%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU492^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 08:32:11 AM UTC 2026
% Result : Theorem 0.19s 0.30s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 17
% Syntax : Number of formulae : 214 ( 31 unt; 0 typ; 12 def)
% Number of atoms : 2288 ( 358 equ; 0 cnn)
% Maximal formula atoms : 6 ( 10 avg)
% Number of connectives : 2692 ( 174 ~; 427 |; 132 &;1631 @)
% ( 12 <=>; 125 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 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 : 68 ( 64 usr; 24 con; 0-4 aty)
% ( 191 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 386 ( 0 sgn 111 !; 0 ?; 386 :)
% 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,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_38,type,
vNOT: $o > $o ).
thf(func_def_39,type,
vOR: $o > $o > $o ).
thf(func_def_40,type,
vAND: $o > $o > $o ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
sK0: $i > $i > $o ).
thf(f7,axiom,
( irrefl
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
~ ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET009^0.ax',asymmetric) ).
thf(f13,axiom,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',transitive) ).
thf(f18,axiom,
( so
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( asymm @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',strict_order) ).
thf(f30,conjecture,
( so
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( irrefl @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alternative_definition_of_strict_order) ).
thf(f31,negated_conjecture,
( so
!= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( irrefl @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f42,plain,
( irrefl
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
~ ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f7]) ).
thf(f43,plain,
( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f50,plain,
( asymm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ~ ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f11]) ).
thf(f51,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f54,plain,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f13]) ).
thf(f55,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f62,plain,
( so
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( asymm @ X0 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f63,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( asymm @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f86,plain,
( so
!= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( irrefl @ X0 ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f87,plain,
( so
!= ( ^ [Y0: $i > $i > $o] :
( ( irrefl @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
( so
!= ( ^ [Y0: $i > $i > $o] :
( ( irrefl @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(flattening,[],[f87]) ).
thf(f95,plain,
( irrefl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f99,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f101,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f106,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( asymm @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f118,plain,
( so
!= ( ^ [Y0: $i > $i > $o] :
( ( irrefl @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f127,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ~ ( Y1 @ Y2 @ Y3 ) ) ) )
@ Y0 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f106,f99,f101]) ).
thf(f136,plain,
( ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 @ Y2 )
=> ~ ( Y1 @ Y2 @ Y3 ) ) ) )
@ Y0 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
@ Y0 ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
~ ( Y1 @ Y2 @ Y2 ) )
@ Y0 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f118,f127,f95,f101]) ).
thf(f137,plain,
( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f145,plain,
( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
@ sK0 )
!= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f137]) ).
thf(f146,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
~ ( Y0 @ Y1 @ Y1 ) )
& ( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK1 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) )
@ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ Y1 @ sK1 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ~ ( sK0 @ sK3 @ Y0 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK4 @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ Y1 @ sK1 ) ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ~ ( sK0 @ sK3 @ Y0 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK4 @ sK4 ) ) ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ Y1 @ sK1 ) ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) )
@ sK6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ~ ( sK0 @ sK3 @ Y0 ) ) ) )
| ( $false
= ( ~ ( sK0 @ sK4 @ sK4 ) ) ) ),
inference(sigma_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ Y1 @ sK1 ) ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ~ ( sK0 @ sK3 @ Y0 ) )
@ sK7 ) )
| ( $false
= ( ~ ( sK0 @ sK4 @ sK4 ) ) ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ Y1 @ sK1 ) ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ~ ( sK0 @ sK3 @ Y0 ) )
@ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK1 ) )
=> ( sK0 @ Y0 @ sK1 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) ) ) )
| ( $false
= ( ( sK0 @ sK7 @ sK3 )
=> ~ ( sK0 @ sK3 @ sK7 ) ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK1 ) )
=> ( sK0 @ Y0 @ sK1 ) )
@ sK8 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) ) ) )
| ( $false
= ( ( sK0 @ sK7 @ sK3 )
=> ~ ( sK0 @ sK3 @ sK7 ) ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK1 ) )
=> ( sK0 @ Y0 @ sK1 ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) )
@ sK9 ) )
| ( $false
= ( ( sK0 @ sK7 @ sK3 )
=> ~ ( sK0 @ sK3 @ sK7 ) ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK1 ) )
=> ( sK0 @ Y0 @ sK1 ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) )
@ sK9 ) )
| ( $false
= ( ~ ( sK0 @ sK3 @ sK7 ) ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK1 ) )
=> ( sK0 @ Y0 @ sK1 ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) )
@ sK9 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( ( $false
= ( ( ( sK0 @ sK8 @ sK5 )
& ( sK0 @ sK5 @ sK1 ) )
=> ( sK0 @ sK8 @ sK1 ) ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ sK9 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( sK0 @ sK8 @ sK1 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ sK9 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $true
= ( ( sK0 @ sK8 @ sK5 )
& ( sK0 @ sK5 @ sK1 ) ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ sK9 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ sK9 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ sK9 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f167]) ).
thf(f170,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( sK0 @ sK9 @ sK2 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f172,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( sK0 @ sK9 @ sK6 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( sK0 @ sK9 @ sK2 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f175,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f176,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK9 @ sK6 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( ( $false
= ( sK0 @ sK8 @ sK1 ) )
| ( $false
= ( sK0 @ sK9 @ sK2 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f179,plain,
( ( $false
= ( sK0 @ sK8 @ sK1 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f180,plain,
( ( $false
= ( sK0 @ sK8 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $false
= ( sK0 @ sK8 @ sK1 ) )
| ( $true
= ( sK0 @ sK9 @ sK6 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK1 ) )
=> ( sK0 @ Y0 @ sK1 ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) )
@ sK9 ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f183,plain,
( ( $false
= ( ( ( sK0 @ sK8 @ sK5 )
& ( sK0 @ sK5 @ sK1 ) )
=> ( sK0 @ sK8 @ sK1 ) ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ sK9 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
( ( $false
= ( sK0 @ sK8 @ sK1 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ sK9 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( $true
= ( ( sK0 @ sK8 @ sK5 )
& ( sK0 @ sK5 @ sK1 ) ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ sK9 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f183]) ).
thf(f186,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ sK9 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ sK9 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f185]) ).
thf(f188,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( sK0 @ sK9 @ sK2 ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f187]) ).
thf(f190,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( sK0 @ sK9 @ sK6 ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f189]) ).
thf(f192,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( sK0 @ sK9 @ sK2 ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f193,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f194,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK9 @ sK6 ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f193]) ).
thf(f196,plain,
( ( $false
= ( sK0 @ sK8 @ sK1 ) )
| ( $false
= ( sK0 @ sK9 @ sK2 ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f197,plain,
( ( $false
= ( sK0 @ sK8 @ sK1 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f198,plain,
( ( $false
= ( sK0 @ sK8 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ( $false
= ( sK0 @ sK8 @ sK1 ) )
| ( $true
= ( sK0 @ sK9 @ sK6 ) )
| ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f197]) ).
thf(f200,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f201,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f200]) ).
thf(f203,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f202]) ).
thf(f205,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f203]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( ~ ( sK0 @ X2 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ~ ( sK0 @ X1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( sK0 @ X2 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ~ ( sK0 @ X1 @ Y0 ) )
@ X3 ) )
| ( $false
= ( sK0 @ X2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( sK0 @ X3 @ X1 )
=> ~ ( sK0 @ X1 @ X3 ) ) )
| ( $false
= ( sK0 @ X2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X2 ) )
| ( $true
= ( ~ ( sK0 @ X1 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X2 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f224,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
~ ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f201]) ).
thf(f225,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f224]) ).
thf(f236,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f225]) ).
thf(f237,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ Y1 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ Y1 @ X2 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ Y1 @ X2 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X4 )
& ( sK0 @ X4 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) )
@ X5 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X4 )
& ( sK0 @ X4 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) )
@ X5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X4 )
& ( sK0 @ X4 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ( ( sK0 @ X5 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ X5 @ X1 ) ) )
| ( $true
= ( ( ( sK0 @ X6 @ X4 )
& ( sK0 @ X4 @ X2 ) )
=> ( sK0 @ X6 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( ( sK0 @ X5 @ X3 )
& ( sK0 @ X3 @ X1 ) ) )
| ( $true
= ( ( ( sK0 @ X6 @ X4 )
& ( sK0 @ X4 @ X2 ) )
=> ( sK0 @ X6 @ X2 ) ) )
| ( $true
= ( sK0 @ X5 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( ( ( sK0 @ X6 @ X4 )
& ( sK0 @ X4 @ X2 ) )
=> ( sK0 @ X6 @ X2 ) ) )
| ( $true
= ( sK0 @ X5 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( ( sK0 @ X6 @ X4 )
& ( sK0 @ X4 @ X2 ) ) )
| ( $true
= ( sK0 @ X5 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X6 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X4 @ X2 ) )
| ( $true
= ( sK0 @ X5 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X6 @ X2 ) )
| ( $false
= ( sK0 @ X6 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f246]) ).
thf(f249,definition,
( spl10_1
<=> ( $true
= ( sK0 @ sK4 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
thf(f251,plain,
( ( $true
= ( sK0 @ sK4 @ sK4 ) )
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f253,definition,
( spl10_2
<=> ( $true
= ( sK0 @ sK7 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f255,plain,
( ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f257,definition,
( spl10_3
<=> ( $true
= ( sK0 @ sK9 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f259,plain,
( ( $true
= ( sK0 @ sK9 @ sK6 ) )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f261,definition,
( spl10_4
<=> ( $true
= ( sK0 @ sK8 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f263,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f261]) ).
thf(f264,plain,
( spl10_1
| spl10_2
| spl10_3
| spl10_4 ),
inference(avatar_split_clause,[],[f173,f261,f257,f253,f249]) ).
thf(f266,definition,
( spl10_5
<=> ( $true
= ( sK0 @ sK6 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
thf(f268,plain,
( ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f269,plain,
( spl10_1
| spl10_2
| spl10_5
| spl10_4 ),
inference(avatar_split_clause,[],[f172,f261,f266,f253,f249]) ).
thf(f271,definition,
( spl10_6
<=> ( $false
= ( sK0 @ sK9 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
thf(f273,plain,
( ( $false
= ( sK0 @ sK9 @ sK2 ) )
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f271]) ).
thf(f274,plain,
( spl10_1
| spl10_2
| spl10_6
| spl10_4 ),
inference(avatar_split_clause,[],[f170,f261,f271,f253,f249]) ).
thf(f276,definition,
( spl10_7
<=> ( $true
= ( sK0 @ sK5 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f278,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f276]) ).
thf(f279,plain,
( spl10_1
| spl10_2
| spl10_3
| spl10_7 ),
inference(avatar_split_clause,[],[f177,f276,f257,f253,f249]) ).
thf(f280,plain,
( spl10_1
| spl10_2
| spl10_5
| spl10_7 ),
inference(avatar_split_clause,[],[f176,f276,f266,f253,f249]) ).
thf(f281,plain,
( spl10_1
| spl10_2
| spl10_6
| spl10_7 ),
inference(avatar_split_clause,[],[f174,f276,f271,f253,f249]) ).
thf(f283,definition,
( spl10_8
<=> ( $false
= ( sK0 @ sK8 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
thf(f285,plain,
( ( $false
= ( sK0 @ sK8 @ sK1 ) )
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f283]) ).
thf(f286,plain,
( spl10_1
| spl10_2
| spl10_3
| spl10_8 ),
inference(avatar_split_clause,[],[f181,f283,f257,f253,f249]) ).
thf(f287,plain,
( spl10_1
| spl10_2
| spl10_5
| spl10_8 ),
inference(avatar_split_clause,[],[f180,f283,f266,f253,f249]) ).
thf(f288,plain,
( spl10_1
| spl10_2
| spl10_6
| spl10_8 ),
inference(avatar_split_clause,[],[f178,f283,f271,f253,f249]) ).
thf(f290,definition,
( spl10_9
<=> ( $true
= ( sK0 @ sK3 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
thf(f292,plain,
( ( $true
= ( sK0 @ sK3 @ sK7 ) )
| ~ spl10_9 ),
inference(avatar_component_clause,[],[f290]) ).
thf(f293,plain,
( spl10_1
| spl10_9
| spl10_3
| spl10_4 ),
inference(avatar_split_clause,[],[f191,f261,f257,f290,f249]) ).
thf(f294,plain,
( spl10_1
| spl10_9
| spl10_5
| spl10_4 ),
inference(avatar_split_clause,[],[f190,f261,f266,f290,f249]) ).
thf(f295,plain,
( spl10_1
| spl10_9
| spl10_6
| spl10_4 ),
inference(avatar_split_clause,[],[f188,f261,f271,f290,f249]) ).
thf(f296,plain,
( spl10_1
| spl10_9
| spl10_3
| spl10_7 ),
inference(avatar_split_clause,[],[f195,f276,f257,f290,f249]) ).
thf(f297,plain,
( spl10_1
| spl10_9
| spl10_5
| spl10_7 ),
inference(avatar_split_clause,[],[f194,f276,f266,f290,f249]) ).
thf(f298,plain,
( spl10_1
| spl10_9
| spl10_6
| spl10_7 ),
inference(avatar_split_clause,[],[f192,f276,f271,f290,f249]) ).
thf(f299,plain,
( spl10_1
| spl10_9
| spl10_3
| spl10_8 ),
inference(avatar_split_clause,[],[f199,f283,f257,f290,f249]) ).
thf(f300,plain,
( spl10_1
| spl10_9
| spl10_5
| spl10_8 ),
inference(avatar_split_clause,[],[f198,f283,f266,f290,f249]) ).
thf(f301,plain,
( spl10_1
| spl10_9
| spl10_6
| spl10_8 ),
inference(avatar_split_clause,[],[f196,f283,f271,f290,f249]) ).
thf(f303,definition,
( spl10_10
<=> ! [X2: $i] :
( $false
= ( sK0 @ X2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
thf(f304,plain,
( ! [X2: $i] :
( $false
= ( sK0 @ X2 @ X2 ) )
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f303]) ).
thf(f306,definition,
( spl10_11
<=> ! [X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
thf(f307,plain,
( ! [X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) ) )
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f306]) ).
thf(f308,plain,
( spl10_10
| spl10_11 ),
inference(avatar_split_clause,[],[f212,f306,f303]) ).
thf(f310,definition,
( spl10_12
<=> ! [X2: $i,X5: $i,X4: $i] :
( ( $false
= ( sK0 @ X4 @ X2 ) )
| ( $false
= ( sK0 @ X5 @ X4 ) )
| ( $true
= ( sK0 @ X5 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
thf(f311,plain,
( ! [X2: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X4 @ X2 ) )
| ( $false
= ( sK0 @ X5 @ X4 ) )
| ( $true
= ( sK0 @ X5 @ X2 ) ) )
| ~ spl10_12 ),
inference(avatar_component_clause,[],[f310]) ).
thf(f314,plain,
( spl10_12
| spl10_12 ),
inference(avatar_split_clause,[],[f247,f310,f310]) ).
thf(f374,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) ) )
| ~ spl10_10
| ~ spl10_12 ),
inference(constrained_superposition,[],[f304,f311]) ).
thf(f385,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ sK9 @ X0 ) ) )
| ~ spl10_6
| ~ spl10_12 ),
inference(constrained_superposition,[],[f273,f311]) ).
thf(f388,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ sK9 @ X0 ) ) )
| ~ spl10_6
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f385]) ).
thf(f398,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) ) )
| ~ spl10_10
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f374]) ).
thf(f421,plain,
( spl10_11
| ~ spl10_10
| ~ spl10_12 ),
inference(avatar_split_clause,[],[f398,f310,f303,f306]) ).
thf(f489,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK6 @ sK2 ) )
| ~ spl10_3
| ~ spl10_6
| ~ spl10_12 ),
inference(constrained_superposition,[],[f259,f388]) ).
thf(f490,plain,
( ( $false
= ( sK0 @ sK6 @ sK2 ) )
| ~ spl10_3
| ~ spl10_6
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f489]) ).
thf(f500,plain,
( ( $true = $false )
| ~ spl10_3
| ~ spl10_5
| ~ spl10_6
| ~ spl10_12 ),
inference(constrained_superposition,[],[f490,f268]) ).
thf(f506,plain,
( $false
| ~ spl10_3
| ~ spl10_5
| ~ spl10_6
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f500]) ).
thf(f507,plain,
( ~ spl10_3
| ~ spl10_5
| ~ spl10_6
| ~ spl10_12 ),
inference(avatar_contradiction_clause,[],[f506]) ).
thf(f512,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK1 ) )
| ( $false
= ( sK0 @ sK8 @ X0 ) ) )
| ~ spl10_8
| ~ spl10_12 ),
inference(constrained_superposition,[],[f311,f285]) ).
thf(f513,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK1 ) )
| ( $false
= ( sK0 @ sK8 @ X0 ) ) )
| ~ spl10_8
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f512]) ).
thf(f576,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ~ spl10_4
| ~ spl10_8
| ~ spl10_12 ),
inference(constrained_superposition,[],[f263,f513]) ).
thf(f577,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ~ spl10_4
| ~ spl10_8
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f576]) ).
thf(f587,plain,
( ( $true = $false )
| ~ spl10_4
| ~ spl10_7
| ~ spl10_8
| ~ spl10_12 ),
inference(constrained_superposition,[],[f577,f278]) ).
thf(f593,plain,
( $false
| ~ spl10_4
| ~ spl10_7
| ~ spl10_8
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f587]) ).
thf(f594,plain,
( ~ spl10_4
| ~ spl10_7
| ~ spl10_8
| ~ spl10_12 ),
inference(avatar_contradiction_clause,[],[f593]) ).
thf(f640,plain,
( ( $true = $false )
| ( $true = $false )
| ~ spl10_1
| ~ spl10_11 ),
inference(constrained_superposition,[],[f307,f251]) ).
thf(f645,plain,
( ( $true = $false )
| ~ spl10_1
| ~ spl10_11 ),
inference(duplicate_literal_removal,[],[f640]) ).
thf(f646,plain,
( $false
| ~ spl10_1
| ~ spl10_11 ),
inference(trivial_inequality_removal,[],[f645]) ).
thf(f647,plain,
( ~ spl10_1
| ~ spl10_11 ),
inference(avatar_contradiction_clause,[],[f646]) ).
thf(f748,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK3 @ sK7 ) )
| ~ spl10_2
| ~ spl10_11 ),
inference(constrained_superposition,[],[f307,f255]) ).
thf(f759,plain,
( ( $false
= ( sK0 @ sK3 @ sK7 ) )
| ~ spl10_2
| ~ spl10_11 ),
inference(trivial_inequality_removal,[],[f748]) ).
thf(f838,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_9
| ~ spl10_11 ),
inference(constrained_superposition,[],[f759,f292]) ).
thf(f844,plain,
( $false
| ~ spl10_2
| ~ spl10_9
| ~ spl10_11 ),
inference(trivial_inequality_removal,[],[f838]) ).
thf(f845,plain,
( ~ spl10_2
| ~ spl10_9
| ~ spl10_11 ),
inference(avatar_contradiction_clause,[],[f844]) ).
cnf(s1,plain,
( spl10_1
| spl10_2
| spl10_3
| spl10_4 ),
inference(sat_conversion,[],[f264]) ).
cnf(s2,plain,
( spl10_1
| spl10_2
| spl10_4
| spl10_5 ),
inference(sat_conversion,[],[f269]) ).
cnf(s3,plain,
( spl10_1
| spl10_2
| spl10_4
| spl10_6 ),
inference(sat_conversion,[],[f274]) ).
cnf(s4,plain,
( spl10_1
| spl10_2
| spl10_3
| spl10_7 ),
inference(sat_conversion,[],[f279]) ).
cnf(s5,plain,
( spl10_1
| spl10_2
| spl10_5
| spl10_7 ),
inference(sat_conversion,[],[f280]) ).
cnf(s6,plain,
( spl10_1
| spl10_2
| spl10_6
| spl10_7 ),
inference(sat_conversion,[],[f281]) ).
cnf(s7,plain,
( spl10_1
| spl10_2
| spl10_3
| spl10_8 ),
inference(sat_conversion,[],[f286]) ).
cnf(s8,plain,
( spl10_1
| spl10_2
| spl10_5
| spl10_8 ),
inference(sat_conversion,[],[f287]) ).
cnf(s9,plain,
( spl10_1
| spl10_2
| spl10_6
| spl10_8 ),
inference(sat_conversion,[],[f288]) ).
cnf(s10,plain,
( spl10_1
| spl10_3
| spl10_4
| spl10_9 ),
inference(sat_conversion,[],[f293]) ).
cnf(s11,plain,
( spl10_1
| spl10_4
| spl10_5
| spl10_9 ),
inference(sat_conversion,[],[f294]) ).
cnf(s12,plain,
( spl10_1
| spl10_4
| spl10_6
| spl10_9 ),
inference(sat_conversion,[],[f295]) ).
cnf(s13,plain,
( spl10_1
| spl10_3
| spl10_7
| spl10_9 ),
inference(sat_conversion,[],[f296]) ).
cnf(s14,plain,
( spl10_1
| spl10_5
| spl10_7
| spl10_9 ),
inference(sat_conversion,[],[f297]) ).
cnf(s15,plain,
( spl10_1
| spl10_6
| spl10_7
| spl10_9 ),
inference(sat_conversion,[],[f298]) ).
cnf(s16,plain,
( spl10_1
| spl10_3
| spl10_8
| spl10_9 ),
inference(sat_conversion,[],[f299]) ).
cnf(s17,plain,
( spl10_1
| spl10_5
| spl10_8
| spl10_9 ),
inference(sat_conversion,[],[f300]) ).
cnf(s18,plain,
( spl10_1
| spl10_6
| spl10_8
| spl10_9 ),
inference(sat_conversion,[],[f301]) ).
cnf(s19,plain,
( spl10_10
| spl10_11 ),
inference(sat_conversion,[],[f308]) ).
cnf(s22,plain,
( spl10_12
| spl10_12 ),
inference(sat_conversion,[],[f314]) ).
cnf(s23,plain,
spl10_12,
inference(rat,[],[s22]) ).
cnf(s24,plain,
( ~ spl10_10
| spl10_11
| ~ spl10_12 ),
inference(sat_conversion,[],[f421]) ).
cnf(s27,plain,
( ~ spl10_3
| ~ spl10_5
| ~ spl10_6
| ~ spl10_12 ),
inference(sat_conversion,[],[f507]) ).
cnf(s29,plain,
( ~ spl10_4
| ~ spl10_7
| ~ spl10_8
| ~ spl10_12 ),
inference(sat_conversion,[],[f594]) ).
cnf(s30,plain,
( ~ spl10_1
| ~ spl10_11 ),
inference(sat_conversion,[],[f647]) ).
cnf(s35,plain,
( ~ spl10_2
| ~ spl10_9
| ~ spl10_11 ),
inference(sat_conversion,[],[f845]) ).
cnf(s36,plain,
( spl10_3
| spl10_2
| spl10_1 ),
inference(rat,[],[s29,s1,s4,s7,s23]) ).
cnf(s37,plain,
( spl10_8
| spl10_2
| spl10_1 ),
inference(rat,[],[s27,s8,s9,s36,s23]) ).
cnf(s38,plain,
( spl10_7
| spl10_2
| spl10_1 ),
inference(rat,[],[s27,s5,s6,s36,s23]) ).
cnf(s39,plain,
( spl10_2
| spl10_1 ),
inference(rat,[],[s27,s2,s3,s29,s38,s37,s36,s23]) ).
cnf(s40,plain,
spl10_11,
inference(rat,[],[s19,s24,s23]) ).
cnf(s41,plain,
( spl10_8
| ~ spl10_3
| spl10_1 ),
inference(rat,[],[s27,s17,s18,s35,s39,s23,s40]) ).
cnf(s42,plain,
( spl10_7
| ~ spl10_3
| spl10_1 ),
inference(rat,[],[s27,s14,s15,s35,s39,s23,s40]) ).
cnf(s43,plain,
( ~ spl10_3
| spl10_1 ),
inference(rat,[],[s27,s11,s12,s29,s42,s41,s35,s39,s23,s40]) ).
cnf(s44,plain,
( spl10_3
| spl10_9
| spl10_1 ),
inference(rat,[],[s29,s13,s16,s10,s23]) ).
cnf(s45,plain,
spl10_1,
inference(rat,[],[s44,s43,s35,s39,s40]) ).
cnf(s46,plain,
$false,
inference(rat,[],[s30,s40,s45]) ).
thf(f848,plain,
$false,
inference(avatar_sat_refutation,[],[s46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU492^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n016.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:50:50 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.30 % (373964)Will run a generic schedule for satisfiability detection.
% 0.19/0.30 % (373982)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1059436419_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.30 % (373988)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=305603083:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.30 % (373985)dis+10_1_sil=32000:sp=arity:random_seed=2373464930:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.30 % (373983)% WARNING: option uhcvi not known.
% 0.19/0.30 % (373987)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2732323107:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.30 % Exception at run slice level
% 0.19/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.30 % (373984)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3837400413:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.30 % (373983)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1466637776:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.30 % (373983)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.30 % (373986)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3410068485:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.30 % (373983)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.30 % (373986)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.30 % (373988) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-373964-373988"...
% 0.19/0.30 % (373996)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2724025489:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.30 % Exception at run slice level
% 0.19/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.30 % (373988)...printing done.
% 0.19/0.30 % (373988)Refutation found. Thanks to Tanya!
% 0.19/0.30 % SZS status Theorem for theBenchmark
% 0.19/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.30 % (373988)------------------------------
% 0.19/0.30 % (373988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.30 % (373988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.30 % (373988)CaDiCaL version: 2.1.3
% 0.19/0.30 % (373988)Termination reason: Refutation
% 0.19/0.30 % (373988)Time elapsed: 0.026 s
% 0.19/0.30 % (373988)Peak memory usage: 12 MB
% 0.19/0.30 % (373988)Instructions burned: 51 (million)
% 0.19/0.30 % (373964)Success in time 0.079 s
% 0.19/0.30 % Vampire exiting
%------------------------------------------------------------------------------