) ).
thf(f740,plain,
( ( $false = $true )
| ~ spl19_7
| ~ spl19_22
| ~ spl19_23
| ~ spl19_31
| ~ spl19_32 ),
inference(forward_demodulation,[],[f736,f340]) ).
thf(f741,plain,
( $false
| ~ spl19_7
| ~ spl19_22
| ~ spl19_23
| ~ spl19_31
| ~ spl19_32 ),
inference(trivial_inequality_removal,[],[f740]) ).
thf(f742,plain,
( ~ spl19_7
| ~ spl19_22
| ~ spl19_23
| ~ spl19_31
| ~ spl19_32 ),
inference(avatar_contradiction_clause,[],[f741]) ).
cnf(s4,plain,
( spl19_5
| spl19_6 ),
inference(sat_conversion,[],[f265]) ).
cnf(s5,plain,
( spl19_6
| spl19_7 ),
inference(sat_conversion,[],[f269]) ).
cnf(s6,plain,
( spl19_6
| spl19_8 ),
inference(sat_conversion,[],[f273]) ).
cnf(s7,plain,
( spl19_6
| spl19_9 ),
inference(sat_conversion,[],[f277]) ).
cnf(s8,plain,
( spl19_6
| spl19_10 ),
inference(sat_conversion,[],[f281]) ).
cnf(s9,plain,
( spl19_6
| spl19_11 ),
inference(sat_conversion,[],[f285]) ).
cnf(s10,plain,
spl19_1,
inference(sat_conversion,[],[f286]) ).
cnf(s11,plain,
( spl19_12
| spl19_13 ),
inference(sat_conversion,[],[f294]) ).
cnf(s15,plain,
spl19_15,
inference(sat_conversion,[],[f314]) ).
cnf(s18,plain,
( spl19_21
| spl19_22 ),
inference(sat_conversion,[],[f336]) ).
cnf(s19,plain,
( spl19_23
| spl19_24 ),
inference(sat_conversion,[],[f345]) ).
cnf(s21,plain,
spl19_18,
inference(sat_conversion,[],[f355]) ).
cnf(s22,plain,
~ spl19_24,
inference(sat_conversion,[],[f356]) ).
cnf(s24,plain,
( ~ spl19_18
| ~ spl19_21 ),
inference(sat_conversion,[],[f374]) ).
cnf(s25,plain,
( ~ spl19_1
| ~ spl19_6 ),
inference(sat_conversion,[],[f381]) ).
cnf(s30,plain,
( ~ spl19_13
| ~ spl19_15 ),
inference(sat_conversion,[],[f441]) ).
cnf(s32,plain,
( ~ spl19_9
| ~ spl19_12
| ~ spl19_23
| spl19_30
| spl19_31 ),
inference(sat_conversion,[],[f457]) ).
cnf(s34,plain,
( ~ spl19_11
| ~ spl19_23
| ~ spl19_30
| spl19_31
| spl19_32 ),
inference(sat_conversion,[],[f479]) ).
cnf(s37,plain,
( ~ spl19_8
| ~ spl19_22
| ~ spl19_23
| ~ spl19_30
| ~ spl19_31
| spl19_32 ),
inference(sat_conversion,[],[f575]) ).
cnf(s39,plain,
( ~ spl19_5
| ~ spl19_12
| ~ spl19_22
| ~ spl19_23
| spl19_30
| ~ spl19_31 ),
inference(sat_conversion,[],[f604]) ).
cnf(s43,plain,
( ~ spl19_10
| ~ spl19_23
| spl19_31
| ~ spl19_32 ),
inference(sat_conversion,[],[f624]) ).
cnf(s48,plain,
( ~ spl19_7
| ~ spl19_22
| ~ spl19_23
| ~ spl19_31
| ~ spl19_32 ),
inference(sat_conversion,[],[f742]) ).
cnf(s50,plain,
~ spl19_21,
inference(rat,[],[s24,s21]) ).
cnf(s51,plain,
spl19_23,
inference(rat,[],[s19,s22]) ).
cnf(s52,plain,
spl19_22,
inference(rat,[],[s18,s50]) ).
cnf(s53,plain,
~ spl19_13,
inference(rat,[],[s30,s15]) ).
cnf(s54,plain,
spl19_12,
inference(rat,[],[s11,s53]) ).
cnf(s55,plain,
~ spl19_6,
inference(rat,[],[s25,s10]) ).
cnf(s56,plain,
spl19_11,
inference(rat,[],[s9,s55]) ).
cnf(s57,plain,
spl19_10,
inference(rat,[],[s8,s55]) ).
cnf(s58,plain,
spl19_9,
inference(rat,[],[s7,s55]) ).
cnf(s59,plain,
spl19_8,
inference(rat,[],[s6,s55]) ).
cnf(s60,plain,
spl19_7,
inference(rat,[],[s5,s55]) ).
cnf(s61,plain,
spl19_5,
inference(rat,[],[s4,s55]) ).
cnf(s62,plain,
spl19_30,
inference(rat,[],[s32,s39,s51,s54,s58,s52,s61]) ).
cnf(s63,plain,
spl19_31,
inference(rat,[],[s34,s43,s51,s56,s62,s57]) ).
cnf(s64,plain,
~ spl19_32,
inference(rat,[],[s48,s60,s52,s51,s63]) ).
cnf(s65,plain,
$false,
inference(rat,[],[s37,s62,s59,s52,s51,s63,s64]) ).
thf(f743,plain,
$false,
inference(avatar_sat_refutation,[],[s65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU462^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.16 % Computer : n011.cluster.edu
% 0.07/0.16 % Model : x86_64 x86_64
% 0.07/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.16 % Memory : 8046.5625MB
% 0.07/0.16 % OS : Linux 6.8.0-71-generic
% 0.07/0.16 % CPULimit : 300
% 0.07/0.16 % WCLimit : 300
% 0.07/0.16 % DateTime : Tue Sep 29 13:42:01 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running higher-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.29 % (112915)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (112927)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2163639881:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (112933)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (112933)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.29 % (112928)lrs+10_16_si=on:nwc=1.5:random_seed=716176650:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (112929)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3453641216:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (112931)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4088190374:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (112932)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3119713267:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (112930)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1121901983:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.29 % (112933)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2739473751:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (112929)Instruction limit reached!
% 0.20/0.29 % (112929)------------------------------
% 0.20/0.29 % (112929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (112929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (112929)CaDiCaL version: 2.1.3
% 0.20/0.29 % (112929)Termination reason: Instruction limit
% 0.20/0.29 % (112929)Termination phase: Property scanning
% 0.20/0.29 % (112929)Time elapsed: 0.002 s
% 0.20/0.29 % (112929)Peak memory usage: 10 MB
% 0.20/0.29 % (112929)Instructions burned: 4 (million)
% 0.20/0.29 % (112928)Instruction limit reached!
% 0.20/0.29 % (112928)------------------------------
% 0.20/0.29 % (112928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (112928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (112928)CaDiCaL version: 2.1.3
% 0.20/0.29 % (112928)Termination reason: Instruction limit
% 0.20/0.29 % (112928)Termination phase: Saturation
% 0.20/0.29 % (112928)Time elapsed: 0.009 s
% 0.20/0.29 % (112928)Peak memory usage: 12 MB
% 0.20/0.29 % (112928)Instructions burned: 19 (million)
% 0.20/0.29 % (112931)Instruction limit reached!
% 0.20/0.29 % (112931)------------------------------
% 0.20/0.29 % (112931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (112931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (112931)CaDiCaL version: 2.1.3
% 0.20/0.29 % (112931)Termination reason: Instruction limit
% 0.20/0.29 % (112931)Termination phase: Saturation
% 0.20/0.29 % (112931)Time elapsed: 0.014 s
% 0.20/0.29 % (112931)Peak memory usage: 12 MB
% 0.20/0.29 % (112931)Instructions burned: 24 (million)
% 0.20/0.29 % (112927)Instruction limit reached!
% 0.20/0.29 % (112927)------------------------------
% 0.20/0.29 % (112927)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (112927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (112927)CaDiCaL version: 2.1.3
% 0.20/0.29 % (112927)Termination reason: Instruction limit
% 0.20/0.29 % (112927)Termination phase: Saturation
% 0.20/0.29 % (112927)Time elapsed: 0.022 s
% 0.20/0.29 % (112927)Peak memory usage: 12 MB
% 0.20/0.29 % (112927)Instructions burned: 91 (million)
% 0.20/0.29 % (112945)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=622568354:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.29 % (112953)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.29 % (112945)Instruction limit reached!
% 0.20/0.29 % (112945)------------------------------
% 0.20/0.29 % (112945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (112945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (112945)CaDiCaL version: 2.1.3
% 0.20/0.29 % (112945)Termination reason: Instruction limit
% 0.20/0.29 % (112945)Termination phase: Property scanning
% 0.20/0.29 % (112945)Time elapsed: 0.002 s
% 0.20/0.29 % (112945)Peak memory usage: 10 MB
% 0.20/0.29 % (112945)Instructions burned: 4 (million)
% 0.20/0.29 % (112933) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-112915-112933"...
% 0.20/0.29 % (112953)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3897612987:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.29 % (112953)Instruction limit reached!
% 0.20/0.29 % (112953)------------------------------
% 0.20/0.29 % (112953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (112953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (112953)CaDiCaL version: 2.1.3
% 0.20/0.29 % (112953)Termination reason: Instruction limit
% 0.20/0.29 % (112953)Termination phase: Function definition elimination
% 0.20/0.29 % (112953)Time elapsed: 0.002 s
% 0.20/0.29 % (112953)Peak memory usage: 10 MB
% 0.20/0.29 % (112953)Instructions burned: 9 (million)
% 0.20/0.29 % (112949)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=37500304:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.29 % (112933)...printing done.
% 0.20/0.29 % (112933)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (112933)------------------------------
% 0.20/0.30 % (112933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (112933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (112933)CaDiCaL version: 2.1.3
% 0.20/0.30 % (112933)Termination reason: Refutation
% 0.20/0.30 % (112933)Time elapsed: 0.029 s
% 0.20/0.30 % (112933)Peak memory usage: 13 MB
% 0.20/0.30 % (112933)Instructions burned: 55 (million)
% 0.20/0.30 % (112915)Success in time 0.068 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------