%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU477^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:29:46 AM UTC 2026
% Result : Theorem 0.69s 0.41s
% Output : Refutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 23
% Syntax : Number of formulae : 269 ( 27 unt; 0 typ; 21 def)
% Number of atoms : 2033 ( 475 equ; 0 cnn)
% Maximal formula atoms : 7 ( 7 avg)
% Number of connectives : 2777 ( 334 ~; 585 |; 116 &;1408 @)
% ( 21 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 179 ( 179 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 75 usr; 28 con; 0-4 aty)
% ( 78 !!; 123 ??; 0 @@+; 0 @@-)
% Number of variables : 502 ( 0 sgn 279 !; 13 ?; 502 :)
% 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,
vAND: $o > $o > $o ).
thf(func_def_33,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_38,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vNOT: $o > $o ).
thf(func_def_40,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
sK0: $i > $i > $o ).
thf(func_def_45,type,
sK1: $i > $o ).
thf(func_def_46,type,
sK2: $i > $o ).
thf(func_def_49,type,
sK5: $i > $i ).
thf(func_def_51,type,
sK7: $i > $i ).
thf(func_def_52,type,
sK8: $i > $i ).
thf(func_def_53,type,
sK9: $i > $i ).
thf(func_def_54,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_55,type,
sK11: ( $i > $o ) > $i ).
thf(f20,axiom,
( term
= ( ^ [X0: $i > $i > $o] :
! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ? [X2: $i] :
( ! [X3: $i] :
( ( X1 @ X3 )
=> ~ ( X0 @ X2 @ X3 ) )
& ( X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET009^0.ax',terminating) ).
thf(f30,conjecture,
( term
= ( ^ [X0: $i > $i > $o] :
~ ? [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) )
& ? [X2: $i] : ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alternative_formulation_of_terminating) ).
thf(f31,negated_conjecture,
( term
!= ( ^ [X0: $i > $i > $o] :
~ ? [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) )
& ? [X2: $i] : ( X1 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
thf(f35,plain,
( term
= ( ^ [X0: $i > $i > $o] :
! [X1: $i > $o] :
( ? [X2: $i] : ( X1 @ X2 )
=> ? [X3: $i] :
( ! [X4: $i] :
( ( X1 @ X4 )
=> ~ ( X0 @ X3 @ X4 ) )
& ( X1 @ X3 ) ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f36,plain,
( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f56,plain,
( term
!= ( ^ [X0: $i > $i > $o] :
~ ? [X1: $i > $o] :
( ! [X2: $i] :
( ( X1 @ X2 )
=> ? [X3: $i] :
( ( X1 @ X3 )
& ( X0 @ X2 @ X3 ) ) )
& ? [X4: $i] : ( X1 @ X4 ) ) ) ),
inference(rectify,[],[f31]) ).
thf(f57,plain,
( term
!= ( ^ [Y0: $i > $i > $o] :
~ ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f88,plain,
( term
!= ( ^ [Y0: $i > $i > $o] :
~ ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f57]) ).
thf(f101,plain,
( term
!= ( ^ [Y0: $i > $i > $o] :
~ ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f118,plain,
( term
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f136,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
~ ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 ) )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f101,f118]) ).
thf(f137,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ) )
!= ( ^ [Y0: $i > $i > $o] :
~ ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f145,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) )
@ sK0 )
!= ( ^ [Y0: $i > $i > $o] :
~ ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
@ sK0 ) ),
inference(negative_extensionality,[],[f137]) ).
thf(f146,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
~ ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
@ sK0 )
= $true ) ),
inference(xor_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] :
~ ( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( ?? @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) ) ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ?? @ $i @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) )
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ~ ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
@ sK1 ) ) ),
inference(not_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( ( ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ) )
@ sK2 )
= $true )
| ( $false
= ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $false
= ( ( ?? @ $i @ sK1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( ( ( ?? @ $i @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) )
| ( ( ( ?? @ $i @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( $true
= ( ?? @ $i @ sK1 ) )
| ( ( ( ?? @ $i @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( ( ?? @ $i @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( ?? @ $i @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( ( ( sK2 @ sK4 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) )
@ X1 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f160,plain,
! [X1: $i] :
( ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK2 @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( sK2 @ Y0 ) ) )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
& ( sK2 @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK0 @ X1 @ ( sK5 @ X1 ) )
& ( sK2 @ ( sK5 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK2 @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( sK2 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK0 @ X1 @ ( sK5 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f163]) ).
thf(f166,plain,
! [X1: $i] :
( ( ( ( ?? @ $i @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f153]) ).
thf(f167,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 ) ) ),
inference(and_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ?? @ $i @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f166]) ).
thf(f169,plain,
! [X1: $i] :
( ( ( sK2 @ sK6 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $false
= ( ( sK1 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ~ ( sK0 @ X1 @ Y0 ) ) ) ) )
| ( ( sK2 @ sK6 )
= $true ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( ( sK2 @ sK6 )
= $true )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ~ ( sK0 @ X1 @ Y0 ) )
@ ( sK7 @ X1 ) ) )
| ( ( sK2 @ sK6 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( ( sK1 @ ( sK7 @ X1 ) )
=> ~ ( sK0 @ X1 @ ( sK7 @ X1 ) ) ) )
| ( ( sK2 @ sK6 )
= $true ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( ( sK2 @ sK6 )
= $true )
| ( $false
= ( ~ ( sK0 @ X1 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( ( sK2 @ sK6 )
= $true )
| ( $false
= ( sK1 @ X1 ) )
| ( ( sK1 @ ( sK7 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f176,plain,
! [X1: $i] :
( ( ( sK2 @ sK6 )
= $true )
| ( ( sK0 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f177,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( sK2 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f178,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK2 @ X2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
& ( sK2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ( sK1 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ~ ( sK0 @ X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( sK1 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ~ ( sK0 @ X1 @ Y0 ) ) ) ) )
| ( $false
= ( sK2 @ X2 ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
& ( sK2 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X1: $i] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
& ( sK2 @ Y0 ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ~ ( sK0 @ X1 @ Y0 ) ) ) )
| ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
& ( sK2 @ Y0 ) )
@ ( sK8 @ X2 ) )
= $true )
| ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ~ ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
& ( sK2 @ Y0 ) )
@ ( sK8 @ X2 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ~ ( sK0 @ X1 @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( $false
= ( sK2 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( ( ( sK0 @ X2 @ ( sK8 @ X2 ) )
& ( sK2 @ ( sK8 @ X2 ) ) )
= $true )
| ( $false
= ( sK2 @ X2 ) )
| ( ( ( sK1 @ ( sK9 @ X1 ) )
=> ~ ( sK0 @ X1 @ ( sK9 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ ( sK8 @ X2 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) )
| ( ( ( sK1 @ ( sK9 @ X1 ) )
=> ~ ( sK0 @ X1 @ ( sK9 @ X1 ) ) )
= $false )
| ( $false
= ( sK2 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( ( ( sK1 @ ( sK9 @ X1 ) )
=> ~ ( sK0 @ X1 @ ( sK9 @ X1 ) ) )
= $false )
| ( ( sK0 @ X2 @ ( sK8 @ X2 ) )
= $true )
| ( $false
= ( sK2 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f183]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( ~ ( sK0 @ X1 @ ( sK9 @ X1 ) ) ) )
| ( ( sK0 @ X2 @ ( sK8 @ X2 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( ( sK1 @ ( sK9 @ X1 ) )
= $true )
| ( $false
= ( sK2 @ X2 ) )
| ( ( sK0 @ X2 @ ( sK8 @ X2 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f185]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( sK1 @ X1 ) )
| ( ( sK0 @ X2 @ ( sK8 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f189,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( ~ ( sK0 @ X1 @ ( sK9 @ X1 ) ) ) )
| ( ( sK2 @ ( sK8 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f190,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ ( sK8 @ X2 ) )
= $true )
| ( $false
= ( sK2 @ X2 ) )
| ( $false
= ( sK1 @ X1 ) )
| ( ( sK1 @ ( sK9 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f191,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( sK2 @ X2 ) )
| ( ( sK2 @ ( sK8 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f192,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f193,plain,
! [X1: $i > $o] :
( ( ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
@ X1 )
= $true )
| ( $true
= ( ~ ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i > $o] :
( ( ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
@ X1 )
= $true )
| ( $false
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( $false
= ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( ?? @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ) )
@ X2 ) )
| ( ( ^ [Y0: $i > $o] :
( ( ?? @ $i @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ~ ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( $false
= ( ( ?? @ $i @ X2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( X2 @ Y1 ) ) ) ) ) ) )
| ( ( ( ?? @ $i @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f197,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( ( ?? @ $i @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( X2 @ Y1 ) ) ) ) ) )
| ( $false
= ( ?? @ $i @ X2 ) ) ),
inference(and_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( $false
= ( ?? @ $i @ X1 ) )
| ( $false
= ( ?? @ $i @ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( X2 @ Y1 ) ) ) ) ) )
| ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( ?? @ $i @ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( X2 @ Y1 ) ) ) ) ) )
| ( ( X1 @ X3 )
= $false ) ),
inference(pi_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( X2 @ Y1 ) ) ) ) ) )
| ( $false
= ( ?? @ $i @ X2 ) )
| ( ( X1 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) )
@ ( sK10 @ X1 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o] :
( ( $false
= ( ?? @ $i @ X2 ) )
| ( ( X1 @ X3 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( X2 @ Y1 ) ) ) )
@ ( sK11 @ X2 ) ) )
| ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) )
@ ( sK10 @ X1 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( X2 @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
& ( X2 @ Y1 ) ) ) )
@ ( sK11 @ X2 ) ) )
| ( $false
= ( X2 @ X4 ) )
| ( ( X1 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ~ ( sK0 @ Y0 @ Y1 ) ) ) )
@ ( sK10 @ X1 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( X2 @ X4 ) )
| ( ( ( X2 @ ( sK11 @ X2 ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ ( sK11 @ X2 ) @ Y0 )
& ( X2 @ Y0 ) ) ) )
= $false )
| ( ( X1 @ X3 )
= $false )
| ( $true
= ( ( X1 @ ( sK10 @ X1 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ~ ( sK0 @ ( sK10 @ X1 ) @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i] :
( ( ( X1 @ X3 )
= $false )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ ( sK11 @ X2 ) @ Y0 )
& ( X2 @ Y0 ) ) ) )
| ( $true
= ( ( X1 @ ( sK10 @ X1 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ~ ( sK0 @ ( sK10 @ X1 ) @ Y0 ) ) ) ) )
| ( $false
= ( X2 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( X2 @ X4 ) )
| ( ( X1 @ X3 )
= $false )
| ( $true
= ( ( X1 @ ( sK10 @ X1 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ~ ( sK0 @ ( sK10 @ X1 ) @ Y0 ) ) ) ) )
| ( ( X2 @ ( sK11 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f206,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ~ ( sK0 @ ( sK10 @ X1 ) @ Y0 ) ) )
= $true )
| ( ( X2 @ ( sK11 @ X2 ) )
= $true )
| ( $false
= ( X2 @ X4 ) )
| ( ( X1 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i] :
( ( ( X1 @ ( sK10 @ X1 ) )
= $true )
| ( ( X1 @ X3 )
= $false )
| ( $false
= ( X2 @ X4 ) )
| ( ( X2 @ ( sK11 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f205]) ).
thf(f208,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( ( X1 @ X3 )
= $false )
| ( $false
= ( X2 @ X4 ) )
| ( ( X2 @ ( sK11 @ X2 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ~ ( sK0 @ ( sK10 @ X1 ) @ Y0 ) )
@ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f206]) ).
thf(f209,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( ( ( X1 @ X5 )
=> ~ ( sK0 @ ( sK10 @ X1 ) @ X5 ) )
= $true )
| ( $false
= ( X2 @ X4 ) )
| ( ( X1 @ X3 )
= $false )
| ( ( X2 @ ( sK11 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( ( X2 @ ( sK11 @ X2 ) )
= $true )
| ( ( ~ ( sK0 @ ( sK10 @ X1 ) @ X5 ) )
= $true )
| ( $false
= ( X2 @ X4 ) )
| ( $false
= ( X1 @ X5 ) )
| ( ( X1 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( ( X1 @ X3 )
= $false )
| ( ( X2 @ ( sK11 @ X2 ) )
= $true )
| ( $false
= ( X2 @ X4 ) )
| ( $false
= ( sK0 @ ( sK10 @ X1 ) @ X5 ) )
| ( $false
= ( X1 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( ( X1 @ ( sK10 @ X1 ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ~ ( sK0 @ ( sK10 @ X1 ) @ Y0 ) ) ) ) )
| ( ( X1 @ X3 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ ( sK11 @ X2 ) @ Y0 )
& ( X2 @ Y0 ) )
@ X5 ) )
| ( $false
= ( X2 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f213,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ~ ( sK0 @ ( sK10 @ X1 ) @ Y0 ) ) )
= $true )
| ( $false
= ( X2 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ ( sK11 @ X2 ) @ Y0 )
& ( X2 @ Y0 ) )
@ X5 ) )
| ( ( X1 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ ( sK11 @ X2 ) @ Y0 )
& ( X2 @ Y0 ) )
@ X5 ) )
| ( ( X1 @ X3 )
= $false )
| ( ( X1 @ ( sK10 @ X1 ) )
= $true )
| ( $false
= ( X2 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f212]) ).
thf(f215,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( ( X1 @ X3 )
= $false )
| ( ( X1 @ ( sK10 @ X1 ) )
= $true )
| ( $false
= ( ( sK0 @ ( sK11 @ X2 ) @ X5 )
& ( X2 @ X5 ) ) )
| ( $false
= ( X2 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ ( sK11 @ X2 ) @ X5 ) )
| ( $false
= ( X2 @ X5 ) )
| ( ( X1 @ ( sK10 @ X1 ) )
= $true )
| ( ( X1 @ X3 )
= $false )
| ( $false
= ( X2 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( X2 @ X4 ) )
| ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ~ ( sK0 @ ( sK10 @ X1 ) @ Y0 ) )
@ X6 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ ( sK11 @ X2 ) @ Y0 )
& ( X2 @ Y0 ) )
@ X5 ) )
| ( ( X1 @ X3 )
= $false ) ),
inference(pi_proxy_clausification,[],[f213]) ).
thf(f218,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X6: $i,X4: $i,X5: $i] :
( ( ( X1 @ X3 )
= $false )
| ( $false
= ( ( sK0 @ ( sK11 @ X2 ) @ X5 )
& ( X2 @ X5 ) ) )
| ( $false
= ( X2 @ X4 ) )
| ( ( ( X1 @ X6 )
=> ~ ( sK0 @ ( sK10 @ X1 ) @ X6 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( X2 @ X4 ) )
| ( ( X1 @ X3 )
= $false )
| ( ( ( X1 @ X6 )
=> ~ ( sK0 @ ( sK10 @ X1 ) @ X6 ) )
= $true )
| ( $false
= ( X2 @ X5 ) )
| ( $false
= ( sK0 @ ( sK11 @ X2 ) @ X5 ) ) ),
inference(and_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X6: $i,X4: $i,X5: $i] :
( ( ( X1 @ X3 )
= $false )
| ( $false
= ( sK0 @ ( sK11 @ X2 ) @ X5 ) )
| ( $false
= ( X1 @ X6 ) )
| ( $false
= ( X2 @ X4 ) )
| ( ( ~ ( sK0 @ ( sK10 @ X1 ) @ X6 ) )
= $true )
| ( $false
= ( X2 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i > $o,X3: $i,X1: $i > $o,X6: $i,X4: $i,X5: $i] :
( ( ( X1 @ X3 )
= $false )
| ( $false
= ( X1 @ X6 ) )
| ( $false
= ( X2 @ X5 ) )
| ( $false
= ( sK0 @ ( sK11 @ X2 ) @ X5 ) )
| ( ( sK0 @ ( sK10 @ X1 ) @ X6 )
= $false )
| ( $false
= ( X2 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f223,definition,
( spl12_1
<=> ( ( sK2 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
thf(f225,plain,
( ( ( sK2 @ sK4 )
= $true )
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f227,definition,
( spl12_2
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
thf(f229,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f227]) ).
thf(f230,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f158,f227,f223]) ).
thf(f232,definition,
( spl12_3
<=> ! [X1: $i] :
( ( $false
= ( sK2 @ X1 ) )
| ( ( sK0 @ X1 @ ( sK5 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
thf(f233,plain,
( ! [X1: $i] :
( ( ( sK0 @ X1 @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f232]) ).
thf(f234,plain,
( spl12_2
| spl12_3 ),
inference(avatar_split_clause,[],[f165,f232,f227]) ).
thf(f236,definition,
( spl12_4
<=> ! [X1: $i] :
( ( ( sK2 @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
thf(f237,plain,
( ! [X1: $i] :
( ( ( sK2 @ ( sK5 @ X1 ) )
= $true )
| ( $false
= ( sK2 @ X1 ) ) )
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f236]) ).
thf(f238,plain,
( spl12_4
| spl12_2 ),
inference(avatar_split_clause,[],[f164,f227,f236]) ).
thf(f240,definition,
( spl12_5
<=> ! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( ( sK1 @ ( sK7 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
thf(f241,plain,
( ! [X1: $i] :
( ( ( sK1 @ ( sK7 @ X1 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) ) )
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f240]) ).
thf(f243,definition,
( spl12_6
<=> ( ( sK2 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
thf(f245,plain,
( ( ( sK2 @ sK6 )
= $true )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f246,plain,
( spl12_5
| spl12_6 ),
inference(avatar_split_clause,[],[f175,f243,f240]) ).
thf(f248,definition,
( spl12_7
<=> ! [X1: $i] :
( ( ( sK0 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
thf(f249,plain,
( ! [X1: $i] :
( ( ( sK0 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) ) )
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f250,plain,
( spl12_6
| spl12_7 ),
inference(avatar_split_clause,[],[f176,f248,f243]) ).
thf(f252,definition,
( spl12_8
<=> ! [X2: $i] :
( ( $false
= ( sK2 @ X2 ) )
| ( ( sK0 @ X2 @ ( sK8 @ X2 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
thf(f253,plain,
( ! [X2: $i] :
( ( ( sK0 @ X2 @ ( sK8 @ X2 ) )
= $true )
| ( $false
= ( sK2 @ X2 ) ) )
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f252]) ).
thf(f255,definition,
( spl12_9
<=> ! [X1: $i] :
( ( ( sK1 @ ( sK9 @ X1 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
thf(f256,plain,
( ! [X1: $i] :
( ( ( sK1 @ ( sK9 @ X1 ) )
= $true )
| ( $false
= ( sK1 @ X1 ) ) )
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f257,plain,
( spl12_8
| spl12_9 ),
inference(avatar_split_clause,[],[f187,f255,f252]) ).
thf(f259,definition,
( spl12_10
<=> ! [X1: $i] :
( ( $true
= ( sK0 @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
thf(f260,plain,
( ! [X1: $i] :
( ( $true
= ( sK0 @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( sK1 @ X1 ) ) )
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f261,plain,
( spl12_8
| spl12_10 ),
inference(avatar_split_clause,[],[f188,f259,f252]) ).
thf(f263,definition,
( spl12_11
<=> ! [X2: $i] :
( ( ( sK2 @ ( sK8 @ X2 ) )
= $true )
| ( $false
= ( sK2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
thf(f264,plain,
( ! [X2: $i] :
( ( ( sK2 @ ( sK8 @ X2 ) )
= $true )
| ( $false
= ( sK2 @ X2 ) ) )
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f263]) ).
thf(f265,plain,
( spl12_9
| spl12_11 ),
inference(avatar_split_clause,[],[f190,f263,f255]) ).
thf(f266,plain,
( spl12_11
| spl12_10 ),
inference(avatar_split_clause,[],[f191,f259,f263]) ).
thf(f268,definition,
( spl12_12
<=> ! [X1: $i > $o,X3: $i] :
( ( ( X1 @ ( sK10 @ X1 ) )
= $true )
| ( ( X1 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
thf(f269,plain,
( ! [X3: $i,X1: $i > $o] :
( ( ( X1 @ ( sK10 @ X1 ) )
= $true )
| ( ( X1 @ X3 )
= $false ) )
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f268]) ).
thf(f271,definition,
( spl12_13
<=> ! [X4: $i,X2: $i > $o] :
( ( $false
= ( X2 @ X4 ) )
| ( ( X2 @ ( sK11 @ X2 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
thf(f272,plain,
( ! [X2: $i > $o,X4: $i] :
( ( ( X2 @ ( sK11 @ X2 ) )
= $true )
| ( $false
= ( X2 @ X4 ) ) )
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f271]) ).
thf(f273,plain,
( spl12_12
| spl12_13 ),
inference(avatar_split_clause,[],[f207,f271,f268]) ).
thf(f275,definition,
( spl12_14
<=> ! [X5: $i,X1: $i > $o,X3: $i] :
( ( ( X1 @ X3 )
= $false )
| ( $false
= ( X1 @ X5 ) )
| ( $false
= ( sK0 @ ( sK10 @ X1 ) @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition]) ).
thf(f276,plain,
( ! [X3: $i,X1: $i > $o,X5: $i] :
( ( $false
= ( sK0 @ ( sK10 @ X1 ) @ X5 ) )
| ( ( X1 @ X3 )
= $false )
| ( $false
= ( X1 @ X5 ) ) )
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f275]) ).
thf(f277,plain,
( spl12_13
| spl12_14 ),
inference(avatar_split_clause,[],[f211,f275,f271]) ).
thf(f279,definition,
( spl12_15
<=> ! [X2: $i > $o,X5: $i,X4: $i] :
( ( $false
= ( sK0 @ ( sK11 @ X2 ) @ X5 ) )
| ( $false
= ( X2 @ X4 ) )
| ( $false
= ( X2 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
thf(f280,plain,
( ! [X2: $i > $o,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ ( sK11 @ X2 ) @ X5 ) )
| ( $false
= ( X2 @ X5 ) )
| ( $false
= ( X2 @ X4 ) ) )
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f279]) ).
thf(f281,plain,
( spl12_12
| spl12_15 ),
inference(avatar_split_clause,[],[f216,f279,f268]) ).
thf(f282,plain,
( spl12_15
| spl12_14 ),
inference(avatar_split_clause,[],[f221,f275,f279]) ).
thf(f284,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ X1 ) )
| ( $false
= ( X0 @ ( sK9 @ ( sK10 @ X0 ) ) ) )
| ( $false
= ( sK1 @ ( sK10 @ X0 ) ) )
| ( $false = $true ) )
| ~ spl12_10
| ~ spl12_14 ),
inference(constrained_superposition,[],[f276,f260]) ).
thf(f290,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK9 @ ( sK10 @ X0 ) ) ) )
| ( $false
= ( sK1 @ ( sK10 @ X0 ) ) )
| ( $false
= ( X0 @ X1 ) ) )
| ~ spl12_10
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f284]) ).
thf(f296,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) ) )
| ( $false = $true )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) ) ) )
| ~ spl12_9
| ~ spl12_10
| ~ spl12_14 ),
inference(constrained_superposition,[],[f256,f290]) ).
thf(f300,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) ) )
| ( $false = $true )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl12_9
| ~ spl12_10
| ~ spl12_14 ),
inference(duplicate_literal_removal,[],[f296]) ).
thf(f301,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) ) ) )
| ~ spl12_9
| ~ spl12_10
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f300]) ).
thf(f305,definition,
( spl12_16
<=> ( $false
= ( sK1 @ ( sK10 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_16])],[avatar_definition]) ).
thf(f307,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) ) )
| ~ spl12_16 ),
inference(avatar_component_clause,[],[f305]) ).
thf(f309,definition,
( spl12_17
<=> ! [X0: $i] :
( $false
= ( sK1 @ X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_17])],[avatar_definition]) ).
thf(f310,plain,
( ! [X0: $i] :
( $false
= ( sK1 @ X0 ) )
| ~ spl12_17 ),
inference(avatar_component_clause,[],[f309]) ).
thf(f312,plain,
( spl12_16
| spl12_17
| ~ spl12_9
| ~ spl12_10
| ~ spl12_14 ),
inference(avatar_split_clause,[],[f301,f275,f259,f255,f309,f305]) ).
thf(f317,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ X1 ) )
| ( $false
= ( X0 @ ( sK8 @ ( sK10 @ X0 ) ) ) )
| ( $false = $true )
| ( $false
= ( sK2 @ ( sK10 @ X0 ) ) ) )
| ~ spl12_8
| ~ spl12_14 ),
inference(constrained_superposition,[],[f253,f276]) ).
thf(f319,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK8 @ ( sK10 @ X0 ) ) ) )
| ( $false
= ( X0 @ X1 ) )
| ( $false
= ( sK2 @ ( sK10 @ X0 ) ) ) )
| ~ spl12_8
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f317]) ).
thf(f325,plain,
( ! [X0: $i] :
( ( $false
= ( sK2 @ ( sK10 @ sK2 ) ) )
| ( $false
= ( sK2 @ X0 ) )
| ( $false
= ( sK2 @ ( sK10 @ sK2 ) ) )
| ( $false = $true ) )
| ~ spl12_8
| ~ spl12_11
| ~ spl12_14 ),
inference(constrained_superposition,[],[f264,f319]) ).
thf(f330,plain,
( ! [X0: $i] :
( ( $false
= ( sK2 @ X0 ) )
| ( $false = $true )
| ( $false
= ( sK2 @ ( sK10 @ sK2 ) ) ) )
| ~ spl12_8
| ~ spl12_11
| ~ spl12_14 ),
inference(duplicate_literal_removal,[],[f325]) ).
thf(f331,plain,
( ! [X0: $i] :
( ( $false
= ( sK2 @ ( sK10 @ sK2 ) ) )
| ( $false
= ( sK2 @ X0 ) ) )
| ~ spl12_8
| ~ spl12_11
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f330]) ).
thf(f334,definition,
( spl12_18
<=> ! [X0: $i] :
( $false
= ( sK2 @ X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_18])],[avatar_definition]) ).
thf(f335,plain,
( ! [X0: $i] :
( $false
= ( sK2 @ X0 ) )
| ~ spl12_18 ),
inference(avatar_component_clause,[],[f334]) ).
thf(f337,definition,
( spl12_19
<=> ( $false
= ( sK2 @ ( sK10 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_19])],[avatar_definition]) ).
thf(f339,plain,
( ( $false
= ( sK2 @ ( sK10 @ sK2 ) ) )
| ~ spl12_19 ),
inference(avatar_component_clause,[],[f337]) ).
thf(f341,plain,
( spl12_19
| spl12_18
| ~ spl12_8
| ~ spl12_11
| ~ spl12_14 ),
inference(avatar_split_clause,[],[f331,f275,f263,f252,f334,f337]) ).
thf(f342,plain,
( ! [X0: $i] :
( ( $false
= ( sK2 @ X0 ) )
| ( $false = $true ) )
| ~ spl12_12
| ~ spl12_19 ),
inference(constrained_superposition,[],[f339,f269]) ).
thf(f346,plain,
( ! [X0: $i] :
( $false
= ( sK2 @ X0 ) )
| ~ spl12_12
| ~ spl12_19 ),
inference(trivial_inequality_removal,[],[f342]) ).
thf(f348,plain,
( spl12_18
| ~ spl12_12
| ~ spl12_19 ),
inference(avatar_split_clause,[],[f346,f337,f268,f334]) ).
thf(f353,plain,
( ( $false = $true )
| ~ spl12_6
| ~ spl12_18 ),
inference(constrained_superposition,[],[f245,f335]) ).
thf(f363,plain,
( $false
| ~ spl12_6
| ~ spl12_18 ),
inference(trivial_inequality_removal,[],[f353]) ).
thf(f364,plain,
( ~ spl12_6
| ~ spl12_18 ),
inference(avatar_contradiction_clause,[],[f363]) ).
thf(f366,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false = $true )
| ( $false
= ( X0 @ ( sK7 @ ( sK10 @ X0 ) ) ) )
| ( $false
= ( X0 @ X1 ) )
| ( $false
= ( sK1 @ ( sK10 @ X0 ) ) ) )
| ~ spl12_7
| ~ spl12_14 ),
inference(constrained_superposition,[],[f249,f276]) ).
thf(f368,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK7 @ ( sK10 @ X0 ) ) ) )
| ( $false
= ( X0 @ X1 ) )
| ( $false
= ( sK1 @ ( sK10 @ X0 ) ) ) )
| ~ spl12_7
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f366]) ).
thf(f372,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) ) )
| ( $false
= ( sK1 @ X0 ) )
| ( $false = $true )
| ( $false
= ( sK1 @ ( sK10 @ sK1 ) ) ) )
| ~ spl12_5
| ~ spl12_7
| ~ spl12_14 ),
inference(constrained_superposition,[],[f241,f368]) ).
thf(f377,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) ) )
| ( $false
= ( sK1 @ X0 ) )
| ( $false = $true ) )
| ~ spl12_5
| ~ spl12_7
| ~ spl12_14 ),
inference(duplicate_literal_removal,[],[f372]) ).
thf(f378,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ ( sK10 @ sK1 ) ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl12_5
| ~ spl12_7
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f377]) ).
thf(f381,plain,
( spl12_16
| spl12_17
| ~ spl12_5
| ~ spl12_7
| ~ spl12_14 ),
inference(avatar_split_clause,[],[f378,f275,f248,f240,f309,f305]) ).
thf(f382,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false = $true ) )
| ~ spl12_12
| ~ spl12_16 ),
inference(constrained_superposition,[],[f307,f269]) ).
thf(f385,plain,
( ! [X0: $i] :
( $false
= ( sK1 @ X0 ) )
| ~ spl12_12
| ~ spl12_16 ),
inference(trivial_inequality_removal,[],[f382]) ).
thf(f388,plain,
( spl12_17
| ~ spl12_12
| ~ spl12_16 ),
inference(avatar_split_clause,[],[f385,f305,f268,f309]) ).
thf(f393,plain,
( ( $false = $true )
| ~ spl12_2
| ~ spl12_17 ),
inference(constrained_superposition,[],[f229,f310]) ).
thf(f399,plain,
( $false
| ~ spl12_2
| ~ spl12_17 ),
inference(trivial_inequality_removal,[],[f393]) ).
thf(f400,plain,
( ~ spl12_2
| ~ spl12_17 ),
inference(avatar_contradiction_clause,[],[f399]) ).
thf(f405,plain,
( ( $false = $true )
| ~ spl12_1
| ~ spl12_18 ),
inference(forward_demodulation,[],[f225,f335]) ).
thf(f406,plain,
( $false
| ~ spl12_1
| ~ spl12_18 ),
inference(trivial_inequality_removal,[],[f405]) ).
thf(f407,plain,
( ~ spl12_1
| ~ spl12_18 ),
inference(avatar_contradiction_clause,[],[f406]) ).
thf(f416,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( sK2 @ ( sK10 @ X0 ) ) )
| ( $false
= ( X0 @ X1 ) )
| ( $false
= ( X0 @ ( sK5 @ ( sK10 @ X0 ) ) ) )
| ( $false = $true ) )
| ~ spl12_3
| ~ spl12_14 ),
inference(constrained_superposition,[],[f233,f276]) ).
thf(f418,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK5 @ ( sK10 @ X0 ) ) ) )
| ( $false
= ( sK2 @ ( sK10 @ X0 ) ) )
| ( $false
= ( X0 @ X1 ) ) )
| ~ spl12_3
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f416]) ).
thf(f420,plain,
( ! [X0: $i] :
( ( $false
= ( sK2 @ ( sK10 @ sK2 ) ) )
| ( $false
= ( sK2 @ X0 ) )
| ( $false
= ( sK2 @ ( sK10 @ sK2 ) ) )
| ( $false = $true ) )
| ~ spl12_3
| ~ spl12_4
| ~ spl12_14 ),
inference(constrained_superposition,[],[f418,f237]) ).
thf(f427,plain,
( ! [X0: $i] :
( ( $false
= ( sK2 @ X0 ) )
| ( $false = $true )
| ( $false
= ( sK2 @ ( sK10 @ sK2 ) ) ) )
| ~ spl12_3
| ~ spl12_4
| ~ spl12_14 ),
inference(duplicate_literal_removal,[],[f420]) ).
thf(f428,plain,
( ! [X0: $i] :
( ( $false
= ( sK2 @ X0 ) )
| ( $false
= ( sK2 @ ( sK10 @ sK2 ) ) ) )
| ~ spl12_3
| ~ spl12_4
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f427]) ).
thf(f434,plain,
( spl12_19
| spl12_18
| ~ spl12_3
| ~ spl12_4
| ~ spl12_14 ),
inference(avatar_split_clause,[],[f428,f275,f236,f232,f334,f337]) ).
thf(f457,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK7 @ ( sK11 @ X0 ) ) ) )
| ( $false
= ( sK1 @ ( sK11 @ X0 ) ) )
| ( $false
= ( X0 @ X1 ) )
| ( $false = $true ) )
| ~ spl12_7
| ~ spl12_15 ),
inference(constrained_superposition,[],[f280,f249]) ).
thf(f458,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false = $true )
| ( $false
= ( X0 @ ( sK8 @ ( sK11 @ X0 ) ) ) )
| ( $false
= ( X0 @ X1 ) )
| ( $false
= ( sK2 @ ( sK11 @ X0 ) ) ) )
| ~ spl12_8
| ~ spl12_15 ),
inference(constrained_superposition,[],[f280,f253]) ).
thf(f461,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ X1 ) )
| ( $false
= ( X0 @ ( sK5 @ ( sK11 @ X0 ) ) ) )
| ( $false = $true )
| ( $false
= ( sK2 @ ( sK11 @ X0 ) ) ) )
| ~ spl12_3
| ~ spl12_15 ),
inference(constrained_superposition,[],[f233,f280]) ).
thf(f465,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK8 @ ( sK11 @ X0 ) ) ) )
| ( $false
= ( sK2 @ ( sK11 @ X0 ) ) )
| ( $false
= ( X0 @ X1 ) ) )
| ~ spl12_8
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f458]) ).
thf(f466,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK5 @ ( sK11 @ X0 ) ) ) )
| ( $false
= ( sK2 @ ( sK11 @ X0 ) ) )
| ( $false
= ( X0 @ X1 ) ) )
| ~ spl12_3
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f461]) ).
thf(f467,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK7 @ ( sK11 @ X0 ) ) ) )
| ( $false
= ( X0 @ X1 ) )
| ( $false
= ( sK1 @ ( sK11 @ X0 ) ) ) )
| ~ spl12_7
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f457]) ).
thf(f474,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK2 @ ( sK11 @ sK2 ) ) )
| ( $false
= ( sK2 @ X0 ) )
| ( $false
= ( sK2 @ ( sK11 @ sK2 ) ) ) )
| ~ spl12_3
| ~ spl12_4
| ~ spl12_15 ),
inference(constrained_superposition,[],[f466,f237]) ).
thf(f480,plain,
( ! [X0: $i] :
( ( $false
= ( sK2 @ X0 ) )
| ( $false
= ( sK2 @ ( sK11 @ sK2 ) ) )
| ( $false = $true ) )
| ~ spl12_3
| ~ spl12_4
| ~ spl12_15 ),
inference(duplicate_literal_removal,[],[f474]) ).
thf(f481,plain,
( ! [X0: $i] :
( ( $false
= ( sK2 @ X0 ) )
| ( $false
= ( sK2 @ ( sK11 @ sK2 ) ) ) )
| ~ spl12_3
| ~ spl12_4
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f480]) ).
thf(f485,definition,
( spl12_20
<=> ( $false
= ( sK2 @ ( sK11 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_20])],[avatar_definition]) ).
thf(f486,plain,
( ( $false
!= ( sK2 @ ( sK11 @ sK2 ) ) )
| spl12_20 ),
inference(avatar_component_clause,[],[f485]) ).
thf(f487,plain,
( ( $false
= ( sK2 @ ( sK11 @ sK2 ) ) )
| ~ spl12_20 ),
inference(avatar_component_clause,[],[f485]) ).
thf(f489,plain,
( spl12_18
| spl12_20
| ~ spl12_3
| ~ spl12_4
| ~ spl12_15 ),
inference(avatar_split_clause,[],[f481,f279,f236,f232,f485,f334]) ).
thf(f490,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK2 @ X0 ) ) )
| ~ spl12_13
| ~ spl12_20 ),
inference(constrained_superposition,[],[f487,f272]) ).
thf(f493,plain,
( ! [X0: $i] :
( $false
= ( sK2 @ X0 ) )
| ~ spl12_13
| ~ spl12_20 ),
inference(trivial_inequality_removal,[],[f490]) ).
thf(f496,plain,
( spl12_18
| ~ spl12_13
| ~ spl12_20 ),
inference(avatar_split_clause,[],[f493,f485,f271,f334]) ).
thf(f531,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK2 @ ( sK11 @ sK2 ) ) )
| ( $false
= ( sK2 @ ( sK11 @ sK2 ) ) )
| ( $false
= ( sK2 @ X0 ) ) )
| ~ spl12_8
| ~ spl12_11
| ~ spl12_15 ),
inference(constrained_superposition,[],[f264,f465]) ).
thf(f533,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK2 @ ( sK11 @ sK2 ) ) )
| ( $false
= ( sK2 @ X0 ) ) )
| ~ spl12_8
| ~ spl12_11
| ~ spl12_15 ),
inference(duplicate_literal_removal,[],[f531]) ).
thf(f534,plain,
( ! [X0: $i] :
( ( $false
= ( sK2 @ ( sK11 @ sK2 ) ) )
| ( $false
= ( sK2 @ X0 ) ) )
| ~ spl12_8
| ~ spl12_11
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f533]) ).
thf(f539,plain,
( ! [X0: $i] :
( $false
= ( sK2 @ X0 ) )
| ~ spl12_8
| ~ spl12_11
| ~ spl12_15
| spl12_20 ),
inference(forward_subsumption_resolution,[],[f534,f486]) ).
thf(f541,plain,
( spl12_18
| ~ spl12_8
| ~ spl12_11
| ~ spl12_15
| spl12_20 ),
inference(avatar_split_clause,[],[f539,f485,f279,f263,f252,f334]) ).
thf(f545,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ X1 ) )
| ( $false
= ( X0 @ ( sK9 @ ( sK11 @ X0 ) ) ) )
| ( $false
= ( sK1 @ ( sK11 @ X0 ) ) )
| ( $false = $true ) )
| ~ spl12_10
| ~ spl12_15 ),
inference(constrained_superposition,[],[f260,f280]) ).
thf(f548,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false
= ( X0 @ ( sK9 @ ( sK11 @ X0 ) ) ) )
| ( $false
= ( sK1 @ ( sK11 @ X0 ) ) )
| ( $false
= ( X0 @ X1 ) ) )
| ~ spl12_10
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f545]) ).
thf(f554,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ ( sK11 @ sK1 ) ) )
| ( $false = $true )
| ( $false
= ( sK1 @ ( sK11 @ sK1 ) ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl12_9
| ~ spl12_10
| ~ spl12_15 ),
inference(constrained_superposition,[],[f548,f256]) ).
thf(f562,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( sK1 @ ( sK11 @ sK1 ) ) )
| ( $false = $true ) )
| ~ spl12_9
| ~ spl12_10
| ~ spl12_15 ),
inference(duplicate_literal_removal,[],[f554]) ).
thf(f563,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( sK1 @ ( sK11 @ sK1 ) ) ) )
| ~ spl12_9
| ~ spl12_10
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f562]) ).
thf(f565,definition,
( spl12_21
<=> ( $false
= ( sK1 @ ( sK11 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_21])],[avatar_definition]) ).
thf(f566,plain,
( ( $false
!= ( sK1 @ ( sK11 @ sK1 ) ) )
| spl12_21 ),
inference(avatar_component_clause,[],[f565]) ).
thf(f567,plain,
( ( $false
= ( sK1 @ ( sK11 @ sK1 ) ) )
| ~ spl12_21 ),
inference(avatar_component_clause,[],[f565]) ).
thf(f569,plain,
( spl12_21
| spl12_17
| ~ spl12_9
| ~ spl12_10
| ~ spl12_15 ),
inference(avatar_split_clause,[],[f563,f279,f259,f255,f309,f565]) ).
thf(f572,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false = $true ) )
| ~ spl12_13
| ~ spl12_21 ),
inference(constrained_superposition,[],[f272,f567]) ).
thf(f573,plain,
( ! [X0: $i] :
( $false
= ( sK1 @ X0 ) )
| ~ spl12_13
| ~ spl12_21 ),
inference(trivial_inequality_removal,[],[f572]) ).
thf(f576,plain,
( spl12_17
| ~ spl12_13
| ~ spl12_21 ),
inference(avatar_split_clause,[],[f573,f565,f271,f309]) ).
thf(f600,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( sK1 @ ( sK11 @ sK1 ) ) )
| ( $false
= ( sK1 @ ( sK11 @ sK1 ) ) )
| ( $false = $true ) )
| ~ spl12_5
| ~ spl12_7
| ~ spl12_15 ),
inference(constrained_superposition,[],[f241,f467]) ).
thf(f611,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK1 @ ( sK11 @ sK1 ) ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl12_5
| ~ spl12_7
| ~ spl12_15 ),
inference(duplicate_literal_removal,[],[f600]) ).
thf(f612,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( sK1 @ ( sK11 @ sK1 ) ) ) )
| ~ spl12_5
| ~ spl12_7
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f611]) ).
thf(f623,plain,
( ! [X0: $i] :
( $false
= ( sK1 @ X0 ) )
| ~ spl12_5
| ~ spl12_7
| ~ spl12_15
| spl12_21 ),
inference(forward_subsumption_resolution,[],[f612,f566]) ).
thf(f627,plain,
( spl12_17
| ~ spl12_5
| ~ spl12_7
| ~ spl12_15
| spl12_21 ),
inference(avatar_split_clause,[],[f623,f565,f279,f248,f240,f309]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f230]) ).
cnf(s2,plain,
( spl12_2
| spl12_3 ),
inference(sat_conversion,[],[f234]) ).
cnf(s3,plain,
( spl12_2
| spl12_4 ),
inference(sat_conversion,[],[f238]) ).
cnf(s4,plain,
( spl12_5
| spl12_6 ),
inference(sat_conversion,[],[f246]) ).
cnf(s5,plain,
( spl12_6
| spl12_7 ),
inference(sat_conversion,[],[f250]) ).
cnf(s6,plain,
( spl12_8
| spl12_9 ),
inference(sat_conversion,[],[f257]) ).
cnf(s7,plain,
( spl12_8
| spl12_10 ),
inference(sat_conversion,[],[f261]) ).
cnf(s8,plain,
( spl12_9
| spl12_11 ),
inference(sat_conversion,[],[f265]) ).
cnf(s9,plain,
( spl12_10
| spl12_11 ),
inference(sat_conversion,[],[f266]) ).
cnf(s10,plain,
( spl12_12
| spl12_13 ),
inference(sat_conversion,[],[f273]) ).
cnf(s11,plain,
( spl12_13
| spl12_14 ),
inference(sat_conversion,[],[f277]) ).
cnf(s12,plain,
( spl12_12
| spl12_15 ),
inference(sat_conversion,[],[f281]) ).
cnf(s13,plain,
( spl12_14
| spl12_15 ),
inference(sat_conversion,[],[f282]) ).
cnf(s15,plain,
( ~ spl12_9
| ~ spl12_10
| ~ spl12_14
| spl12_16
| spl12_17 ),
inference(sat_conversion,[],[f312]) ).
cnf(s17,plain,
( ~ spl12_8
| ~ spl12_11
| ~ spl12_14
| spl12_18
| spl12_19 ),
inference(sat_conversion,[],[f341]) ).
cnf(s18,plain,
( ~ spl12_12
| spl12_18
| ~ spl12_19 ),
inference(sat_conversion,[],[f348]) ).
cnf(s21,plain,
( ~ spl12_6
| ~ spl12_18 ),
inference(sat_conversion,[],[f364]) ).
cnf(s23,plain,
( ~ spl12_5
| ~ spl12_7
| ~ spl12_14
| spl12_16
| spl12_17 ),
inference(sat_conversion,[],[f381]) ).
cnf(s24,plain,
( ~ spl12_12
| ~ spl12_16
| spl12_17 ),
inference(sat_conversion,[],[f388]) ).
cnf(s27,plain,
( ~ spl12_2
| ~ spl12_17 ),
inference(sat_conversion,[],[f400]) ).
cnf(s28,plain,
( ~ spl12_1
| ~ spl12_18 ),
inference(sat_conversion,[],[f407]) ).
cnf(s32,plain,
( ~ spl12_3
| ~ spl12_4
| ~ spl12_14
| spl12_18
| spl12_19 ),
inference(sat_conversion,[],[f434]) ).
cnf(s34,plain,
( ~ spl12_3
| ~ spl12_4
| ~ spl12_15
| spl12_18
| spl12_20 ),
inference(sat_conversion,[],[f489]) ).
cnf(s35,plain,
( ~ spl12_13
| spl12_18
| ~ spl12_20 ),
inference(sat_conversion,[],[f496]) ).
cnf(s37,plain,
( ~ spl12_8
| ~ spl12_11
| ~ spl12_15
| spl12_18
| spl12_20 ),
inference(sat_conversion,[],[f541]) ).
cnf(s40,plain,
( ~ spl12_9
| ~ spl12_10
| ~ spl12_15
| spl12_17
| spl12_21 ),
inference(sat_conversion,[],[f569]) ).
cnf(s41,plain,
( ~ spl12_13
| spl12_17
| ~ spl12_21 ),
inference(sat_conversion,[],[f576]) ).
cnf(s45,plain,
( ~ spl12_5
| ~ spl12_7
| ~ spl12_15
| spl12_17
| spl12_21 ),
inference(sat_conversion,[],[f627]) ).
cnf(s47,plain,
( spl12_12
| spl12_8
| spl12_17 ),
inference(rat,[],[s41,s40,s10,s12,s7,s6]) ).
cnf(s48,plain,
( spl12_16
| ~ spl12_10
| spl12_17
| ~ spl12_9 ),
inference(rat,[],[s41,s40,s11,s13,s15]) ).
cnf(s49,plain,
( spl12_8
| spl12_17 ),
inference(rat,[],[s48,s24,s47,s6,s7]) ).
cnf(s50,plain,
( ~ spl12_10
| ~ spl12_9
| spl12_17 ),
inference(rat,[],[s41,s40,s10,s12,s24,s48]) ).
cnf(s51,plain,
( spl12_12
| ~ spl12_11
| spl12_18
| ~ spl12_8 ),
inference(rat,[],[s35,s37,s10,s12]) ).
cnf(s52,plain,
( spl12_19
| ~ spl12_11
| ~ spl12_8
| spl12_18 ),
inference(rat,[],[s35,s37,s11,s13,s17]) ).
cnf(s53,plain,
( ~ spl12_11
| spl12_18
| ~ spl12_8 ),
inference(rat,[],[s52,s18,s51]) ).
cnf(s54,plain,
( spl12_11
| spl12_17 ),
inference(rat,[],[s50,s8,s9]) ).
cnf(s55,plain,
( spl12_12
| spl12_17 ),
inference(rat,[],[s41,s45,s10,s12,s5,s4,s21,s53,s54,s49]) ).
cnf(s56,plain,
( spl12_16
| spl12_17
| ~ spl12_7
| ~ spl12_5 ),
inference(rat,[],[s41,s45,s11,s13,s23]) ).
cnf(s57,plain,
spl12_17,
inference(rat,[],[s56,s24,s55,s4,s5,s21,s53,s54,s49]) ).
cnf(s58,plain,
~ spl12_2,
inference(rat,[],[s27,s57]) ).
cnf(s59,plain,
spl12_4,
inference(rat,[],[s3,s58]) ).
cnf(s60,plain,
spl12_3,
inference(rat,[],[s2,s58]) ).
cnf(s61,plain,
spl12_1,
inference(rat,[],[s1,s58]) ).
cnf(s62,plain,
~ spl12_18,
inference(rat,[],[s28,s61]) ).
cnf(s63,plain,
spl12_15,
inference(rat,[],[s18,s32,s12,s13,s62,s59,s60]) ).
cnf(s64,plain,
spl12_20,
inference(rat,[],[s34,s59,s62,s60,s63]) ).
cnf(s65,plain,
~ spl12_13,
inference(rat,[],[s35,s62,s64]) ).
cnf(s66,plain,
spl12_14,
inference(rat,[],[s11,s65]) ).
cnf(s67,plain,
spl12_12,
inference(rat,[],[s10,s65]) ).
cnf(s68,plain,
spl12_19,
inference(rat,[],[s32,s62,s60,s59,s66]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s18,s62,s67,s68]) ).
thf(f628,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU477^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n008.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 13:43:24 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.28 Running higher-order theorem proving
% 0.27/0.30 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.69/0.41 % (3174468)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.69/0.41 % (3174473)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=787928665:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.69/0.41 % (3174475)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3345176918:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.69/0.41 % (3174475)Instruction limit reached!
% 0.69/0.41 % (3174475)------------------------------
% 0.69/0.41 % (3174475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.41 % (3174475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.41 % (3174475)CaDiCaL version: 2.1.3
% 0.69/0.41 % (3174475)Termination reason: Instruction limit
% 0.69/0.41 % (3174475)Termination phase: Property scanning
% 0.69/0.41 % (3174475)Time elapsed: 0.002 s
% 0.69/0.41 % (3174475)Peak memory usage: 10 MB
% 0.69/0.41 % (3174475)Instructions burned: 3 (million)
% 0.69/0.41 % (3174479)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.69/0.41 % (3174479)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
% 0.69/0.41 % (3174474)lrs+10_16_si=on:nwc=1.5:random_seed=2595458880:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.69/0.41 % (3174476)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=1770350561: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)
% 0.69/0.41 % (3174477)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4210164147:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.69/0.41 % (3174478)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1945214817:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.69/0.41 % (3174479)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=2279522826:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.69/0.41 % (3174474)Instruction limit reached!
% 0.69/0.41 % (3174474)------------------------------
% 0.69/0.41 % (3174474)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.41 % (3174474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.41 % (3174474)CaDiCaL version: 2.1.3
% 0.69/0.41 % (3174474)Termination reason: Instruction limit
% 0.69/0.41 % (3174474)Termination phase: Saturation
% 0.69/0.41 % (3174474)Time elapsed: 0.016 s
% 0.69/0.41 % (3174474)Peak memory usage: 12 MB
% 0.69/0.41 % (3174474)Instructions burned: 18 (million)
% 0.69/0.41 % (3174477)Instruction limit reached!
% 0.69/0.41 % (3174477)------------------------------
% 0.69/0.41 % (3174477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.41 % (3174477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.41 % (3174477)CaDiCaL version: 2.1.3
% 0.69/0.41 % (3174477)Termination reason: Instruction limit
% 0.69/0.41 % (3174477)Termination phase: Saturation
% 0.69/0.41 % (3174477)Time elapsed: 0.023 s
% 0.69/0.41 % (3174477)Peak memory usage: 11 MB
% 0.69/0.41 % (3174477)Instructions burned: 24 (million)
% 0.69/0.41 % (3174483)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2396539267:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.69/0.41 % (3174473)Instruction limit reached!
% 0.69/0.41 % (3174473)------------------------------
% 0.69/0.41 % (3174473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.41 % (3174473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.41 % (3174473)CaDiCaL version: 2.1.3
% 0.69/0.41 % (3174473)Termination reason: Instruction limit
% 0.69/0.41 % (3174473)Termination phase: Saturation
% 0.69/0.41 % (3174473)Time elapsed: 0.043 s
% 0.69/0.41 % (3174473)Peak memory usage: 12 MB
% 0.69/0.41 % (3174473)Instructions burned: 88 (million)
% 0.69/0.41 % (3174483)Instruction limit reached!
% 0.69/0.41 % (3174483)------------------------------
% 0.69/0.41 % (3174483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.41 % (3174483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.41 % (3174483)CaDiCaL version: 2.1.3
% 0.69/0.41 % (3174483)Termination reason: Instruction limit
% 0.69/0.41 % (3174483)Termination phase: Property scanning
% 0.69/0.41 % (3174483)Time elapsed: 0.003 s
% 0.69/0.41 % (3174483)Peak memory usage: 9 MB
% 0.69/0.41 % (3174483)Instructions burned: 3 (million)
% 0.69/0.41 % (3174479) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3174468-3174479"...
% 0.69/0.41 % (3174494)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
% 0.69/0.41 % (3174494)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.69/0.41 % (3174494)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4180383043:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.69/0.41 % (3174489)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=870872194:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.69/0.41 % (3174492)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.69/0.41 % (3174479)...printing done.
% 0.69/0.41 % (3174489)Instruction limit reached!
% 0.69/0.41 % (3174489)------------------------------
% 0.69/0.41 % (3174489)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.41 % (3174489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.41 % (3174489)CaDiCaL version: 2.1.3
% 0.69/0.41 % (3174489)Termination reason: Instruction limit
% 0.69/0.41 % (3174489)Termination phase: Property scanning
% 0.69/0.41 % (3174489)Time elapsed: 0.005 s
% 0.69/0.41 % (3174489)Peak memory usage: 10 MB
% 0.69/0.41 % (3174489)Instructions burned: 5 (million)
% 0.69/0.41 % (3174479)Refutation found. Thanks to Tanya!
% 0.69/0.41 % SZS status Theorem for theBenchmark
% 0.69/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.69/0.41 % (3174479)------------------------------
% 0.69/0.41 % (3174479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.41 % (3174479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.41 % (3174479)CaDiCaL version: 2.1.3
% 0.69/0.41 % (3174479)Termination reason: Refutation
% 0.69/0.41 % (3174479)Time elapsed: 0.051 s
% 0.69/0.41 % (3174479)Peak memory usage: 13 MB
% 0.69/0.41 % (3174479)Instructions burned: 52 (million)
% 0.69/0.41 % (3174468)Success in time 0.093 s
% 0.69/0.41 % Vampire exiting
%------------------------------------------------------------------------------