%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN045^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:41:49 AM UTC 2026
% Result : Theorem 2.43s 0.72s
% Output : Refutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 57
% Syntax : Number of formulae : 951 ( 44 unt; 0 typ; 50 def)
% Number of atoms : 13790 (2324 equ; 0 cnn)
% Maximal formula atoms : 44 ( 14 avg)
% Number of connectives : 15284 (2463 ~;4152 |; 0 &;7928 @)
% ( 50 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 118 ( 118 >; 0 *; 0 +; 0 <<)
% Number of symbols : 132 ( 128 usr; 78 con; 0-4 aty)
% ( 691 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1714 ( 0 sgn 592 !; 0 ?;1714 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
qmltpeq: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
mtrue: $i > $o ).
thf(func_def_8,type,
mfalse: $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
exists_in_world: mu > $i > $o ).
thf(func_def_16,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_18,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_33,type,
rel_s4: $i > $i > $o ).
thf(func_def_34,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
r: $i > $o ).
thf(func_def_37,type,
q: $i > $o ).
thf(func_def_38,type,
p: $i > $o ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vIMP: $o > $o > $o ).
thf(func_def_51,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
vAND: $o > $o > $o ).
thf(func_def_53,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
sK0: $i > mu ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f8,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(f9,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f37,conjecture,
mvalid @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel13) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f40,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f41,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f43,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f49,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f50,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f83,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f84,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f91,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f92,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f100,plain,
~ ( mvalid @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f101,plain,
( ( mvalid @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f100]) ).
thf(f102,plain,
( ( mvalid @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f101]) ).
thf(f107,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f108,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f113,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f114,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f133,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f137,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f142,plain,
( ( mvalid @ ( mand @ ( mbox_s4 @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) ) ) @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ r ) ) ) @ ( mor @ ( mbox_s4 @ p ) @ ( mand @ ( mbox_s4 @ q ) @ ( mbox_s4 @ r ) ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f102]) ).
thf(f146,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f113,f107,f108,f107,f107]) ).
thf(f147,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f114,f108,f107]) ).
thf(f157,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ r ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ r ) ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ r ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ r ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f142,f133,f146,f137,f147,f108,f137,f146,f137,f137,f146,f108,f137,f137,f108,f137,f137,f137,f147,f146,f108,f137,f137,f108,f137,f137,f108,f137,f146,f137,f137]) ).
thf(f158,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( r @ Y2 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( r @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ~ ( ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( r @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( r @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( r @ Y2 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( r @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ~ ( ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( r @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( r @ Y2 ) ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
@ sK2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
@ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ Y1 ) ) ) ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 )
| ~ ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
( ( $false
= ( ~ ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f254,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f255,plain,
( ( $false
= ( ~ ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f256,plain,
( ( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f255]) ).
thf(f257,plain,
( ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f256]) ).
thf(f258,plain,
( ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f257]) ).
thf(f259,plain,
( ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f257]) ).
thf(f260,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f259]) ).
thf(f261,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f262]) ).
thf(f272,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f263]) ).
thf(f273,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f263]) ).
thf(f274,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f275]) ).
thf(f277,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f276]) ).
thf(f279,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f279]) ).
thf(f281,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f282]) ).
thf(f284,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f283]) ).
thf(f285,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f284]) ).
thf(f286,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f285]) ).
thf(f287,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f288]) ).
thf(f290,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( $false
= ( rel_s4 @ sK3 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f290]) ).
thf(f292,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f277]) ).
thf(f293,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f292]) ).
thf(f294,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f293]) ).
thf(f295,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f294]) ).
thf(f296,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f295]) ).
thf(f297,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f296]) ).
thf(f298,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f298]) ).
thf(f300,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f299]) ).
thf(f301,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f301]) ).
thf(f303,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( $false
= ( rel_s4 @ sK3 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f272]) ).
thf(f306,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f305]) ).
thf(f307,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f306]) ).
thf(f308,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f309,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f310,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK10 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f309]) ).
thf(f311,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK10 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f310]) ).
thf(f312,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK10 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f311]) ).
thf(f314,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK10 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f312]) ).
thf(f315,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK10 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK11 ) ) ),
inference(sigma_proxy_clausification,[],[f314]) ).
thf(f316,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK10 )
| ( p @ sK10 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK11 )
| ( p @ sK11 ) ) ) ),
inference(beta-eta_normalization,[],[f315]) ).
thf(f317,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK10 )
| ( p @ sK10 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK11 )
| ( p @ sK11 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ sK10 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK11 )
| ( p @ sK11 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f317]) ).
thf(f319,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK10 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK11 )
| ( p @ sK11 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f317]) ).
thf(f320,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK10 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK11 )
| ( p @ sK11 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f319]) ).
thf(f321,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK11 )
| ( p @ sK11 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f320]) ).
thf(f322,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( p @ sK11 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK11 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f321]) ).
thf(f324,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK11 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK11 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f324]) ).
thf(f326,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK11 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f322]) ).
thf(f328,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f327]) ).
thf(f329,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK11 )
| ( p @ sK11 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f318]) ).
thf(f330,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( p @ sK11 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f329]) ).
thf(f331,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK11 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f329]) ).
thf(f332,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK11 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f331]) ).
thf(f333,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK11 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f332]) ).
thf(f334,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK11 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f333]) ).
thf(f335,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f330]) ).
thf(f336,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ sK10 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f335]) ).
thf(f359,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK13 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f308]) ).
thf(f360,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK13 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK13 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f360]) ).
thf(f362,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK13 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f361]) ).
thf(f386,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK13 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK15 ) ) ),
inference(sigma_proxy_clausification,[],[f362]) ).
thf(f387,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK13 )
| ( r @ sK13 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK15 )
| ( q @ sK15 ) ) ) ),
inference(beta-eta_normalization,[],[f386]) ).
thf(f388,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK13 )
| ( r @ sK13 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK15 )
| ( q @ sK15 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f387]) ).
thf(f389,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( r @ sK13 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK15 )
| ( q @ sK15 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f388]) ).
thf(f390,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK13 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK15 )
| ( q @ sK15 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f388]) ).
thf(f391,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK13 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK15 )
| ( q @ sK15 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f390]) ).
thf(f392,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK15 )
| ( q @ sK15 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f391]) ).
thf(f393,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( q @ sK15 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f392]) ).
thf(f394,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK15 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f392]) ).
thf(f395,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f394]) ).
thf(f396,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f395]) ).
thf(f397,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f396]) ).
thf(f398,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( q @ sK15 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f393]) ).
thf(f399,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( q @ sK15 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f398]) ).
thf(f400,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( r @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK15 )
| ( q @ sK15 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f389]) ).
thf(f401,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( r @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( q @ sK15 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f400]) ).
thf(f402,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( r @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK15 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f400]) ).
thf(f403,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( r @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f402]) ).
thf(f404,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( r @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f403]) ).
thf(f405,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( r @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f404]) ).
thf(f406,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( r @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( q @ sK15 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f401]) ).
thf(f407,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( r @ sK13 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( q @ sK15 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f406]) ).
thf(f408,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f258]) ).
thf(f409,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f408]) ).
thf(f410,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f409]) ).
thf(f411,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f410]) ).
thf(f420,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f411]) ).
thf(f421,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f411]) ).
thf(f422,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f421]) ).
thf(f423,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f422]) ).
thf(f424,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f423]) ).
thf(f425,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f424]) ).
thf(f426,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f424]) ).
thf(f427,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f426]) ).
thf(f428,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f427]) ).
thf(f429,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f428]) ).
thf(f430,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f429]) ).
thf(f431,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( r @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f430]) ).
thf(f432,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f431]) ).
thf(f433,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f432]) ).
thf(f434,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f433]) ).
thf(f435,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f434]) ).
thf(f436,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f435]) ).
thf(f437,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f436]) ).
thf(f438,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f437]) ).
thf(f439,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( $false
= ( rel_s4 @ sK3 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f438]) ).
thf(f440,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f425]) ).
thf(f441,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f440]) ).
thf(f442,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f441]) ).
thf(f443,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f442]) ).
thf(f444,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( r @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f443]) ).
thf(f445,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f444]) ).
thf(f446,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f445]) ).
thf(f447,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f446]) ).
thf(f448,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f447]) ).
thf(f449,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f448]) ).
thf(f450,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f449]) ).
thf(f451,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f450]) ).
thf(f452,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( r @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( $false
= ( rel_s4 @ sK3 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f451]) ).
thf(f453,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f420]) ).
thf(f454,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f453]) ).
thf(f455,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f454]) ).
thf(f456,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f455]) ).
thf(f457,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f455]) ).
thf(f458,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK16 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f457]) ).
thf(f459,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK16 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f458]) ).
thf(f460,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK16 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f459]) ).
thf(f462,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK16 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f460]) ).
thf(f463,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK16 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK17 ) ) ),
inference(sigma_proxy_clausification,[],[f462]) ).
thf(f464,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( r @ X1 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK16 )
| ( p @ sK16 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK17 )
| ( p @ sK17 ) ) ) ),
inference(beta-eta_normalization,[],[f463]) ).
thf(f465,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK16 )
| ( p @ sK16 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK17 )
| ( p @ sK17 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f464]) ).
thf(f466,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( p @ sK16 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK17 )
| ( p @ sK17 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f465]) ).
thf(f467,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK16 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK17 )
| ( p @ sK17 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f465]) ).
thf(f468,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK16 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK17 )
| ( p @ sK17 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f467]) ).
thf(f469,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK17 )
| ( p @ sK17 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f468]) ).
thf(f470,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( p @ sK17 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f469]) ).
thf(f471,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK17 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f469]) ).
thf(f472,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK17 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f471]) ).
thf(f473,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK17 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f472]) ).
thf(f474,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK17 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f473]) ).
thf(f475,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( p @ sK17 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f470]) ).
thf(f476,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( p @ sK17 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f475]) ).
thf(f477,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( p @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK17 )
| ( p @ sK17 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f466]) ).
thf(f478,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( p @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( p @ sK17 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f477]) ).
thf(f479,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( p @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK17 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f477]) ).
thf(f480,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( p @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK17 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f479]) ).
thf(f481,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( p @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK17 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f480]) ).
thf(f482,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( p @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK17 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f481]) ).
thf(f483,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( p @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( p @ sK17 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f478]) ).
thf(f484,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( p @ sK16 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( p @ sK17 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f483]) ).
thf(f507,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK19 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f456]) ).
thf(f508,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK19 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f507]) ).
thf(f509,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK19 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f508]) ).
thf(f510,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK19 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f509]) ).
thf(f534,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK19 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK21 ) ) ),
inference(sigma_proxy_clausification,[],[f510]) ).
thf(f535,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( r @ X1 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK19 )
| ( r @ sK19 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK21 )
| ( q @ sK21 ) ) ) ),
inference(beta-eta_normalization,[],[f534]) ).
thf(f536,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK19 )
| ( r @ sK19 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK21 )
| ( q @ sK21 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f535]) ).
thf(f537,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( r @ sK19 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK21 )
| ( q @ sK21 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f536]) ).
thf(f538,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK19 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK21 )
| ( q @ sK21 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f536]) ).
thf(f539,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK19 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK21 )
| ( q @ sK21 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f538]) ).
thf(f540,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK21 )
| ( q @ sK21 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f539]) ).
thf(f541,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( q @ sK21 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f540]) ).
thf(f542,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK21 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f540]) ).
thf(f543,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK21 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f542]) ).
thf(f544,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK21 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f543]) ).
thf(f545,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK21 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f544]) ).
thf(f546,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( q @ sK21 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f541]) ).
thf(f547,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( q @ sK21 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f546]) ).
thf(f548,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( r @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK21 )
| ( q @ sK21 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f537]) ).
thf(f549,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( r @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( q @ sK21 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f548]) ).
thf(f550,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( r @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK21 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f548]) ).
thf(f551,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( r @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK21 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f550]) ).
thf(f552,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( r @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK21 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f551]) ).
thf(f553,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( r @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK21 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f552]) ).
thf(f554,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( r @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( q @ sK21 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f549]) ).
thf(f555,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( r @ sK19 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( q @ sK21 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f554]) ).
thf(f556,plain,
( ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f254]) ).
thf(f557,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f254]) ).
thf(f558,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f557]) ).
thf(f559,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f558]) ).
thf(f566,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f559]) ).
thf(f567,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f559]) ).
thf(f568,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f567]) ).
thf(f569,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f568]) ).
thf(f570,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f569]) ).
thf(f571,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f570]) ).
thf(f572,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f570]) ).
thf(f573,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f572]) ).
thf(f574,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f573]) ).
thf(f575,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f574]) ).
thf(f576,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK22 )
| ( p @ sK22 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f575]) ).
thf(f577,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f576]) ).
thf(f578,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK22 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f576]) ).
thf(f579,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f578]) ).
thf(f580,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f579]) ).
thf(f581,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f580]) ).
thf(f582,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f581]) ).
thf(f583,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f582]) ).
thf(f584,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f577]) ).
thf(f585,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f584]) ).
thf(f586,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f585]) ).
thf(f587,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f586]) ).
thf(f588,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f571]) ).
thf(f589,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f588]) ).
thf(f590,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f589]) ).
thf(f591,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK22 )
| ( p @ sK22 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( r @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f590]) ).
thf(f592,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( r @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f591]) ).
thf(f593,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK22 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( r @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f591]) ).
thf(f594,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( r @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f593]) ).
thf(f595,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f594]) ).
thf(f596,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f595]) ).
thf(f597,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f596]) ).
thf(f598,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f597]) ).
thf(f599,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f592]) ).
thf(f600,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f599]) ).
thf(f601,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f600]) ).
thf(f602,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f601]) ).
thf(f603,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f566]) ).
thf(f604,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f603]) ).
thf(f605,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f604]) ).
thf(f606,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f605]) ).
thf(f607,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f605]) ).
thf(f608,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK23 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f607]) ).
thf(f609,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK23 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f608]) ).
thf(f611,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK23 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f609]) ).
thf(f612,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK23 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK24 ) ) ),
inference(sigma_proxy_clausification,[],[f611]) ).
thf(f613,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK22 )
| ( p @ sK22 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK23 )
| ( p @ sK23 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 )
| ( p @ sK24 ) ) ) ),
inference(beta-eta_normalization,[],[f612]) ).
thf(f614,plain,
( ( $false
= ( p @ sK22 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK23 )
| ( p @ sK23 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 )
| ( p @ sK24 ) ) ) ),
inference(or_proxy_clausification,[],[f613]) ).
thf(f615,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK22 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK23 )
| ( p @ sK23 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 )
| ( p @ sK24 ) ) ) ),
inference(or_proxy_clausification,[],[f613]) ).
thf(f616,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK23 )
| ( p @ sK23 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 )
| ( p @ sK24 ) ) ) ),
inference(not_proxy_clausification,[],[f615]) ).
thf(f617,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $false
= ( p @ sK23 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 )
| ( p @ sK24 ) ) ) ),
inference(or_proxy_clausification,[],[f616]) ).
thf(f618,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK23 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 )
| ( p @ sK24 ) ) ) ),
inference(or_proxy_clausification,[],[f616]) ).
thf(f619,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK23 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 )
| ( p @ sK24 ) ) ) ),
inference(not_proxy_clausification,[],[f618]) ).
thf(f620,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK23 ) )
| ( $false
= ( p @ sK24 ) ) ),
inference(or_proxy_clausification,[],[f619]) ).
thf(f621,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK23 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 ) ) ) ),
inference(or_proxy_clausification,[],[f619]) ).
thf(f622,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK23 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK24 ) ) ),
inference(not_proxy_clausification,[],[f621]) ).
thf(f623,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $false
= ( p @ sK23 ) )
| ( $false
= ( p @ sK24 ) ) ),
inference(or_proxy_clausification,[],[f617]) ).
thf(f624,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $false
= ( p @ sK23 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 ) ) ) ),
inference(or_proxy_clausification,[],[f617]) ).
thf(f625,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $false
= ( p @ sK23 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK24 ) ) ),
inference(not_proxy_clausification,[],[f624]) ).
thf(f626,plain,
( ( $false
= ( p @ sK22 ) )
| ( $false
= ( p @ sK23 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 )
| ( p @ sK24 ) ) ) ),
inference(or_proxy_clausification,[],[f614]) ).
thf(f627,plain,
( ( $false
= ( p @ sK22 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK23 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 )
| ( p @ sK24 ) ) ) ),
inference(or_proxy_clausification,[],[f614]) ).
thf(f628,plain,
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK23 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 )
| ( p @ sK24 ) ) ) ),
inference(not_proxy_clausification,[],[f627]) ).
thf(f629,plain,
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK23 ) )
| ( $false
= ( p @ sK24 ) ) ),
inference(or_proxy_clausification,[],[f628]) ).
thf(f630,plain,
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK23 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 ) ) ) ),
inference(or_proxy_clausification,[],[f628]) ).
thf(f631,plain,
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK23 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK24 ) ) ),
inference(not_proxy_clausification,[],[f630]) ).
thf(f632,plain,
( ( $false
= ( p @ sK22 ) )
| ( $false
= ( p @ sK23 ) )
| ( $false
= ( p @ sK24 ) ) ),
inference(or_proxy_clausification,[],[f626]) ).
thf(f633,plain,
( ( $false
= ( p @ sK22 ) )
| ( $false
= ( p @ sK23 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK24 ) ) ) ),
inference(or_proxy_clausification,[],[f626]) ).
thf(f634,plain,
( ( $false
= ( p @ sK22 ) )
| ( $false
= ( p @ sK23 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK24 ) ) ),
inference(not_proxy_clausification,[],[f633]) ).
thf(f658,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK26 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f606]) ).
thf(f659,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK26 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f658]) ).
thf(f660,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK26 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f659]) ).
thf(f685,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK22 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK26 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK28 ) ) ),
inference(sigma_proxy_clausification,[],[f660]) ).
thf(f686,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK22 )
| ( p @ sK22 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK26 )
| ( r @ sK26 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 )
| ( q @ sK28 ) ) ) ),
inference(beta-eta_normalization,[],[f685]) ).
thf(f687,plain,
( ( $false
= ( p @ sK22 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK26 )
| ( r @ sK26 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 )
| ( q @ sK28 ) ) ) ),
inference(or_proxy_clausification,[],[f686]) ).
thf(f688,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK22 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK26 )
| ( r @ sK26 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 )
| ( q @ sK28 ) ) ) ),
inference(or_proxy_clausification,[],[f686]) ).
thf(f689,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK26 )
| ( r @ sK26 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 )
| ( q @ sK28 ) ) ) ),
inference(not_proxy_clausification,[],[f688]) ).
thf(f690,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $false
= ( r @ sK26 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 )
| ( q @ sK28 ) ) ) ),
inference(or_proxy_clausification,[],[f689]) ).
thf(f691,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK26 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 )
| ( q @ sK28 ) ) ) ),
inference(or_proxy_clausification,[],[f689]) ).
thf(f692,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK26 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 )
| ( q @ sK28 ) ) ) ),
inference(not_proxy_clausification,[],[f691]) ).
thf(f693,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK26 ) )
| ( $false
= ( q @ sK28 ) ) ),
inference(or_proxy_clausification,[],[f692]) ).
thf(f694,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK26 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 ) ) ) ),
inference(or_proxy_clausification,[],[f692]) ).
thf(f695,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK26 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK28 ) ) ),
inference(not_proxy_clausification,[],[f694]) ).
thf(f696,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $false
= ( r @ sK26 ) )
| ( $false
= ( q @ sK28 ) ) ),
inference(or_proxy_clausification,[],[f690]) ).
thf(f697,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $false
= ( r @ sK26 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 ) ) ) ),
inference(or_proxy_clausification,[],[f690]) ).
thf(f698,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ( $false
= ( r @ sK26 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK28 ) ) ),
inference(not_proxy_clausification,[],[f697]) ).
thf(f699,plain,
( ( $false
= ( p @ sK22 ) )
| ( $false
= ( r @ sK26 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 )
| ( q @ sK28 ) ) ) ),
inference(or_proxy_clausification,[],[f687]) ).
thf(f700,plain,
( ( $false
= ( p @ sK22 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK26 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 )
| ( q @ sK28 ) ) ) ),
inference(or_proxy_clausification,[],[f687]) ).
thf(f701,plain,
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK26 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 )
| ( q @ sK28 ) ) ) ),
inference(not_proxy_clausification,[],[f700]) ).
thf(f702,plain,
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK26 ) )
| ( $false
= ( q @ sK28 ) ) ),
inference(or_proxy_clausification,[],[f701]) ).
thf(f703,plain,
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK26 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 ) ) ) ),
inference(or_proxy_clausification,[],[f701]) ).
thf(f704,plain,
( ( $false
= ( p @ sK22 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK26 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK28 ) ) ),
inference(not_proxy_clausification,[],[f703]) ).
thf(f705,plain,
( ( $false
= ( p @ sK22 ) )
| ( $false
= ( r @ sK26 ) )
| ( $false
= ( q @ sK28 ) ) ),
inference(or_proxy_clausification,[],[f699]) ).
thf(f706,plain,
( ( $false
= ( p @ sK22 ) )
| ( $false
= ( r @ sK26 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK28 ) ) ) ),
inference(or_proxy_clausification,[],[f699]) ).
thf(f707,plain,
( ( $false
= ( p @ sK22 ) )
| ( $false
= ( r @ sK26 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK28 ) ) ),
inference(not_proxy_clausification,[],[f706]) ).
thf(f708,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f556]) ).
thf(f709,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f708]) ).
thf(f710,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f709]) ).
thf(f711,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f710]) ).
thf(f712,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f711]) ).
thf(f727,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f712]) ).
thf(f728,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f712]) ).
thf(f729,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f728]) ).
thf(f730,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f729]) ).
thf(f731,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f730]) ).
thf(f732,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f731]) ).
thf(f733,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f731]) ).
thf(f734,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f733]) ).
thf(f735,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f734]) ).
thf(f736,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f735]) ).
thf(f737,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK31 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f736]) ).
thf(f738,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK31 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f737]) ).
thf(f739,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK29 )
| ( r @ sK29 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f738]) ).
thf(f740,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f739]) ).
thf(f741,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK29 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f739]) ).
thf(f742,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f741]) ).
thf(f743,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f742]) ).
thf(f744,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK31 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f743]) ).
thf(f745,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK31 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f743]) ).
thf(f746,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK31 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f745]) ).
thf(f747,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK31 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f746]) ).
thf(f748,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK31 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f747]) ).
thf(f749,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK31 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f748]) ).
thf(f750,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK31 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f744]) ).
thf(f751,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK31 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f750]) ).
thf(f752,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK31 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f751]) ).
thf(f753,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f740]) ).
thf(f754,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK31 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f753]) ).
thf(f755,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK31 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f753]) ).
thf(f756,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK31 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f755]) ).
thf(f757,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK31 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f756]) ).
thf(f758,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK31 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f757]) ).
thf(f759,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK31 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f758]) ).
thf(f760,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK31 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f754]) ).
thf(f761,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK31 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f760]) ).
thf(f762,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK31 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f761]) ).
thf(f763,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f732]) ).
thf(f764,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f763]) ).
thf(f765,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f764]) ).
thf(f766,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK32 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f765]) ).
thf(f767,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK32 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f766]) ).
thf(f768,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK29 )
| ( r @ sK29 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( r @ X1 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK32 )
| ( q @ sK32 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f767]) ).
thf(f769,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( r @ X1 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK32 )
| ( q @ sK32 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f768]) ).
thf(f770,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK29 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( r @ X1 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK32 )
| ( q @ sK32 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f768]) ).
thf(f771,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 )
| ( r @ X1 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK32 )
| ( q @ sK32 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f770]) ).
thf(f772,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK32 )
| ( q @ sK32 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f771]) ).
thf(f773,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( q @ sK32 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f772]) ).
thf(f774,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK32 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f772]) ).
thf(f775,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK32 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f774]) ).
thf(f776,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK32 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f775]) ).
thf(f777,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK32 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f776]) ).
thf(f778,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK32 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f777]) ).
thf(f779,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( q @ sK32 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f773]) ).
thf(f780,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( q @ sK32 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f779]) ).
thf(f781,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( q @ sK32 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f780]) ).
thf(f782,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK32 )
| ( q @ sK32 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f769]) ).
thf(f783,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( q @ sK32 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f782]) ).
thf(f784,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK32 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f782]) ).
thf(f785,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK32 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f784]) ).
thf(f786,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK32 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f785]) ).
thf(f787,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK32 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f786]) ).
thf(f788,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK32 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f787]) ).
thf(f789,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( q @ sK32 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f783]) ).
thf(f790,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( q @ sK32 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f789]) ).
thf(f791,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( r @ X1 ) )
| ( $false
= ( q @ sK32 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f790]) ).
thf(f792,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f727]) ).
thf(f793,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f792]) ).
thf(f794,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f793]) ).
thf(f795,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f794]) ).
thf(f796,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f794]) ).
thf(f797,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK33 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f796]) ).
thf(f798,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK33 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f797]) ).
thf(f799,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK33 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK34 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f798]) ).
thf(f800,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK33 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK34 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f799]) ).
thf(f802,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK33 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK34 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f800]) ).
thf(f803,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK33 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK34 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK35 ) ) ),
inference(sigma_proxy_clausification,[],[f802]) ).
thf(f804,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK29 )
| ( r @ sK29 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 )
| ( p @ sK33 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 )
| ( q @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(beta-eta_normalization,[],[f803]) ).
thf(f805,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 )
| ( p @ sK33 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 )
| ( q @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f804]) ).
thf(f806,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK29 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 )
| ( p @ sK33 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 )
| ( q @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f804]) ).
thf(f807,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 )
| ( p @ sK33 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 )
| ( q @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(not_proxy_clausification,[],[f806]) ).
thf(f808,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 )
| ( q @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f807]) ).
thf(f809,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 )
| ( q @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f807]) ).
thf(f810,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 )
| ( q @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(not_proxy_clausification,[],[f809]) ).
thf(f811,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f810]) ).
thf(f812,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f810]) ).
thf(f813,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(not_proxy_clausification,[],[f812]) ).
thf(f814,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $false
= ( p @ sK35 ) ) ),
inference(or_proxy_clausification,[],[f813]) ).
thf(f815,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f813]) ).
thf(f816,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK35 ) ) ),
inference(not_proxy_clausification,[],[f815]) ).
thf(f817,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $false
= ( p @ sK35 ) ) ),
inference(or_proxy_clausification,[],[f811]) ).
thf(f818,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f811]) ).
thf(f819,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK35 ) ) ),
inference(not_proxy_clausification,[],[f818]) ).
thf(f820,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f808]) ).
thf(f821,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f808]) ).
thf(f822,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(not_proxy_clausification,[],[f821]) ).
thf(f823,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $false
= ( p @ sK35 ) ) ),
inference(or_proxy_clausification,[],[f822]) ).
thf(f824,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f822]) ).
thf(f825,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK35 ) ) ),
inference(not_proxy_clausification,[],[f824]) ).
thf(f826,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $false
= ( p @ sK35 ) ) ),
inference(or_proxy_clausification,[],[f820]) ).
thf(f827,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f820]) ).
thf(f828,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK35 ) ) ),
inference(not_proxy_clausification,[],[f827]) ).
thf(f829,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 )
| ( q @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f805]) ).
thf(f830,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 )
| ( q @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f805]) ).
thf(f831,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 )
| ( q @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(not_proxy_clausification,[],[f830]) ).
thf(f832,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f831]) ).
thf(f833,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f831]) ).
thf(f834,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(not_proxy_clausification,[],[f833]) ).
thf(f835,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $false
= ( p @ sK35 ) ) ),
inference(or_proxy_clausification,[],[f834]) ).
thf(f836,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f834]) ).
thf(f837,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK35 ) ) ),
inference(not_proxy_clausification,[],[f836]) ).
thf(f838,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $false
= ( p @ sK35 ) ) ),
inference(or_proxy_clausification,[],[f832]) ).
thf(f839,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f832]) ).
thf(f840,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK35 ) ) ),
inference(not_proxy_clausification,[],[f839]) ).
thf(f841,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f829]) ).
thf(f842,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f829]) ).
thf(f843,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 )
| ( p @ sK35 ) ) ) ),
inference(not_proxy_clausification,[],[f842]) ).
thf(f844,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $false
= ( p @ sK35 ) ) ),
inference(or_proxy_clausification,[],[f843]) ).
thf(f845,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f843]) ).
thf(f846,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK35 ) ) ),
inference(not_proxy_clausification,[],[f845]) ).
thf(f847,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $false
= ( p @ sK35 ) ) ),
inference(or_proxy_clausification,[],[f841]) ).
thf(f848,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK35 ) ) ) ),
inference(or_proxy_clausification,[],[f841]) ).
thf(f849,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( p @ sK33 ) )
| ( $false
= ( q @ sK34 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK35 ) ) ),
inference(not_proxy_clausification,[],[f848]) ).
thf(f897,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK37 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f795]) ).
thf(f898,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK37 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f897]) ).
thf(f899,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK37 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK38 ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f898]) ).
thf(f900,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK37 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK38 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f899]) ).
thf(f901,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK37 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK38 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f900]) ).
thf(f950,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK37 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK38 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK40 ) ) ),
inference(sigma_proxy_clausification,[],[f901]) ).
thf(f951,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK29 )
| ( r @ sK29 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK37 )
| ( r @ sK37 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 )
| ( q @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(beta-eta_normalization,[],[f950]) ).
thf(f952,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK37 )
| ( r @ sK37 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 )
| ( q @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f951]) ).
thf(f953,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK29 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK37 )
| ( r @ sK37 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 )
| ( q @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f951]) ).
thf(f954,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK37 )
| ( r @ sK37 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 )
| ( q @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(not_proxy_clausification,[],[f953]) ).
thf(f955,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 )
| ( q @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f954]) ).
thf(f956,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK37 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 )
| ( q @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f954]) ).
thf(f957,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 )
| ( q @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(not_proxy_clausification,[],[f956]) ).
thf(f958,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f957]) ).
thf(f959,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f957]) ).
thf(f960,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(not_proxy_clausification,[],[f959]) ).
thf(f961,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $false
= ( q @ sK40 ) ) ),
inference(or_proxy_clausification,[],[f960]) ).
thf(f962,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f960]) ).
thf(f963,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK40 ) ) ),
inference(not_proxy_clausification,[],[f962]) ).
thf(f964,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $false
= ( q @ sK40 ) ) ),
inference(or_proxy_clausification,[],[f958]) ).
thf(f965,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f958]) ).
thf(f966,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK40 ) ) ),
inference(not_proxy_clausification,[],[f965]) ).
thf(f967,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f955]) ).
thf(f968,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f955]) ).
thf(f969,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(not_proxy_clausification,[],[f968]) ).
thf(f970,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $false
= ( q @ sK40 ) ) ),
inference(or_proxy_clausification,[],[f969]) ).
thf(f971,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f969]) ).
thf(f972,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK40 ) ) ),
inference(not_proxy_clausification,[],[f971]) ).
thf(f973,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $false
= ( q @ sK40 ) ) ),
inference(or_proxy_clausification,[],[f967]) ).
thf(f974,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f967]) ).
thf(f975,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK40 ) ) ),
inference(not_proxy_clausification,[],[f974]) ).
thf(f976,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 )
| ( q @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f952]) ).
thf(f977,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK37 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 )
| ( q @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f952]) ).
thf(f978,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 )
| ( q @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(not_proxy_clausification,[],[f977]) ).
thf(f979,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f978]) ).
thf(f980,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f978]) ).
thf(f981,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(not_proxy_clausification,[],[f980]) ).
thf(f982,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $false
= ( q @ sK40 ) ) ),
inference(or_proxy_clausification,[],[f981]) ).
thf(f983,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f981]) ).
thf(f984,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK40 ) ) ),
inference(not_proxy_clausification,[],[f983]) ).
thf(f985,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $false
= ( q @ sK40 ) ) ),
inference(or_proxy_clausification,[],[f979]) ).
thf(f986,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f979]) ).
thf(f987,plain,
( ( $false
= ( r @ sK29 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK40 ) ) ),
inference(not_proxy_clausification,[],[f986]) ).
thf(f988,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f976]) ).
thf(f989,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK38 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f976]) ).
thf(f990,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( q @ sK40 ) ) ) ),
inference(not_proxy_clausification,[],[f989]) ).
thf(f991,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $false
= ( q @ sK40 ) ) ),
inference(or_proxy_clausification,[],[f990]) ).
thf(f992,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f990]) ).
thf(f993,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK40 ) ) ),
inference(not_proxy_clausification,[],[f992]) ).
thf(f994,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $false
= ( q @ sK40 ) ) ),
inference(or_proxy_clausification,[],[f988]) ).
thf(f995,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK40 ) ) ) ),
inference(or_proxy_clausification,[],[f988]) ).
thf(f996,plain,
( ( $false
= ( r @ sK29 ) )
| ( $false
= ( r @ sK37 ) )
| ( $false
= ( q @ sK38 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK40 ) ) ),
inference(not_proxy_clausification,[],[f995]) ).
thf(f1019,definition,
( spl41_3
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl41_3])],[avatar_definition]) ).
thf(f1020,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s4 @ sK3 @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl41_3 ),
inference(avatar_component_clause,[],[f1019]) ).
thf(f1022,definition,
( spl41_4
<=> ! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl41_4])],[avatar_definition]) ).
thf(f1023,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl41_4 ),
inference(avatar_component_clause,[],[f1022]) ).
thf(f1026,definition,
( spl41_5
<=> ! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl41_5])],[avatar_definition]) ).
thf(f1027,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK3 @ X1 ) )
| ( $true
= ( r @ X1 ) ) )
| ~ spl41_5 ),
inference(avatar_component_clause,[],[f1026]) ).
thf(f1094,definition,
( spl41_18
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl41_18])],[avatar_definition]) ).
thf(f1095,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl41_18 ),
inference(avatar_component_clause,[],[f1094]) ).
thf(f1097,definition,
( spl41_19
<=> ! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl41_19])],[avatar_definition]) ).
thf(f1098,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl41_19 ),
inference(avatar_component_clause,[],[f1097]) ).
thf(f1100,plain,
( spl41_3
| spl41_18
| spl41_4
| spl41_19 ),
inference(avatar_split_clause,[],[f291,f1097,f1022,f1094,f1019]) ).
thf(f1101,plain,
( spl41_3
| spl41_18
| spl41_5
| spl41_19 ),
inference(avatar_split_clause,[],[f304,f1097,f1026,f1094,f1019]) ).
thf(f1103,definition,
( spl41_20
<=> ( $true
= ( rel_s4 @ sK3 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_20])],[avatar_definition]) ).
thf(f1105,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK11 ) )
| ~ spl41_20 ),
inference(avatar_component_clause,[],[f1103]) ).
thf(f1107,definition,
( spl41_21
<=> ( $true
= ( rel_s4 @ sK3 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_21])],[avatar_definition]) ).
thf(f1109,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK10 ) )
| ~ spl41_21 ),
inference(avatar_component_clause,[],[f1107]) ).
thf(f1110,plain,
( spl41_20
| spl41_18
| spl41_21
| spl41_19 ),
inference(avatar_split_clause,[],[f326,f1097,f1107,f1094,f1103]) ).
thf(f1112,definition,
( spl41_22
<=> ( $false
= ( p @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_22])],[avatar_definition]) ).
thf(f1114,plain,
( ( $false
= ( p @ sK11 ) )
| ~ spl41_22 ),
inference(avatar_component_clause,[],[f1112]) ).
thf(f1115,plain,
( spl41_22
| spl41_18
| spl41_21
| spl41_19 ),
inference(avatar_split_clause,[],[f328,f1097,f1107,f1094,f1112]) ).
thf(f1117,definition,
( spl41_23
<=> ( $false
= ( p @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_23])],[avatar_definition]) ).
thf(f1119,plain,
( ( $false
= ( p @ sK10 ) )
| ~ spl41_23 ),
inference(avatar_component_clause,[],[f1117]) ).
thf(f1120,plain,
( spl41_20
| spl41_18
| spl41_23
| spl41_19 ),
inference(avatar_split_clause,[],[f334,f1097,f1117,f1094,f1103]) ).
thf(f1121,plain,
( spl41_22
| spl41_18
| spl41_23
| spl41_19 ),
inference(avatar_split_clause,[],[f336,f1097,f1117,f1094,f1112]) ).
thf(f1139,definition,
( spl41_27
<=> ( $true
= ( rel_s4 @ sK3 @ sK13 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_27])],[avatar_definition]) ).
thf(f1141,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK13 ) )
| ~ spl41_27 ),
inference(avatar_component_clause,[],[f1139]) ).
thf(f1149,definition,
( spl41_29
<=> ( $false
= ( r @ sK13 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_29])],[avatar_definition]) ).
thf(f1151,plain,
( ( $false
= ( r @ sK13 ) )
| ~ spl41_29 ),
inference(avatar_component_clause,[],[f1149]) ).
thf(f1155,definition,
( spl41_30
<=> ( $true
= ( rel_s4 @ sK3 @ sK15 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_30])],[avatar_definition]) ).
thf(f1157,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ~ spl41_30 ),
inference(avatar_component_clause,[],[f1155]) ).
thf(f1158,plain,
( spl41_30
| spl41_18
| spl41_27
| spl41_19 ),
inference(avatar_split_clause,[],[f397,f1097,f1139,f1094,f1155]) ).
thf(f1160,definition,
( spl41_31
<=> ( $false
= ( q @ sK15 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_31])],[avatar_definition]) ).
thf(f1162,plain,
( ( $false
= ( q @ sK15 ) )
| ~ spl41_31 ),
inference(avatar_component_clause,[],[f1160]) ).
thf(f1163,plain,
( spl41_31
| spl41_18
| spl41_27
| spl41_19 ),
inference(avatar_split_clause,[],[f399,f1097,f1139,f1094,f1160]) ).
thf(f1164,plain,
( spl41_30
| spl41_18
| spl41_29
| spl41_19 ),
inference(avatar_split_clause,[],[f405,f1097,f1149,f1094,f1155]) ).
thf(f1165,plain,
( spl41_31
| spl41_18
| spl41_29
| spl41_19 ),
inference(avatar_split_clause,[],[f407,f1097,f1149,f1094,f1160]) ).
thf(f1167,definition,
( spl41_32
<=> ! [X1: $i] :
( ( $true
= ( r @ X1 ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl41_32])],[avatar_definition]) ).
thf(f1168,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( r @ X1 ) ) )
| ~ spl41_32 ),
inference(avatar_component_clause,[],[f1167]) ).
thf(f1170,plain,
( spl41_3
| spl41_18
| spl41_4
| spl41_32 ),
inference(avatar_split_clause,[],[f439,f1167,f1022,f1094,f1019]) ).
thf(f1171,plain,
( spl41_3
| spl41_18
| spl41_5
| spl41_32 ),
inference(avatar_split_clause,[],[f452,f1167,f1026,f1094,f1019]) ).
thf(f1173,definition,
( spl41_33
<=> ( $true
= ( rel_s4 @ sK3 @ sK17 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_33])],[avatar_definition]) ).
thf(f1175,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK17 ) )
| ~ spl41_33 ),
inference(avatar_component_clause,[],[f1173]) ).
thf(f1177,definition,
( spl41_34
<=> ( $true
= ( rel_s4 @ sK3 @ sK16 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_34])],[avatar_definition]) ).
thf(f1179,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK16 ) )
| ~ spl41_34 ),
inference(avatar_component_clause,[],[f1177]) ).
thf(f1180,plain,
( spl41_33
| spl41_18
| spl41_34
| spl41_32 ),
inference(avatar_split_clause,[],[f474,f1167,f1177,f1094,f1173]) ).
thf(f1182,definition,
( spl41_35
<=> ( $false
= ( p @ sK17 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_35])],[avatar_definition]) ).
thf(f1184,plain,
( ( $false
= ( p @ sK17 ) )
| ~ spl41_35 ),
inference(avatar_component_clause,[],[f1182]) ).
thf(f1185,plain,
( spl41_35
| spl41_18
| spl41_34
| spl41_32 ),
inference(avatar_split_clause,[],[f476,f1167,f1177,f1094,f1182]) ).
thf(f1187,definition,
( spl41_36
<=> ( $false
= ( p @ sK16 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_36])],[avatar_definition]) ).
thf(f1189,plain,
( ( $false
= ( p @ sK16 ) )
| ~ spl41_36 ),
inference(avatar_component_clause,[],[f1187]) ).
thf(f1190,plain,
( spl41_33
| spl41_18
| spl41_36
| spl41_32 ),
inference(avatar_split_clause,[],[f482,f1167,f1187,f1094,f1173]) ).
thf(f1191,plain,
( spl41_35
| spl41_18
| spl41_36
| spl41_32 ),
inference(avatar_split_clause,[],[f484,f1167,f1187,f1094,f1182]) ).
thf(f1209,definition,
( spl41_40
<=> ( $true
= ( rel_s4 @ sK3 @ sK19 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_40])],[avatar_definition]) ).
thf(f1211,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK19 ) )
| ~ spl41_40 ),
inference(avatar_component_clause,[],[f1209]) ).
thf(f1219,definition,
( spl41_42
<=> ( $false
= ( r @ sK19 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_42])],[avatar_definition]) ).
thf(f1221,plain,
( ( $false
= ( r @ sK19 ) )
| ~ spl41_42 ),
inference(avatar_component_clause,[],[f1219]) ).
thf(f1225,definition,
( spl41_43
<=> ( $true
= ( rel_s4 @ sK3 @ sK21 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_43])],[avatar_definition]) ).
thf(f1227,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK21 ) )
| ~ spl41_43 ),
inference(avatar_component_clause,[],[f1225]) ).
thf(f1228,plain,
( spl41_43
| spl41_18
| spl41_40
| spl41_32 ),
inference(avatar_split_clause,[],[f545,f1167,f1209,f1094,f1225]) ).
thf(f1230,definition,
( spl41_44
<=> ( $false
= ( q @ sK21 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_44])],[avatar_definition]) ).
thf(f1232,plain,
( ( $false
= ( q @ sK21 ) )
| ~ spl41_44 ),
inference(avatar_component_clause,[],[f1230]) ).
thf(f1233,plain,
( spl41_44
| spl41_18
| spl41_40
| spl41_32 ),
inference(avatar_split_clause,[],[f547,f1167,f1209,f1094,f1230]) ).
thf(f1234,plain,
( spl41_43
| spl41_18
| spl41_42
| spl41_32 ),
inference(avatar_split_clause,[],[f553,f1167,f1219,f1094,f1225]) ).
thf(f1235,plain,
( spl41_44
| spl41_18
| spl41_42
| spl41_32 ),
inference(avatar_split_clause,[],[f555,f1167,f1219,f1094,f1230]) ).
thf(f1237,definition,
( spl41_45
<=> ( $true
= ( rel_s4 @ sK2 @ sK22 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_45])],[avatar_definition]) ).
thf(f1239,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK22 ) )
| ~ spl41_45 ),
inference(avatar_component_clause,[],[f1237]) ).
thf(f1242,definition,
( spl41_46
<=> ( $false
= ( p @ sK22 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_46])],[avatar_definition]) ).
thf(f1244,plain,
( ( $false
= ( p @ sK22 ) )
| ~ spl41_46 ),
inference(avatar_component_clause,[],[f1242]) ).
thf(f1246,plain,
( spl41_3
| spl41_4
| spl41_45 ),
inference(avatar_split_clause,[],[f583,f1237,f1022,f1019]) ).
thf(f1247,plain,
( spl41_3
| spl41_4
| spl41_46 ),
inference(avatar_split_clause,[],[f587,f1242,f1022,f1019]) ).
thf(f1248,plain,
( spl41_3
| spl41_5
| spl41_45 ),
inference(avatar_split_clause,[],[f598,f1237,f1026,f1019]) ).
thf(f1249,plain,
( spl41_3
| spl41_5
| spl41_46 ),
inference(avatar_split_clause,[],[f602,f1242,f1026,f1019]) ).
thf(f1251,definition,
( spl41_47
<=> ( $true
= ( rel_s4 @ sK3 @ sK24 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_47])],[avatar_definition]) ).
thf(f1253,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK24 ) )
| ~ spl41_47 ),
inference(avatar_component_clause,[],[f1251]) ).
thf(f1255,definition,
( spl41_48
<=> ( $true
= ( rel_s4 @ sK3 @ sK23 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_48])],[avatar_definition]) ).
thf(f1257,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK23 ) )
| ~ spl41_48 ),
inference(avatar_component_clause,[],[f1255]) ).
thf(f1258,plain,
( spl41_47
| spl41_48
| spl41_45 ),
inference(avatar_split_clause,[],[f622,f1237,f1255,f1251]) ).
thf(f1260,definition,
( spl41_49
<=> ( $false
= ( p @ sK24 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_49])],[avatar_definition]) ).
thf(f1262,plain,
( ( $false
= ( p @ sK24 ) )
| ~ spl41_49 ),
inference(avatar_component_clause,[],[f1260]) ).
thf(f1263,plain,
( spl41_49
| spl41_48
| spl41_45 ),
inference(avatar_split_clause,[],[f620,f1237,f1255,f1260]) ).
thf(f1265,definition,
( spl41_50
<=> ( $false
= ( p @ sK23 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_50])],[avatar_definition]) ).
thf(f1267,plain,
( ( $false
= ( p @ sK23 ) )
| ~ spl41_50 ),
inference(avatar_component_clause,[],[f1265]) ).
thf(f1268,plain,
( spl41_47
| spl41_50
| spl41_45 ),
inference(avatar_split_clause,[],[f625,f1237,f1265,f1251]) ).
thf(f1269,plain,
( spl41_49
| spl41_50
| spl41_45 ),
inference(avatar_split_clause,[],[f623,f1237,f1265,f1260]) ).
thf(f1270,plain,
( spl41_47
| spl41_48
| spl41_46 ),
inference(avatar_split_clause,[],[f631,f1242,f1255,f1251]) ).
thf(f1271,plain,
( spl41_49
| spl41_48
| spl41_46 ),
inference(avatar_split_clause,[],[f629,f1242,f1255,f1260]) ).
thf(f1272,plain,
( spl41_47
| spl41_50
| spl41_46 ),
inference(avatar_split_clause,[],[f634,f1242,f1265,f1251]) ).
thf(f1273,plain,
( spl41_49
| spl41_50
| spl41_46 ),
inference(avatar_split_clause,[],[f632,f1242,f1265,f1260]) ).
thf(f1295,definition,
( spl41_54
<=> ( $true
= ( rel_s4 @ sK3 @ sK26 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_54])],[avatar_definition]) ).
thf(f1297,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK26 ) )
| ~ spl41_54 ),
inference(avatar_component_clause,[],[f1295]) ).
thf(f1305,definition,
( spl41_56
<=> ( $false
= ( r @ sK26 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_56])],[avatar_definition]) ).
thf(f1307,plain,
( ( $false
= ( r @ sK26 ) )
| ~ spl41_56 ),
inference(avatar_component_clause,[],[f1305]) ).
thf(f1315,definition,
( spl41_57
<=> ( $true
= ( rel_s4 @ sK3 @ sK28 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_57])],[avatar_definition]) ).
thf(f1317,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK28 ) )
| ~ spl41_57 ),
inference(avatar_component_clause,[],[f1315]) ).
thf(f1318,plain,
( spl41_57
| spl41_54
| spl41_45 ),
inference(avatar_split_clause,[],[f695,f1237,f1295,f1315]) ).
thf(f1320,definition,
( spl41_58
<=> ( $false
= ( q @ sK28 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_58])],[avatar_definition]) ).
thf(f1322,plain,
( ( $false
= ( q @ sK28 ) )
| ~ spl41_58 ),
inference(avatar_component_clause,[],[f1320]) ).
thf(f1323,plain,
( spl41_58
| spl41_54
| spl41_45 ),
inference(avatar_split_clause,[],[f693,f1237,f1295,f1320]) ).
thf(f1324,plain,
( spl41_57
| spl41_56
| spl41_45 ),
inference(avatar_split_clause,[],[f698,f1237,f1305,f1315]) ).
thf(f1325,plain,
( spl41_58
| spl41_56
| spl41_45 ),
inference(avatar_split_clause,[],[f696,f1237,f1305,f1320]) ).
thf(f1326,plain,
( spl41_57
| spl41_54
| spl41_46 ),
inference(avatar_split_clause,[],[f704,f1242,f1295,f1315]) ).
thf(f1327,plain,
( spl41_58
| spl41_54
| spl41_46 ),
inference(avatar_split_clause,[],[f702,f1242,f1295,f1320]) ).
thf(f1328,plain,
( spl41_57
| spl41_56
| spl41_46 ),
inference(avatar_split_clause,[],[f707,f1242,f1305,f1315]) ).
thf(f1329,plain,
( spl41_58
| spl41_56
| spl41_46 ),
inference(avatar_split_clause,[],[f705,f1242,f1305,f1320]) ).
thf(f1335,definition,
( spl41_60
<=> ( $true
= ( rel_s4 @ sK2 @ sK29 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_60])],[avatar_definition]) ).
thf(f1337,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK29 ) )
| ~ spl41_60 ),
inference(avatar_component_clause,[],[f1335]) ).
thf(f1345,definition,
( spl41_62
<=> ( $false
= ( r @ sK29 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_62])],[avatar_definition]) ).
thf(f1347,plain,
( ( $false
= ( r @ sK29 ) )
| ~ spl41_62 ),
inference(avatar_component_clause,[],[f1345]) ).
thf(f1351,definition,
( spl41_63
<=> ( $true
= ( rel_s4 @ sK2 @ sK31 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_63])],[avatar_definition]) ).
thf(f1353,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK31 ) )
| ~ spl41_63 ),
inference(avatar_component_clause,[],[f1351]) ).
thf(f1354,plain,
( spl41_3
| spl41_63
| spl41_4
| spl41_60 ),
inference(avatar_split_clause,[],[f749,f1335,f1022,f1351,f1019]) ).
thf(f1356,definition,
( spl41_64
<=> ( $false
= ( q @ sK31 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_64])],[avatar_definition]) ).
thf(f1358,plain,
( ( $false
= ( q @ sK31 ) )
| ~ spl41_64 ),
inference(avatar_component_clause,[],[f1356]) ).
thf(f1359,plain,
( spl41_3
| spl41_64
| spl41_4
| spl41_60 ),
inference(avatar_split_clause,[],[f752,f1335,f1022,f1356,f1019]) ).
thf(f1360,plain,
( spl41_3
| spl41_63
| spl41_4
| spl41_62 ),
inference(avatar_split_clause,[],[f759,f1345,f1022,f1351,f1019]) ).
thf(f1361,plain,
( spl41_3
| spl41_64
| spl41_4
| spl41_62 ),
inference(avatar_split_clause,[],[f762,f1345,f1022,f1356,f1019]) ).
thf(f1363,definition,
( spl41_65
<=> ( $true
= ( rel_s4 @ sK2 @ sK32 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_65])],[avatar_definition]) ).
thf(f1365,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK32 ) )
| ~ spl41_65 ),
inference(avatar_component_clause,[],[f1363]) ).
thf(f1366,plain,
( spl41_3
| spl41_65
| spl41_5
| spl41_60 ),
inference(avatar_split_clause,[],[f778,f1335,f1026,f1363,f1019]) ).
thf(f1368,definition,
( spl41_66
<=> ( $false
= ( q @ sK32 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_66])],[avatar_definition]) ).
thf(f1370,plain,
( ( $false
= ( q @ sK32 ) )
| ~ spl41_66 ),
inference(avatar_component_clause,[],[f1368]) ).
thf(f1371,plain,
( spl41_3
| spl41_66
| spl41_5
| spl41_60 ),
inference(avatar_split_clause,[],[f781,f1335,f1026,f1368,f1019]) ).
thf(f1372,plain,
( spl41_3
| spl41_65
| spl41_5
| spl41_62 ),
inference(avatar_split_clause,[],[f788,f1345,f1026,f1363,f1019]) ).
thf(f1373,plain,
( spl41_3
| spl41_66
| spl41_5
| spl41_62 ),
inference(avatar_split_clause,[],[f791,f1345,f1026,f1368,f1019]) ).
thf(f1375,definition,
( spl41_67
<=> ( $true
= ( rel_s4 @ sK3 @ sK35 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_67])],[avatar_definition]) ).
thf(f1377,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK35 ) )
| ~ spl41_67 ),
inference(avatar_component_clause,[],[f1375]) ).
thf(f1379,definition,
( spl41_68
<=> ( $true
= ( rel_s4 @ sK2 @ sK34 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_68])],[avatar_definition]) ).
thf(f1381,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK34 ) )
| ~ spl41_68 ),
inference(avatar_component_clause,[],[f1379]) ).
thf(f1383,definition,
( spl41_69
<=> ( $true
= ( rel_s4 @ sK3 @ sK33 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_69])],[avatar_definition]) ).
thf(f1385,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK33 ) )
| ~ spl41_69 ),
inference(avatar_component_clause,[],[f1383]) ).
thf(f1386,plain,
( spl41_67
| spl41_68
| spl41_69
| spl41_60 ),
inference(avatar_split_clause,[],[f816,f1335,f1383,f1379,f1375]) ).
thf(f1388,definition,
( spl41_70
<=> ( $false
= ( p @ sK35 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_70])],[avatar_definition]) ).
thf(f1390,plain,
( ( $false
= ( p @ sK35 ) )
| ~ spl41_70 ),
inference(avatar_component_clause,[],[f1388]) ).
thf(f1391,plain,
( spl41_70
| spl41_68
| spl41_69
| spl41_60 ),
inference(avatar_split_clause,[],[f814,f1335,f1383,f1379,f1388]) ).
thf(f1393,definition,
( spl41_71
<=> ( $false
= ( q @ sK34 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_71])],[avatar_definition]) ).
thf(f1395,plain,
( ( $false
= ( q @ sK34 ) )
| ~ spl41_71 ),
inference(avatar_component_clause,[],[f1393]) ).
thf(f1396,plain,
( spl41_67
| spl41_71
| spl41_69
| spl41_60 ),
inference(avatar_split_clause,[],[f819,f1335,f1383,f1393,f1375]) ).
thf(f1397,plain,
( spl41_70
| spl41_71
| spl41_69
| spl41_60 ),
inference(avatar_split_clause,[],[f817,f1335,f1383,f1393,f1388]) ).
thf(f1399,definition,
( spl41_72
<=> ( $false
= ( p @ sK33 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_72])],[avatar_definition]) ).
thf(f1401,plain,
( ( $false
= ( p @ sK33 ) )
| ~ spl41_72 ),
inference(avatar_component_clause,[],[f1399]) ).
thf(f1402,plain,
( spl41_67
| spl41_68
| spl41_72
| spl41_60 ),
inference(avatar_split_clause,[],[f825,f1335,f1399,f1379,f1375]) ).
thf(f1403,plain,
( spl41_70
| spl41_68
| spl41_72
| spl41_60 ),
inference(avatar_split_clause,[],[f823,f1335,f1399,f1379,f1388]) ).
thf(f1404,plain,
( spl41_67
| spl41_71
| spl41_72
| spl41_60 ),
inference(avatar_split_clause,[],[f828,f1335,f1399,f1393,f1375]) ).
thf(f1405,plain,
( spl41_70
| spl41_71
| spl41_72
| spl41_60 ),
inference(avatar_split_clause,[],[f826,f1335,f1399,f1393,f1388]) ).
thf(f1406,plain,
( spl41_67
| spl41_68
| spl41_69
| spl41_62 ),
inference(avatar_split_clause,[],[f837,f1345,f1383,f1379,f1375]) ).
thf(f1407,plain,
( spl41_70
| spl41_68
| spl41_69
| spl41_62 ),
inference(avatar_split_clause,[],[f835,f1345,f1383,f1379,f1388]) ).
thf(f1408,plain,
( spl41_67
| spl41_71
| spl41_69
| spl41_62 ),
inference(avatar_split_clause,[],[f840,f1345,f1383,f1393,f1375]) ).
thf(f1409,plain,
( spl41_70
| spl41_71
| spl41_69
| spl41_62 ),
inference(avatar_split_clause,[],[f838,f1345,f1383,f1393,f1388]) ).
thf(f1410,plain,
( spl41_67
| spl41_68
| spl41_72
| spl41_62 ),
inference(avatar_split_clause,[],[f846,f1345,f1399,f1379,f1375]) ).
thf(f1411,plain,
( spl41_70
| spl41_68
| spl41_72
| spl41_62 ),
inference(avatar_split_clause,[],[f844,f1345,f1399,f1379,f1388]) ).
thf(f1412,plain,
( spl41_67
| spl41_71
| spl41_72
| spl41_62 ),
inference(avatar_split_clause,[],[f849,f1345,f1399,f1393,f1375]) ).
thf(f1413,plain,
( spl41_70
| spl41_71
| spl41_72
| spl41_62 ),
inference(avatar_split_clause,[],[f847,f1345,f1399,f1393,f1388]) ).
thf(f1443,definition,
( spl41_76
<=> ( $true
= ( rel_s4 @ sK2 @ sK38 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_76])],[avatar_definition]) ).
thf(f1445,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK38 ) )
| ~ spl41_76 ),
inference(avatar_component_clause,[],[f1443]) ).
thf(f1447,definition,
( spl41_77
<=> ( $true
= ( rel_s4 @ sK3 @ sK37 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_77])],[avatar_definition]) ).
thf(f1449,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK37 ) )
| ~ spl41_77 ),
inference(avatar_component_clause,[],[f1447]) ).
thf(f1457,definition,
( spl41_79
<=> ( $false
= ( q @ sK38 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_79])],[avatar_definition]) ).
thf(f1459,plain,
( ( $false
= ( q @ sK38 ) )
| ~ spl41_79 ),
inference(avatar_component_clause,[],[f1457]) ).
thf(f1463,definition,
( spl41_80
<=> ( $false
= ( r @ sK37 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_80])],[avatar_definition]) ).
thf(f1465,plain,
( ( $false
= ( r @ sK37 ) )
| ~ spl41_80 ),
inference(avatar_component_clause,[],[f1463]) ).
thf(f1479,definition,
( spl41_81
<=> ( $true
= ( rel_s4 @ sK3 @ sK40 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_81])],[avatar_definition]) ).
thf(f1481,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK40 ) )
| ~ spl41_81 ),
inference(avatar_component_clause,[],[f1479]) ).
thf(f1482,plain,
( spl41_81
| spl41_76
| spl41_77
| spl41_60 ),
inference(avatar_split_clause,[],[f963,f1335,f1447,f1443,f1479]) ).
thf(f1484,definition,
( spl41_82
<=> ( $false
= ( q @ sK40 ) ) ),
introduced(definition,[new_symbols(definition,[spl41_82])],[avatar_definition]) ).
thf(f1486,plain,
( ( $false
= ( q @ sK40 ) )
| ~ spl41_82 ),
inference(avatar_component_clause,[],[f1484]) ).
thf(f1487,plain,
( spl41_82
| spl41_76
| spl41_77
| spl41_60 ),
inference(avatar_split_clause,[],[f961,f1335,f1447,f1443,f1484]) ).
thf(f1488,plain,
( spl41_81
| spl41_79
| spl41_77
| spl41_60 ),
inference(avatar_split_clause,[],[f966,f1335,f1447,f1457,f1479]) ).
thf(f1489,plain,
( spl41_82
| spl41_79
| spl41_77
| spl41_60 ),
inference(avatar_split_clause,[],[f964,f1335,f1447,f1457,f1484]) ).
thf(f1490,plain,
( spl41_81
| spl41_76
| spl41_80
| spl41_60 ),
inference(avatar_split_clause,[],[f972,f1335,f1463,f1443,f1479]) ).
thf(f1491,plain,
( spl41_82
| spl41_76
| spl41_80
| spl41_60 ),
inference(avatar_split_clause,[],[f970,f1335,f1463,f1443,f1484]) ).
thf(f1492,plain,
( spl41_81
| spl41_79
| spl41_80
| spl41_60 ),
inference(avatar_split_clause,[],[f975,f1335,f1463,f1457,f1479]) ).
thf(f1493,plain,
( spl41_82
| spl41_79
| spl41_80
| spl41_60 ),
inference(avatar_split_clause,[],[f973,f1335,f1463,f1457,f1484]) ).
thf(f1494,plain,
( spl41_81
| spl41_76
| spl41_77
| spl41_62 ),
inference(avatar_split_clause,[],[f984,f1345,f1447,f1443,f1479]) ).
thf(f1495,plain,
( spl41_82
| spl41_76
| spl41_77
| spl41_62 ),
inference(avatar_split_clause,[],[f982,f1345,f1447,f1443,f1484]) ).
thf(f1496,plain,
( spl41_81
| spl41_79
| spl41_77
| spl41_62 ),
inference(avatar_split_clause,[],[f987,f1345,f1447,f1457,f1479]) ).
thf(f1497,plain,
( spl41_82
| spl41_79
| spl41_77
| spl41_62 ),
inference(avatar_split_clause,[],[f985,f1345,f1447,f1457,f1484]) ).
thf(f1498,plain,
( spl41_81
| spl41_76
| spl41_80
| spl41_62 ),
inference(avatar_split_clause,[],[f993,f1345,f1463,f1443,f1479]) ).
thf(f1499,plain,
( spl41_82
| spl41_76
| spl41_80
| spl41_62 ),
inference(avatar_split_clause,[],[f991,f1345,f1463,f1443,f1484]) ).
thf(f1500,plain,
( spl41_81
| spl41_79
| spl41_80
| spl41_62 ),
inference(avatar_split_clause,[],[f996,f1345,f1463,f1457,f1479]) ).
thf(f1501,plain,
( spl41_82
| spl41_79
| spl41_80
| spl41_62 ),
inference(avatar_split_clause,[],[f994,f1345,f1463,f1457,f1484]) ).
thf(f1530,plain,
( ( $true = $false )
| ( $true
= ( p @ sK22 ) )
| ~ spl41_18
| ~ spl41_45 ),
inference(constrained_superposition,[],[f1095,f1239]) ).
thf(f1540,plain,
( ( $true
= ( p @ sK22 ) )
| ~ spl41_18
| ~ spl41_45 ),
inference(trivial_inequality_removal,[],[f1530]) ).
thf(f1546,plain,
( ( $true = $false )
| ~ spl41_18
| ~ spl41_45
| ~ spl41_46 ),
inference(forward_demodulation,[],[f1540,f1244]) ).
thf(f1547,plain,
( $false
| ~ spl41_18
| ~ spl41_45
| ~ spl41_46 ),
inference(trivial_inequality_removal,[],[f1546]) ).
thf(f1548,plain,
( ~ spl41_18
| ~ spl41_45
| ~ spl41_46 ),
inference(avatar_contradiction_clause,[],[f1547]) ).
thf(f1563,plain,
( ( $true = $false )
| ( $true
= ( p @ sK23 ) )
| ~ spl41_3
| ~ spl41_48 ),
inference(constrained_superposition,[],[f1020,f1257]) ).
thf(f1573,plain,
( ( $true
= ( p @ sK23 ) )
| ~ spl41_3
| ~ spl41_48 ),
inference(trivial_inequality_removal,[],[f1563]) ).
thf(f1579,plain,
( ( $true = $false )
| ~ spl41_3
| ~ spl41_48
| ~ spl41_50 ),
inference(forward_demodulation,[],[f1573,f1267]) ).
thf(f1580,plain,
( $false
| ~ spl41_3
| ~ spl41_48
| ~ spl41_50 ),
inference(trivial_inequality_removal,[],[f1579]) ).
thf(f1581,plain,
( ~ spl41_3
| ~ spl41_48
| ~ spl41_50 ),
inference(avatar_contradiction_clause,[],[f1580]) ).
thf(f1588,plain,
( ( $true = $false )
| ( $true
= ( p @ sK24 ) )
| ~ spl41_3
| ~ spl41_47 ),
inference(constrained_superposition,[],[f1253,f1020]) ).
thf(f1593,plain,
( ( $true
= ( p @ sK24 ) )
| ~ spl41_3
| ~ spl41_47 ),
inference(trivial_inequality_removal,[],[f1588]) ).
thf(f1597,plain,
( ( $true = $false )
| ~ spl41_3
| ~ spl41_47
| ~ spl41_49 ),
inference(forward_demodulation,[],[f1593,f1262]) ).
thf(f1598,plain,
( $false
| ~ spl41_3
| ~ spl41_47
| ~ spl41_49 ),
inference(trivial_inequality_removal,[],[f1597]) ).
thf(f1599,plain,
( ~ spl41_3
| ~ spl41_47
| ~ spl41_49 ),
inference(avatar_contradiction_clause,[],[f1598]) ).
thf(f1620,plain,
( ( $true = $false )
| ( $true
= ( r @ sK29 ) )
| ~ spl41_32
| ~ spl41_60 ),
inference(constrained_superposition,[],[f1168,f1337]) ).
thf(f1628,plain,
( ( $true
= ( r @ sK29 ) )
| ~ spl41_32
| ~ spl41_60 ),
inference(trivial_inequality_removal,[],[f1620]) ).
thf(f1635,plain,
( ( $true = $false )
| ~ spl41_32
| ~ spl41_60
| ~ spl41_62 ),
inference(forward_demodulation,[],[f1628,f1347]) ).
thf(f1636,plain,
( $false
| ~ spl41_32
| ~ spl41_60
| ~ spl41_62 ),
inference(trivial_inequality_removal,[],[f1635]) ).
thf(f1637,plain,
( ~ spl41_32
| ~ spl41_60
| ~ spl41_62 ),
inference(avatar_contradiction_clause,[],[f1636]) ).
thf(f1653,plain,
( ( $true = $false )
| ( $true
= ( p @ sK16 ) )
| ~ spl41_3
| ~ spl41_34 ),
inference(constrained_superposition,[],[f1020,f1179]) ).
thf(f1663,plain,
( ( $true
= ( p @ sK16 ) )
| ~ spl41_3
| ~ spl41_34 ),
inference(trivial_inequality_removal,[],[f1653]) ).
thf(f1669,plain,
( ( $true = $false )
| ~ spl41_3
| ~ spl41_34
| ~ spl41_36 ),
inference(forward_demodulation,[],[f1663,f1189]) ).
thf(f1670,plain,
( $false
| ~ spl41_3
| ~ spl41_34
| ~ spl41_36 ),
inference(trivial_inequality_removal,[],[f1669]) ).
thf(f1671,plain,
( ~ spl41_3
| ~ spl41_34
| ~ spl41_36 ),
inference(avatar_contradiction_clause,[],[f1670]) ).
thf(f1690,plain,
( ( $true = $false )
| ( $true
= ( r @ sK19 ) )
| ~ spl41_5
| ~ spl41_40 ),
inference(constrained_superposition,[],[f1027,f1211]) ).
thf(f1698,plain,
( ( $true
= ( r @ sK19 ) )
| ~ spl41_5
| ~ spl41_40 ),
inference(trivial_inequality_removal,[],[f1690]) ).
thf(f1705,plain,
( ( $true = $false )
| ~ spl41_5
| ~ spl41_40
| ~ spl41_42 ),
inference(forward_demodulation,[],[f1698,f1221]) ).
thf(f1706,plain,
( $false
| ~ spl41_5
| ~ spl41_40
| ~ spl41_42 ),
inference(trivial_inequality_removal,[],[f1705]) ).
thf(f1707,plain,
( ~ spl41_5
| ~ spl41_40
| ~ spl41_42 ),
inference(avatar_contradiction_clause,[],[f1706]) ).
thf(f1727,plain,
( ( $true = $false )
| ( $true
= ( q @ sK21 ) )
| ~ spl41_4
| ~ spl41_43 ),
inference(constrained_superposition,[],[f1227,f1023]) ).
thf(f1734,plain,
( ( $true
= ( q @ sK21 ) )
| ~ spl41_4
| ~ spl41_43 ),
inference(trivial_inequality_removal,[],[f1727]) ).
thf(f1739,plain,
( ( $true = $false )
| ~ spl41_4
| ~ spl41_43
| ~ spl41_44 ),
inference(forward_demodulation,[],[f1734,f1232]) ).
thf(f1740,plain,
( $false
| ~ spl41_4
| ~ spl41_43
| ~ spl41_44 ),
inference(trivial_inequality_removal,[],[f1739]) ).
thf(f1741,plain,
( ~ spl41_4
| ~ spl41_43
| ~ spl41_44 ),
inference(avatar_contradiction_clause,[],[f1740]) ).
thf(f1786,plain,
( ( $true = $false )
| ( $true
= ( r @ sK26 ) )
| ~ spl41_5
| ~ spl41_54 ),
inference(constrained_superposition,[],[f1297,f1027]) ).
thf(f1795,plain,
( ( $true
= ( r @ sK26 ) )
| ~ spl41_5
| ~ spl41_54 ),
inference(trivial_inequality_removal,[],[f1786]) ).
thf(f1799,plain,
( ( $true = $false )
| ~ spl41_5
| ~ spl41_54
| ~ spl41_56 ),
inference(forward_demodulation,[],[f1795,f1307]) ).
thf(f1800,plain,
( $false
| ~ spl41_5
| ~ spl41_54
| ~ spl41_56 ),
inference(trivial_inequality_removal,[],[f1799]) ).
thf(f1801,plain,
( ~ spl41_5
| ~ spl41_54
| ~ spl41_56 ),
inference(avatar_contradiction_clause,[],[f1800]) ).
thf(f1857,plain,
( ( $true = $false )
| ( $true
= ( q @ sK31 ) )
| ~ spl41_19
| ~ spl41_63 ),
inference(constrained_superposition,[],[f1353,f1098]) ).
thf(f1864,plain,
( ( $true
= ( q @ sK31 ) )
| ~ spl41_19
| ~ spl41_63 ),
inference(trivial_inequality_removal,[],[f1857]) ).
thf(f1869,plain,
( ( $true = $false )
| ~ spl41_19
| ~ spl41_63
| ~ spl41_64 ),
inference(forward_demodulation,[],[f1864,f1358]) ).
thf(f1870,plain,
( $false
| ~ spl41_19
| ~ spl41_63
| ~ spl41_64 ),
inference(trivial_inequality_removal,[],[f1869]) ).
thf(f1871,plain,
( ~ spl41_19
| ~ spl41_63
| ~ spl41_64 ),
inference(avatar_contradiction_clause,[],[f1870]) ).
thf(f1877,plain,
( ( $true = $false )
| ( $true
= ( q @ sK32 ) )
| ~ spl41_19
| ~ spl41_65 ),
inference(constrained_superposition,[],[f1365,f1098]) ).
thf(f1884,plain,
( ( $true
= ( q @ sK32 ) )
| ~ spl41_19
| ~ spl41_65 ),
inference(trivial_inequality_removal,[],[f1877]) ).
thf(f1889,plain,
( ( $true = $false )
| ~ spl41_19
| ~ spl41_65
| ~ spl41_66 ),
inference(forward_demodulation,[],[f1884,f1370]) ).
thf(f1890,plain,
( $false
| ~ spl41_19
| ~ spl41_65
| ~ spl41_66 ),
inference(trivial_inequality_removal,[],[f1889]) ).
thf(f1891,plain,
( ~ spl41_19
| ~ spl41_65
| ~ spl41_66 ),
inference(avatar_contradiction_clause,[],[f1890]) ).
thf(f1925,plain,
( ( $true = $false )
| ( $true
= ( r @ sK37 ) )
| ~ spl41_5
| ~ spl41_77 ),
inference(constrained_superposition,[],[f1027,f1449]) ).
thf(f1934,plain,
( ( $true
= ( r @ sK37 ) )
| ~ spl41_5
| ~ spl41_77 ),
inference(trivial_inequality_removal,[],[f1925]) ).
thf(f1941,plain,
( ( $true = $false )
| ~ spl41_5
| ~ spl41_77
| ~ spl41_80 ),
inference(forward_demodulation,[],[f1934,f1465]) ).
thf(f1942,plain,
( $false
| ~ spl41_5
| ~ spl41_77
| ~ spl41_80 ),
inference(trivial_inequality_removal,[],[f1941]) ).
thf(f1943,plain,
( ~ spl41_5
| ~ spl41_77
| ~ spl41_80 ),
inference(avatar_contradiction_clause,[],[f1942]) ).
thf(f1949,plain,
( ( $true = $false )
| ( $true
= ( q @ sK38 ) )
| ~ spl41_19
| ~ spl41_76 ),
inference(constrained_superposition,[],[f1445,f1098]) ).
thf(f1956,plain,
( ( $true
= ( q @ sK38 ) )
| ~ spl41_19
| ~ spl41_76 ),
inference(trivial_inequality_removal,[],[f1949]) ).
thf(f1961,plain,
( ( $true = $false )
| ~ spl41_19
| ~ spl41_76
| ~ spl41_79 ),
inference(forward_demodulation,[],[f1956,f1459]) ).
thf(f1962,plain,
( $false
| ~ spl41_19
| ~ spl41_76
| ~ spl41_79 ),
inference(trivial_inequality_removal,[],[f1961]) ).
thf(f1963,plain,
( ~ spl41_19
| ~ spl41_76
| ~ spl41_79 ),
inference(avatar_contradiction_clause,[],[f1962]) ).
thf(f1980,plain,
( ( $true = $false )
| ( $true
= ( q @ sK40 ) )
| ~ spl41_4
| ~ spl41_81 ),
inference(constrained_superposition,[],[f1481,f1023]) ).
thf(f1987,plain,
( ( $true
= ( q @ sK40 ) )
| ~ spl41_4
| ~ spl41_81 ),
inference(trivial_inequality_removal,[],[f1980]) ).
thf(f1992,plain,
( ( $true = $false )
| ~ spl41_4
| ~ spl41_81
| ~ spl41_82 ),
inference(forward_demodulation,[],[f1987,f1486]) ).
thf(f1993,plain,
( $false
| ~ spl41_4
| ~ spl41_81
| ~ spl41_82 ),
inference(trivial_inequality_removal,[],[f1992]) ).
thf(f1994,plain,
( ~ spl41_4
| ~ spl41_81
| ~ spl41_82 ),
inference(avatar_contradiction_clause,[],[f1993]) ).
thf(f2014,plain,
( ( $true = $false )
| ( $true
= ( r @ sK13 ) )
| ~ spl41_5
| ~ spl41_27 ),
inference(constrained_superposition,[],[f1141,f1027]) ).
thf(f2023,plain,
( ( $true
= ( r @ sK13 ) )
| ~ spl41_5
| ~ spl41_27 ),
inference(trivial_inequality_removal,[],[f2014]) ).
thf(f2027,plain,
( ( $true = $false )
| ~ spl41_5
| ~ spl41_27
| ~ spl41_29 ),
inference(forward_demodulation,[],[f2023,f1151]) ).
thf(f2028,plain,
( $false
| ~ spl41_5
| ~ spl41_27
| ~ spl41_29 ),
inference(trivial_inequality_removal,[],[f2027]) ).
thf(f2029,plain,
( ~ spl41_5
| ~ spl41_27
| ~ spl41_29 ),
inference(avatar_contradiction_clause,[],[f2028]) ).
thf(f2054,plain,
( ( $true = $false )
| ( $true
= ( p @ sK10 ) )
| ~ spl41_3
| ~ spl41_21 ),
inference(constrained_superposition,[],[f1020,f1109]) ).
thf(f2056,plain,
( ( $true = $false )
| ( $true
= ( p @ sK17 ) )
| ~ spl41_3
| ~ spl41_33 ),
inference(constrained_superposition,[],[f1020,f1175]) ).
thf(f2059,plain,
( ( $true = $false )
| ( $true
= ( p @ sK33 ) )
| ~ spl41_3
| ~ spl41_69 ),
inference(constrained_superposition,[],[f1020,f1385]) ).
thf(f2080,plain,
( ( $true
= ( p @ sK33 ) )
| ~ spl41_3
| ~ spl41_69 ),
inference(trivial_inequality_removal,[],[f2059]) ).
thf(f2083,plain,
( ( $true
= ( p @ sK17 ) )
| ~ spl41_3
| ~ spl41_33 ),
inference(trivial_inequality_removal,[],[f2056]) ).
thf(f2085,plain,
( ( $true
= ( p @ sK10 ) )
| ~ spl41_3
| ~ spl41_21 ),
inference(trivial_inequality_removal,[],[f2054]) ).
thf(f2097,plain,
( ( $true = $false )
| ~ spl41_3
| ~ spl41_69
| ~ spl41_72 ),
inference(forward_demodulation,[],[f2080,f1401]) ).
thf(f2098,plain,
( $false
| ~ spl41_3
| ~ spl41_69
| ~ spl41_72 ),
inference(trivial_inequality_removal,[],[f2097]) ).
thf(f2099,plain,
( ~ spl41_3
| ~ spl41_69
| ~ spl41_72 ),
inference(avatar_contradiction_clause,[],[f2098]) ).
thf(f2100,plain,
( ( $true = $false )
| ~ spl41_3
| ~ spl41_33
| ~ spl41_35 ),
inference(forward_demodulation,[],[f2083,f1184]) ).
thf(f2101,plain,
( $false
| ~ spl41_3
| ~ spl41_33
| ~ spl41_35 ),
inference(trivial_inequality_removal,[],[f2100]) ).
thf(f2102,plain,
( ~ spl41_3
| ~ spl41_33
| ~ spl41_35 ),
inference(avatar_contradiction_clause,[],[f2101]) ).
thf(f2103,plain,
( ( $true = $false )
| ~ spl41_3
| ~ spl41_21
| ~ spl41_23 ),
inference(forward_demodulation,[],[f2085,f1119]) ).
thf(f2104,plain,
( $false
| ~ spl41_3
| ~ spl41_21
| ~ spl41_23 ),
inference(trivial_inequality_removal,[],[f2103]) ).
thf(f2105,plain,
( ~ spl41_3
| ~ spl41_21
| ~ spl41_23 ),
inference(avatar_contradiction_clause,[],[f2104]) ).
thf(f2210,plain,
( ( $true = $false )
| ( $true
= ( q @ sK15 ) )
| ~ spl41_4
| ~ spl41_30 ),
inference(constrained_superposition,[],[f1157,f1023]) ).
thf(f2217,plain,
( ( $true
= ( q @ sK15 ) )
| ~ spl41_4
| ~ spl41_30 ),
inference(trivial_inequality_removal,[],[f2210]) ).
thf(f2222,plain,
( ( $true = $false )
| ~ spl41_4
| ~ spl41_30
| ~ spl41_31 ),
inference(forward_demodulation,[],[f2217,f1162]) ).
thf(f2223,plain,
( $false
| ~ spl41_4
| ~ spl41_30
| ~ spl41_31 ),
inference(trivial_inequality_removal,[],[f2222]) ).
thf(f2224,plain,
( ~ spl41_4
| ~ spl41_30
| ~ spl41_31 ),
inference(avatar_contradiction_clause,[],[f2223]) ).
thf(f2361,plain,
( ( $true = $false )
| ( $true
= ( q @ sK28 ) )
| ~ spl41_4
| ~ spl41_57 ),
inference(constrained_superposition,[],[f1317,f1023]) ).
thf(f2372,plain,
( ( $true
= ( q @ sK28 ) )
| ~ spl41_4
| ~ spl41_57 ),
inference(trivial_inequality_removal,[],[f2361]) ).
thf(f2377,plain,
( ( $true = $false )
| ~ spl41_4
| ~ spl41_57
| ~ spl41_58 ),
inference(forward_demodulation,[],[f2372,f1322]) ).
thf(f2378,plain,
( $false
| ~ spl41_4
| ~ spl41_57
| ~ spl41_58 ),
inference(trivial_inequality_removal,[],[f2377]) ).
thf(f2379,plain,
( ~ spl41_4
| ~ spl41_57
| ~ spl41_58 ),
inference(avatar_contradiction_clause,[],[f2378]) ).
thf(f2476,plain,
( ( $true = $false )
| ( $true
= ( q @ sK34 ) )
| ~ spl41_19
| ~ spl41_68 ),
inference(constrained_superposition,[],[f1098,f1381]) ).
thf(f2495,plain,
( ( $true
= ( q @ sK34 ) )
| ~ spl41_19
| ~ spl41_68 ),
inference(trivial_inequality_removal,[],[f2476]) ).
thf(f2507,plain,
( ( $true = $false )
| ~ spl41_19
| ~ spl41_68
| ~ spl41_71 ),
inference(forward_demodulation,[],[f2495,f1395]) ).
thf(f2508,plain,
( $false
| ~ spl41_19
| ~ spl41_68
| ~ spl41_71 ),
inference(trivial_inequality_removal,[],[f2507]) ).
thf(f2509,plain,
( ~ spl41_19
| ~ spl41_68
| ~ spl41_71 ),
inference(avatar_contradiction_clause,[],[f2508]) ).
thf(f2547,plain,
( ( $true = $false )
| ( $true
= ( p @ sK35 ) )
| ~ spl41_3
| ~ spl41_67 ),
inference(constrained_superposition,[],[f1377,f1020]) ).
thf(f2556,plain,
( ( $true
= ( p @ sK35 ) )
| ~ spl41_3
| ~ spl41_67 ),
inference(trivial_inequality_removal,[],[f2547]) ).
thf(f2560,plain,
( ( $true = $false )
| ~ spl41_3
| ~ spl41_67
| ~ spl41_70 ),
inference(forward_demodulation,[],[f2556,f1390]) ).
thf(f2561,plain,
( $false
| ~ spl41_3
| ~ spl41_67
| ~ spl41_70 ),
inference(trivial_inequality_removal,[],[f2560]) ).
thf(f2562,plain,
( ~ spl41_3
| ~ spl41_67
| ~ spl41_70 ),
inference(avatar_contradiction_clause,[],[f2561]) ).
thf(f2573,plain,
( ( $true = $false )
| ( $true
= ( p @ sK11 ) )
| ~ spl41_3
| ~ spl41_20 ),
inference(constrained_superposition,[],[f1105,f1020]) ).
thf(f2582,plain,
( ( $true
= ( p @ sK11 ) )
| ~ spl41_3
| ~ spl41_20 ),
inference(trivial_inequality_removal,[],[f2573]) ).
thf(f2586,plain,
( ( $true = $false )
| ~ spl41_3
| ~ spl41_20
| ~ spl41_22 ),
inference(forward_demodulation,[],[f2582,f1114]) ).
thf(f2587,plain,
( $false
| ~ spl41_3
| ~ spl41_20
| ~ spl41_22 ),
inference(trivial_inequality_removal,[],[f2586]) ).
thf(f2588,plain,
( ~ spl41_3
| ~ spl41_20
| ~ spl41_22 ),
inference(avatar_contradiction_clause,[],[f2587]) ).
cnf(s21,plain,
( spl41_3
| spl41_4
| spl41_18
| spl41_19 ),
inference(sat_conversion,[],[f1100]) ).
cnf(s22,plain,
( spl41_3
| spl41_5
| spl41_18
| spl41_19 ),
inference(sat_conversion,[],[f1101]) ).
cnf(s23,plain,
( spl41_18
| spl41_19
| spl41_20
| spl41_21 ),
inference(sat_conversion,[],[f1110]) ).
cnf(s24,plain,
( spl41_18
| spl41_19
| spl41_21
| spl41_22 ),
inference(sat_conversion,[],[f1115]) ).
cnf(s25,plain,
( spl41_18
| spl41_19
| spl41_20
| spl41_23 ),
inference(sat_conversion,[],[f1120]) ).
cnf(s26,plain,
( spl41_18
| spl41_19
| spl41_22
| spl41_23 ),
inference(sat_conversion,[],[f1121]) ).
cnf(s35,plain,
( spl41_18
| spl41_19
| spl41_27
| spl41_30 ),
inference(sat_conversion,[],[f1158]) ).
cnf(s36,plain,
( spl41_18
| spl41_19
| spl41_27
| spl41_31 ),
inference(sat_conversion,[],[f1163]) ).
cnf(s37,plain,
( spl41_18
| spl41_19
| spl41_29
| spl41_30 ),
inference(sat_conversion,[],[f1164]) ).
cnf(s38,plain,
( spl41_18
| spl41_19
| spl41_29
| spl41_31 ),
inference(sat_conversion,[],[f1165]) ).
cnf(s40,plain,
( spl41_3
| spl41_4
| spl41_18
| spl41_32 ),
inference(sat_conversion,[],[f1170]) ).
cnf(s41,plain,
( spl41_3
| spl41_5
| spl41_18
| spl41_32 ),
inference(sat_conversion,[],[f1171]) ).
cnf(s42,plain,
( spl41_18
| spl41_32
| spl41_33
| spl41_34 ),
inference(sat_conversion,[],[f1180]) ).
cnf(s43,plain,
( spl41_18
| spl41_32
| spl41_34
| spl41_35 ),
inference(sat_conversion,[],[f1185]) ).
cnf(s44,plain,
( spl41_18
| spl41_32
| spl41_33
| spl41_36 ),
inference(sat_conversion,[],[f1190]) ).
cnf(s45,plain,
( spl41_18
| spl41_32
| spl41_35
| spl41_36 ),
inference(sat_conversion,[],[f1191]) ).
cnf(s54,plain,
( spl41_18
| spl41_32
| spl41_40
| spl41_43 ),
inference(sat_conversion,[],[f1228]) ).
cnf(s55,plain,
( spl41_18
| spl41_32
| spl41_40
| spl41_44 ),
inference(sat_conversion,[],[f1233]) ).
cnf(s56,plain,
( spl41_18
| spl41_32
| spl41_42
| spl41_43 ),
inference(sat_conversion,[],[f1234]) ).
cnf(s57,plain,
( spl41_18
| spl41_32
| spl41_42
| spl41_44 ),
inference(sat_conversion,[],[f1235]) ).
cnf(s60,plain,
( spl41_3
| spl41_4
| spl41_45 ),
inference(sat_conversion,[],[f1246]) ).
cnf(s61,plain,
( spl41_3
| spl41_4
| spl41_46 ),
inference(sat_conversion,[],[f1247]) ).
cnf(s62,plain,
( spl41_3
| spl41_5
| spl41_45 ),
inference(sat_conversion,[],[f1248]) ).
cnf(s63,plain,
( spl41_3
| spl41_5
| spl41_46 ),
inference(sat_conversion,[],[f1249]) ).
cnf(s64,plain,
( spl41_45
| spl41_47
| spl41_48 ),
inference(sat_conversion,[],[f1258]) ).
cnf(s65,plain,
( spl41_45
| spl41_48
| spl41_49 ),
inference(sat_conversion,[],[f1263]) ).
cnf(s66,plain,
( spl41_45
| spl41_47
| spl41_50 ),
inference(sat_conversion,[],[f1268]) ).
cnf(s67,plain,
( spl41_45
| spl41_49
| spl41_50 ),
inference(sat_conversion,[],[f1269]) ).
cnf(s68,plain,
( spl41_46
| spl41_47
| spl41_48 ),
inference(sat_conversion,[],[f1270]) ).
cnf(s69,plain,
( spl41_46
| spl41_48
| spl41_49 ),
inference(sat_conversion,[],[f1271]) ).
cnf(s70,plain,
( spl41_46
| spl41_47
| spl41_50 ),
inference(sat_conversion,[],[f1272]) ).
cnf(s71,plain,
( spl41_46
| spl41_49
| spl41_50 ),
inference(sat_conversion,[],[f1273]) ).
cnf(s88,plain,
( spl41_45
| spl41_54
| spl41_57 ),
inference(sat_conversion,[],[f1318]) ).
cnf(s89,plain,
( spl41_45
| spl41_54
| spl41_58 ),
inference(sat_conversion,[],[f1323]) ).
cnf(s90,plain,
( spl41_45
| spl41_56
| spl41_57 ),
inference(sat_conversion,[],[f1324]) ).
cnf(s91,plain,
( spl41_45
| spl41_56
| spl41_58 ),
inference(sat_conversion,[],[f1325]) ).
cnf(s92,plain,
( spl41_46
| spl41_54
| spl41_57 ),
inference(sat_conversion,[],[f1326]) ).
cnf(s93,plain,
( spl41_46
| spl41_54
| spl41_58 ),
inference(sat_conversion,[],[f1327]) ).
cnf(s94,plain,
( spl41_46
| spl41_56
| spl41_57 ),
inference(sat_conversion,[],[f1328]) ).
cnf(s95,plain,
( spl41_46
| spl41_56
| spl41_58 ),
inference(sat_conversion,[],[f1329]) ).
cnf(s100,plain,
( spl41_3
| spl41_4
| spl41_60
| spl41_63 ),
inference(sat_conversion,[],[f1354]) ).
cnf(s101,plain,
( spl41_3
| spl41_4
| spl41_60
| spl41_64 ),
inference(sat_conversion,[],[f1359]) ).
cnf(s102,plain,
( spl41_3
| spl41_4
| spl41_62
| spl41_63 ),
inference(sat_conversion,[],[f1360]) ).
cnf(s103,plain,
( spl41_3
| spl41_4
| spl41_62
| spl41_64 ),
inference(sat_conversion,[],[f1361]) ).
cnf(s104,plain,
( spl41_3
| spl41_5
| spl41_60
| spl41_65 ),
inference(sat_conversion,[],[f1366]) ).
cnf(s105,plain,
( spl41_3
| spl41_5
| spl41_60
| spl41_66 ),
inference(sat_conversion,[],[f1371]) ).
cnf(s106,plain,
( spl41_3
| spl41_5
| spl41_62
| spl41_65 ),
inference(sat_conversion,[],[f1372]) ).
cnf(s107,plain,
( spl41_3
| spl41_5
| spl41_62
| spl41_66 ),
inference(sat_conversion,[],[f1373]) ).
cnf(s108,plain,
( spl41_60
| spl41_67
| spl41_68
| spl41_69 ),
inference(sat_conversion,[],[f1386]) ).
cnf(s109,plain,
( spl41_60
| spl41_68
| spl41_69
| spl41_70 ),
inference(sat_conversion,[],[f1391]) ).
cnf(s110,plain,
( spl41_60
| spl41_67
| spl41_69
| spl41_71 ),
inference(sat_conversion,[],[f1396]) ).
cnf(s111,plain,
( spl41_60
| spl41_69
| spl41_70
| spl41_71 ),
inference(sat_conversion,[],[f1397]) ).
cnf(s112,plain,
( spl41_60
| spl41_67
| spl41_68
| spl41_72 ),
inference(sat_conversion,[],[f1402]) ).
cnf(s113,plain,
( spl41_60
| spl41_68
| spl41_70
| spl41_72 ),
inference(sat_conversion,[],[f1403]) ).
cnf(s114,plain,
( spl41_60
| spl41_67
| spl41_71
| spl41_72 ),
inference(sat_conversion,[],[f1404]) ).
cnf(s115,plain,
( spl41_60
| spl41_70
| spl41_71
| spl41_72 ),
inference(sat_conversion,[],[f1405]) ).
cnf(s116,plain,
( spl41_62
| spl41_67
| spl41_68
| spl41_69 ),
inference(sat_conversion,[],[f1406]) ).
cnf(s117,plain,
( spl41_62
| spl41_68
| spl41_69
| spl41_70 ),
inference(sat_conversion,[],[f1407]) ).
cnf(s118,plain,
( spl41_62
| spl41_67
| spl41_69
| spl41_71 ),
inference(sat_conversion,[],[f1408]) ).
cnf(s119,plain,
( spl41_62
| spl41_69
| spl41_70
| spl41_71 ),
inference(sat_conversion,[],[f1409]) ).
cnf(s120,plain,
( spl41_62
| spl41_67
| spl41_68
| spl41_72 ),
inference(sat_conversion,[],[f1410]) ).
cnf(s121,plain,
( spl41_62
| spl41_68
| spl41_70
| spl41_72 ),
inference(sat_conversion,[],[f1411]) ).
cnf(s122,plain,
( spl41_62
| spl41_67
| spl41_71
| spl41_72 ),
inference(sat_conversion,[],[f1412]) ).
cnf(s123,plain,
( spl41_62
| spl41_70
| spl41_71
| spl41_72 ),
inference(sat_conversion,[],[f1413]) ).
cnf(s156,plain,
( spl41_60
| spl41_76
| spl41_77
| spl41_81 ),
inference(sat_conversion,[],[f1482]) ).
cnf(s157,plain,
( spl41_60
| spl41_76
| spl41_77
| spl41_82 ),
inference(sat_conversion,[],[f1487]) ).
cnf(s158,plain,
( spl41_60
| spl41_77
| spl41_79
| spl41_81 ),
inference(sat_conversion,[],[f1488]) ).
cnf(s159,plain,
( spl41_60
| spl41_77
| spl41_79
| spl41_82 ),
inference(sat_conversion,[],[f1489]) ).
cnf(s160,plain,
( spl41_60
| spl41_76
| spl41_80
| spl41_81 ),
inference(sat_conversion,[],[f1490]) ).
cnf(s161,plain,
( spl41_60
| spl41_76
| spl41_80
| spl41_82 ),
inference(sat_conversion,[],[f1491]) ).
cnf(s162,plain,
( spl41_60
| spl41_79
| spl41_80
| spl41_81 ),
inference(sat_conversion,[],[f1492]) ).
cnf(s163,plain,
( spl41_60
| spl41_79
| spl41_80
| spl41_82 ),
inference(sat_conversion,[],[f1493]) ).
cnf(s164,plain,
( spl41_62
| spl41_76
| spl41_77
| spl41_81 ),
inference(sat_conversion,[],[f1494]) ).
cnf(s165,plain,
( spl41_62
| spl41_76
| spl41_77
| spl41_82 ),
inference(sat_conversion,[],[f1495]) ).
cnf(s166,plain,
( spl41_62
| spl41_77
| spl41_79
| spl41_81 ),
inference(sat_conversion,[],[f1496]) ).
cnf(s167,plain,
( spl41_62
| spl41_77
| spl41_79
| spl41_82 ),
inference(sat_conversion,[],[f1497]) ).
cnf(s168,plain,
( spl41_62
| spl41_76
| spl41_80
| spl41_81 ),
inference(sat_conversion,[],[f1498]) ).
cnf(s169,plain,
( spl41_62
| spl41_76
| spl41_80
| spl41_82 ),
inference(sat_conversion,[],[f1499]) ).
cnf(s170,plain,
( spl41_62
| spl41_79
| spl41_80
| spl41_81 ),
inference(sat_conversion,[],[f1500]) ).
cnf(s171,plain,
( spl41_62
| spl41_79
| spl41_80
| spl41_82 ),
inference(sat_conversion,[],[f1501]) ).
cnf(s173,plain,
( ~ spl41_18
| ~ spl41_45
| ~ spl41_46 ),
inference(sat_conversion,[],[f1548]) ).
cnf(s175,plain,
( ~ spl41_3
| ~ spl41_48
| ~ spl41_50 ),
inference(sat_conversion,[],[f1581]) ).
cnf(s177,plain,
( ~ spl41_3
| ~ spl41_47
| ~ spl41_49 ),
inference(sat_conversion,[],[f1599]) ).
cnf(s179,plain,
( ~ spl41_32
| ~ spl41_60
| ~ spl41_62 ),
inference(sat_conversion,[],[f1637]) ).
cnf(s181,plain,
( ~ spl41_3
| ~ spl41_34
| ~ spl41_36 ),
inference(sat_conversion,[],[f1671]) ).
cnf(s183,plain,
( ~ spl41_5
| ~ spl41_40
| ~ spl41_42 ),
inference(sat_conversion,[],[f1707]) ).
cnf(s185,plain,
( ~ spl41_4
| ~ spl41_43
| ~ spl41_44 ),
inference(sat_conversion,[],[f1741]) ).
cnf(s187,plain,
( ~ spl41_5
| ~ spl41_54
| ~ spl41_56 ),
inference(sat_conversion,[],[f1801]) ).
cnf(s191,plain,
( ~ spl41_19
| ~ spl41_63
| ~ spl41_64 ),
inference(sat_conversion,[],[f1871]) ).
cnf(s193,plain,
( ~ spl41_19
| ~ spl41_65
| ~ spl41_66 ),
inference(sat_conversion,[],[f1891]) ).
cnf(s195,plain,
( ~ spl41_5
| ~ spl41_77
| ~ spl41_80 ),
inference(sat_conversion,[],[f1943]) ).
cnf(s197,plain,
( ~ spl41_19
| ~ spl41_76
| ~ spl41_79 ),
inference(sat_conversion,[],[f1963]) ).
cnf(s199,plain,
( ~ spl41_4
| ~ spl41_81
| ~ spl41_82 ),
inference(sat_conversion,[],[f1994]) ).
cnf(s201,plain,
( ~ spl41_5
| ~ spl41_27
| ~ spl41_29 ),
inference(sat_conversion,[],[f2029]) ).
cnf(s205,plain,
( ~ spl41_3
| ~ spl41_69
| ~ spl41_72 ),
inference(sat_conversion,[],[f2099]) ).
cnf(s206,plain,
( ~ spl41_3
| ~ spl41_33
| ~ spl41_35 ),
inference(sat_conversion,[],[f2102]) ).
cnf(s207,plain,
( ~ spl41_3
| ~ spl41_21
| ~ spl41_23 ),
inference(sat_conversion,[],[f2105]) ).
cnf(s209,plain,
( ~ spl41_4
| ~ spl41_30
| ~ spl41_31 ),
inference(sat_conversion,[],[f2224]) ).
cnf(s211,plain,
( ~ spl41_4
| ~ spl41_57
| ~ spl41_58 ),
inference(sat_conversion,[],[f2379]) ).
cnf(s213,plain,
( ~ spl41_19
| ~ spl41_68
| ~ spl41_71 ),
inference(sat_conversion,[],[f2509]) ).
cnf(s215,plain,
( ~ spl41_3
| ~ spl41_67
| ~ spl41_70 ),
inference(sat_conversion,[],[f2562]) ).
cnf(s217,plain,
( ~ spl41_3
| ~ spl41_20
| ~ spl41_22 ),
inference(sat_conversion,[],[f2588]) ).
cnf(s221,plain,
( spl41_4
| spl41_3
| ~ spl41_19
| spl41_62 ),
inference(rat,[],[s191,s102,s103]) ).
cnf(s222,plain,
( spl41_5
| spl41_3
| ~ spl41_19
| spl41_62 ),
inference(rat,[],[s193,s106,s107]) ).
cnf(s225,plain,
( spl41_80
| spl41_76
| ~ spl41_4
| spl41_62 ),
inference(rat,[],[s199,s168,s169]) ).
cnf(s226,plain,
( spl41_76
| ~ spl41_5
| ~ spl41_4
| spl41_62 ),
inference(rat,[],[s199,s164,s165,s195,s225]) ).
cnf(s227,plain,
( spl41_80
| spl41_79
| ~ spl41_4
| spl41_62 ),
inference(rat,[],[s199,s170,s171]) ).
cnf(s228,plain,
( spl41_3
| ~ spl41_19
| spl41_62 ),
inference(rat,[],[s199,s166,s167,s195,s227,s197,s226,s222,s221]) ).
cnf(s229,plain,
( spl41_68
| spl41_67
| ~ spl41_3
| spl41_62 ),
inference(rat,[],[s205,s116,s120]) ).
cnf(s230,plain,
( spl41_67
| ~ spl41_19
| spl41_62 ),
inference(rat,[],[s205,s118,s122,s213,s229,s228]) ).
cnf(s231,plain,
( spl41_68
| ~ spl41_19
| spl41_62 ),
inference(rat,[],[s205,s117,s121,s215,s230,s228]) ).
cnf(s232,plain,
( ~ spl41_19
| spl41_62 ),
inference(rat,[],[s205,s119,s123,s213,s231,s215,s230,s228]) ).
cnf(s234,plain,
( spl41_27
| ~ spl41_4
| spl41_18
| spl41_19 ),
inference(rat,[],[s209,s36,s35]) ).
cnf(s235,plain,
( spl41_3
| spl41_18
| spl41_19 ),
inference(rat,[],[s209,s37,s38,s201,s234,s21,s22]) ).
cnf(s238,plain,
( spl41_20
| spl41_18
| spl41_19 ),
inference(rat,[],[s207,s23,s25,s235]) ).
cnf(s239,plain,
( spl41_18
| spl41_19 ),
inference(rat,[],[s207,s24,s26,s217,s238,s235]) ).
cnf(s241,plain,
( spl41_54
| spl41_46
| ~ spl41_4 ),
inference(rat,[],[s211,s93,s92]) ).
cnf(s242,plain,
( spl41_46
| ~ spl41_4
| ~ spl41_5 ),
inference(rat,[],[s211,s94,s95,s187,s241]) ).
cnf(s243,plain,
( spl41_54
| spl41_45
| ~ spl41_4 ),
inference(rat,[],[s211,s89,s88]) ).
cnf(s244,plain,
( ~ spl41_4
| ~ spl41_5
| ~ spl41_18 ),
inference(rat,[],[s211,s90,s91,s187,s243,s173,s242]) ).
cnf(s245,plain,
( spl41_4
| spl41_3
| ~ spl41_18 ),
inference(rat,[],[s173,s60,s61]) ).
cnf(s246,plain,
( spl41_3
| ~ spl41_18 ),
inference(rat,[],[s173,s62,s63,s244,s245]) ).
cnf(s247,plain,
( spl41_47
| spl41_46
| ~ spl41_3 ),
inference(rat,[],[s175,s68,s70]) ).
cnf(s248,plain,
( spl41_46
| ~ spl41_3 ),
inference(rat,[],[s175,s69,s71,s177,s247]) ).
cnf(s249,plain,
( spl41_47
| ~ spl41_18 ),
inference(rat,[],[s175,s64,s66,s173,s248,s246]) ).
cnf(s250,plain,
~ spl41_18,
inference(rat,[],[s175,s65,s67,s177,s249,s173,s248,s246]) ).
cnf(s251,plain,
spl41_19,
inference(rat,[],[s239,s250]) ).
cnf(s252,plain,
spl41_62,
inference(rat,[],[s232,s251]) ).
cnf(s253,plain,
( spl41_80
| spl41_76
| ~ spl41_4
| spl41_60 ),
inference(rat,[],[s199,s160,s161]) ).
cnf(s254,plain,
( spl41_76
| ~ spl41_4
| ~ spl41_5
| spl41_60 ),
inference(rat,[],[s199,s156,s157,s195,s253]) ).
cnf(s255,plain,
( spl41_80
| spl41_79
| ~ spl41_4
| spl41_60 ),
inference(rat,[],[s199,s162,s163]) ).
cnf(s256,plain,
( ~ spl41_4
| ~ spl41_5
| spl41_60 ),
inference(rat,[],[s199,s158,s159,s195,s255,s197,s254,s251]) ).
cnf(s257,plain,
( spl41_4
| spl41_3
| spl41_60 ),
inference(rat,[],[s191,s100,s101,s251]) ).
cnf(s258,plain,
( spl41_5
| spl41_3
| spl41_60 ),
inference(rat,[],[s193,s104,s105,s251]) ).
cnf(s259,plain,
( spl41_3
| spl41_60 ),
inference(rat,[],[s258,s256,s257]) ).
cnf(s260,plain,
( spl41_72
| spl41_68
| spl41_60 ),
inference(rat,[],[s215,s113,s112,s259]) ).
cnf(s261,plain,
( spl41_68
| spl41_60 ),
inference(rat,[],[s215,s109,s108,s205,s260,s259]) ).
cnf(s262,plain,
( spl41_72
| spl41_60 ),
inference(rat,[],[s215,s115,s114,s259,s213,s261,s251]) ).
cnf(s263,plain,
spl41_60,
inference(rat,[],[s215,s111,s110,s205,s262,s213,s261,s259,s251]) ).
cnf(s264,plain,
~ spl41_32,
inference(rat,[],[s179,s252,s263]) ).
cnf(s266,plain,
( spl41_40
| ~ spl41_4 ),
inference(rat,[],[s185,s54,s55,s264,s250]) ).
cnf(s267,plain,
spl41_3,
inference(rat,[],[s185,s56,s57,s183,s266,s41,s40,s264,s250]) ).
cnf(s270,plain,
spl41_33,
inference(rat,[],[s181,s42,s44,s267,s264,s250]) ).
cnf(s271,plain,
~ spl41_35,
inference(rat,[],[s206,s267,s270]) ).
cnf(s272,plain,
spl41_36,
inference(rat,[],[s45,s250,s264,s271]) ).
cnf(s273,plain,
spl41_34,
inference(rat,[],[s43,s250,s264,s271]) ).
cnf(s274,plain,
$false,
inference(rat,[],[s181,s267,s272,s273]) ).
thf(f2589,plain,
$false,
inference(avatar_sat_refutation,[],[s274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN045^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.29 % Computer : n016.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8046.5625MB
% 0.11/0.29 % OS : Linux 6.8.0-71-generic
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Sep 29 16:19:20 UTC 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.29/0.34 Running first-order model finding
% 0.29/0.34 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.43/0.72 % (542281)Will run a generic schedule for satisfiability detection.
% 2.43/0.72 % (542289)dis+10_1_sil=32000:sp=arity:random_seed=2417500141:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.43/0.72 % (542287)% WARNING: option uhcvi not known.
% 2.43/0.72 % (542286)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3813686723_2999 on theBenchmark for (2999ds/0Mi)
% 2.43/0.72 % (542288)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2869575285:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.43/0.72 % (542287)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3967052267:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.43/0.72 % (542291)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1056733893:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.43/0.72 % (542292)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1830140540:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.43/0.72 % (542290)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1271993683:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.43/0.72 % (542287)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.43/0.72 % (542290)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.43/0.72 % Exception at run slice level
% 2.43/0.72 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.43/0.72 % (542287)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.43/0.72 % (542289)Instruction limit reached!
% 2.43/0.72 % (542289)------------------------------
% 2.43/0.72 % (542289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.72 % (542289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.72 % (542289)CaDiCaL version: 2.1.3
% 2.43/0.72 % (542289)Termination reason: Instruction limit
% 2.43/0.72 % (542289)Termination phase: Saturation
% 2.43/0.72 % (542289)Time elapsed: 0.046 s
% 2.43/0.72 % (542289)Peak memory usage: 12 MB
% 2.43/0.72 % (542289)Instructions burned: 103 (million)
% 2.43/0.72 % (542300)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2292603055:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 2.43/0.72 % (542301)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1063170548:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 2.43/0.72 % Exception at run slice level
% 2.43/0.72 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.43/0.72 % (542304)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=666815287:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.43/0.72 % (542304)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.43/0.72 % (542290)Instruction limit reached!
% 2.43/0.72 % (542290)------------------------------
% 2.43/0.72 % (542290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.72 % (542290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.72 % (542290)CaDiCaL version: 2.1.3
% 2.43/0.72 % (542290)Termination reason: Instruction limit
% 2.43/0.72 % (542290)Termination phase: Saturation
% 2.43/0.72 % (542290)Time elapsed: 0.096 s
% 2.43/0.72 % (542290)Peak memory usage: 12 MB
% 2.43/0.72 % (542290)Instructions burned: 117 (million)
% 2.43/0.72 % (542304)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 2.43/0.72 % (542291)Instruction limit reached!
% 2.43/0.72 % (542291)------------------------------
% 2.43/0.72 % (542291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.72 % (542291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.72 % (542291)CaDiCaL version: 2.1.3
% 2.43/0.72 % (542291)Termination reason: Instruction limit
% 2.43/0.72 % (542291)Termination phase: Saturation
% 2.43/0.72 % (542291)Time elapsed: 0.103 s
% 2.43/0.72 % (542291)Peak memory usage: 12 MB
% 2.43/0.72 % (542291)Instructions burned: 132 (million)
% 2.43/0.72 % (542301)Instruction limit reached!
% 2.43/0.72 % (542301)------------------------------
% 2.43/0.72 % (542301)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.72 % (542301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.72 % (542301)CaDiCaL version: 2.1.3
% 2.43/0.72 % (542301)Termination reason: Instruction limit
% 2.43/0.72 % (542301)Termination phase: Saturation
% 2.43/0.72 % (542301)Time elapsed: 0.059 s
% 2.43/0.72 % (542301)Peak memory usage: 13 MB
% 2.43/0.72 % (542301)Instructions burned: 131 (million)
% 2.43/0.72 % (542308)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2125622976:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.43/0.72 % (542306)ott-21_1_sil=16000:fs=off:random_seed=2327398051:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.43/0.72 % Exception at run slice level
% 2.43/0.72 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.43/0.72 % (542307)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=308315874:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.43/0.72 % (542292)Instruction limit reached!
% 2.43/0.72 % (542292)------------------------------
% 2.43/0.72 % (542292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.72 % (542292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.72 % (542292)CaDiCaL version: 2.1.3
% 2.43/0.72 % (542292)Termination reason: Instruction limit
% 2.43/0.72 % (542292)Termination phase: Saturation
% 2.43/0.72 % (542292)Time elapsed: 0.137 s
% 2.43/0.72 % (542292)Peak memory usage: 13 MB
% 2.43/0.72 % (542292)Instructions burned: 163 (million)
% 2.43/0.72 % (542313)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1374509538:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 2.43/0.72 % (542311)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=368330888:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 2.43/0.72 % Exception at run slice level
% 2.43/0.72 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 2.43/0.72 % (542316)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=4214889625:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 2.43/0.72 % (542316)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 2.43/0.72 % (542304) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-542281-542304"...
% 2.43/0.72 % (542316) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-542281-542316"...
% 2.43/0.72 % (542306)Instruction limit reached!
% 2.43/0.72 % (542306)------------------------------
% 2.43/0.72 % (542306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.72 % (542306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.72 % (542306)CaDiCaL version: 2.1.3
% 2.43/0.72 % (542306)Termination reason: Instruction limit
% 2.43/0.72 % (542306)Termination phase: Saturation
% 2.43/0.72 % (542306)Time elapsed: 0.146 s
% 2.43/0.72 % (542306)Peak memory usage: 12 MB
% 2.43/0.72 % (542306)Instructions burned: 180 (million)
% 2.43/0.72 % (542318)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4048263249:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 2.43/0.72 % (542316)...printing done.
% 2.43/0.72 % (542316)Refutation found. Thanks to Tanya!
% 2.43/0.72 % SZS status Theorem for theBenchmark
% 2.43/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 2.43/0.74 % (542316)------------------------------
% 2.43/0.74 % (542316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.43/0.74 % (542316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.43/0.74 % (542316)CaDiCaL version: 2.1.3
% 2.43/0.74 % (542316)Termination reason: Refutation
% 2.43/0.74 % (542316)Time elapsed: 0.110 s
% 2.43/0.74 % (542316)Peak memory usage: 14 MB
% 2.43/0.74 % (542316)Instructions burned: 223 (million)
% 2.43/0.74 % (542281)Success in time 0.365 s
% 2.43/0.74 % Vampire exiting
%------------------------------------------------------------------------------