%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU492^1 : 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 : 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 : Wed Sep 30 08:29:48 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 15
% Syntax : Number of formulae : 155 ( 39 unt; 0 typ; 10 def)
% Number of atoms : 1266 ( 208 equ; 0 cnn)
% Maximal formula atoms : 4 ( 8 avg)
% Number of connectives : 1798 ( 154 ~; 195 |; 86 &;1098 @)
% ( 10 <=>; 87 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 20 con; 0-4 aty)
% ( 168 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 299 ( 0 sgn 64 !; 0 ?; 299 :)
% 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,
vNOT: $o > $o ).
thf(func_def_32,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_35,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
vAND: $o > $o > $o ).
thf(func_def_37,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vIMP: $o > $o > $o ).
thf(func_def_40,type,
vOR: $o > $o > $o ).
thf(func_def_41,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_44,type,
sK0: $i > $i > $o ).
thf(f7,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
~ ( X0 @ X1 @ X1 ) )
= irrefl ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',irreflexive) ).
thf(f11,axiom,
( asymm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ~ ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',asymmetric) ).
thf(f13,axiom,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $i,X2: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',transitive) ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
( ( asymm @ X0 )
& ( trans @ X0 ) ) )
= so ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',strict_order) ).
thf(f30,conjecture,
( ( ^ [X0: $i > $i > $o] :
( ( irrefl @ X0 )
& ( trans @ X0 ) ) )
= so ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',alternative_definition_of_strict_order) ).
thf(f31,negated_conjecture,
( ( ^ [X0: $i > $i > $o] :
( ( irrefl @ X0 )
& ( trans @ X0 ) ) )
!= so ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f32,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
~ ( X0 @ X1 @ X1 ) )
= irrefl ),
inference(rectify,[],[f7]) ).
thf(f33,plain,
( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f42,plain,
( ( ^ [X0: $i > $i > $o] :
( ( irrefl @ X0 )
& ( trans @ X0 ) ) )
!= so ),
inference(rectify,[],[f31]) ).
thf(f43,plain,
( so
!= ( ^ [Y0: $i > $i > $o] :
( ( trans @ Y0 )
& ( irrefl @ Y0 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f69,plain,
( asymm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ~ ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f70,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f80,plain,
( ( ^ [X0: $i > $i > $o] :
( ( asymm @ X0 )
& ( trans @ X0 ) ) )
= so ),
inference(rectify,[],[f18]) ).
thf(f81,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( trans @ Y0 )
& ( asymm @ Y0 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f84,plain,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f85,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,[],[f84]) ).
thf(f88,plain,
( so
!= ( ^ [Y0: $i > $i > $o] :
( ( trans @ Y0 )
& ( irrefl @ Y0 ) ) ) ),
inference(flattening,[],[f43]) ).
thf(f89,plain,
( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f94,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f105,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,[],[f85]) ).
thf(f112,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( trans @ Y0 )
& ( asymm @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f113,plain,
( so
!= ( ^ [Y0: $i > $i > $o] :
( ( trans @ Y0 )
& ( irrefl @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f127,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
@ Y0 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ~ ( Y1 @ Y2 @ Y3 ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f112,f105,f94]) ).
thf(f136,plain,
( ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
@ Y0 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y1 @ Y2 @ Y2 ) )
@ Y0 ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
@ Y0 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ~ ( Y1 @ Y2 @ Y3 ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f113,f127,f105,f89]) ).
thf(f137,plain,
( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,plain,
( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
@ sK0 )
!= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f137]) ).
thf(f139,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f138]) ).
thf(f140,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f138]) ).
thf(f141,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) )
@ sK3 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK1 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) )
@ sK3 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 )
@ sK2 ) ) ),
inference(duplicate_literal_removal,[],[f146]) ).
thf(f148,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ~ ( sK0 @ sK3 @ Y0 ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK1 )
& ( sK0 @ sK1 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
| ( ( ~ ( sK0 @ sK2 @ sK2 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ~ ( sK0 @ sK3 @ Y0 ) )
@ sK4 ) )
| ( ( ~ ( sK0 @ sK2 @ sK2 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK1 )
& ( sK0 @ sK1 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ~ ( sK0 @ sK3 @ Y0 ) )
@ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK1 )
& ( sK0 @ sK1 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
| ( ( sK0 @ sK2 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ~ ( sK0 @ sK3 @ Y0 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK1 )
& ( sK0 @ sK1 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK5 ) )
| ( ( sK0 @ sK2 @ sK2 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( ( sK0 @ sK2 @ sK2 )
= $true )
| ( $false
= ( ( sK0 @ sK4 @ sK3 )
=> ~ ( sK0 @ sK3 @ sK4 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK1 )
& ( sK0 @ sK1 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK1 )
& ( sK0 @ sK1 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK3 @ sK4 ) ) )
| ( ( sK0 @ sK2 @ sK2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK1 )
& ( sK0 @ sK1 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) ) ) )
| ( ( sK0 @ sK4 @ sK3 )
= $true )
| ( ( sK0 @ sK2 @ sK2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK1 )
& ( sK0 @ sK1 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) )
@ sK6 ) )
| ( ( sK0 @ sK4 @ sK3 )
= $true )
| ( ( sK0 @ sK2 @ sK2 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( ( sK0 @ sK4 @ sK3 )
= $true )
| ( $false
= ( ( ( sK0 @ sK6 @ sK1 )
& ( sK0 @ sK1 @ sK5 ) )
=> ( sK0 @ sK6 @ sK5 ) ) )
| ( ( sK0 @ sK2 @ sK2 )
= $true ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
( ( ( sK0 @ sK4 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK6 @ sK5 ) )
| ( ( sK0 @ sK2 @ sK2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( ( sK0 @ sK4 @ sK3 )
= $true )
| ( $true
= ( ( sK0 @ sK6 @ sK1 )
& ( sK0 @ sK1 @ sK5 ) ) )
| ( ( sK0 @ sK2 @ sK2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f159,plain,
( ( ( sK0 @ sK4 @ sK3 )
= $true )
| ( ( sK0 @ sK2 @ sK2 )
= $true )
| ( $true
= ( sK0 @ sK1 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( ( sK0 @ sK6 @ sK1 )
= $true )
| ( ( sK0 @ sK4 @ sK3 )
= $true )
| ( ( sK0 @ sK2 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f158]) ).
thf(f161,plain,
( ( ( sK0 @ sK2 @ sK2 )
= $true )
| ( $false
= ( ~ ( sK0 @ sK3 @ sK4 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK1 )
& ( sK0 @ sK1 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f162,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK1 )
& ( sK0 @ sK1 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) )
@ sK7 ) )
| ( ( sK0 @ sK3 @ sK4 )
= $true )
| ( ( sK0 @ sK2 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( ( sK0 @ sK3 @ sK4 )
= $true )
| ( ( sK0 @ sK2 @ sK2 )
= $true )
| ( $false
= ( ( ( sK0 @ sK7 @ sK1 )
& ( sK0 @ sK1 @ sK5 ) )
=> ( sK0 @ sK7 @ sK5 ) ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
( ( ( sK0 @ sK2 @ sK2 )
= $true )
| ( ( sK0 @ sK3 @ sK4 )
= $true )
| ( $false
= ( sK0 @ sK7 @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( ( sK0 @ sK3 @ sK4 )
= $true )
| ( $true
= ( ( sK0 @ sK7 @ sK1 )
& ( sK0 @ sK1 @ sK5 ) ) )
| ( ( sK0 @ sK2 @ sK2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f163]) ).
thf(f166,plain,
( ( ( sK0 @ sK2 @ sK2 )
= $true )
| ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ( ( sK0 @ sK3 @ sK4 )
= $true ) ),
inference(and_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( ( sK0 @ sK2 @ sK2 )
= $true )
| ( ( sK0 @ sK3 @ sK4 )
= $true )
| ( ( sK0 @ sK7 @ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f169,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f168]) ).
thf(f172,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f170]) ).
thf(f173,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(duplicate_literal_removal,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( sK0 @ X3 @ X1 )
& ( sK0 @ X1 @ X2 ) )
=> ( sK0 @ X3 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X3 @ X1 )
& ( sK0 @ X1 @ X2 ) ) )
| ( ( sK0 @ X3 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X3 @ X1 ) )
| ( ( sK0 @ X3 @ X2 )
= $true ) ),
inference(and_proxy_clausification,[],[f180]) ).
thf(f194,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f169]) ).
thf(f206,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f194]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( sK0 @ X2 @ X2 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ~ ( sK0 @ X1 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ~ ( sK0 @ X1 @ Y0 ) ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ~ ( sK0 @ X1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( sK0 @ X2 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X2 ) )
| ( $true
= ( ( sK0 @ X3 @ X1 )
=> ~ ( sK0 @ X1 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( sK0 @ X1 @ X3 ) ) )
| ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( $false
= ( sK0 @ X2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f215,definition,
( spl8_1
<=> ( ( sK0 @ sK4 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f216,plain,
( ( ( sK0 @ sK4 @ sK3 )
= $true )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f215]) ).
thf(f218,definition,
( spl8_2
<=> ( ( sK0 @ sK2 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f219,plain,
( ( ( sK0 @ sK2 @ sK2 )
= $true )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f221,definition,
( spl8_3
<=> ( ( sK0 @ sK6 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f222,plain,
( ( ( sK0 @ sK6 @ sK1 )
= $true )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f221]) ).
thf(f223,plain,
( spl8_1
| spl8_2
| spl8_3 ),
inference(avatar_split_clause,[],[f160,f221,f218,f215]) ).
thf(f225,definition,
( spl8_4
<=> ( $true
= ( sK0 @ sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f226,plain,
( ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f225]) ).
thf(f227,plain,
( spl8_4
| spl8_2
| spl8_1 ),
inference(avatar_split_clause,[],[f159,f215,f218,f225]) ).
thf(f229,definition,
( spl8_5
<=> ( $false
= ( sK0 @ sK6 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f230,plain,
( ( $false
= ( sK0 @ sK6 @ sK5 ) )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f229]) ).
thf(f231,plain,
( spl8_5
| spl8_2
| spl8_1 ),
inference(avatar_split_clause,[],[f157,f215,f218,f229]) ).
thf(f233,definition,
( spl8_6
<=> ( ( sK0 @ sK3 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
thf(f234,plain,
( ( ( sK0 @ sK3 @ sK4 )
= $true )
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f236,definition,
( spl8_7
<=> ( ( sK0 @ sK7 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
thf(f237,plain,
( ( ( sK0 @ sK7 @ sK1 )
= $true )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f236]) ).
thf(f238,plain,
( spl8_6
| spl8_2
| spl8_7 ),
inference(avatar_split_clause,[],[f167,f236,f218,f233]) ).
thf(f239,plain,
( spl8_6
| spl8_2
| spl8_4 ),
inference(avatar_split_clause,[],[f166,f225,f218,f233]) ).
thf(f241,definition,
( spl8_8
<=> ( $false
= ( sK0 @ sK7 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
thf(f242,plain,
( ( $false
= ( sK0 @ sK7 @ sK5 ) )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f243,plain,
( spl8_2
| spl8_6
| spl8_8 ),
inference(avatar_split_clause,[],[f164,f241,f233,f218]) ).
thf(f245,definition,
( spl8_9
<=> ! [X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
thf(f246,plain,
( ! [X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) ) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f248,definition,
( spl8_10
<=> ! [X2: $i] :
( $false
= ( sK0 @ X2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
thf(f249,plain,
( ! [X2: $i] :
( $false
= ( sK0 @ X2 @ X2 ) )
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f250,plain,
( spl8_9
| spl8_10 ),
inference(avatar_split_clause,[],[f213,f248,f245]) ).
thf(f251,plain,
( ( $false = $true )
| ( $false = $true )
| ~ spl8_2
| ~ spl8_9 ),
inference(constrained_superposition,[],[f246,f219]) ).
thf(f259,plain,
( ( $false = $true )
| ~ spl8_2
| ~ spl8_9 ),
inference(duplicate_literal_removal,[],[f251]) ).
thf(f260,plain,
( $false
| ~ spl8_2
| ~ spl8_9 ),
inference(trivial_inequality_removal,[],[f259]) ).
thf(f261,plain,
( ~ spl8_2
| ~ spl8_9 ),
inference(avatar_contradiction_clause,[],[f260]) ).
thf(f264,plain,
( ( $false = $true )
| ~ spl8_2
| ~ spl8_10 ),
inference(backward_demodulation,[],[f219,f249]) ).
thf(f265,plain,
( $false
| ~ spl8_2
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f264]) ).
thf(f266,plain,
( ~ spl8_2
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[],[f265]) ).
thf(f269,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false = $true ) )
| ~ spl8_10 ),
inference(constrained_superposition,[],[f181,f249]) ).
thf(f276,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) ) )
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f281,plain,
( spl8_9
| ~ spl8_10 ),
inference(avatar_split_clause,[],[f276,f248,f245]) ).
thf(f299,plain,
( ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ( $false = $true )
| ~ spl8_1
| ~ spl8_9 ),
inference(constrained_superposition,[],[f216,f246]) ).
thf(f304,plain,
( ( $false
= ( sK0 @ sK3 @ sK4 ) )
| ~ spl8_1
| ~ spl8_9 ),
inference(trivial_inequality_removal,[],[f299]) ).
thf(f312,plain,
( ( $false = $true )
| ~ spl8_1
| ~ spl8_6
| ~ spl8_9 ),
inference(backward_demodulation,[],[f234,f304]) ).
thf(f313,plain,
( $false
| ~ spl8_1
| ~ spl8_6
| ~ spl8_9 ),
inference(trivial_inequality_removal,[],[f312]) ).
thf(f314,plain,
( ~ spl8_1
| ~ spl8_6
| ~ spl8_9 ),
inference(avatar_contradiction_clause,[],[f313]) ).
thf(f316,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( sK0 @ X0 @ sK5 )
= $false )
| ( ( sK0 @ sK6 @ X0 )
= $false ) )
| ~ spl8_5 ),
inference(constrained_superposition,[],[f181,f230]) ).
thf(f317,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK6 @ X0 )
= $false )
| ( ( sK0 @ X0 @ sK5 )
= $false ) )
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f316]) ).
thf(f351,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $false = $true )
| ~ spl8_3
| ~ spl8_5 ),
inference(constrained_superposition,[],[f222,f317]) ).
thf(f354,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ~ spl8_3
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f351]) ).
thf(f359,plain,
( ( $false = $true )
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(backward_demodulation,[],[f226,f354]) ).
thf(f360,plain,
( $false
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f359]) ).
thf(f361,plain,
( ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(avatar_contradiction_clause,[],[f360]) ).
thf(f367,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK7 @ X0 ) )
| ( ( sK0 @ X0 @ sK5 )
= $false )
| ( $false = $true ) )
| ~ spl8_8 ),
inference(constrained_superposition,[],[f181,f242]) ).
thf(f368,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK7 @ X0 ) )
| ( ( sK0 @ X0 @ sK5 )
= $false ) )
| ~ spl8_8 ),
inference(trivial_inequality_removal,[],[f367]) ).
thf(f414,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ~ spl8_7
| ~ spl8_8 ),
inference(constrained_superposition,[],[f237,f368]) ).
thf(f416,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ~ spl8_7
| ~ spl8_8 ),
inference(trivial_inequality_removal,[],[f414]) ).
thf(f422,plain,
( ( $false = $true )
| ~ spl8_4
| ~ spl8_7
| ~ spl8_8 ),
inference(backward_demodulation,[],[f226,f416]) ).
thf(f423,plain,
( $false
| ~ spl8_4
| ~ spl8_7
| ~ spl8_8 ),
inference(trivial_inequality_removal,[],[f422]) ).
thf(f424,plain,
( ~ spl8_4
| ~ spl8_7
| ~ spl8_8 ),
inference(avatar_contradiction_clause,[],[f423]) ).
cnf(s1,plain,
( spl8_1
| spl8_2
| spl8_3 ),
inference(sat_conversion,[],[f223]) ).
cnf(s2,plain,
( spl8_1
| spl8_2
| spl8_4 ),
inference(sat_conversion,[],[f227]) ).
cnf(s3,plain,
( spl8_1
| spl8_2
| spl8_5 ),
inference(sat_conversion,[],[f231]) ).
cnf(s4,plain,
( spl8_2
| spl8_6
| spl8_7 ),
inference(sat_conversion,[],[f238]) ).
cnf(s5,plain,
( spl8_2
| spl8_4
| spl8_6 ),
inference(sat_conversion,[],[f239]) ).
cnf(s6,plain,
( spl8_2
| spl8_6
| spl8_8 ),
inference(sat_conversion,[],[f243]) ).
cnf(s7,plain,
( spl8_9
| spl8_10 ),
inference(sat_conversion,[],[f250]) ).
cnf(s9,plain,
( ~ spl8_2
| ~ spl8_9 ),
inference(sat_conversion,[],[f261]) ).
cnf(s12,plain,
( ~ spl8_2
| ~ spl8_10 ),
inference(sat_conversion,[],[f266]) ).
cnf(s13,plain,
( spl8_9
| ~ spl8_10 ),
inference(sat_conversion,[],[f281]) ).
cnf(s15,plain,
( ~ spl8_1
| ~ spl8_6
| ~ spl8_9 ),
inference(sat_conversion,[],[f314]) ).
cnf(s16,plain,
( ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(sat_conversion,[],[f361]) ).
cnf(s17,plain,
( ~ spl8_4
| ~ spl8_7
| ~ spl8_8 ),
inference(sat_conversion,[],[f424]) ).
cnf(s18,plain,
( spl8_2
| spl8_1 ),
inference(rat,[],[s16,s2,s3,s1]) ).
cnf(s19,plain,
~ spl8_2,
inference(rat,[],[s7,s9,s12]) ).
cnf(s20,plain,
spl8_1,
inference(rat,[],[s18,s19]) ).
cnf(s21,plain,
( spl8_6
| ~ spl8_4 ),
inference(rat,[],[s17,s6,s4,s19]) ).
cnf(s22,plain,
spl8_9,
inference(rat,[],[s7,s13]) ).
cnf(s24,plain,
~ spl8_6,
inference(rat,[],[s15,s20,s22]) ).
cnf(s26,plain,
spl8_4,
inference(rat,[],[s5,s19,s24]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s21,s26,s24]) ).
thf(f425,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU492^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n013.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:45:06 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.22/0.30 % (2134441)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (2134451)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1755186456:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (2134452)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (2134452)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
% 0.22/0.30 % (2134447)lrs+10_16_si=on:nwc=1.5:random_seed=3858638473:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (2134446)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1945668803:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (2134448)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=738343985:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (2134449)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=220421722: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)
% 0.22/0.30 % (2134452)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=2248792783:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (2134450)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2711354628:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (2134448)Instruction limit reached!
% 0.22/0.30 % (2134448)------------------------------
% 0.22/0.30 % (2134448)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2134448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2134448)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2134448)Termination reason: Instruction limit
% 0.22/0.30 % (2134448)Termination phase: Property scanning
% 0.22/0.30 % (2134448)Time elapsed: 0.002 s
% 0.22/0.30 % (2134448)Peak memory usage: 10 MB
% 0.22/0.30 % (2134448)Instructions burned: 4 (million)
% 0.22/0.30 % (2134451) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2134441-2134451"...
% 0.22/0.30 % (2134447)Instruction limit reached!
% 0.22/0.30 % (2134447)------------------------------
% 0.22/0.30 % (2134447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2134447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2134447)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2134447)Termination reason: Instruction limit
% 0.22/0.30 % (2134447)Termination phase: Saturation
% 0.22/0.30 % (2134447)Time elapsed: 0.009 s
% 0.22/0.30 % (2134447)Peak memory usage: 12 MB
% 0.22/0.30 % (2134447)Instructions burned: 18 (million)
% 0.22/0.30 % (2134451)...printing done.
% 0.22/0.30 % (2134451)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (2134451)------------------------------
% 0.22/0.30 % (2134451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2134451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2134451)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2134451)Termination reason: Refutation
% 0.22/0.30 % (2134451)Time elapsed: 0.014 s
% 0.22/0.30 % (2134451)Peak memory usage: 13 MB
% 0.22/0.30 % (2134451)Instructions burned: 34 (million)
% 0.22/0.30 % (2134441)Success in time 0.047 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------