%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU498^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 17
% Syntax : Number of formulae : 193 ( 54 unt; 0 typ; 10 def)
% Number of atoms : 1512 ( 357 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 1543 ( 235 ~; 174 |; 182 &; 790 @)
% ( 10 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 58 usr; 18 con; 0-4 aty)
% ( 84 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 211 ( 0 sgn 52 !; 1 ?; 211 :)
% 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(f6,axiom,
( refl
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',reflexive) ).
thf(f10,axiom,
( antisymm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',antisymmetric) ).
thf(f11,axiom,
( asymm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ~ ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',asymmetric) ).
thf(f13,axiom,
( trans
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET009^0.ax',transitive) ).
thf(f17,axiom,
( po
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( antisymm @ X0 )
& ( refl @ 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] :
( ( po @ X0 )
=> ( so
@ ^ [X1: $i,X2: $i] :
( ( X1 != X2 )
& ( X0 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partial_order_induces_strict_order) ).
thf(f31,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( po @ X0 )
=> ( so
@ ^ [X1: $i,X2: $i] :
( ( X1 != X2 )
& ( X0 @ X1 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f40,plain,
( refl
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f6]) ).
thf(f41,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f48,plain,
( antisymm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f10]) ).
thf(f49,plain,
( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f48]) ).
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(f60,plain,
( po
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( antisymm @ X0 )
& ( refl @ X0 ) ) ) ),
inference(rectify,[],[f17]) ).
thf(f61,plain,
( po
= ( ^ [Y0: $i > $i > $o] :
( ( refl @ Y0 )
& ( antisymm @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(fool_elimination,[],[f60]) ).
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,
~ ! [X0: $i > $i > $o] :
( ( po @ X0 )
=> ( so
@ ^ [X1: $i,X2: $i] :
( ( X1 != X2 )
& ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f87,plain,
~ ! [X0: $i > $i > $o] :
( ( ( po @ X0 )
= $true )
=> ( $true
= ( so
@ ^ [Y0: $i,Y1: $i] :
( ( X0 @ Y0 @ Y1 )
& ( Y0 != Y1 ) ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( $true
!= ( so
@ ^ [Y0: $i,Y1: $i] :
( ( X0 @ Y0 @ Y1 )
& ( Y0 != Y1 ) ) ) )
& ( ( po @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f87]) ).
thf(f89,plain,
( ( $true
!= ( so
@ ^ [Y0: $i,Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( Y0 != Y1 ) ) ) )
& ( $true
= ( po @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
thf(f95,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f99,plain,
( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f100,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f102,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,
( po
= ( ^ [Y0: $i > $i > $o] :
( ( refl @ Y0 )
& ( antisymm @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f107,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( asymm @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f119,plain,
( $true
= ( po @ sK0 ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f120,plain,
( $true
!= ( so
@ ^ [Y0: $i,Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( Y0 != Y1 ) ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f128,plain,
( po
= ( ^ [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] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y3 = 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,[],[f106,f95,f99,f102]) ).
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 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f107,f100,f102]) ).
thf(f138,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 @ Y3 )
& ( Y1 @ Y3 @ Y2 ) )
=> ( Y1 @ Y4 @ Y2 ) ) ) ) )
@ Y0 ) )
@ ^ [Y0: $i,Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( Y0 != Y1 ) ) ) ),
inference(definition_unfolding,[],[f120,f129]) ).
thf(f139,plain,
( $true
= ( ^ [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] :
( ( ( Y1 @ Y3 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y3 = 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 ) )
@ sK0 ) ),
inference(definition_unfolding,[],[f119,f128]) ).
thf(f140,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( Y1 = Y0 ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( Y1 = Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f140]) ).
thf(f143,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f147,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f143]) ).
thf(f148,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X1 @ X2 ) )
=> ( X2 = X1 ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X1 @ X2 ) ) )
| ( $true
= ( X2 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( X2 = X1 ) )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f141]) ).
thf(f155,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X2 @ X1 ) ) )
| ( $true
= ( sK0 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $true
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( $true
!= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( Y1 != Y0 ) )
=> ~ ( ( sK0 @ Y0 @ Y1 )
& ( Y0 != Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y2 != Y1 )
& ( sK0 @ Y1 @ Y0 )
& ( Y1 != Y0 ) )
=> ( ( sK0 @ Y2 @ Y0 )
& ( Y2 != Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f163,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y2 != Y1 )
& ( sK0 @ Y1 @ Y0 )
& ( Y1 != Y0 ) )
=> ( ( sK0 @ Y2 @ Y0 )
& ( Y2 != Y0 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( Y1 != Y0 ) )
=> ~ ( ( sK0 @ Y0 @ Y1 )
& ( Y0 != Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y2 != Y1 )
& ( sK0 @ Y1 @ Y0 )
& ( Y1 != Y0 ) )
=> ( ( sK0 @ Y2 @ Y0 )
& ( Y2 != Y0 ) ) ) ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( Y1 != Y0 ) )
=> ~ ( ( sK0 @ Y0 @ Y1 )
& ( Y0 != Y1 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y2 != Y1 )
& ( sK0 @ Y1 @ Y0 )
& ( Y1 != Y0 ) )
=> ( ( sK0 @ Y2 @ Y0 )
& ( Y2 != Y0 ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( Y1 != Y0 ) )
=> ~ ( ( sK0 @ Y0 @ Y1 )
& ( Y0 != Y1 ) ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( Y1 != Y0 )
& ( sK0 @ Y0 @ sK1 )
& ( Y0 != sK1 ) )
=> ( ( sK0 @ Y1 @ sK1 )
& ( Y1 != sK1 ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK2 )
& ( Y0 != sK2 ) )
=> ~ ( ( sK0 @ sK2 @ Y0 )
& ( sK2 != Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( Y1 != Y0 )
& ( sK0 @ Y0 @ sK1 )
& ( Y0 != sK1 ) )
=> ( ( sK0 @ Y1 @ sK1 )
& ( Y1 != sK1 ) ) ) )
@ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK2 )
& ( Y0 != sK2 ) )
=> ~ ( ( sK0 @ sK2 @ Y0 )
& ( sK2 != Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( Y1 != Y0 )
& ( sK0 @ Y0 @ sK1 )
& ( Y0 != sK1 ) )
=> ( ( sK0 @ Y1 @ sK1 )
& ( Y1 != sK1 ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK2 )
& ( Y0 != sK2 ) )
=> ~ ( ( sK0 @ sK2 @ Y0 )
& ( sK2 != Y0 ) ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( Y0 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) )
=> ( ( sK0 @ Y0 @ sK1 )
& ( Y0 != sK1 ) ) ) ) )
| ( $false
= ( ( ( sK0 @ sK4 @ sK2 )
& ( sK4 != sK2 ) )
=> ~ ( ( sK0 @ sK2 @ sK4 )
& ( sK2 != sK4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( Y0 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) )
=> ( ( sK0 @ Y0 @ sK1 )
& ( Y0 != sK1 ) ) )
@ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK4 @ sK2 )
& ( sK4 != sK2 ) )
=> ~ ( ( sK0 @ sK2 @ sK4 )
& ( sK2 != sK4 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( Y0 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) )
=> ( ( sK0 @ Y0 @ sK1 )
& ( Y0 != sK1 ) ) )
@ sK5 ) )
| ( $false
= ( ~ ( ( sK0 @ sK2 @ sK4 )
& ( sK2 != sK4 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( Y0 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) )
=> ( ( sK0 @ Y0 @ sK1 )
& ( Y0 != sK1 ) ) )
@ sK5 ) )
| ( $true
= ( ( sK0 @ sK4 @ sK2 )
& ( sK4 != sK2 ) ) ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f174,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( Y0 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) )
=> ( ( sK0 @ Y0 @ sK1 )
& ( Y0 != sK1 ) ) )
@ sK5 ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( ( $false
= ( ( ( sK0 @ sK5 @ sK3 )
& ( sK5 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) )
=> ( ( sK0 @ sK5 @ sK1 )
& ( sK5 != sK1 ) ) ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
( ( $false
= ( ( sK0 @ sK5 @ sK1 )
& ( sK5 != sK1 ) ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $true
= ( ( sK0 @ sK5 @ sK3 )
& ( sK5 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( ( $true
= ( ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( $true
= ( ( sK0 @ sK5 @ sK3 )
& ( sK5 != sK3 ) ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f177]) ).
thf(f181,plain,
( ( $true
= ( sK0 @ sK5 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f179]) ).
thf(f184,plain,
( ( $true
= ( sK3 != sK1 ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f178]) ).
thf(f185,plain,
( ( $true
= ( sK0 @ sK3 @ sK1 ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f178]) ).
thf(f186,plain,
( ( $false
= ( sK3 = sK1 ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f187,plain,
( ( sK1 != sK3 )
| ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
inference(equality_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( $false
= ( sK5 != sK1 ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) )
| ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f176]) ).
thf(f189,plain,
( ( $true
= ( sK5 = sK1 ) )
| ( $true
= ( sK0 @ sK4 @ sK2 ) )
| ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( sK1 = sK5 )
| ( $true
= ( sK0 @ sK4 @ sK2 ) )
| ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f189]) ).
thf(f209,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( Y0 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) )
=> ( ( sK0 @ Y0 @ sK1 )
& ( Y0 != sK1 ) ) )
@ sK5 ) )
| ( $true
= ( ( sK0 @ sK2 @ sK4 )
& ( sK2 != sK4 ) ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f210,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( Y0 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) )
=> ( ( sK0 @ Y0 @ sK1 )
& ( Y0 != sK1 ) ) )
@ sK5 ) )
| ( $true
= ( sK2 != sK4 ) ) ),
inference(and_proxy_clausification,[],[f209]) ).
thf(f211,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( Y0 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) )
=> ( ( sK0 @ Y0 @ sK1 )
& ( Y0 != sK1 ) ) )
@ sK5 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f209]) ).
thf(f212,plain,
( ( $false
= ( ( ( sK0 @ sK5 @ sK3 )
& ( sK5 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) )
=> ( ( sK0 @ sK5 @ sK1 )
& ( sK5 != sK1 ) ) ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f213,plain,
( ( $false
= ( ( sK0 @ sK5 @ sK1 )
& ( sK5 != sK1 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( $true
= ( ( sK0 @ sK5 @ sK3 )
& ( sK5 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f212]) ).
thf(f215,plain,
( ( $true
= ( ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( ( $true
= ( ( sK0 @ sK5 @ sK3 )
& ( sK5 != sK3 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f214]) ).
thf(f218,plain,
( ( $true
= ( sK0 @ sK5 @ sK3 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f216]) ).
thf(f221,plain,
( ( $true
= ( sK3 != sK1 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f215]) ).
thf(f222,plain,
( ( $true
= ( sK0 @ sK3 @ sK1 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f215]) ).
thf(f223,plain,
( ( $false
= ( sK3 = sK1 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f224,plain,
( ( sK1 != sK3 )
| ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
inference(equality_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ( $false
= ( sK5 != sK1 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f213]) ).
thf(f226,plain,
( ( $true
= ( sK5 = sK1 ) )
| ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
( ( sK1 = sK5 )
| ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( Y0 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) )
=> ( ( sK0 @ Y0 @ sK1 )
& ( Y0 != sK1 ) ) )
@ sK5 ) )
| ( $false
= ( sK2 = sK4 ) ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f229,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( Y0 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) )
=> ( ( sK0 @ Y0 @ sK1 )
& ( Y0 != sK1 ) ) )
@ sK5 ) )
| ( sK2 != sK4 ) ),
inference(equality_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( ( $false
= ( ( ( sK0 @ sK5 @ sK3 )
& ( sK5 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) )
=> ( ( sK0 @ sK5 @ sK1 )
& ( sK5 != sK1 ) ) ) )
| ( sK2 != sK4 ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
( ( $false
= ( ( sK0 @ sK5 @ sK1 )
& ( sK5 != sK1 ) ) )
| ( sK2 != sK4 ) ),
inference(imp_proxy_clausification,[],[f230]) ).
thf(f232,plain,
( ( $true
= ( ( sK0 @ sK5 @ sK3 )
& ( sK5 != sK3 )
& ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) ) )
| ( sK2 != sK4 ) ),
inference(imp_proxy_clausification,[],[f230]) ).
thf(f233,plain,
( ( $true
= ( ( sK0 @ sK3 @ sK1 )
& ( sK3 != sK1 ) ) )
| ( sK2 != sK4 ) ),
inference(and_proxy_clausification,[],[f232]) ).
thf(f234,plain,
( ( $true
= ( ( sK0 @ sK5 @ sK3 )
& ( sK5 != sK3 ) ) )
| ( sK2 != sK4 ) ),
inference(and_proxy_clausification,[],[f232]) ).
thf(f236,plain,
( ( $true
= ( sK0 @ sK5 @ sK3 ) )
| ( sK2 != sK4 ) ),
inference(and_proxy_clausification,[],[f234]) ).
thf(f239,plain,
( ( $true
= ( sK3 != sK1 ) )
| ( sK2 != sK4 ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f240,plain,
( ( $true
= ( sK0 @ sK3 @ sK1 ) )
| ( sK2 != sK4 ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f241,plain,
( ( $false
= ( sK3 = sK1 ) )
| ( sK2 != sK4 ) ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f242,plain,
( ( sK1 != sK3 )
| ( sK2 != sK4 ) ),
inference(equality_proxy_clausification,[],[f241]) ).
thf(f243,plain,
( ( $false
= ( sK5 != sK1 ) )
| ( sK2 != sK4 )
| ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f231]) ).
thf(f244,plain,
( ( $true
= ( sK5 = sK1 ) )
| ( sK2 != sK4 )
| ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f243]) ).
thf(f245,plain,
( ( sK1 = sK5 )
| ( sK2 != sK4 )
| ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
inference(equality_proxy_clausification,[],[f244]) ).
thf(f247,definition,
( spl6_1
<=> ( $true
= ( sK0 @ sK4 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f249,plain,
( ( $true
= ( sK0 @ sK4 @ sK2 ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f247]) ).
thf(f251,definition,
( spl6_2
<=> ( $true
= ( sK0 @ sK5 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f253,plain,
( ( $true
= ( sK0 @ sK5 @ sK3 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f251]) ).
thf(f254,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f181,f251,f247]) ).
thf(f261,definition,
( spl6_4
<=> ( $true
= ( sK0 @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f263,plain,
( ( $true
= ( sK0 @ sK3 @ sK1 ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f261]) ).
thf(f264,plain,
( spl6_1
| spl6_4 ),
inference(avatar_split_clause,[],[f185,f261,f247]) ).
thf(f266,definition,
( spl6_5
<=> ( sK1 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f269,plain,
( spl6_1
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f187,f266,f247]) ).
thf(f271,definition,
( spl6_6
<=> ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f273,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f271]) ).
thf(f275,definition,
( spl6_7
<=> ( sK1 = sK5 ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f277,plain,
( ( sK1 = sK5 )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f275]) ).
thf(f278,plain,
( spl6_6
| spl6_1
| spl6_7 ),
inference(avatar_split_clause,[],[f190,f275,f247,f271]) ).
thf(f280,definition,
( spl6_8
<=> ( sK2 = sK4 ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f289,definition,
( spl6_9
<=> ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
thf(f291,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f289]) ).
thf(f292,plain,
( spl6_9
| spl6_2 ),
inference(avatar_split_clause,[],[f218,f251,f289]) ).
thf(f294,plain,
( spl6_9
| spl6_4 ),
inference(avatar_split_clause,[],[f222,f261,f289]) ).
thf(f295,plain,
( spl6_9
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f224,f266,f289]) ).
thf(f296,plain,
( spl6_6
| spl6_9
| spl6_7 ),
inference(avatar_split_clause,[],[f227,f275,f289,f271]) ).
thf(f297,plain,
( ~ spl6_8
| spl6_2 ),
inference(avatar_split_clause,[],[f236,f251,f280]) ).
thf(f299,plain,
( ~ spl6_8
| spl6_4 ),
inference(avatar_split_clause,[],[f240,f261,f280]) ).
thf(f300,plain,
( ~ spl6_8
| ~ spl6_5 ),
inference(avatar_split_clause,[],[f242,f266,f280]) ).
thf(f301,plain,
( spl6_6
| ~ spl6_8
| spl6_7 ),
inference(avatar_split_clause,[],[f245,f275,f280,f271]) ).
thf(f303,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK1 @ sK3 ) )
| ( sK1 = sK3 )
| ~ spl6_4 ),
inference(constrained_superposition,[],[f153,f263]) ).
thf(f320,plain,
( ( $false
= ( sK0 @ sK1 @ sK3 ) )
| ( sK1 = sK3 )
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f303]) ).
thf(f328,definition,
( spl6_11
<=> ( $false
= ( sK0 @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition]) ).
thf(f330,plain,
( ( $false
= ( sK0 @ sK1 @ sK3 ) )
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f328]) ).
thf(f336,plain,
( spl6_5
| spl6_11
| ~ spl6_4 ),
inference(avatar_split_clause,[],[f320,f261,f328,f266]) ).
thf(f339,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK2 @ sK4 ) )
| ( sK2 = sK4 )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f249,f153]) ).
thf(f346,plain,
( ( $false
= ( sK0 @ sK2 @ sK4 ) )
| ( sK2 = sK4 )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f339]) ).
thf(f348,definition,
( spl6_12
<=> ( $false
= ( sK0 @ sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_12])],[avatar_definition]) ).
thf(f350,plain,
( ( $false
= ( sK0 @ sK2 @ sK4 ) )
| ~ spl6_12 ),
inference(avatar_component_clause,[],[f348]) ).
thf(f354,plain,
( spl6_8
| spl6_12
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f346,f247,f348,f280]) ).
thf(f378,plain,
( ( $true = $false )
| ~ spl6_9
| ~ spl6_12 ),
inference(constrained_superposition,[],[f350,f291]) ).
thf(f379,plain,
( ( $true = $false )
| ~ spl6_9
| ~ spl6_12 ),
inference(constrained_superposition,[],[f291,f350]) ).
thf(f380,plain,
( $false
| ~ spl6_9
| ~ spl6_12 ),
inference(trivial_inequality_removal,[],[f379]) ).
thf(f381,plain,
( ~ spl6_9
| ~ spl6_12 ),
inference(avatar_contradiction_clause,[],[f380]) ).
thf(f382,plain,
( $false
| ~ spl6_9
| ~ spl6_12 ),
inference(trivial_inequality_removal,[],[f378]) ).
thf(f383,plain,
( ~ spl6_9
| ~ spl6_12 ),
inference(avatar_contradiction_clause,[],[f382]) ).
thf(f431,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK1 ) )
| ( $false
= ( sK0 @ sK5 @ X0 ) ) )
| ~ spl6_6 ),
inference(constrained_superposition,[],[f273,f161]) ).
thf(f442,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK1 ) )
| ( $false
= ( sK0 @ sK5 @ X0 ) ) )
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f431]) ).
thf(f482,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK3 @ sK1 ) )
| ~ spl6_2
| ~ spl6_6 ),
inference(constrained_superposition,[],[f253,f442]) ).
thf(f483,plain,
( ( $false
= ( sK0 @ sK3 @ sK1 ) )
| ~ spl6_2
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f482]) ).
thf(f495,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_4
| ~ spl6_6 ),
inference(constrained_superposition,[],[f483,f263]) ).
thf(f501,plain,
( $false
| ~ spl6_2
| ~ spl6_4
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f495]) ).
thf(f502,plain,
( ~ spl6_2
| ~ spl6_4
| ~ spl6_6 ),
inference(avatar_contradiction_clause,[],[f501]) ).
thf(f506,plain,
( ( $true
= ( sK0 @ sK1 @ sK3 ) )
| ~ spl6_2
| ~ spl6_7 ),
inference(constrained_superposition,[],[f253,f277]) ).
thf(f527,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_7
| ~ spl6_11 ),
inference(constrained_superposition,[],[f506,f330]) ).
thf(f533,plain,
( $false
| ~ spl6_2
| ~ spl6_7
| ~ spl6_11 ),
inference(trivial_inequality_removal,[],[f527]) ).
thf(f534,plain,
( ~ spl6_2
| ~ spl6_7
| ~ spl6_11 ),
inference(avatar_contradiction_clause,[],[f533]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f254]) ).
cnf(s3,plain,
( spl6_1
| spl6_4 ),
inference(sat_conversion,[],[f264]) ).
cnf(s4,plain,
( spl6_1
| ~ spl6_5 ),
inference(sat_conversion,[],[f269]) ).
cnf(s5,plain,
( spl6_1
| spl6_6
| spl6_7 ),
inference(sat_conversion,[],[f278]) ).
cnf(s11,plain,
( spl6_2
| spl6_9 ),
inference(sat_conversion,[],[f292]) ).
cnf(s13,plain,
( spl6_4
| spl6_9 ),
inference(sat_conversion,[],[f294]) ).
cnf(s14,plain,
( ~ spl6_5
| spl6_9 ),
inference(sat_conversion,[],[f295]) ).
cnf(s15,plain,
( spl6_6
| spl6_7
| spl6_9 ),
inference(sat_conversion,[],[f296]) ).
cnf(s16,plain,
( spl6_2
| ~ spl6_8 ),
inference(sat_conversion,[],[f297]) ).
cnf(s18,plain,
( spl6_4
| ~ spl6_8 ),
inference(sat_conversion,[],[f299]) ).
cnf(s19,plain,
( ~ spl6_5
| ~ spl6_8 ),
inference(sat_conversion,[],[f300]) ).
cnf(s20,plain,
( spl6_6
| spl6_7
| ~ spl6_8 ),
inference(sat_conversion,[],[f301]) ).
cnf(s27,plain,
( ~ spl6_4
| spl6_5
| spl6_11 ),
inference(sat_conversion,[],[f336]) ).
cnf(s32,plain,
( ~ spl6_1
| spl6_8
| spl6_12 ),
inference(sat_conversion,[],[f354]) ).
cnf(s33,plain,
( ~ spl6_9
| ~ spl6_12 ),
inference(sat_conversion,[],[f381]) ).
cnf(s34,plain,
( ~ spl6_9
| ~ spl6_12 ),
inference(sat_conversion,[],[f383]) ).
cnf(s36,plain,
( ~ spl6_2
| ~ spl6_4
| ~ spl6_6 ),
inference(sat_conversion,[],[f502]) ).
cnf(s38,plain,
( ~ spl6_2
| ~ spl6_7
| ~ spl6_11 ),
inference(sat_conversion,[],[f534]) ).
cnf(s39,plain,
spl6_1,
inference(rat,[],[s38,s5,s27,s36,s1,s3,s4]) ).
cnf(s40,plain,
( spl6_7
| spl6_6 ),
inference(rat,[],[s32,s34,s20,s15,s39]) ).
cnf(s41,plain,
~ spl6_5,
inference(rat,[],[s33,s32,s14,s19,s39]) ).
cnf(s42,plain,
( ~ spl6_4
| ~ spl6_2 ),
inference(rat,[],[s38,s40,s27,s36,s41]) ).
cnf(s43,plain,
spl6_4,
inference(rat,[],[s33,s32,s13,s18,s39]) ).
cnf(s44,plain,
~ spl6_2,
inference(rat,[],[s42,s43]) ).
cnf(s46,plain,
~ spl6_8,
inference(rat,[],[s16,s44]) ).
cnf(s47,plain,
spl6_9,
inference(rat,[],[s11,s44]) ).
cnf(s48,plain,
spl6_12,
inference(rat,[],[s32,s39,s46]) ).
cnf(s49,plain,
$false,
inference(rat,[],[s33,s48,s47]) ).
thf(f536,plain,
$false,
inference(avatar_sat_refutation,[],[s49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU498^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:46:10 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.28 % (737928)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (737942)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2314517803_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (737943)% WARNING: option uhcvi not known.
% 0.19/0.28 % (737943)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=731738545:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (737944)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=196810132:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.28 % (737945)dis+10_1_sil=32000:sp=arity:random_seed=1722069098:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (737946)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=419775380:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.28 % (737948)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4173528284:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.28 % (737947)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1407465776:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (737943)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (737946)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (737956)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1812900764:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.28 % (737943)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (737948) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-737928-737948"...
% 0.19/0.28 % (737966)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=232606453:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.28 % (737948)...printing done.
% 0.19/0.28 % (737948)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (737948)------------------------------
% 0.19/0.28 % (737948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (737948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (737948)CaDiCaL version: 2.1.3
% 0.19/0.28 % (737948)Termination reason: Refutation
% 0.19/0.28 % (737948)Time elapsed: 0.018 s
% 0.19/0.28 % (737948)Peak memory usage: 13 MB
% 0.19/0.28 % (737948)Instructions burned: 33 (million)
% 0.19/0.28 % (737928)Success in time 0.055 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------