%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU497^1 : 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 : n018.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 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 24
% Syntax : Number of formulae : 240 ( 54 unt; 0 typ; 16 def)
% Number of atoms : 2225 ( 539 equ; 0 cnn)
% Maximal formula atoms : 5 ( 9 avg)
% Number of connectives : 2039 ( 168 ~; 542 |; 103 &;1008 @)
% ( 14 <=>; 86 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 128 ( 128 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 65 usr; 25 con; 0-4 aty)
% ( 118 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 282 ( 0 sgn 60 !; 1 ?; 282 :)
% 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,
vNOT: $o > $o ).
thf(func_def_31,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vIMP: $o > $o > $o ).
thf(func_def_42,type,
vAND: $o > $o > $o ).
thf(func_def_43,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
sK0: $i > $i > $o ).
thf(func_def_45,type,
sF1: $o ).
thf(func_def_46,type,
sF2: $o ).
thf(f6,axiom,
( refl
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',reflexive) ).
thf(f8,axiom,
( rc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',reflexive_closure) ).
thf(f10,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X1 ) )
=> ( X1 = X2 ) ) )
= antisymm ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',antisymmetric) ).
thf(f11,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ~ ( X0 @ X2 @ X1 ) ) )
= asymm ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',asymmetric) ).
thf(f13,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
= trans ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',transitive) ).
thf(f17,axiom,
( po
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( refl @ X0 )
& ( antisymm @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',partial_order) ).
thf(f18,axiom,
( so
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( asymm @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',strict_order) ).
thf(f30,conjecture,
! [X0: $i > $i > $o] :
( ( so @ X0 )
=> ( po @ ( rc @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strict_order_induces_partial_order) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( so @ X0 )
=> ( po @ ( rc @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f34,plain,
~ ! [X0: $i > $i > $o] :
( ( so @ X0 )
=> ( po @ ( rc @ X0 ) ) ),
inference(rectify,[],[f31]) ).
thf(f35,plain,
~ ! [X0: $i > $i > $o] :
( ( ( so @ X0 )
= $true )
=> ( ( po @ ( rc @ X0 ) )
= $true ) ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
( rc
= ( ^ [X0: $i > $i > $o,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f37,plain,
( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f50,plain,
( refl
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f6]) ).
thf(f51,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f54,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ~ ( X0 @ X2 @ X1 ) ) )
= asymm ),
inference(rectify,[],[f11]) ).
thf(f55,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f61,plain,
( so
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( asymm @ X0 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f62,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( asymm @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f63,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X2 @ X3 ) ) )
= trans ),
inference(rectify,[],[f13]) ).
thf(f64,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f67,plain,
( po
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( refl @ X0 )
& ( antisymm @ X0 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f68,plain,
( po
= ( ^ [Y0: $i > $i > $o] :
( ( antisymm @ Y0 )
& ( refl @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f74,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X1 ) )
=> ( X1 = X2 ) ) )
= antisymm ),
inference(rectify,[],[f10]) ).
thf(f75,plain,
( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( po @ ( rc @ X0 ) )
!= $true )
& ( ( so @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f35]) ).
thf(f89,plain,
( ( $true
!= ( po @ ( rc @ sK0 ) ) )
& ( $true
= ( so @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
thf(f101,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( asymm @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f103,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f104,plain,
( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y2 = Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f106,plain,
( trans
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f108,plain,
( $true
= ( so @ sK0 ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f109,plain,
( $true
!= ( po @ ( rc @ sK0 ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f111,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f119,plain,
( rc
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f120,plain,
( po
= ( ^ [Y0: $i > $i > $o] :
( ( antisymm @ Y0 )
& ( refl @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f128,plain,
( po
= ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) )
@ Y0 )
& ( ^ [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 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f120,f104,f111,f106]) ).
thf(f129,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 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f101,f103,f106]) ).
thf(f138,plain,
( $true
!= ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) )
@ Y0 )
& ( ^ [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 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f109,f128,f119]) ).
thf(f139,plain,
( $true
= ( ^ [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 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
@ Y0 ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f108,f129]) ).
thf(f140,definition,
( sF1
= ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) )
@ Y0 )
& ( ^ [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 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) )
@ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f141,plain,
$true != sF1,
inference(definition_folding,[],[f138,f140]) ).
thf(f142,definition,
( sF2
= ( ^ [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 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
@ Y0 ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f143,plain,
$true = sF2,
inference(definition_folding,[],[f139,f142]) ).
thf(f145,plain,
( ( $true
= ( ^ [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 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
@ Y0 ) )
@ sK0 ) )
| ( sF2 = $false ) ),
inference(iff_proxy_clausification,[],[f142]) ).
thf(f146,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 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) )
| ( sF2 = $false ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
( ( sF2 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f146]) ).
thf(f148,plain,
( ( sF2 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f146]) ).
thf(f149,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( sF2 = $false ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( ( sF2 = $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ~ ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ~ ( sK0 @ X1 @ Y0 ) )
@ X2 ) )
| ( sF2 = $false ) ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( sK0 @ X2 @ X1 )
=> ~ ( sK0 @ X1 @ X2 ) ) )
| ( sF2 = $false ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( sK0 @ X1 @ X2 ) ) )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( sF2 = $false ) ),
inference(imp_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X2 @ X1 ) )
| ( sF2 = $false ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( sF2 = $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f147]) ).
thf(f156,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X1 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ X1 ) ) ) ) )
| ( sF2 = $false ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( ( sF2 = $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X1 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ X1 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X2 @ Y0 ) )
=> ( sK0 @ X2 @ X1 ) ) ) )
| ( sF2 = $false ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF2 = $false )
| ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X2 @ Y0 ) )
=> ( sK0 @ X2 @ X1 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF2 = $false )
| ( $true
= ( ( ( sK0 @ X3 @ X1 )
& ( sK0 @ X2 @ X3 ) )
=> ( sK0 @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ X1 ) )
| ( sF2 = $false )
| ( ( ( sK0 @ X3 @ X1 )
& ( sK0 @ X2 @ X3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF2 = $false )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X3 @ X1 )
= $false )
| ( $false
= ( sK0 @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f161]) ).
thf(f186,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y1 @ Y2 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y3 = Y2 ) ) ) )
@ Y0 )
& ( ^ [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 @ Y2 )
& ( Y1 @ Y3 @ Y4 ) )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) )
@ sK0 ) )
= $false )
| ( $true = sF1 ) ),
inference(iff_proxy_clausification,[],[f140]) ).
thf(f235,plain,
( ( $true = sF1 )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y0 @ Y1 )
| ( Y0 = Y1 ) )
& ( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ Y0 )
| ( Y0 = Y0 ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK0 @ Y2 @ Y0 )
| ( Y2 = Y0 ) )
& ( ( sK0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) )
=> ( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f236,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y0 @ Y1 )
| ( Y0 = Y1 ) )
& ( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ Y0 )
| ( Y0 = Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK0 @ Y2 @ Y0 )
| ( Y2 = Y0 ) )
& ( ( sK0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) )
=> ( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(and_proxy_clausification,[],[f235]) ).
thf(f237,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y0 @ Y1 )
| ( Y0 = Y1 ) )
& ( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) )
=> ( Y1 = Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK0 @ Y2 @ Y0 )
| ( Y2 = Y0 ) )
& ( ( sK0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) )
=> ( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) ) ) ) ) )
| ( $true = sF1 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ Y0 )
| ( Y0 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f236]) ).
thf(f238,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y0 @ Y1 )
| ( Y0 = Y1 ) )
& ( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) )
=> ( Y1 = Y0 ) ) )
@ sK9 ) )
| ( $true = sF1 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ Y0 )
| ( Y0 = Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK0 @ Y2 @ Y0 )
| ( Y2 = Y0 ) )
& ( ( sK0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) )
=> ( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f237]) ).
thf(f239,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK0 @ Y2 @ Y0 )
| ( Y2 = Y0 ) )
& ( ( sK0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) )
=> ( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ Y0 )
| ( Y0 = Y0 ) )
@ sK10 )
= $false )
| ( $true = sF1 )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y0 @ Y1 )
| ( Y0 = Y1 ) )
& ( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) )
=> ( Y1 = Y0 ) ) )
@ sK9 ) ) ),
inference(sigma_proxy_clausification,[],[f238]) ).
thf(f240,plain,
( ( $true = sF1 )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y0 @ Y1 )
| ( Y0 = Y1 ) )
& ( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) )
=> ( Y1 = Y0 ) ) )
@ sK9 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ( sK0 @ Y2 @ Y0 )
| ( Y2 = Y0 ) )
& ( ( sK0 @ Y1 @ Y2 )
| ( Y1 = Y2 ) ) )
=> ( ( sK0 @ Y1 @ Y0 )
| ( Y1 = Y0 ) ) ) ) )
@ sK11 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ Y0 )
| ( Y0 = Y0 ) )
@ sK10 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f239]) ).
thf(f241,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( sK0 @ sK9 @ Y0 )
| ( sK9 = Y0 ) )
& ( ( sK0 @ Y0 @ sK9 )
| ( Y0 = sK9 ) ) )
=> ( Y0 = sK9 ) ) ) )
| ( $true = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y1 @ sK11 )
| ( Y1 = sK11 ) )
& ( ( sK0 @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) )
=> ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) ) ) ) )
= $false )
| ( $false
= ( ( sK0 @ sK10 @ sK10 )
| ( sK10 = sK10 ) ) ) ),
inference(beta-eta_normalization,[],[f240]) ).
thf(f242,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y1 @ sK11 )
| ( Y1 = sK11 ) )
& ( ( sK0 @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) )
=> ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) ) ) ) )
= $false )
| ( $false
= ( ( sK0 @ sK10 @ sK10 )
| ( sK10 = sK10 ) ) )
| ( $true = sF1 )
| ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ sK9 @ Y0 )
| ( sK9 = Y0 ) )
& ( ( sK0 @ Y0 @ sK9 )
| ( Y0 = sK9 ) ) )
=> ( Y0 = sK9 ) )
@ sK12 ) ) ),
inference(sigma_proxy_clausification,[],[f241]) ).
thf(f243,plain,
( ( $false
= ( ( sK0 @ sK10 @ sK10 )
| ( sK10 = sK10 ) ) )
| ( $true = sF1 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y1 @ sK11 )
| ( Y1 = sK11 ) )
& ( ( sK0 @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) )
=> ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) ) ) )
@ sK13 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ sK9 @ Y0 )
| ( sK9 = Y0 ) )
& ( ( sK0 @ Y0 @ sK9 )
| ( Y0 = sK9 ) ) )
=> ( Y0 = sK9 ) )
@ sK12 ) ) ),
inference(sigma_proxy_clausification,[],[f242]) ).
thf(f244,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y1 @ sK11 )
| ( Y1 = sK11 ) )
& ( ( sK0 @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) )
=> ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) ) ) )
@ sK13 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ sK9 @ Y0 )
| ( sK9 = Y0 ) )
& ( ( sK0 @ Y0 @ sK9 )
| ( Y0 = sK9 ) ) )
=> ( Y0 = sK9 ) )
@ sK12 ) )
| ( $true = sF1 )
| ( ( sK10 = sK10 )
= $false ) ),
inference(or_proxy_clausification,[],[f243]) ).
thf(f294,plain,
( ( $true = sF1 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y1 @ sK11 )
| ( Y1 = sK11 ) )
& ( ( sK0 @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) )
=> ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) ) ) )
@ sK13 )
= $false )
| ( sK10 != sK10 )
| ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ sK9 @ Y0 )
| ( sK9 = Y0 ) )
& ( ( sK0 @ Y0 @ sK9 )
| ( Y0 = sK9 ) ) )
=> ( Y0 = sK9 ) )
@ sK12 ) ) ),
inference(equality_proxy_clausification,[],[f244]) ).
thf(f295,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ( sK0 @ Y1 @ sK11 )
| ( Y1 = sK11 ) )
& ( ( sK0 @ Y0 @ Y1 )
| ( Y0 = Y1 ) ) )
=> ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) ) ) )
@ sK13 )
= $false )
| ( $true = sF1 )
| ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ sK9 @ Y0 )
| ( sK9 = Y0 ) )
& ( ( sK0 @ Y0 @ sK9 )
| ( Y0 = sK9 ) ) )
=> ( Y0 = sK9 ) )
@ sK12 ) ) ),
inference(trivial_inequality_removal,[],[f294]) ).
thf(f296,plain,
( ( $true = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) )
& ( ( sK0 @ sK13 @ Y0 )
| ( sK13 = Y0 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) ) )
= $false )
| ( $false
= ( ( ( ( sK0 @ sK9 @ sK12 )
| ( sK9 = sK12 ) )
& ( ( sK0 @ sK12 @ sK9 )
| ( sK12 = sK9 ) ) )
=> ( sK12 = sK9 ) ) ) ),
inference(beta-eta_normalization,[],[f295]) ).
thf(f297,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) )
& ( ( sK0 @ sK13 @ Y0 )
| ( sK13 = Y0 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) )
@ sK16 ) )
| ( $true = sF1 )
| ( $false
= ( ( ( ( sK0 @ sK9 @ sK12 )
| ( sK9 = sK12 ) )
& ( ( sK0 @ sK12 @ sK9 )
| ( sK12 = sK9 ) ) )
=> ( sK12 = sK9 ) ) ) ),
inference(sigma_proxy_clausification,[],[f296]) ).
thf(f298,plain,
( ( ( sK12 = sK9 )
= $false )
| ( $true = sF1 )
| ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) )
& ( ( sK0 @ sK13 @ Y0 )
| ( sK13 = Y0 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) )
@ sK16 ) ) ),
inference(imp_proxy_clausification,[],[f297]) ).
thf(f299,plain,
( ( $true = sF1 )
| ( $true
= ( ( ( sK0 @ sK9 @ sK12 )
| ( sK9 = sK12 ) )
& ( ( sK0 @ sK12 @ sK9 )
| ( sK12 = sK9 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) )
& ( ( sK0 @ sK13 @ Y0 )
| ( sK13 = Y0 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) )
@ sK16 ) ) ),
inference(imp_proxy_clausification,[],[f297]) ).
thf(f300,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) )
& ( ( sK0 @ sK13 @ Y0 )
| ( sK13 = Y0 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) )
@ sK16 ) )
| ( $true = sF1 )
| ( ( ( sK0 @ sK12 @ sK9 )
| ( sK12 = sK9 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f299]) ).
thf(f301,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) )
& ( ( sK0 @ sK13 @ Y0 )
| ( sK13 = Y0 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) )
@ sK16 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK12 )
| ( sK9 = sK12 ) ) )
| ( $true = sF1 ) ),
inference(and_proxy_clausification,[],[f299]) ).
thf(f302,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) )
& ( ( sK0 @ sK13 @ Y0 )
| ( sK13 = Y0 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) )
@ sK16 ) )
| ( $true
= ( sK9 = sK12 ) )
| ( $true = sF1 )
| ( $true
= ( sK0 @ sK9 @ sK12 ) ) ),
inference(or_proxy_clausification,[],[f301]) ).
thf(f303,plain,
( ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) )
& ( ( sK0 @ sK13 @ Y0 )
| ( sK13 = Y0 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) )
@ sK16 ) )
| ( $true = sF1 )
| ( sK9 = sK12 ) ),
inference(equality_proxy_clausification,[],[f302]) ).
thf(f304,plain,
( ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ( sK9 = sK12 )
| ( $false
= ( ( ( ( sK0 @ sK16 @ sK11 )
| ( sK16 = sK11 ) )
& ( ( sK0 @ sK13 @ sK16 )
| ( sK13 = sK16 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) ) )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f303]) ).
thf(f305,plain,
( ( ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) )
= $false )
| ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ( sK9 = sK12 )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f304]) ).
thf(f306,plain,
( ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ( sK9 = sK12 )
| ( $true
= ( ( ( sK0 @ sK16 @ sK11 )
| ( sK16 = sK11 ) )
& ( ( sK0 @ sK13 @ sK16 )
| ( sK13 = sK16 ) ) ) )
| ( $true = sF1 ) ),
inference(imp_proxy_clausification,[],[f304]) ).
thf(f307,plain,
( ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ( $true = sF1 )
| ( sK9 = sK12 )
| ( $true
= ( ( sK0 @ sK13 @ sK16 )
| ( sK13 = sK16 ) ) ) ),
inference(and_proxy_clausification,[],[f306]) ).
thf(f308,plain,
( ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ( $true
= ( ( sK0 @ sK16 @ sK11 )
| ( sK16 = sK11 ) ) )
| ( sK9 = sK12 )
| ( $true = sF1 ) ),
inference(and_proxy_clausification,[],[f306]) ).
thf(f309,plain,
( ( $true
= ( sK0 @ sK16 @ sK11 ) )
| ( sK9 = sK12 )
| ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ( $true = sF1 )
| ( $true
= ( sK16 = sK11 ) ) ),
inference(or_proxy_clausification,[],[f308]) ).
thf(f310,plain,
( ( $true = sF1 )
| ( sK9 = sK12 )
| ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ( sK11 = sK16 )
| ( $true
= ( sK0 @ sK16 @ sK11 ) ) ),
inference(equality_proxy_clausification,[],[f309]) ).
thf(f311,plain,
( ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ( sK9 = sK12 )
| ( $true
= ( sK0 @ sK13 @ sK16 ) )
| ( $true = sF1 )
| ( $true
= ( sK13 = sK16 ) ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f312,plain,
( ( $true
= ( sK0 @ sK13 @ sK16 ) )
| ( sK9 = sK12 )
| ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ( $true = sF1 )
| ( sK13 = sK16 ) ),
inference(equality_proxy_clausification,[],[f311]) ).
thf(f313,plain,
( ( $true = sF1 )
| ( sK9 = sK12 )
| ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ( ( sK13 = sK11 )
= $false ) ),
inference(or_proxy_clausification,[],[f305]) ).
thf(f314,plain,
( ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ( $true = sF1 )
| ( sK9 = sK12 )
| ( $false
= ( sK0 @ sK13 @ sK11 ) ) ),
inference(or_proxy_clausification,[],[f305]) ).
thf(f315,plain,
( ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ( sK11 != sK13 )
| ( $true = sF1 )
| ( sK9 = sK12 ) ),
inference(equality_proxy_clausification,[],[f313]) ).
thf(f316,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) )
& ( ( sK0 @ sK13 @ Y0 )
| ( sK13 = Y0 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) )
@ sK16 ) )
| ( $true
= ( sK12 = sK9 ) )
| ( $true = sF1 )
| ( $true
= ( sK0 @ sK12 @ sK9 ) ) ),
inference(or_proxy_clausification,[],[f300]) ).
thf(f317,plain,
( ( sK9 = sK12 )
| ( $true
= ( sK0 @ sK12 @ sK9 ) )
| ( $true = sF1 )
| ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) )
& ( ( sK0 @ sK13 @ Y0 )
| ( sK13 = Y0 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) )
@ sK16 ) ) ),
inference(equality_proxy_clausification,[],[f316]) ).
thf(f318,plain,
( ( $true
= ( sK0 @ sK12 @ sK9 ) )
| ( sK9 = sK12 )
| ( $true = sF1 )
| ( $false
= ( ( ( ( sK0 @ sK16 @ sK11 )
| ( sK16 = sK11 ) )
& ( ( sK0 @ sK13 @ sK16 )
| ( sK13 = sK16 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) ) ) ),
inference(beta-eta_normalization,[],[f317]) ).
thf(f319,plain,
( ( sK9 = sK12 )
| ( ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) )
= $false )
| ( $true = sF1 )
| ( $true
= ( sK0 @ sK12 @ sK9 ) ) ),
inference(imp_proxy_clausification,[],[f318]) ).
thf(f320,plain,
( ( $true = sF1 )
| ( $true
= ( sK0 @ sK12 @ sK9 ) )
| ( $true
= ( ( ( sK0 @ sK16 @ sK11 )
| ( sK16 = sK11 ) )
& ( ( sK0 @ sK13 @ sK16 )
| ( sK13 = sK16 ) ) ) )
| ( sK9 = sK12 ) ),
inference(imp_proxy_clausification,[],[f318]) ).
thf(f321,plain,
( ( sK9 = sK12 )
| ( $true
= ( ( sK0 @ sK13 @ sK16 )
| ( sK13 = sK16 ) ) )
| ( $true = sF1 )
| ( $true
= ( sK0 @ sK12 @ sK9 ) ) ),
inference(and_proxy_clausification,[],[f320]) ).
thf(f322,plain,
( ( $true = sF1 )
| ( sK9 = sK12 )
| ( $true
= ( ( sK0 @ sK16 @ sK11 )
| ( sK16 = sK11 ) ) )
| ( $true
= ( sK0 @ sK12 @ sK9 ) ) ),
inference(and_proxy_clausification,[],[f320]) ).
thf(f323,plain,
( ( $true
= ( sK0 @ sK12 @ sK9 ) )
| ( sK9 = sK12 )
| ( $true = sF1 )
| ( $true
= ( sK16 = sK11 ) )
| ( $true
= ( sK0 @ sK16 @ sK11 ) ) ),
inference(or_proxy_clausification,[],[f322]) ).
thf(f324,plain,
( ( $true = sF1 )
| ( $true
= ( sK0 @ sK12 @ sK9 ) )
| ( sK9 = sK12 )
| ( sK11 = sK16 )
| ( $true
= ( sK0 @ sK16 @ sK11 ) ) ),
inference(equality_proxy_clausification,[],[f323]) ).
thf(f325,plain,
( ( sK9 = sK12 )
| ( $true
= ( sK13 = sK16 ) )
| ( $true
= ( sK0 @ sK13 @ sK16 ) )
| ( $true
= ( sK0 @ sK12 @ sK9 ) )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f321]) ).
thf(f326,plain,
( ( $true = sF1 )
| ( sK9 = sK12 )
| ( $true
= ( sK0 @ sK13 @ sK16 ) )
| ( $true
= ( sK0 @ sK12 @ sK9 ) )
| ( sK13 = sK16 ) ),
inference(equality_proxy_clausification,[],[f325]) ).
thf(f327,plain,
( ( $true
= ( sK0 @ sK12 @ sK9 ) )
| ( ( sK13 = sK11 )
= $false )
| ( sK9 = sK12 )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f319]) ).
thf(f328,plain,
( ( $false
= ( sK0 @ sK13 @ sK11 ) )
| ( sK9 = sK12 )
| ( $true
= ( sK0 @ sK12 @ sK9 ) )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f319]) ).
thf(f329,plain,
( ( $true = sF1 )
| ( $true
= ( sK0 @ sK12 @ sK9 ) )
| ( sK11 != sK13 )
| ( sK9 = sK12 ) ),
inference(equality_proxy_clausification,[],[f327]) ).
thf(f330,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( ( sK0 @ Y0 @ sK11 )
| ( Y0 = sK11 ) )
& ( ( sK0 @ sK13 @ Y0 )
| ( sK13 = Y0 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) )
@ sK16 ) )
| ( $true = sF1 )
| ( sK9 != sK12 ) ),
inference(equality_proxy_clausification,[],[f298]) ).
thf(f331,plain,
( ( $true = sF1 )
| ( $false
= ( ( ( ( sK0 @ sK16 @ sK11 )
| ( sK16 = sK11 ) )
& ( ( sK0 @ sK13 @ sK16 )
| ( sK13 = sK16 ) ) )
=> ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) ) ) )
| ( sK9 != sK12 ) ),
inference(beta-eta_normalization,[],[f330]) ).
thf(f332,plain,
( ( $true = sF1 )
| ( ( ( sK0 @ sK13 @ sK11 )
| ( sK13 = sK11 ) )
= $false )
| ( sK9 != sK12 ) ),
inference(imp_proxy_clausification,[],[f331]) ).
thf(f333,plain,
( ( $true = sF1 )
| ( sK9 != sK12 )
| ( $true
= ( ( ( sK0 @ sK16 @ sK11 )
| ( sK16 = sK11 ) )
& ( ( sK0 @ sK13 @ sK16 )
| ( sK13 = sK16 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f331]) ).
thf(f334,plain,
( ( $true = sF1 )
| ( sK9 != sK12 )
| ( $true
= ( ( sK0 @ sK13 @ sK16 )
| ( sK13 = sK16 ) ) ) ),
inference(and_proxy_clausification,[],[f333]) ).
thf(f335,plain,
( ( $true
= ( ( sK0 @ sK16 @ sK11 )
| ( sK16 = sK11 ) ) )
| ( $true = sF1 )
| ( sK9 != sK12 ) ),
inference(and_proxy_clausification,[],[f333]) ).
thf(f336,plain,
( ( $true
= ( sK0 @ sK16 @ sK11 ) )
| ( $true
= ( sK16 = sK11 ) )
| ( sK9 != sK12 )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f335]) ).
thf(f337,plain,
( ( sK9 != sK12 )
| ( sK11 = sK16 )
| ( $true = sF1 )
| ( $true
= ( sK0 @ sK16 @ sK11 ) ) ),
inference(equality_proxy_clausification,[],[f336]) ).
thf(f338,plain,
( ( $true
= ( sK0 @ sK13 @ sK16 ) )
| ( $true
= ( sK13 = sK16 ) )
| ( $true = sF1 )
| ( sK9 != sK12 ) ),
inference(or_proxy_clausification,[],[f334]) ).
thf(f339,plain,
( ( $true = sF1 )
| ( sK13 = sK16 )
| ( sK9 != sK12 )
| ( $true
= ( sK0 @ sK13 @ sK16 ) ) ),
inference(equality_proxy_clausification,[],[f338]) ).
thf(f340,plain,
( ( ( sK13 = sK11 )
= $false )
| ( $true = sF1 )
| ( sK9 != sK12 ) ),
inference(or_proxy_clausification,[],[f332]) ).
thf(f341,plain,
( ( $true = sF1 )
| ( sK9 != sK12 )
| ( $false
= ( sK0 @ sK13 @ sK11 ) ) ),
inference(or_proxy_clausification,[],[f332]) ).
thf(f342,plain,
( ( $true = sF1 )
| ( sK11 != sK13 )
| ( sK9 != sK12 ) ),
inference(equality_proxy_clausification,[],[f340]) ).
thf(f344,definition,
( spl17_1
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
thf(f345,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f344]) ).
thf(f347,definition,
( spl17_2
<=> ( sF2 = $false ) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
thf(f349,plain,
( ( sF2 = $false )
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f347]) ).
thf(f350,plain,
( spl17_1
| spl17_2 ),
inference(avatar_split_clause,[],[f154,f347,f344]) ).
thf(f352,definition,
( spl17_3
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( sK0 @ X3 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
thf(f353,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X3 @ X1 )
= $false )
| ( $false
= ( sK0 @ X2 @ X3 ) ) )
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f352]) ).
thf(f354,plain,
( spl17_3
| spl17_2 ),
inference(avatar_split_clause,[],[f162,f347,f352]) ).
thf(f364,definition,
( spl17_6
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl17_6])],[avatar_definition]) ).
thf(f366,plain,
( ( $true = sF2 )
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f364]) ).
thf(f418,definition,
( spl17_18
<=> ( sK9 = sK12 ) ),
introduced(definition,[new_symbols(definition,[spl17_18])],[avatar_definition]) ).
thf(f434,definition,
( spl17_22
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl17_22])],[avatar_definition]) ).
thf(f438,definition,
( spl17_23
<=> ( $true
= ( sK0 @ sK9 @ sK12 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_23])],[avatar_definition]) ).
thf(f440,plain,
( ( $true
= ( sK0 @ sK9 @ sK12 ) )
| ~ spl17_23 ),
inference(avatar_component_clause,[],[f438]) ).
thf(f452,definition,
( spl17_26
<=> ( $false
= ( sK0 @ sK13 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_26])],[avatar_definition]) ).
thf(f454,plain,
( ( $false
= ( sK0 @ sK13 @ sK11 ) )
| ~ spl17_26 ),
inference(avatar_component_clause,[],[f452]) ).
thf(f457,definition,
( spl17_27
<=> ( sK11 = sK13 ) ),
introduced(definition,[new_symbols(definition,[spl17_27])],[avatar_definition]) ).
thf(f459,plain,
( ( sK11 != sK13 )
| spl17_27 ),
inference(avatar_component_clause,[],[f457]) ).
thf(f462,definition,
( spl17_28
<=> ( $true
= ( sK0 @ sK12 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_28])],[avatar_definition]) ).
thf(f464,plain,
( ( $true
= ( sK0 @ sK12 @ sK9 ) )
| ~ spl17_28 ),
inference(avatar_component_clause,[],[f462]) ).
thf(f490,definition,
( spl17_33
<=> ( sK11 = sK16 ) ),
introduced(definition,[new_symbols(definition,[spl17_33])],[avatar_definition]) ).
thf(f492,plain,
( ( sK11 = sK16 )
| ~ spl17_33 ),
inference(avatar_component_clause,[],[f490]) ).
thf(f494,definition,
( spl17_34
<=> ( $true
= ( sK0 @ sK16 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_34])],[avatar_definition]) ).
thf(f496,plain,
( ( $true
= ( sK0 @ sK16 @ sK11 ) )
| ~ spl17_34 ),
inference(avatar_component_clause,[],[f494]) ).
thf(f497,plain,
( spl17_33
| spl17_34
| spl17_18
| spl17_23
| spl17_22 ),
inference(avatar_split_clause,[],[f310,f434,f438,f418,f494,f490]) ).
thf(f499,definition,
( spl17_35
<=> ( $true
= ( sK0 @ sK13 @ sK16 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_35])],[avatar_definition]) ).
thf(f501,plain,
( ( $true
= ( sK0 @ sK13 @ sK16 ) )
| ~ spl17_35 ),
inference(avatar_component_clause,[],[f499]) ).
thf(f503,definition,
( spl17_36
<=> ( sK13 = sK16 ) ),
introduced(definition,[new_symbols(definition,[spl17_36])],[avatar_definition]) ).
thf(f505,plain,
( ( sK13 = sK16 )
| ~ spl17_36 ),
inference(avatar_component_clause,[],[f503]) ).
thf(f506,plain,
( spl17_35
| spl17_23
| spl17_36
| spl17_18
| spl17_22 ),
inference(avatar_split_clause,[],[f312,f434,f418,f503,f438,f499]) ).
thf(f507,plain,
( spl17_22
| spl17_26
| spl17_18
| spl17_23 ),
inference(avatar_split_clause,[],[f314,f438,f418,f452,f434]) ).
thf(f508,plain,
( ~ spl17_27
| spl17_23
| spl17_18
| spl17_22 ),
inference(avatar_split_clause,[],[f315,f434,f418,f438,f457]) ).
thf(f509,plain,
( spl17_34
| spl17_18
| spl17_28
| spl17_22
| spl17_33 ),
inference(avatar_split_clause,[],[f324,f490,f434,f462,f418,f494]) ).
thf(f510,plain,
( spl17_18
| spl17_28
| spl17_36
| spl17_22
| spl17_35 ),
inference(avatar_split_clause,[],[f326,f499,f434,f503,f462,f418]) ).
thf(f511,plain,
( spl17_28
| spl17_18
| spl17_26
| spl17_22 ),
inference(avatar_split_clause,[],[f328,f434,f452,f418,f462]) ).
thf(f512,plain,
( ~ spl17_27
| spl17_18
| spl17_22
| spl17_28 ),
inference(avatar_split_clause,[],[f329,f462,f434,f418,f457]) ).
thf(f513,plain,
( ~ spl17_18
| spl17_34
| spl17_22
| spl17_33 ),
inference(avatar_split_clause,[],[f337,f490,f434,f494,f418]) ).
thf(f514,plain,
( spl17_35
| spl17_22
| ~ spl17_18
| spl17_36 ),
inference(avatar_split_clause,[],[f339,f503,f418,f434,f499]) ).
thf(f515,plain,
( spl17_26
| spl17_22
| ~ spl17_18 ),
inference(avatar_split_clause,[],[f341,f418,f434,f452]) ).
thf(f516,plain,
( ~ spl17_18
| ~ spl17_27
| spl17_22 ),
inference(avatar_split_clause,[],[f342,f434,f457,f418]) ).
thf(f517,plain,
~ spl17_22,
inference(avatar_split_clause,[],[f141,f434]) ).
thf(f518,plain,
spl17_6,
inference(avatar_split_clause,[],[f143,f364]) ).
thf(f528,plain,
( ( $true = $false )
| ~ spl17_2
| ~ spl17_6 ),
inference(forward_demodulation,[],[f366,f349]) ).
thf(f529,plain,
( $false
| ~ spl17_2
| ~ spl17_6 ),
inference(trivial_inequality_removal,[],[f528]) ).
thf(f530,plain,
( ~ spl17_2
| ~ spl17_6 ),
inference(avatar_contradiction_clause,[],[f529]) ).
thf(f546,plain,
( ( $true = $false )
| ( ( sK0 @ sK9 @ sK12 )
= $false )
| ~ spl17_1
| ~ spl17_28 ),
inference(constrained_superposition,[],[f464,f345]) ).
thf(f549,plain,
( ( ( sK0 @ sK9 @ sK12 )
= $false )
| ~ spl17_1
| ~ spl17_28 ),
inference(trivial_inequality_removal,[],[f546]) ).
thf(f553,plain,
( ( $true = $false )
| ~ spl17_1
| ~ spl17_23
| ~ spl17_28 ),
inference(forward_demodulation,[],[f549,f440]) ).
thf(f554,plain,
( $false
| ~ spl17_1
| ~ spl17_23
| ~ spl17_28 ),
inference(trivial_inequality_removal,[],[f553]) ).
thf(f555,plain,
( ~ spl17_1
| ~ spl17_23
| ~ spl17_28 ),
inference(avatar_contradiction_clause,[],[f554]) ).
thf(f561,plain,
( ( $true
= ( sK0 @ sK13 @ sK11 ) )
| ~ spl17_33
| ~ spl17_35 ),
inference(forward_demodulation,[],[f501,f492]) ).
thf(f562,plain,
( ( $true = $false )
| ~ spl17_26
| ~ spl17_33
| ~ spl17_35 ),
inference(forward_demodulation,[],[f561,f454]) ).
thf(f563,plain,
( $false
| ~ spl17_26
| ~ spl17_33
| ~ spl17_35 ),
inference(trivial_inequality_removal,[],[f562]) ).
thf(f564,plain,
( ~ spl17_26
| ~ spl17_33
| ~ spl17_35 ),
inference(avatar_contradiction_clause,[],[f563]) ).
thf(f571,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( sK0 @ X0 @ sK11 )
= $false )
| ( ( sK0 @ sK13 @ X0 )
= $false ) )
| ~ spl17_3
| ~ spl17_26 ),
inference(constrained_superposition,[],[f454,f353]) ).
thf(f577,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK13 @ X0 )
= $false )
| ( ( sK0 @ X0 @ sK11 )
= $false ) )
| ~ spl17_3
| ~ spl17_26 ),
inference(trivial_inequality_removal,[],[f571]) ).
thf(f636,plain,
( ( $true = $false )
| ( ( sK0 @ sK16 @ sK11 )
= $false )
| ~ spl17_3
| ~ spl17_26
| ~ spl17_35 ),
inference(constrained_superposition,[],[f501,f577]) ).
thf(f642,plain,
( ( ( sK0 @ sK16 @ sK11 )
= $false )
| ~ spl17_3
| ~ spl17_26
| ~ spl17_35 ),
inference(trivial_inequality_removal,[],[f636]) ).
thf(f646,plain,
( ( $true = $false )
| ~ spl17_3
| ~ spl17_26
| ~ spl17_34
| ~ spl17_35 ),
inference(forward_demodulation,[],[f642,f496]) ).
thf(f647,plain,
( $false
| ~ spl17_3
| ~ spl17_26
| ~ spl17_34
| ~ spl17_35 ),
inference(trivial_inequality_removal,[],[f646]) ).
thf(f648,plain,
( ~ spl17_3
| ~ spl17_26
| ~ spl17_34
| ~ spl17_35 ),
inference(avatar_contradiction_clause,[],[f647]) ).
thf(f650,plain,
( ( $true
= ( sK0 @ sK13 @ sK11 ) )
| ~ spl17_34
| ~ spl17_36 ),
inference(constrained_superposition,[],[f496,f505]) ).
thf(f652,plain,
( ( $true = $false )
| ~ spl17_26
| ~ spl17_34
| ~ spl17_36 ),
inference(forward_demodulation,[],[f650,f454]) ).
thf(f653,plain,
( $false
| ~ spl17_26
| ~ spl17_34
| ~ spl17_36 ),
inference(trivial_inequality_removal,[],[f652]) ).
thf(f654,plain,
( ~ spl17_26
| ~ spl17_34
| ~ spl17_36 ),
inference(avatar_contradiction_clause,[],[f653]) ).
thf(f655,plain,
( ( sK11 = sK13 )
| ~ spl17_33
| ~ spl17_36 ),
inference(forward_demodulation,[],[f492,f505]) ).
thf(f657,plain,
( $false
| spl17_27
| ~ spl17_33
| ~ spl17_36 ),
inference(forward_subsumption_resolution,[],[f655,f459]) ).
thf(f658,plain,
( spl17_27
| ~ spl17_33
| ~ spl17_36 ),
inference(avatar_contradiction_clause,[],[f657]) ).
cnf(s1,plain,
( spl17_1
| spl17_2 ),
inference(sat_conversion,[],[f350]) ).
cnf(s2,plain,
( spl17_2
| spl17_3 ),
inference(sat_conversion,[],[f354]) ).
cnf(s26,plain,
( spl17_18
| spl17_22
| spl17_23
| spl17_33
| spl17_34 ),
inference(sat_conversion,[],[f497]) ).
cnf(s27,plain,
( spl17_18
| spl17_22
| spl17_23
| spl17_35
| spl17_36 ),
inference(sat_conversion,[],[f506]) ).
cnf(s28,plain,
( spl17_18
| spl17_22
| spl17_23
| spl17_26 ),
inference(sat_conversion,[],[f507]) ).
cnf(s29,plain,
( spl17_18
| spl17_22
| spl17_23
| ~ spl17_27 ),
inference(sat_conversion,[],[f508]) ).
cnf(s30,plain,
( spl17_18
| spl17_22
| spl17_28
| spl17_33
| spl17_34 ),
inference(sat_conversion,[],[f509]) ).
cnf(s31,plain,
( spl17_18
| spl17_22
| spl17_28
| spl17_35
| spl17_36 ),
inference(sat_conversion,[],[f510]) ).
cnf(s32,plain,
( spl17_18
| spl17_22
| spl17_26
| spl17_28 ),
inference(sat_conversion,[],[f511]) ).
cnf(s33,plain,
( spl17_18
| spl17_22
| ~ spl17_27
| spl17_28 ),
inference(sat_conversion,[],[f512]) ).
cnf(s34,plain,
( ~ spl17_18
| spl17_22
| spl17_33
| spl17_34 ),
inference(sat_conversion,[],[f513]) ).
cnf(s35,plain,
( ~ spl17_18
| spl17_22
| spl17_35
| spl17_36 ),
inference(sat_conversion,[],[f514]) ).
cnf(s36,plain,
( ~ spl17_18
| spl17_22
| spl17_26 ),
inference(sat_conversion,[],[f515]) ).
cnf(s37,plain,
( ~ spl17_18
| spl17_22
| ~ spl17_27 ),
inference(sat_conversion,[],[f516]) ).
cnf(s38,plain,
~ spl17_22,
inference(sat_conversion,[],[f517]) ).
cnf(s39,plain,
spl17_6,
inference(sat_conversion,[],[f518]) ).
cnf(s40,plain,
( ~ spl17_2
| ~ spl17_6 ),
inference(sat_conversion,[],[f530]) ).
cnf(s42,plain,
( ~ spl17_1
| ~ spl17_23
| ~ spl17_28 ),
inference(sat_conversion,[],[f555]) ).
cnf(s43,plain,
( ~ spl17_26
| ~ spl17_33
| ~ spl17_35 ),
inference(sat_conversion,[],[f564]) ).
cnf(s45,plain,
( ~ spl17_3
| ~ spl17_26
| ~ spl17_34
| ~ spl17_35 ),
inference(sat_conversion,[],[f648]) ).
cnf(s46,plain,
( ~ spl17_26
| ~ spl17_34
| ~ spl17_36 ),
inference(sat_conversion,[],[f654]) ).
cnf(s47,plain,
( spl17_27
| ~ spl17_33
| ~ spl17_36 ),
inference(sat_conversion,[],[f658]) ).
cnf(s48,plain,
~ spl17_2,
inference(rat,[],[s40,s39]) ).
cnf(s49,plain,
( ~ spl17_18
| ~ spl17_27 ),
inference(rat,[],[s37,s38]) ).
cnf(s50,plain,
( ~ spl17_18
| spl17_26 ),
inference(rat,[],[s36,s38]) ).
cnf(s51,plain,
( ~ spl17_18
| spl17_35
| spl17_36 ),
inference(rat,[],[s35,s38]) ).
cnf(s52,plain,
( ~ spl17_18
| spl17_33
| spl17_34 ),
inference(rat,[],[s34,s38]) ).
cnf(s53,plain,
( spl17_18
| ~ spl17_27
| spl17_28 ),
inference(rat,[],[s33,s38]) ).
cnf(s54,plain,
( spl17_18
| spl17_26
| spl17_28 ),
inference(rat,[],[s32,s38]) ).
cnf(s55,plain,
( spl17_18
| spl17_28
| spl17_35
| spl17_36 ),
inference(rat,[],[s31,s38]) ).
cnf(s56,plain,
( spl17_18
| spl17_28
| spl17_33
| spl17_34 ),
inference(rat,[],[s30,s38]) ).
cnf(s57,plain,
( spl17_18
| spl17_23
| ~ spl17_27 ),
inference(rat,[],[s29,s38]) ).
cnf(s58,plain,
( spl17_18
| spl17_23
| spl17_26 ),
inference(rat,[],[s28,s38]) ).
cnf(s59,plain,
( spl17_18
| spl17_23
| spl17_35
| spl17_36 ),
inference(rat,[],[s27,s38]) ).
cnf(s60,plain,
( spl17_18
| spl17_23
| spl17_33
| spl17_34 ),
inference(rat,[],[s26,s38]) ).
cnf(s73,plain,
spl17_3,
inference(rat,[],[s2,s48]) ).
cnf(s74,plain,
spl17_1,
inference(rat,[],[s1,s48]) ).
cnf(s76,plain,
( ~ spl17_34
| spl17_28
| spl17_18 ),
inference(rat,[],[s55,s45,s46,s54,s73]) ).
cnf(s77,plain,
( spl17_28
| spl17_18 ),
inference(rat,[],[s55,s43,s47,s56,s76,s54,s53]) ).
cnf(s78,plain,
( ~ spl17_34
| spl17_18 ),
inference(rat,[],[s59,s45,s46,s58,s42,s77,s73,s74]) ).
cnf(s79,plain,
( spl17_23
| spl17_18 ),
inference(rat,[],[s59,s43,s47,s60,s78,s58,s57]) ).
cnf(s80,plain,
spl17_18,
inference(rat,[],[s79,s42,s77,s74]) ).
cnf(s81,plain,
~ spl17_27,
inference(rat,[],[s49,s80]) ).
cnf(s82,plain,
spl17_26,
inference(rat,[],[s50,s80]) ).
cnf(s83,plain,
~ spl17_34,
inference(rat,[],[s51,s45,s46,s80,s73,s82]) ).
cnf(s84,plain,
spl17_33,
inference(rat,[],[s52,s80,s83]) ).
cnf(s85,plain,
~ spl17_36,
inference(rat,[],[s47,s81,s84]) ).
cnf(s86,plain,
~ spl17_35,
inference(rat,[],[s43,s82,s84]) ).
cnf(s87,plain,
$false,
inference(rat,[],[s51,s80,s85,s86]) ).
thf(f660,plain,
$false,
inference(avatar_sat_refutation,[],[s87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU497^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:48:36 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.31 % (90465)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (90473)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=863197089: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)
% 0.21/0.31 % (90476)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (90476)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
% 0.21/0.31 % (90472)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=923603292:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (90470)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3066603374:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (90475)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3165152931:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (90471)lrs+10_16_si=on:nwc=1.5:random_seed=3605907153:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (90474)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2971786905:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (90476)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=1183437791:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (90472)Instruction limit reached!
% 0.21/0.31 % (90472)------------------------------
% 0.21/0.31 % (90472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (90472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (90472)CaDiCaL version: 2.1.3
% 0.21/0.31 % (90472)Termination reason: Instruction limit
% 0.21/0.31 % (90472)Termination phase: Property scanning
% 0.21/0.31 % (90472)Time elapsed: 0.002 s
% 0.21/0.31 % (90472)Peak memory usage: 10 MB
% 0.21/0.31 % (90472)Instructions burned: 4 (million)
% 0.21/0.31 % (90471)Instruction limit reached!
% 0.21/0.31 % (90471)------------------------------
% 0.21/0.31 % (90471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (90471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (90471)CaDiCaL version: 2.1.3
% 0.21/0.31 % (90471)Termination reason: Instruction limit
% 0.21/0.31 % (90471)Termination phase: Saturation
% 0.21/0.31 % (90471)Time elapsed: 0.009 s
% 0.21/0.31 % (90471)Peak memory usage: 12 MB
% 0.21/0.31 % (90471)Instructions burned: 18 (million)
% 0.21/0.31 % (90476) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-90465-90476"...
% 0.21/0.31 % (90474)Instruction limit reached!
% 0.21/0.31 % (90474)------------------------------
% 0.21/0.31 % (90474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (90474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (90474)CaDiCaL version: 2.1.3
% 0.21/0.31 % (90474)Termination reason: Instruction limit
% 0.21/0.31 % (90474)Termination phase: Saturation
% 0.21/0.31 % (90474)Time elapsed: 0.014 s
% 0.21/0.31 % (90474)Peak memory usage: 12 MB
% 0.21/0.31 % (90474)Instructions burned: 24 (million)
% 0.21/0.31 % (90470) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-90465-90470"...
% 0.21/0.31 % (90484)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2548253501:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.31 % (90476)...printing done.
% 0.21/0.31 % (90476)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (90476)------------------------------
% 0.21/0.31 % (90476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (90476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (90476)CaDiCaL version: 2.1.3
% 0.21/0.31 % (90476)Termination reason: Refutation
% 0.21/0.31 % (90476)Time elapsed: 0.019 s
% 0.21/0.31 % (90476)Peak memory usage: 13 MB
% 0.21/0.31 % (90476)Instructions burned: 36 (million)
% 0.21/0.31 % (90465)Success in time 0.06 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------