%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n003.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 08:29:49 AM UTC 2026
% Result : Theorem 0.24s 0.36s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 18
% Syntax : Number of formulae : 204 ( 55 unt; 0 typ; 11 def)
% Number of atoms : 1623 ( 376 equ; 0 cnn)
% Maximal formula atoms : 5 ( 7 avg)
% Number of connectives : 1652 ( 260 ~; 209 |; 188 &; 826 @)
% ( 11 <=>; 69 =>; 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 : 64 ( 60 usr; 20 con; 0-4 aty)
% ( 89 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 216 ( 0 sgn 54 !; 1 ?; 216 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_34,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_35,type,
vNOT: $o > $o ).
thf(func_def_36,type,
vIMP: $o > $o > $o ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vOR: $o > $o > $o ).
thf(func_def_41,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_44,type,
sK0: $i > $i > $o ).
thf(f6,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= refl ),
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,
( ( ^ [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,
( 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,
( ( ^ [X0: $i > $i > $o] :
( ( refl @ X0 )
& ( trans @ X0 )
& ( antisymm @ X0 ) ) )
= po ),
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] :
( ( X0 @ X1 @ X2 )
& ( 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] :
( ( X0 @ X1 @ X2 )
& ( X1 != X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f39,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(f40,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,[],[f39]) ).
thf(f41,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ~ ( X0 @ X2 @ X1 ) ) )
= asymm ),
inference(rectify,[],[f11]) ).
thf(f42,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f51,plain,
( so
= ( ^ [X0: $i > $i > $o] :
( ( trans @ X0 )
& ( asymm @ X0 ) ) ) ),
inference(rectify,[],[f18]) ).
thf(f52,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( asymm @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f63,plain,
( antisymm
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ( X1 = X2 ) ) ) ),
inference(rectify,[],[f10]) ).
thf(f64,plain,
( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f71,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= refl ),
inference(rectify,[],[f6]) ).
thf(f72,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
( ( ^ [X0: $i > $i > $o] :
( ( refl @ X0 )
& ( trans @ X0 )
& ( antisymm @ X0 ) ) )
= po ),
inference(rectify,[],[f17]) ).
thf(f74,plain,
( po
= ( ^ [Y0: $i > $i > $o] :
( ( antisymm @ Y0 )
& ( trans @ Y0 )
& ( refl @ Y0 ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f75,plain,
~ ! [X0: $i > $i > $o] :
( ( po @ X0 )
=> ( so
@ ^ [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
& ( X1 != X2 ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f76,plain,
~ ! [X0: $i > $i > $o] :
( ( ( po @ X0 )
= $true )
=> ( $true
= ( so
@ ^ [Y0: $i,Y1: $i] :
( ( Y0 != Y1 )
& ( X0 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( $true
!= ( so
@ ^ [Y0: $i,Y1: $i] :
( ( Y0 != Y1 )
& ( X0 @ Y0 @ Y1 ) ) ) )
& ( ( po @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f76]) ).
thf(f89,plain,
( ( $true
!= ( so
@ ^ [Y0: $i,Y1: $i] :
( ( Y0 != Y1 )
& ( sK0 @ Y0 @ Y1 ) ) ) )
& ( $true
= ( po @ sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
thf(f90,plain,
( po
= ( ^ [Y0: $i > $i > $o] :
( ( antisymm @ Y0 )
& ( trans @ Y0 )
& ( refl @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f91,plain,
( asymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ~ ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f92,plain,
( antisymm
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y2 = Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f108,plain,
( refl
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f113,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,[],[f40]) ).
thf(f116,plain,
( so
= ( ^ [Y0: $i > $i > $o] :
( ( asymm @ Y0 )
& ( trans @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f117,plain,
( $true
= ( po @ sK0 ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f118,plain,
( $true
!= ( so
@ ^ [Y0: $i,Y1: $i] :
( ( Y0 != Y1 )
& ( sK0 @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f128,plain,
( po
= ( ^ [Y0: $i > $i > $o] :
( ( ^ [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 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f90,f92,f113,f108]) ).
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,[],[f116,f91,f113]) ).
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] :
( ( Y0 != Y1 )
& ( sK0 @ Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f118,f129]) ).
thf(f139,plain,
( ( ^ [Y0: $i > $i > $o] :
( ( ^ [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 )
& ( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
@ Y0 ) )
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f117,f128]) ).
thf(f140,plain,
( $true
= ( ( !! @ $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 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f142,plain,
( $true
= ( ( !! @ $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(and_proxy_clausification,[],[f140]) ).
thf(f143,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f142]) ).
thf(f145,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f147,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f146]) ).
thf(f148,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X1 @ X2 ) )
=> ( X2 = X1 ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( X2 = X1 ) )
| ( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X1 @ X2 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X1 @ X2 ) )
= $false )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( X1 = X2 ) ),
inference(and_proxy_clausification,[],[f150]) ).
thf(f152,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,[],[f143]) ).
thf(f153,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,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,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK0 @ X3 @ X1 ) )
| ( ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X2 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK0 @ X3 @ X1 ) )
| ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X3 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f158]) ).
thf(f162,plain,
( $true
!= ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( Y1 != Y0 )
& ( sK0 @ Y1 @ Y0 ) )
=> ~ ( ( Y0 != Y1 )
& ( sK0 @ Y0 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y2 != Y1 )
& ( sK0 @ Y2 @ Y1 )
& ( Y1 != Y0 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( ( Y2 != Y0 )
& ( sK0 @ Y2 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f163,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y2 != Y1 )
& ( sK0 @ Y2 @ Y1 )
& ( Y1 != Y0 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( ( Y2 != Y0 )
& ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( Y1 != Y0 )
& ( sK0 @ Y1 @ Y0 ) )
=> ~ ( ( Y0 != Y1 )
& ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y2 != Y1 )
& ( sK0 @ Y2 @ Y1 )
& ( Y1 != Y0 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( ( Y2 != Y0 )
& ( sK0 @ Y2 @ Y0 ) ) ) ) )
@ sK1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( Y1 != Y0 )
& ( sK0 @ Y1 @ Y0 ) )
=> ~ ( ( Y0 != Y1 )
& ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( Y1 != Y0 )
& ( sK0 @ Y1 @ Y0 ) )
=> ~ ( ( Y0 != Y1 )
& ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK2 )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( Y2 != Y1 )
& ( sK0 @ Y2 @ Y1 )
& ( Y1 != Y0 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( ( Y2 != Y0 )
& ( sK0 @ Y2 @ Y0 ) ) ) ) )
@ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( Y0 != sK2 )
& ( sK0 @ Y0 @ sK2 ) )
=> ~ ( ( sK2 != Y0 )
& ( sK0 @ sK2 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( Y1 != Y0 )
& ( sK0 @ Y1 @ Y0 )
& ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( ( Y1 != sK1 )
& ( sK0 @ Y1 @ sK1 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( Y0 != sK2 )
& ( sK0 @ Y0 @ sK2 ) )
=> ~ ( ( sK2 != Y0 )
& ( sK0 @ sK2 @ Y0 ) ) )
@ sK3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( Y1 != Y0 )
& ( sK0 @ Y1 @ Y0 )
& ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( ( Y1 != sK1 )
& ( sK0 @ Y1 @ sK1 ) ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( Y1 != Y0 )
& ( sK0 @ Y1 @ Y0 )
& ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( ( Y1 != sK1 )
& ( sK0 @ Y1 @ sK1 ) ) ) )
@ sK4 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( ( Y0 != sK2 )
& ( sK0 @ Y0 @ sK2 ) )
=> ~ ( ( sK2 != Y0 )
& ( sK0 @ sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( ( ( ( sK3 != sK2 )
& ( sK0 @ sK3 @ sK2 ) )
=> ~ ( ( sK2 != sK3 )
& ( sK0 @ sK2 @ sK3 ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( Y0 != sK4 )
& ( sK0 @ Y0 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
( ( ( ~ ( ( sK2 != sK3 )
& ( sK0 @ sK2 @ sK3 ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( Y0 != sK4 )
& ( sK0 @ Y0 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( Y0 != sK4 )
& ( sK0 @ Y0 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) ) ) ) )
| ( ( ( sK3 != sK2 )
& ( sK0 @ sK3 @ sK2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f172,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( Y0 != sK4 )
& ( sK0 @ Y0 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) ) )
@ sK5 ) )
| ( ( ( sK3 != sK2 )
& ( sK0 @ sK3 @ sK2 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( Y0 != sK4 )
& ( sK0 @ Y0 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) ) )
@ sK5 ) )
| ( ( sK0 @ sK3 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f172]) ).
thf(f193,plain,
( ( ( sK0 @ sK3 @ sK2 )
= $true )
| ( ( ( ( sK5 != sK4 )
& ( sK0 @ sK5 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( sK5 != sK1 )
& ( sK0 @ sK5 @ sK1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f194,plain,
( ( ( sK0 @ sK3 @ sK2 )
= $true )
| ( $false
= ( ( sK5 != sK1 )
& ( sK0 @ sK5 @ sK1 ) ) ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( ( ( sK0 @ sK3 @ sK2 )
= $true )
| ( $true
= ( ( sK5 != sK4 )
& ( sK0 @ sK5 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) ) ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f196,plain,
( ( ( sK0 @ sK3 @ sK2 )
= $true )
| ( $true
= ( ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) ) ) ),
inference(and_proxy_clausification,[],[f195]) ).
thf(f197,plain,
( ( $true
= ( ( sK5 != sK4 )
& ( sK0 @ sK5 @ sK4 ) ) )
| ( ( sK0 @ sK3 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f195]) ).
thf(f198,plain,
( ( ( sK0 @ sK3 @ sK2 )
= $true )
| ( ( sK0 @ sK5 @ sK4 )
= $true ) ),
inference(and_proxy_clausification,[],[f197]) ).
thf(f202,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( ( sK0 @ sK3 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f196]) ).
thf(f203,plain,
( ( ( sK4 != sK1 )
= $true )
| ( ( sK0 @ sK3 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f196]) ).
thf(f204,plain,
( ( $false
= ( sK4 = sK1 ) )
| ( ( sK0 @ sK3 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
( ( ( sK0 @ sK3 @ sK2 )
= $true )
| ( sK4 != sK1 ) ),
inference(equality_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( ( ( sK0 @ sK3 @ sK2 )
= $true )
| ( $false
= ( sK5 != sK1 ) )
| ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f194]) ).
thf(f207,plain,
( ( ( sK0 @ sK3 @ sK2 )
= $true )
| ( $true
= ( sK5 = sK1 ) )
| ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( ( sK0 @ sK3 @ sK2 )
= $true )
| ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ( sK1 = sK5 ) ),
inference(equality_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( Y0 != sK4 )
& ( sK0 @ Y0 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) ) ) ) )
| ( $true
= ( ( sK2 != sK3 )
& ( sK0 @ sK2 @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f210,plain,
( ( $true
= ( ( sK2 != sK3 )
& ( sK0 @ sK2 @ sK3 ) ) )
| ( ( ^ [Y0: $i] :
( ( ( Y0 != sK4 )
& ( sK0 @ Y0 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f209]) ).
thf(f211,plain,
( ( ( sK0 @ sK2 @ sK3 )
= $true )
| ( ( ^ [Y0: $i] :
( ( ( Y0 != sK4 )
& ( sK0 @ Y0 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 )
= $false ) ),
inference(and_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( ( ^ [Y0: $i] :
( ( ( Y0 != sK4 )
& ( sK0 @ Y0 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 )
= $false )
| ( $true
= ( sK2 != sK3 ) ) ),
inference(and_proxy_clausification,[],[f210]) ).
thf(f213,plain,
( ( ( ^ [Y0: $i] :
( ( ( Y0 != sK4 )
& ( sK0 @ Y0 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 )
= $false )
| ( ( sK2 = sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( ( ^ [Y0: $i] :
( ( ( Y0 != sK4 )
& ( sK0 @ Y0 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( Y0 != sK1 )
& ( sK0 @ Y0 @ sK1 ) ) )
@ sK6 )
= $false )
| ( sK2 != sK3 ) ),
inference(equality_proxy_clausification,[],[f213]) ).
thf(f215,plain,
( ( ( ( ( sK6 != sK4 )
& ( sK0 @ sK6 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( sK6 != sK1 )
& ( sK0 @ sK6 @ sK1 ) ) )
= $false )
| ( sK2 != sK3 ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
( ( sK2 != sK3 )
| ( ( ( sK6 != sK1 )
& ( sK0 @ sK6 @ sK1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f215]) ).
thf(f217,plain,
( ( sK2 != sK3 )
| ( $true
= ( ( sK6 != sK4 )
& ( sK0 @ sK6 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) ) ) ),
inference(imp_proxy_clausification,[],[f215]) ).
thf(f218,plain,
( ( sK2 != sK3 )
| ( $true
= ( ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) ) ) ),
inference(and_proxy_clausification,[],[f217]) ).
thf(f219,plain,
( ( $true
= ( ( sK6 != sK4 )
& ( sK0 @ sK6 @ sK4 ) ) )
| ( sK2 != sK3 ) ),
inference(and_proxy_clausification,[],[f217]) ).
thf(f220,plain,
( ( sK2 != sK3 )
| ( $true
= ( sK0 @ sK6 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f219]) ).
thf(f224,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( sK2 != sK3 ) ),
inference(and_proxy_clausification,[],[f218]) ).
thf(f225,plain,
( ( sK2 != sK3 )
| ( ( sK4 != sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f218]) ).
thf(f226,plain,
( ( $false
= ( sK4 = sK1 ) )
| ( sK2 != sK3 ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
( ( sK2 != sK3 )
| ( sK4 != sK1 ) ),
inference(equality_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( ( $false
= ( sK6 != sK1 ) )
| ( sK2 != sK3 )
| ( ( sK0 @ sK6 @ sK1 )
= $false ) ),
inference(and_proxy_clausification,[],[f216]) ).
thf(f229,plain,
( ( $true
= ( sK6 = sK1 ) )
| ( ( sK0 @ sK6 @ sK1 )
= $false )
| ( sK2 != sK3 ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( ( sK1 = sK6 )
| ( sK2 != sK3 )
| ( ( sK0 @ sK6 @ sK1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( ( ( sK0 @ sK2 @ sK3 )
= $true )
| ( ( ( ( sK6 != sK4 )
& ( sK0 @ sK6 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) )
=> ( ( sK6 != sK1 )
& ( sK0 @ sK6 @ sK1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f232,plain,
( ( ( ( sK6 != sK1 )
& ( sK0 @ sK6 @ sK1 ) )
= $false )
| ( ( sK0 @ sK2 @ sK3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f231]) ).
thf(f233,plain,
( ( $true
= ( ( sK6 != sK4 )
& ( sK0 @ sK6 @ sK4 )
& ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) ) )
| ( ( sK0 @ sK2 @ sK3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f231]) ).
thf(f234,plain,
( ( ( sK0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( ( sK4 != sK1 )
& ( sK0 @ sK4 @ sK1 ) ) ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f235,plain,
( ( $true
= ( ( sK6 != sK4 )
& ( sK0 @ sK6 @ sK4 ) ) )
| ( ( sK0 @ sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f236,plain,
( ( ( sK0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK6 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f235]) ).
thf(f240,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ( ( sK0 @ sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f234]) ).
thf(f241,plain,
( ( ( sK4 != sK1 )
= $true )
| ( ( sK0 @ sK2 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f234]) ).
thf(f242,plain,
( ( ( sK0 @ sK2 @ sK3 )
= $true )
| ( $false
= ( sK4 = sK1 ) ) ),
inference(not_proxy_clausification,[],[f241]) ).
thf(f243,plain,
( ( ( sK0 @ sK2 @ sK3 )
= $true )
| ( sK4 != sK1 ) ),
inference(equality_proxy_clausification,[],[f242]) ).
thf(f244,plain,
( ( ( sK0 @ sK2 @ sK3 )
= $true )
| ( $false
= ( sK6 != sK1 ) )
| ( ( sK0 @ sK6 @ sK1 )
= $false ) ),
inference(and_proxy_clausification,[],[f232]) ).
thf(f245,plain,
( ( $true
= ( sK6 = sK1 ) )
| ( ( sK0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK6 @ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( ( ( sK0 @ sK2 @ sK3 )
= $true )
| ( sK1 = sK6 )
| ( ( sK0 @ sK6 @ sK1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f245]) ).
thf(f252,definition,
( spl7_2
<=> ( sK2 = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f254,plain,
( ( sK2 != sK3 )
| spl7_2 ),
inference(avatar_component_clause,[],[f252]) ).
thf(f257,definition,
( spl7_3
<=> ( ( sK0 @ sK5 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f259,plain,
( ( ( sK0 @ sK5 @ sK4 )
= $true )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f262,definition,
( spl7_4
<=> ( sK4 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f264,plain,
( ( sK4 != sK1 )
| spl7_4 ),
inference(avatar_component_clause,[],[f262]) ).
thf(f267,definition,
( spl7_5
<=> ( $true
= ( sK0 @ sK4 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f269,plain,
( ( $true
= ( sK0 @ sK4 @ sK1 ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f267]) ).
thf(f272,definition,
( spl7_6
<=> ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f274,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f276,definition,
( spl7_7
<=> ( sK1 = sK5 ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f278,plain,
( ( sK1 = sK5 )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f276]) ).
thf(f281,definition,
( spl7_8
<=> ( ( sK0 @ sK3 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f283,plain,
( ( ( sK0 @ sK3 @ sK2 )
= $true )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f281]) ).
thf(f285,plain,
( spl7_8
| spl7_3 ),
inference(avatar_split_clause,[],[f198,f257,f281]) ).
thf(f286,plain,
( spl7_8
| ~ spl7_4 ),
inference(avatar_split_clause,[],[f205,f262,f281]) ).
thf(f287,plain,
( spl7_8
| spl7_5 ),
inference(avatar_split_clause,[],[f202,f267,f281]) ).
thf(f288,plain,
( spl7_8
| spl7_7
| spl7_6 ),
inference(avatar_split_clause,[],[f208,f272,f276,f281]) ).
thf(f295,definition,
( spl7_10
<=> ( $true
= ( sK0 @ sK6 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition]) ).
thf(f297,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ~ spl7_10 ),
inference(avatar_component_clause,[],[f295]) ).
thf(f298,plain,
( spl7_10
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f220,f252,f295]) ).
thf(f299,plain,
( ~ spl7_4
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f227,f252,f262]) ).
thf(f300,plain,
( spl7_5
| ~ spl7_2 ),
inference(avatar_split_clause,[],[f224,f252,f267]) ).
thf(f302,definition,
( spl7_11
<=> ( ( sK0 @ sK6 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl7_11])],[avatar_definition]) ).
thf(f304,plain,
( ( ( sK0 @ sK6 @ sK1 )
= $false )
| ~ spl7_11 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f306,definition,
( spl7_12
<=> ( sK1 = sK6 ) ),
introduced(definition,[new_symbols(definition,[spl7_12])],[avatar_definition]) ).
thf(f308,plain,
( ( sK1 = sK6 )
| ~ spl7_12 ),
inference(avatar_component_clause,[],[f306]) ).
thf(f309,plain,
( ~ spl7_2
| spl7_11
| spl7_12 ),
inference(avatar_split_clause,[],[f230,f306,f302,f252]) ).
thf(f311,definition,
( spl7_13
<=> ( ( sK0 @ sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl7_13])],[avatar_definition]) ).
thf(f313,plain,
( ( ( sK0 @ sK2 @ sK3 )
= $true )
| ~ spl7_13 ),
inference(avatar_component_clause,[],[f311]) ).
thf(f315,plain,
( spl7_10
| spl7_13 ),
inference(avatar_split_clause,[],[f236,f311,f295]) ).
thf(f316,plain,
( ~ spl7_4
| spl7_13 ),
inference(avatar_split_clause,[],[f243,f311,f262]) ).
thf(f317,plain,
( spl7_5
| spl7_13 ),
inference(avatar_split_clause,[],[f240,f311,f267]) ).
thf(f318,plain,
( spl7_12
| spl7_11
| spl7_13 ),
inference(avatar_split_clause,[],[f246,f311,f302,f306]) ).
thf(f325,plain,
( ( $true = $false )
| ( sK4 = sK1 )
| ( ( sK0 @ sK1 @ sK4 )
= $false )
| ~ spl7_5 ),
inference(constrained_superposition,[],[f269,f151]) ).
thf(f334,plain,
( ( sK4 = sK1 )
| ( ( sK0 @ sK1 @ sK4 )
= $false )
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f325]) ).
thf(f346,plain,
( ( ( sK0 @ sK1 @ sK4 )
= $false )
| spl7_4
| ~ spl7_5 ),
inference(forward_subsumption_resolution,[],[f334,f264]) ).
thf(f364,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK1 )
= $false )
| ( $true = $false )
| ( $false
= ( sK0 @ sK5 @ X0 ) ) )
| ~ spl7_6 ),
inference(constrained_superposition,[],[f159,f274]) ).
thf(f365,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK6 @ X0 )
= $false )
| ( ( sK0 @ X0 @ sK1 )
= $false )
| ( $true = $false ) )
| ~ spl7_11 ),
inference(constrained_superposition,[],[f159,f304]) ).
thf(f399,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK1 )
= $false )
| ( $false
= ( sK0 @ sK5 @ X0 ) ) )
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f364]) ).
thf(f417,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK1 )
= $false )
| ( ( sK0 @ sK6 @ X0 )
= $false ) )
| ~ spl7_11 ),
inference(trivial_inequality_removal,[],[f365]) ).
thf(f426,plain,
( ( $true = $false )
| ( ( sK0 @ sK4 @ sK1 )
= $false )
| ~ spl7_3
| ~ spl7_6 ),
inference(constrained_superposition,[],[f399,f259]) ).
thf(f436,plain,
( ( ( sK0 @ sK4 @ sK1 )
= $false )
| ~ spl7_3
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f426]) ).
thf(f442,plain,
( ( $true = $false )
| ~ spl7_3
| ~ spl7_5
| ~ spl7_6 ),
inference(forward_demodulation,[],[f436,f269]) ).
thf(f443,plain,
( $false
| ~ spl7_3
| ~ spl7_5
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f442]) ).
thf(f444,plain,
( ~ spl7_3
| ~ spl7_5
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f443]) ).
thf(f448,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl7_3
| ~ spl7_7 ),
inference(constrained_superposition,[],[f259,f278]) ).
thf(f450,plain,
( ( $true = $false )
| ~ spl7_3
| spl7_4
| ~ spl7_5
| ~ spl7_7 ),
inference(forward_demodulation,[],[f448,f346]) ).
thf(f451,plain,
( $false
| ~ spl7_3
| spl7_4
| ~ spl7_5
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f450]) ).
thf(f452,plain,
( ~ spl7_3
| spl7_4
| ~ spl7_5
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[],[f451]) ).
thf(f460,plain,
( ( sK2 = sK3 )
| ( $true = $false )
| ( ( sK0 @ sK2 @ sK3 )
= $false )
| ~ spl7_8 ),
inference(constrained_superposition,[],[f283,f151]) ).
thf(f466,plain,
( ( ( sK0 @ sK2 @ sK3 )
= $false )
| ( sK2 = sK3 )
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f460]) ).
thf(f474,plain,
( ( ( sK0 @ sK2 @ sK3 )
= $false )
| spl7_2
| ~ spl7_8 ),
inference(forward_subsumption_resolution,[],[f466,f254]) ).
thf(f485,plain,
( ( ( sK0 @ sK4 @ sK1 )
= $false )
| ( $true = $false )
| ~ spl7_10
| ~ spl7_11 ),
inference(constrained_superposition,[],[f417,f297]) ).
thf(f493,plain,
( ( ( sK0 @ sK4 @ sK1 )
= $false )
| ~ spl7_10
| ~ spl7_11 ),
inference(trivial_inequality_removal,[],[f485]) ).
thf(f501,plain,
( ( $true = $false )
| ~ spl7_5
| ~ spl7_10
| ~ spl7_11 ),
inference(forward_demodulation,[],[f493,f269]) ).
thf(f502,plain,
( $false
| ~ spl7_5
| ~ spl7_10
| ~ spl7_11 ),
inference(trivial_inequality_removal,[],[f501]) ).
thf(f503,plain,
( ~ spl7_5
| ~ spl7_10
| ~ spl7_11 ),
inference(avatar_contradiction_clause,[],[f502]) ).
thf(f505,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl7_10
| ~ spl7_12 ),
inference(constrained_superposition,[],[f297,f308]) ).
thf(f510,plain,
( ( $true = $false )
| spl7_4
| ~ spl7_5
| ~ spl7_10
| ~ spl7_12 ),
inference(forward_demodulation,[],[f505,f346]) ).
thf(f511,plain,
( $false
| spl7_4
| ~ spl7_5
| ~ spl7_10
| ~ spl7_12 ),
inference(trivial_inequality_removal,[],[f510]) ).
thf(f512,plain,
( spl7_4
| ~ spl7_5
| ~ spl7_10
| ~ spl7_12 ),
inference(avatar_contradiction_clause,[],[f511]) ).
thf(f513,plain,
( ( $true = $false )
| spl7_2
| ~ spl7_8
| ~ spl7_13 ),
inference(forward_demodulation,[],[f313,f474]) ).
thf(f514,plain,
( $false
| spl7_2
| ~ spl7_8
| ~ spl7_13 ),
inference(trivial_inequality_removal,[],[f513]) ).
thf(f515,plain,
( spl7_2
| ~ spl7_8
| ~ spl7_13 ),
inference(avatar_contradiction_clause,[],[f514]) ).
cnf(s7,plain,
( spl7_3
| spl7_8 ),
inference(sat_conversion,[],[f285]) ).
cnf(s8,plain,
( ~ spl7_4
| spl7_8 ),
inference(sat_conversion,[],[f286]) ).
cnf(s9,plain,
( spl7_5
| spl7_8 ),
inference(sat_conversion,[],[f287]) ).
cnf(s10,plain,
( spl7_6
| spl7_7
| spl7_8 ),
inference(sat_conversion,[],[f288]) ).
cnf(s12,plain,
( ~ spl7_2
| spl7_10 ),
inference(sat_conversion,[],[f298]) ).
cnf(s13,plain,
( ~ spl7_2
| ~ spl7_4 ),
inference(sat_conversion,[],[f299]) ).
cnf(s14,plain,
( ~ spl7_2
| spl7_5 ),
inference(sat_conversion,[],[f300]) ).
cnf(s15,plain,
( ~ spl7_2
| spl7_11
| spl7_12 ),
inference(sat_conversion,[],[f309]) ).
cnf(s17,plain,
( spl7_10
| spl7_13 ),
inference(sat_conversion,[],[f315]) ).
cnf(s18,plain,
( ~ spl7_4
| spl7_13 ),
inference(sat_conversion,[],[f316]) ).
cnf(s19,plain,
( spl7_5
| spl7_13 ),
inference(sat_conversion,[],[f317]) ).
cnf(s20,plain,
( spl7_11
| spl7_12
| spl7_13 ),
inference(sat_conversion,[],[f318]) ).
cnf(s22,plain,
( ~ spl7_3
| ~ spl7_5
| ~ spl7_6 ),
inference(sat_conversion,[],[f444]) ).
cnf(s23,plain,
( ~ spl7_3
| spl7_4
| ~ spl7_5
| ~ spl7_7 ),
inference(sat_conversion,[],[f452]) ).
cnf(s26,plain,
( ~ spl7_5
| ~ spl7_10
| ~ spl7_11 ),
inference(sat_conversion,[],[f503]) ).
cnf(s28,plain,
( spl7_4
| ~ spl7_5
| ~ spl7_10
| ~ spl7_12 ),
inference(sat_conversion,[],[f512]) ).
cnf(s29,plain,
( spl7_2
| ~ spl7_8
| ~ spl7_13 ),
inference(sat_conversion,[],[f515]) ).
cnf(s30,plain,
spl7_13,
inference(rat,[],[s20,s28,s26,s17,s18,s19]) ).
cnf(s31,plain,
spl7_8,
inference(rat,[],[s10,s22,s23,s7,s8,s9]) ).
cnf(s32,plain,
spl7_2,
inference(rat,[],[s29,s30,s31]) ).
cnf(s33,plain,
spl7_5,
inference(rat,[],[s14,s32]) ).
cnf(s34,plain,
~ spl7_4,
inference(rat,[],[s13,s32]) ).
cnf(s35,plain,
spl7_10,
inference(rat,[],[s12,s32]) ).
cnf(s38,plain,
~ spl7_11,
inference(rat,[],[s26,s33,s35]) ).
cnf(s39,plain,
~ spl7_12,
inference(rat,[],[s28,s33,s34,s35]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s15,s32,s39,s38]) ).
thf(f516,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU498^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n003.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 13:48:13 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.28 Running higher-order theorem proving
% 0.24/0.31 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
% 0.24/0.36 % (2522440)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.36 % (2522445)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4123574157:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.36 % (2522451)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.36 % (2522451)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
% 0.24/0.36 % (2522445) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2522440-2522445"...
% 0.24/0.36 % (2522447)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1770423002:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.36 % (2522446)lrs+10_16_si=on:nwc=1.5:random_seed=1808756671:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.36 % (2522449)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3274489863:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.36 % (2522448)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=3530400954: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)
% 0.24/0.36 % (2522450)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=448011598:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.36 % (2522451)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=4240012665:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.36 % (2522447)Instruction limit reached!
% 0.24/0.36 % (2522447)------------------------------
% 0.24/0.36 % (2522447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.36 % (2522447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.36 % (2522447)CaDiCaL version: 2.1.3
% 0.24/0.36 % (2522447)Termination reason: Instruction limit
% 0.24/0.36 % (2522447)Termination phase: Property scanning
% 0.24/0.36 % (2522447)Time elapsed: 0.003 s
% 0.24/0.36 % (2522447)Peak memory usage: 9 MB
% 0.24/0.36 % (2522447)Instructions burned: 3 (million)
% 0.24/0.36 % (2522445)...printing done.
% 0.24/0.36 % (2522445)Refutation found. Thanks to Tanya!
% 0.24/0.36 % SZS status Theorem for theBenchmark
% 0.24/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.37 % (2522445)------------------------------
% 0.24/0.37 % (2522445)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (2522445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (2522445)CaDiCaL version: 2.1.3
% 0.24/0.37 % (2522445)Termination reason: Refutation
% 0.24/0.37 % (2522445)Time elapsed: 0.018 s
% 0.24/0.37 % (2522445)Peak memory usage: 13 MB
% 0.24/0.37 % (2522445)Instructions burned: 35 (million)
% 0.24/0.37 % (2522440)Success in time 0.043 s
% 0.24/0.37 % Vampire exiting
%------------------------------------------------------------------------------