%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN045^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:41:38 AM UTC 2026
% Result : Theorem 0.21s 0.36s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 68
% Number of leaves : 55
% Syntax : Number of formulae : 881 ( 46 unt; 0 typ; 48 def)
% Number of atoms : 12343 (2055 equ; 0 cnn)
% Maximal formula atoms : 44 ( 14 avg)
% Number of connectives : 14161 (2341 ~;3740 |; 0 &;7362 @)
% ( 48 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 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 : 129 ( 125 usr; 75 con; 0-4 aty)
% ( 670 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1655 ( 0 sgn 564 !; 0 ?;1655 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vOR: $o > $o > $o ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_46,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_54,type,
sK0: $i > mu ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(f9,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox/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/sandbox/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(f39,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f40,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f42,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f51,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f52,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f58,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(f59,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,[],[f58]) ).
thf(f71,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f79,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f83,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f84,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
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,[],[f59]) ).
thf(f112,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f121,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f126,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(f132,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f135,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f141,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f143,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f147,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f121,f143,f135,f143,f143]) ).
thf(f148,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f132,f135,f143]) ).
thf(f158,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] :
( ( Y3 @ Y4 )
| ( Y2 @ 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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ 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] :
( ( Y3 @ Y4 )
| ( Y2 @ 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] :
( ( Y3 @ Y4 )
| ( Y2 @ 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] :
( ( Y1 @ Y2 )
| ( Y0 @ 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] :
( ( Y1 @ Y2 )
| ( Y0 @ 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] :
( ( Y3 @ Y4 )
| ( Y2 @ 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] :
( ( Y3 @ Y4 )
| ( Y2 @ 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] :
( ( Y1 @ Y2 )
| ( Y0 @ 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] :
( ( Y1 @ Y2 )
| ( Y0 @ 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] :
( ( Y1 @ Y2 )
| ( Y0 @ 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] :
( ( Y3 @ Y4 )
| ( Y2 @ 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,[],[f126,f112,f147,f141,f148,f135,f141,f147,f141,f141,f147,f135,f141,f141,f135,f141,f141,f141,f148,f147,f135,f141,f141,f135,f141,f141,f135,f141,f147,f141,f141]) ).
thf(f171,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( r @ 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 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( ( !! @ $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
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f172,plain,
( ( ^ [Y0: $i] :
~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( r @ 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 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( ( !! @ $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
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ 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 )
| ( p @ Y1 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( ( !! @ $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
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ 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 )
| ( p @ Y1 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( ( !! @ $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
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( ( !! @ $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
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ 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 )
| ( p @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ 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 )
| ( p @ Y1 ) ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( ( !! @ $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
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ 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 )
| ( p @ Y1 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( ( !! @ $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
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( ( !! @ $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
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ 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 )
| ( p @ Y1 ) ) ) ) ) )
@ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( r @ 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 )
| ( p @ Y1 ) ) ) ) ) )
@ sK2 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( ~ ( ( !! @ $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
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
@ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ~ ( ~ ( ( !! @ $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 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ 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 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
( ( ( ~ ( ~ ( ( !! @ $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 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ 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 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f234,plain,
( ( ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ 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 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f235,plain,
( ( $false
= ( ~ ( ~ ( ( !! @ $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 ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ 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 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f236,plain,
( ( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ 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 )
| ( p @ 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 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f235]) ).
thf(f237,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ 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 )
| ( p @ Y0 ) ) ) ) ) )
= $false )
| ( ( ~ ( ( !! @ $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 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f236]) ).
thf(f298,plain,
( ( ( ~ ( ( !! @ $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 ) ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f237]) ).
thf(f299,plain,
( ( ( ~ ( ( !! @ $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 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f237]) ).
thf(f300,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f299]) ).
thf(f301,plain,
( ( $false
= ( ( !! @ $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 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f300]) ).
thf(f302,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f301]) ).
thf(f303,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f301]) ).
thf(f304,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f303]) ).
thf(f305,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f304]) ).
thf(f306,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f304]) ).
thf(f307,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f306]) ).
thf(f309,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
= $false )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f310,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK15 )
= $false )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f309]) ).
thf(f311,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK15 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f310]) ).
thf(f312,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK15 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f311]) ).
thf(f313,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK15 )
= $false )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f312]) ).
thf(f314,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK15 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f313]) ).
thf(f315,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK16 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK15 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f314]) ).
thf(f316,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK15 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK17 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK16 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f315]) ).
thf(f317,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK15 )
| ( q @ sK15 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK16 )
| ( r @ sK16 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 )
| ( q @ sK17 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f316]) ).
thf(f318,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK16 )
| ( r @ sK16 ) )
= $false )
| ( ( q @ sK15 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 )
| ( q @ sK17 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f317]) ).
thf(f319,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK17 )
| ( q @ sK17 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK15 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK16 )
| ( r @ sK16 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f317]) ).
thf(f320,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK16 )
| ( r @ sK16 ) )
= $false )
| ( ( q @ sK17 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK15 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f319]) ).
thf(f321,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK16 )
| ( r @ sK16 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK15 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f319]) ).
thf(f322,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK17 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( $false
= ( r @ sK16 ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK15 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f321]) ).
thf(f323,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK15 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK16 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f321]) ).
thf(f324,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 ) )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK16 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f323]) ).
thf(f325,plain,
( ( ( r @ sK14 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK16 ) )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) ) ),
inference(or_proxy_clausification,[],[f324]) ).
thf(f326,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK17 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK16 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f324]) ).
thf(f327,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK16 ) )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f326]) ).
thf(f328,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK16 ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) ) ),
inference(not_proxy_clausification,[],[f327]) ).
thf(f329,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK16 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) ) ),
inference(not_proxy_clausification,[],[f328]) ).
thf(f330,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK16 ) )
= $false )
| ( ( r @ sK14 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) ) ),
inference(not_proxy_clausification,[],[f325]) ).
thf(f331,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( ( r @ sK14 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK16 ) ) ),
inference(not_proxy_clausification,[],[f330]) ).
thf(f332,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK15 ) )
= $false )
| ( $false
= ( r @ sK16 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f322]) ).
thf(f333,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( $false
= ( r @ sK16 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) ) ),
inference(not_proxy_clausification,[],[f332]) ).
thf(f334,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( $false
= ( r @ sK16 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) )
| ( ( r @ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f333]) ).
thf(f335,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( $false
= ( r @ sK16 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f333]) ).
thf(f336,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) )
| ( $false
= ( r @ sK16 ) ) ),
inference(not_proxy_clausification,[],[f335]) ).
thf(f337,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK15 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( $false
= ( r @ sK16 ) )
| ( ( q @ sK17 )
= $false ) ),
inference(or_proxy_clausification,[],[f320]) ).
thf(f338,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK15 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK16 ) )
= $false )
| ( ( q @ sK17 )
= $false ) ),
inference(or_proxy_clausification,[],[f320]) ).
thf(f339,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK16 ) )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( ( q @ sK17 )
= $false ) ),
inference(not_proxy_clausification,[],[f338]) ).
thf(f340,plain,
( ( ( q @ sK17 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK16 ) ) ),
inference(not_proxy_clausification,[],[f339]) ).
thf(f341,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( ( q @ sK17 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK16 ) )
| ( ( r @ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f340]) ).
thf(f342,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK16 ) )
| ( ( q @ sK17 )
= $false ) ),
inference(or_proxy_clausification,[],[f340]) ).
thf(f343,plain,
( ( ( q @ sK17 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK16 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true ) ),
inference(not_proxy_clausification,[],[f342]) ).
thf(f344,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( $false
= ( r @ sK16 ) )
| ( ( q @ sK17 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f337]) ).
thf(f345,plain,
( ( $false
= ( r @ sK16 ) )
| ( ( q @ sK17 )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( ( r @ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f344]) ).
thf(f346,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( ( q @ sK17 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false )
| ( $false
= ( r @ sK16 ) ) ),
inference(or_proxy_clausification,[],[f344]) ).
thf(f347,plain,
( ( $false
= ( r @ sK16 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true )
| ( ( q @ sK17 )
= $false ) ),
inference(not_proxy_clausification,[],[f346]) ).
thf(f348,plain,
( ( $false
= ( r @ sK16 ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 )
| ( q @ sK17 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( ( q @ sK15 )
= $false ) ),
inference(or_proxy_clausification,[],[f318]) ).
thf(f349,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 )
| ( q @ sK17 ) )
= $false )
| ( ( q @ sK15 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK16 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f318]) ).
thf(f350,plain,
( ( ( q @ sK15 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK16 ) )
= $false )
| ( ( r @ sK14 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 )
| ( q @ sK17 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f349]) ).
thf(f351,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK16 ) )
= $false )
| ( ( q @ sK15 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 )
| ( q @ sK17 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f349]) ).
thf(f352,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK17 )
| ( q @ sK17 ) )
= $false )
| ( ( q @ sK15 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK16 ) ) ),
inference(not_proxy_clausification,[],[f351]) ).
thf(f353,plain,
( ( ( q @ sK17 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false )
| ( ( q @ sK15 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK16 ) ) ),
inference(or_proxy_clausification,[],[f352]) ).
thf(f354,plain,
( ( ( q @ sK15 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK16 ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f352]) ).
thf(f355,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK16 ) )
| ( ( q @ sK15 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 ) )
= $false )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true ) ),
inference(not_proxy_clausification,[],[f354]) ).
thf(f356,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK16 ) )
| ( ( q @ sK15 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true ) ),
inference(not_proxy_clausification,[],[f355]) ).
thf(f357,plain,
( ( ( q @ sK17 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK16 ) )
| ( ( q @ sK15 )
= $false )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true ) ),
inference(not_proxy_clausification,[],[f353]) ).
thf(f358,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK16 ) )
| ( ( r @ sK14 )
= $false )
| ( ( q @ sK15 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 )
| ( q @ sK17 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f350]) ).
thf(f359,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK16 ) )
| ( ( q @ sK15 )
= $false )
| ( ( r @ sK14 )
= $false )
| ( ( q @ sK17 )
= $false ) ),
inference(or_proxy_clausification,[],[f358]) ).
thf(f360,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK17 ) )
= $false )
| ( ( r @ sK14 )
= $false )
| ( ( q @ sK15 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK16 ) ) ),
inference(or_proxy_clausification,[],[f358]) ).
thf(f361,plain,
( ( ( q @ sK15 )
= $false )
| ( ( r @ sK14 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK16 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) ) ),
inference(not_proxy_clausification,[],[f360]) ).
thf(f362,plain,
( ( $false
= ( r @ sK16 ) )
| ( ( q @ sK17 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( ( q @ sK15 )
= $false ) ),
inference(or_proxy_clausification,[],[f348]) ).
thf(f363,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 ) )
= $false )
| ( $false
= ( r @ sK16 ) )
| ( ( q @ sK15 )
= $false ) ),
inference(or_proxy_clausification,[],[f348]) ).
thf(f364,plain,
( ( $false
= ( r @ sK16 ) )
| ( ( r @ sK14 )
= $false )
| ( ( q @ sK15 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f363]) ).
thf(f365,plain,
( ( ( q @ sK15 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 ) )
= $false )
| ( $false
= ( r @ sK16 ) ) ),
inference(or_proxy_clausification,[],[f363]) ).
thf(f366,plain,
( ( ( q @ sK15 )
= $false )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK17 ) )
= $false )
| ( $false
= ( r @ sK16 ) ) ),
inference(not_proxy_clausification,[],[f365]) ).
thf(f367,plain,
( ( ( rel_s4 @ sK3 @ sK14 )
= $true )
| ( ( q @ sK15 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) )
| ( $false
= ( r @ sK16 ) ) ),
inference(not_proxy_clausification,[],[f366]) ).
thf(f368,plain,
( ( ( r @ sK14 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK17 ) )
| ( $false
= ( r @ sK16 ) )
| ( ( q @ sK15 )
= $false ) ),
inference(not_proxy_clausification,[],[f364]) ).
thf(f369,plain,
( ( $false
= ( r @ sK16 ) )
| ( ( q @ sK17 )
= $false )
| ( ( q @ sK15 )
= $false )
| ( ( r @ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f362]) ).
thf(f370,plain,
( ( ( q @ sK15 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false )
| ( $false
= ( r @ sK16 ) )
| ( ( q @ sK17 )
= $false ) ),
inference(or_proxy_clausification,[],[f362]) ).
thf(f371,plain,
( ( $false
= ( r @ sK16 ) )
| ( ( q @ sK15 )
= $false )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true )
| ( ( q @ sK17 )
= $false ) ),
inference(not_proxy_clausification,[],[f370]) ).
thf(f431,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK21 ) )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f305]) ).
thf(f432,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK21 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false ) ),
inference(not_proxy_clausification,[],[f431]) ).
thf(f434,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK21 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f432]) ).
thf(f435,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK14 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK21 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK22 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f434]) ).
thf(f436,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK22 )
| ( q @ sK22 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK21 )
| ( p @ sK21 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f435]) ).
thf(f437,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( ( q @ sK22 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK21 )
| ( p @ sK21 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f436]) ).
thf(f438,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK14 )
| ( r @ sK14 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK21 )
| ( p @ sK21 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK22 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f436]) ).
thf(f439,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK21 )
| ( p @ sK21 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK22 ) )
= $false )
| ( ( r @ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f438]) ).
thf(f440,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK22 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK21 )
| ( p @ sK21 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f438]) ).
thf(f441,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK22 ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK21 )
| ( p @ sK21 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f440]) ).
thf(f442,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK22 ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK21 )
| ( p @ sK21 ) )
= $false )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true ) ),
inference(not_proxy_clausification,[],[f441]) ).
thf(f443,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK22 ) )
| ( ( p @ sK21 )
= $false )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true ) ),
inference(or_proxy_clausification,[],[f442]) ).
thf(f444,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK21 ) )
= $false )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true )
| ( $true
= ( rel_s4 @ sK3 @ sK22 ) ) ),
inference(or_proxy_clausification,[],[f442]) ).
thf(f445,plain,
( ( ( rel_s4 @ sK3 @ sK14 )
= $true )
| ( $true
= ( rel_s4 @ sK3 @ sK22 ) )
| ( ( rel_s4 @ sK2 @ sK21 )
= $true ) ),
inference(not_proxy_clausification,[],[f444]) ).
thf(f446,plain,
( ( ( p @ sK21 )
= $false )
| ( ( r @ sK14 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK22 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f439]) ).
thf(f447,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK21 ) )
= $false )
| ( ( r @ sK14 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK22 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f439]) ).
thf(f448,plain,
( ( ( rel_s4 @ sK2 @ sK21 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK22 ) )
= $false )
| ( ( r @ sK14 )
= $false ) ),
inference(not_proxy_clausification,[],[f447]) ).
thf(f449,plain,
( ( ( rel_s4 @ sK2 @ sK21 )
= $true )
| ( ( r @ sK14 )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK22 ) ) ),
inference(not_proxy_clausification,[],[f448]) ).
thf(f450,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK22 ) )
| ( ( r @ sK14 )
= $false )
| ( ( p @ sK21 )
= $false ) ),
inference(not_proxy_clausification,[],[f446]) ).
thf(f451,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK21 )
| ( p @ sK21 ) )
= $false )
| ( ( q @ sK22 )
= $false )
| ( ( r @ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f437]) ).
thf(f452,plain,
( ( ( q @ sK22 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK14 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK21 )
| ( p @ sK21 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f437]) ).
thf(f453,plain,
( ( ( q @ sK22 )
= $false )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK21 )
| ( p @ sK21 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f452]) ).
thf(f454,plain,
( ( ( rel_s4 @ sK3 @ sK14 )
= $true )
| ( ( p @ sK21 )
= $false )
| ( ( q @ sK22 )
= $false ) ),
inference(or_proxy_clausification,[],[f453]) ).
thf(f455,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK21 ) )
= $false )
| ( ( q @ sK22 )
= $false )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true ) ),
inference(or_proxy_clausification,[],[f453]) ).
thf(f456,plain,
( ( ( rel_s4 @ sK2 @ sK21 )
= $true )
| ( ( rel_s4 @ sK3 @ sK14 )
= $true )
| ( ( q @ sK22 )
= $false ) ),
inference(not_proxy_clausification,[],[f455]) ).
thf(f457,plain,
( ( ( p @ sK21 )
= $false )
| ( ( r @ sK14 )
= $false )
| ( ( q @ sK22 )
= $false ) ),
inference(or_proxy_clausification,[],[f451]) ).
thf(f458,plain,
( ( ( r @ sK14 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK21 ) )
= $false )
| ( ( q @ sK22 )
= $false ) ),
inference(or_proxy_clausification,[],[f451]) ).
thf(f459,plain,
( ( ( q @ sK22 )
= $false )
| ( ( r @ sK14 )
= $false )
| ( ( rel_s4 @ sK2 @ sK21 )
= $true ) ),
inference(not_proxy_clausification,[],[f458]) ).
thf(f483,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f302]) ).
thf(f484,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f483]) ).
thf(f578,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) ) ),
inference(sigma_proxy_clausification,[],[f484]) ).
thf(f579,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) ) ),
inference(or_proxy_clausification,[],[f578]) ).
thf(f580,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f578]) ).
thf(f581,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) ) ),
inference(not_proxy_clausification,[],[f580]) ).
thf(f582,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) ) ),
inference(or_proxy_clausification,[],[f581]) ).
thf(f583,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) ) ),
inference(not_proxy_clausification,[],[f582]) ).
thf(f584,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK30 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) ) ),
inference(sigma_proxy_clausification,[],[f583]) ).
thf(f585,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK30 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) ) ),
inference(not_proxy_clausification,[],[f584]) ).
thf(f586,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK31 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK30 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) ) ),
inference(sigma_proxy_clausification,[],[f585]) ).
thf(f587,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK30 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK31 ) ) ),
inference(duplicate_literal_removal,[],[f586]) ).
thf(f588,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK30 )
| ( r @ sK30 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK29 )
| ( p @ sK29 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f587]) ).
thf(f589,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) )
= $false )
| ( ( r @ sK30 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK29 )
| ( p @ sK29 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f588]) ).
thf(f590,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK29 )
| ( p @ sK29 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK30 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f588]) ).
thf(f591,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK30 ) )
= $false )
| ( ( p @ sK29 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f590]) ).
thf(f592,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK29 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK30 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f590]) ).
thf(f593,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK30 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK29 ) ) ),
inference(not_proxy_clausification,[],[f592]) ).
thf(f594,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK30 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK29 ) ) ),
inference(not_proxy_clausification,[],[f593]) ).
thf(f595,plain,
( ( ( q @ sK31 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK30 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK29 ) ) ),
inference(or_proxy_clausification,[],[f594]) ).
thf(f596,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK31 ) )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK29 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK30 ) ) ),
inference(or_proxy_clausification,[],[f594]) ).
thf(f597,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK30 ) )
| ( ( rel_s4 @ sK2 @ sK31 )
= $true )
| ( $true
= ( rel_s4 @ sK3 @ sK29 ) ) ),
inference(not_proxy_clausification,[],[f596]) ).
thf(f598,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK30 ) )
| ( ( p @ sK29 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK31 )
| ( q @ sK31 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f591]) ).
thf(f599,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK30 ) )
| ( ( p @ sK29 )
= $false )
| ( ( q @ sK31 )
= $false ) ),
inference(or_proxy_clausification,[],[f598]) ).
thf(f600,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK30 ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK31 ) )
= $false )
| ( ( p @ sK29 )
= $false ) ),
inference(or_proxy_clausification,[],[f598]) ).
thf(f601,plain,
( ( ( rel_s4 @ sK2 @ sK31 )
= $true )
| ( ( p @ sK29 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK30 ) ) ),
inference(not_proxy_clausification,[],[f600]) ).
thf(f602,plain,
( ( ( q @ sK31 )
= $false )
| ( ( r @ sK30 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK29 )
| ( p @ sK29 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f589]) ).
thf(f603,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK31 ) )
= $false )
| ( ( r @ sK30 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK29 )
| ( p @ sK29 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f589]) ).
thf(f604,plain,
( ( ( rel_s4 @ sK2 @ sK31 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK29 )
| ( p @ sK29 ) )
= $false )
| ( ( r @ sK30 )
= $false ) ),
inference(not_proxy_clausification,[],[f603]) ).
thf(f605,plain,
( ( ( p @ sK29 )
= $false )
| ( ( rel_s4 @ sK2 @ sK31 )
= $true )
| ( ( r @ sK30 )
= $false ) ),
inference(or_proxy_clausification,[],[f604]) ).
thf(f606,plain,
( ( ( rel_s4 @ sK2 @ sK31 )
= $true )
| ( ( r @ sK30 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK29 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f604]) ).
thf(f607,plain,
( ( ( r @ sK30 )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK29 ) )
| ( ( rel_s4 @ sK2 @ sK31 )
= $true ) ),
inference(not_proxy_clausification,[],[f606]) ).
thf(f608,plain,
( ( ( r @ sK30 )
= $false )
| ( ( q @ sK31 )
= $false )
| ( ( p @ sK29 )
= $false ) ),
inference(or_proxy_clausification,[],[f602]) ).
thf(f609,plain,
( ( ( q @ sK31 )
= $false )
| ( ( r @ sK30 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK29 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f602]) ).
thf(f610,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK29 ) )
| ( ( q @ sK31 )
= $false )
| ( ( r @ sK30 )
= $false ) ),
inference(not_proxy_clausification,[],[f609]) ).
thf(f611,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK32 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) ) ),
inference(sigma_proxy_clausification,[],[f579]) ).
thf(f612,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK29 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK32 ) ) ),
inference(duplicate_literal_removal,[],[f611]) ).
thf(f613,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK29 )
| ( p @ sK29 ) )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK32 )
| ( p @ sK32 ) ) ) ),
inference(beta-eta_normalization,[],[f612]) ).
thf(f614,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK32 )
| ( p @ sK32 ) ) )
| ( ( p @ sK29 )
= $false ) ),
inference(or_proxy_clausification,[],[f613]) ).
thf(f615,plain,
( ( ( ~ ( rel_s4 @ sK3 @ sK29 ) )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK32 )
| ( p @ sK32 ) ) ) ),
inference(or_proxy_clausification,[],[f613]) ).
thf(f616,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK32 )
| ( p @ sK32 ) ) )
| ( $true
= ( rel_s4 @ sK3 @ sK29 ) ) ),
inference(not_proxy_clausification,[],[f615]) ).
thf(f617,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK29 ) )
| ( ( p @ sK32 )
= $false ) ),
inference(or_proxy_clausification,[],[f616]) ).
thf(f618,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK29 ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK32 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f616]) ).
thf(f619,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK32 ) )
| ( $true
= ( rel_s4 @ sK3 @ sK29 ) ) ),
inference(not_proxy_clausification,[],[f618]) ).
thf(f620,plain,
( ( ( p @ sK32 )
= $false )
| ( ( p @ sK29 )
= $false ) ),
inference(or_proxy_clausification,[],[f614]) ).
thf(f621,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK32 ) )
= $false )
| ( ( p @ sK29 )
= $false ) ),
inference(or_proxy_clausification,[],[f614]) ).
thf(f622,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK32 ) )
| ( ( p @ sK29 )
= $false ) ),
inference(not_proxy_clausification,[],[f621]) ).
thf(f623,plain,
( ( $true
= ( ~ ( ( !! @ $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 ) ) ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f298]) ).
thf(f624,plain,
( ( ( ~ ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f623]) ).
thf(f625,plain,
( ( $false
= ( ( !! @ $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 ) ) ) ) )
= $true )
| ( $true
= ( ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f624]) ).
thf(f626,plain,
( ( $true
= ( ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) ) )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f625]) ).
thf(f627,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f625]) ).
thf(f628,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f627]) ).
thf(f630,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
= $false )
| ( $true
= ( ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f628]) ).
thf(f631,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK33 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f630]) ).
thf(f632,plain,
( ( $true
= ( ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK33 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK34 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f631]) ).
thf(f633,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK33 )
= $false )
| ( ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK34 )
= $false ) ),
inference(not_proxy_clausification,[],[f632]) ).
thf(f634,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK34 )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK33 )
= $false ) ),
inference(or_proxy_clausification,[],[f633]) ).
thf(f635,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK33 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK34 )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f633]) ).
thf(f636,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK33 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK34 )
= $false ) ),
inference(not_proxy_clausification,[],[f635]) ).
thf(f637,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK34 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK33 )
= $false ) ),
inference(or_proxy_clausification,[],[f636]) ).
thf(f638,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK33 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK34 )
= $false ) ),
inference(pi_proxy_clausification,[],[f637]) ).
thf(f639,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X1 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK33 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK34 )
= $false ) ),
inference(pi_proxy_clausification,[],[f638]) ).
thf(f640,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ X1 )
| ( r @ X1 ) )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK34 )
| ( r @ sK34 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 )
| ( q @ sK33 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f639]) ).
thf(f641,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 )
| ( q @ sK33 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK34 )
| ( r @ sK34 ) ) )
| ( ( r @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f640]) ).
thf(f642,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( ( r @ X1 )
= $true )
| ( ( q @ sK33 )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK34 )
| ( r @ sK34 ) ) ) ),
inference(or_proxy_clausification,[],[f641]) ).
thf(f643,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK34 )
| ( r @ sK34 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK33 ) )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( ( r @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f641]) ).
thf(f644,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK3 @ sK34 )
| ( r @ sK34 ) ) )
| ( ( r @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK33 ) )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f643]) ).
thf(f645,plain,
! [X2: $i,X1: $i] :
( ( ( r @ sK34 )
= $false )
| ( ( r @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK33 ) )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f644]) ).
thf(f646,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ sK34 ) )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK33 ) )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( ( r @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f644]) ).
thf(f647,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK33 ) )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK34 ) )
| ( ( r @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f646]) ).
thf(f648,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( r @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK33 ) )
= $false )
| ( ( p @ X2 )
= $true )
| ( $true
= ( rel_s4 @ sK3 @ sK34 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f647]) ).
thf(f649,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ sK33 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( ( p @ X2 )
= $true )
| ( ( r @ X1 )
= $true )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK34 ) ) ),
inference(not_proxy_clausification,[],[f648]) ).
thf(f650,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X2 )
= $true )
| ( ( r @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ sK33 )
= $true )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK34 ) ) ),
inference(not_proxy_clausification,[],[f649]) ).
thf(f651,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ sK33 ) )
= $false )
| ( ( r @ X1 )
= $true )
| ( ( p @ X2 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( r @ sK34 )
= $false ) ),
inference(or_proxy_clausification,[],[f645]) ).
thf(f652,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X2 )
= $true )
| ( ( r @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ sK33 )
= $true )
| ( ( r @ sK34 )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f651]) ).
thf(f653,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( r @ X1 )
= $true )
| ( ( p @ X2 )
= $true )
| ( ( rel_s4 @ sK3 @ sK33 )
= $true )
| ( ( r @ sK34 )
= $false )
| ( ( rel_s4 @ sK2 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f652]) ).
thf(f654,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( ( q @ sK33 )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK34 )
| ( r @ sK34 ) ) )
| ( ( r @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f642]) ).
thf(f655,plain,
! [X2: $i,X1: $i] :
( ( ( r @ X1 )
= $true )
| ( ( q @ sK33 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK34 )
| ( r @ sK34 ) ) )
| ( ( p @ X2 )
= $true ) ),
inference(or_proxy_clausification,[],[f654]) ).
thf(f656,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X2 )
= $true )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( q @ sK33 )
= $false )
| ( ( r @ X1 )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK34 )
| ( r @ sK34 ) ) ) ),
inference(not_proxy_clausification,[],[f655]) ).
thf(f657,plain,
! [X2: $i,X1: $i] :
( ( ( r @ X1 )
= $true )
| ( ( q @ sK33 )
= $false )
| ( ( r @ sK34 )
= $false )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( p @ X2 )
= $true )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f656]) ).
thf(f658,plain,
! [X2: $i,X1: $i] :
( ( ( q @ sK33 )
= $false )
| ( ( p @ X2 )
= $true )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( r @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK34 ) )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f656]) ).
thf(f659,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( q @ sK33 )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK34 ) )
| ( ( p @ X2 )
= $true )
| ( ( r @ X1 )
= $true )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f658]) ).
thf(f660,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK34 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK33 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f634]) ).
thf(f661,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK33 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK34 )
= $false ) ),
inference(or_proxy_clausification,[],[f660]) ).
thf(f662,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK34 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK33 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f661]) ).
thf(f663,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ sK34 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK33 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f662]) ).
thf(f664,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( q @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 )
| ( q @ sK33 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK34 )
| ( r @ sK34 ) ) ) ),
inference(beta-eta_normalization,[],[f663]) ).
thf(f665,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK3 @ sK34 )
| ( r @ sK34 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( q @ X2 ) ) )
| ( ( p @ X1 )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 )
| ( q @ sK33 ) ) )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f664]) ).
thf(f666,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( q @ X2 ) ) )
| ( ( r @ sK34 )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 )
| ( q @ sK33 ) ) )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f665]) ).
thf(f667,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( q @ X2 ) ) )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK34 ) )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 )
| ( q @ sK33 ) ) ) ),
inference(or_proxy_clausification,[],[f665]) ).
thf(f668,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 )
| ( q @ sK33 ) ) )
| ( $true
= ( q @ X2 ) )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK34 ) )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f667]) ).
thf(f669,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( ( p @ X1 )
= $true )
| ( ( q @ sK33 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK34 ) )
= $false )
| ( $true
= ( q @ X2 ) ) ),
inference(or_proxy_clausification,[],[f668]) ).
thf(f670,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ sK34 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK33 ) )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f668]) ).
thf(f671,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( $true
= ( q @ X2 ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK33 ) )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK34 ) )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f670]) ).
thf(f672,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK34 ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK33 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f671]) ).
thf(f673,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK3 @ sK34 ) )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK3 @ sK33 )
= $true )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f672]) ).
thf(f674,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ sK33 )
= $true )
| ( ( p @ X1 )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK34 ) )
| ( ( rel_s4 @ sK2 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f673]) ).
thf(f675,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK34 ) )
= $false )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( q @ sK33 )
= $false ) ),
inference(not_proxy_clausification,[],[f669]) ).
thf(f676,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( q @ sK33 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK34 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f675]) ).
thf(f677,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( q @ sK33 )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK34 ) )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK2 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f676]) ).
thf(f678,plain,
! [X2: $i,X1: $i] :
( ( ( r @ sK34 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( ( p @ X1 )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 )
| ( q @ sK33 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f666]) ).
thf(f679,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( r @ sK34 )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK3 @ sK33 )
| ( q @ sK33 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f678]) ).
thf(f680,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( q @ sK33 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( $true
= ( q @ X2 ) )
| ( ( r @ sK34 )
= $false ) ),
inference(or_proxy_clausification,[],[f679]) ).
thf(f681,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( $true
= ( q @ X2 ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK33 ) )
= $false )
| ( ( r @ sK34 )
= $false )
| ( ( p @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f679]) ).
thf(f682,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK33 ) )
= $false )
| ( ( r @ sK34 )
= $false )
| ( ( rel_s4 @ sK2 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f681]) ).
thf(f683,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ sK33 )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( r @ sK34 )
= $false )
| ( ( rel_s4 @ sK2 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f682]) ).
thf(f684,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( p @ X1 )
= $true )
| ( ( q @ sK33 )
= $false )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( r @ sK34 )
= $false ) ),
inference(not_proxy_clausification,[],[f680]) ).
thf(f741,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ 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 )
| ( p @ Y0 ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f626]) ).
thf(f742,plain,
( ( ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f741]) ).
thf(f743,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f742]) ).
thf(f744,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f742]) ).
thf(f745,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK38 )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f744]) ).
thf(f746,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK38 )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f745]) ).
thf(f775,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK38 )
= $false )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f746]) ).
thf(f776,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK40 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK38 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f775]) ).
thf(f777,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK38 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK40 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f776]) ).
thf(f778,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK40 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK38 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f777]) ).
thf(f779,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK38 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK40 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f778]) ).
thf(f780,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK3 @ sK38 )
| ( p @ sK38 ) ) )
| ( ( ~ ( rel_s4 @ sK2 @ X2 )
| ( r @ X2 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( p @ sK40 ) )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( p @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f779]) ).
thf(f781,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ X2 )
| ( r @ X2 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( p @ X1 ) ) )
| ( ( p @ sK38 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( p @ sK40 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f780]) ).
thf(f782,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK3 @ sK38 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( p @ X1 ) ) )
| ( ( ~ ( rel_s4 @ sK2 @ X2 )
| ( r @ X2 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( p @ sK40 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f780]) ).
thf(f783,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( p @ X1 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( p @ sK40 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ X2 )
| ( r @ X2 ) )
= $true )
| ( ( rel_s4 @ sK3 @ sK38 )
= $true ) ),
inference(not_proxy_clausification,[],[f782]) ).
thf(f784,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ X2 )
| ( r @ X2 ) )
= $true )
| ( ( rel_s4 @ sK3 @ sK38 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( p @ sK40 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f783]) ).
thf(f785,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ sK38 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ X2 )
| ( r @ X2 ) )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( p @ sK40 ) )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f784]) ).
thf(f786,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( p @ sK40 ) )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK3 @ sK38 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f785]) ).
thf(f787,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( r @ X2 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( ( p @ sK40 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ sK38 )
= $true ) ),
inference(or_proxy_clausification,[],[f786]) ).
thf(f788,plain,
! [X2: $i,X1: $i] :
( ( ( r @ X2 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK40 ) )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( rel_s4 @ sK3 @ sK38 )
= $true ) ),
inference(or_proxy_clausification,[],[f786]) ).
thf(f789,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( $true
= ( rel_s4 @ sK3 @ sK40 ) )
| ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK3 @ sK38 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f788]) ).
thf(f790,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( rel_s4 @ sK3 @ sK38 )
= $true )
| ( $true
= ( rel_s4 @ sK3 @ sK40 ) )
| ( ( r @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f789]) ).
thf(f791,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ sK38 )
= $true )
| ( ( p @ sK40 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK2 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f787]) ).
thf(f792,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( ( p @ sK38 )
= $false )
| ( ( r @ X2 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( p @ X1 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( p @ sK40 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f781]) ).
thf(f793,plain,
! [X2: $i,X1: $i] :
( ( ( p @ sK38 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( p @ X1 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( p @ sK40 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f792]) ).
thf(f794,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( p @ sK40 ) )
= $false )
| ( ( p @ sK38 )
= $false )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( p @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f793]) ).
thf(f795,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK40 )
| ( p @ sK40 ) )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( p @ sK38 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK2 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f794]) ).
thf(f796,plain,
! [X2: $i,X1: $i] :
( ( ( p @ sK38 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( p @ sK40 )
= $false )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f795]) ).
thf(f797,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ sK40 ) )
= $false )
| ( ( p @ sK38 )
= $false ) ),
inference(or_proxy_clausification,[],[f795]) ).
thf(f798,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( p @ sK38 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( $true
= ( rel_s4 @ sK3 @ sK40 ) )
| ( ( r @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f797]) ).
thf(f799,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f743]) ).
thf(f800,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f799]) ).
thf(f801,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f800]) ).
thf(f828,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK43 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK43 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f801]) ).
thf(f829,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK43 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK43 )
= $false ) ),
inference(pi_proxy_clausification,[],[f828]) ).
thf(f830,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK43 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK43 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f829]) ).
thf(f831,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ sK43 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(duplicate_literal_removal,[],[f830]) ).
thf(f832,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ sK43 )
| ( p @ sK43 ) )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( q @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f831]) ).
thf(f833,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( p @ X1 ) ) )
| ( ( p @ sK43 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( q @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f832]) ).
thf(f834,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ( p @ X1 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ sK43 ) )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( q @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f832]) ).
thf(f835,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( q @ X2 ) ) )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK43 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f834]) ).
thf(f836,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ sK43 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f835]) ).
thf(f837,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ sK43 ) )
= $false )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f836]) ).
thf(f838,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( rel_s4 @ sK3 @ sK43 )
= $true ) ),
inference(not_proxy_clausification,[],[f837]) ).
thf(f839,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK3 @ sK43 )
= $true ) ),
inference(not_proxy_clausification,[],[f838]) ).
thf(f840,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 )
| ( q @ X2 ) ) )
| ( ( p @ sK43 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f833]) ).
thf(f841,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( ( p @ X1 )
= $true )
| ( ( p @ sK43 )
= $false ) ),
inference(or_proxy_clausification,[],[f840]) ).
thf(f842,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X2 ) ) )
| ( ( p @ X1 )
= $true )
| ( ( p @ sK43 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f841]) ).
thf(f843,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( p @ sK43 )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( q @ X2 ) ) ),
inference(not_proxy_clausification,[],[f842]) ).
thf(f844,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ 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 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f234]) ).
thf(f845,plain,
( ( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ 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 )
| ( p @ Y0 ) ) ) ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f844]) ).
thf(f846,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ 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 )
| ( p @ Y0 ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f845]) ).
thf(f867,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ 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 )
| ( p @ Y0 ) ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f846]) ).
thf(f868,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ 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 )
| ( p @ Y0 ) ) ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f867]) ).
thf(f869,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ 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 )
| ( p @ Y0 ) ) ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f867]) ).
thf(f870,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ 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 )
| ( p @ Y0 ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f869]) ).
thf(f871,plain,
( ( $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 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f869]) ).
thf(f872,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f871]) ).
thf(f873,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f872]) ).
thf(f874,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f873]) ).
thf(f875,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f874]) ).
thf(f876,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f874]) ).
thf(f877,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f876]) ).
thf(f878,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f877]) ).
thf(f879,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f878]) ).
thf(f880,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK44 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f879]) ).
thf(f881,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK44 )
= $false ) ),
inference(not_proxy_clausification,[],[f880]) ).
thf(f882,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK45 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK44 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f881]) ).
thf(f883,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK45 )
| ( q @ sK45 ) )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK44 )
| ( r @ sK44 ) ) ) ),
inference(beta-eta_normalization,[],[f882]) ).
thf(f884,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK45 )
| ( q @ sK45 ) )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK44 )
| ( r @ sK44 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f883]) ).
thf(f885,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK44 )
| ( r @ sK44 ) ) )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( q @ sK45 )
= $false ) ),
inference(or_proxy_clausification,[],[f884]) ).
thf(f886,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK44 )
| ( r @ sK44 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK45 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f884]) ).
thf(f887,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( r @ sK44 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK45 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f886]) ).
thf(f888,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK45 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK44 ) ) ) ),
inference(or_proxy_clausification,[],[f886]) ).
thf(f889,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK45 ) )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( r @ X2 )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK44 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f888]) ).
thf(f890,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK45 ) )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK44 ) ) )
| ( ( p @ X1 )
= $true )
| ( ( r @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f889]) ).
thf(f891,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ sK45 ) )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( r @ X2 )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK44 ) ) ) ),
inference(not_proxy_clausification,[],[f890]) ).
thf(f892,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK45 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK44 ) ) )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f891]) ).
thf(f893,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK45 ) )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK2 @ sK44 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f892]) ).
thf(f894,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK45 ) )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( r @ sK44 )
= $false ) ),
inference(not_proxy_clausification,[],[f887]) ).
thf(f895,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( r @ sK44 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( r @ X2 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK45 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f894]) ).
thf(f896,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK45 ) )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( r @ sK44 )
= $false ) ),
inference(not_proxy_clausification,[],[f895]) ).
thf(f897,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK45 ) )
| ( ( r @ sK44 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( rel_s4 @ sK3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f896]) ).
thf(f898,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK44 )
| ( r @ sK44 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( r @ X2 )
= $true )
| ( ( q @ sK45 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( p @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f885]) ).
thf(f899,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( r @ sK44 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( q @ sK45 )
= $false )
| ( ( p @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f898]) ).
thf(f900,plain,
! [X2: $i,X1: $i] :
( ( ( q @ sK45 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK44 ) ) )
| ( ( p @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f898]) ).
thf(f901,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK44 ) ) )
| ( ( q @ sK45 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( r @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f900]) ).
thf(f902,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( q @ sK45 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK2 @ sK44 )
= $true ) ),
inference(not_proxy_clausification,[],[f901]) ).
thf(f903,plain,
! [X2: $i,X1: $i] :
( ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( q @ sK45 )
= $false )
| ( ( rel_s4 @ sK2 @ sK44 )
= $true ) ),
inference(not_proxy_clausification,[],[f902]) ).
thf(f904,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( r @ X2 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( q @ sK45 )
= $false )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( r @ sK44 )
= $false ) ),
inference(not_proxy_clausification,[],[f899]) ).
thf(f905,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( q @ sK45 )
= $false )
| ( ( r @ sK44 )
= $false ) ),
inference(not_proxy_clausification,[],[f904]) ).
thf(f906,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK46 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f875]) ).
thf(f907,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK46 )
| ( p @ sK46 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f906]) ).
thf(f908,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ sK46 )
| ( p @ sK46 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( r @ X2 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f907]) ).
thf(f909,plain,
! [X2: $i,X1: $i] :
( ( ( p @ sK46 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f908]) ).
thf(f910,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK46 ) )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f908]) ).
thf(f911,plain,
! [X2: $i,X1: $i] :
( ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK46 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f910]) ).
thf(f912,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ sK46 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( p @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f911]) ).
thf(f913,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK2 @ sK46 )
= $true )
| ( ( r @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f912]) ).
thf(f914,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( rel_s4 @ sK2 @ sK46 )
= $true ) ),
inference(not_proxy_clausification,[],[f913]) ).
thf(f915,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( r @ X2 )
= $true )
| ( ( p @ sK46 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f909]) ).
thf(f916,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( r @ X2 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( p @ sK46 )
= $false ) ),
inference(or_proxy_clausification,[],[f915]) ).
thf(f917,plain,
! [X2: $i,X1: $i] :
( ( ( r @ X2 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( p @ sK46 )
= $false )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( rel_s4 @ sK3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f916]) ).
thf(f918,plain,
! [X1: $i] :
( ( ( ~ ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f870]) ).
thf(f919,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f918]) ).
thf(f920,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f919]) ).
thf(f921,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f920]) ).
thf(f922,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f921]) ).
thf(f923,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f922]) ).
thf(f924,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f922]) ).
thf(f925,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f924]) ).
thf(f926,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f925]) ).
thf(f927,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f926]) ).
thf(f928,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X4 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X3 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f927]) ).
thf(f929,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( ( ~ ( rel_s4 @ sK2 @ X4 )
| ( r @ X4 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f928]) ).
thf(f930,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( $true
= ( p @ X3 ) )
| ( ( ~ ( rel_s4 @ sK2 @ X4 )
| ( r @ X4 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f929]) ).
thf(f931,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( p @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( ( ~ ( rel_s4 @ sK2 @ X4 )
| ( r @ X4 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f930]) ).
thf(f932,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( p @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( ~ ( rel_s4 @ sK2 @ X4 )
| ( r @ X4 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f931]) ).
thf(f933,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( r @ X2 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ X4 )
| ( r @ X4 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( $true
= ( p @ X3 ) )
| ( ( p @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f932]) ).
thf(f934,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( r @ X2 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ X4 )
| ( r @ X4 ) )
= $true )
| ( $true
= ( p @ X3 ) )
| ( ( rel_s4 @ sK3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f933]) ).
thf(f935,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( r @ X2 )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( ~ ( rel_s4 @ sK2 @ X4 )
| ( r @ X4 ) )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( p @ X1 )
= $true )
| ( $true
= ( p @ X3 ) ) ),
inference(not_proxy_clausification,[],[f934]) ).
thf(f936,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( r @ X4 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 ) ) )
| ( ( p @ X1 )
= $true )
| ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f935]) ).
thf(f937,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( p @ X1 )
= $true )
| ( ( r @ X4 )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( $true
= ( p @ X3 ) )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( r @ X2 )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X4 ) )
| ( ( rel_s4 @ sK3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f936]) ).
thf(f938,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) ) ),
inference(not_proxy_clausification,[],[f923]) ).
thf(f939,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f938]) ).
thf(f940,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f939]) ).
thf(f941,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( r @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f940]) ).
thf(f942,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( q @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 )
| ( p @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f941]) ).
thf(f943,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( ( q @ X3 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f942]) ).
thf(f944,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 )
| ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( q @ X3 )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f943]) ).
thf(f945,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( r @ X2 ) ) )
| ( ( q @ X3 )
= $true )
| ( ( p @ X4 )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f944]) ).
thf(f946,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( q @ X3 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( r @ X2 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( p @ X4 )
= $true ) ),
inference(or_proxy_clausification,[],[f945]) ).
thf(f947,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( r @ X2 )
= $true )
| ( ( q @ X3 )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( p @ X4 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 ) ) )
| ( ( rel_s4 @ sK3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f946]) ).
thf(f948,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( r @ X2 )
= $true )
| ( ( p @ X4 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 ) ) )
| ( ( q @ X3 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f947]) ).
thf(f949,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( r @ X2 )
= $true )
| ( ( q @ X3 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X4 ) )
| ( ( p @ X4 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f948]) ).
thf(f950,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( p @ X4 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( q @ X3 )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f949]) ).
thf(f951,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f868]) ).
thf(f952,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f868]) ).
thf(f953,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f952]) ).
thf(f954,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f953]) ).
thf(f955,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f954]) ).
thf(f956,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f955]) ).
thf(f957,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f955]) ).
thf(f958,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f957]) ).
thf(f959,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f958]) ).
thf(f960,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f959]) ).
thf(f961,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f960]) ).
thf(f962,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK47 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f961]) ).
thf(f963,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK48 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ sK47 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f962]) ).
thf(f964,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ sK47 )
| ( r @ sK47 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK48 )
| ( q @ sK48 ) )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f963]) ).
thf(f965,plain,
! [X2: $i,X1: $i] :
( ( ( r @ sK47 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ sK48 )
| ( q @ sK48 ) )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f964]) ).
thf(f966,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK48 )
| ( q @ sK48 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK47 ) ) ) ),
inference(or_proxy_clausification,[],[f964]) ).
thf(f967,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK48 )
| ( q @ sK48 ) )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK47 ) ) ) ),
inference(or_proxy_clausification,[],[f966]) ).
thf(f968,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK48 )
| ( q @ sK48 ) )
= $false )
| ( ( p @ X1 )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK47 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f967]) ).
thf(f969,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK47 ) ) )
| ( $true
= ( q @ X2 ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK48 )
| ( q @ sK48 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f968]) ).
thf(f970,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ sK47 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK48 )
| ( q @ sK48 ) )
= $false )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f969]) ).
thf(f971,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK2 @ sK47 )
= $true )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( q @ sK48 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( $true
= ( q @ X2 ) ) ),
inference(or_proxy_clausification,[],[f970]) ).
thf(f972,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK2 @ sK47 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK48 ) ) ) ),
inference(or_proxy_clausification,[],[f970]) ).
thf(f973,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK48 ) ) )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( rel_s4 @ sK2 @ sK47 )
= $true )
| ( ( p @ X1 )
= $true )
| ( $true
= ( q @ X2 ) ) ),
inference(not_proxy_clausification,[],[f972]) ).
thf(f974,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK48 ) )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK2 @ sK47 )
= $true ) ),
inference(not_proxy_clausification,[],[f973]) ).
thf(f975,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( ( q @ sK48 )
= $false )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK2 @ sK47 )
= $true ) ),
inference(not_proxy_clausification,[],[f971]) ).
thf(f976,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( ( r @ sK47 )
= $false )
| ( ( q @ sK48 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f965]) ).
thf(f977,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( r @ sK47 )
= $false )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK48 ) ) ) ),
inference(or_proxy_clausification,[],[f965]) ).
thf(f978,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $false
= ( ~ ( rel_s4 @ sK2 @ sK48 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( r @ sK47 )
= $false ) ),
inference(or_proxy_clausification,[],[f977]) ).
thf(f979,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK48 ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( r @ sK47 )
= $false ) ),
inference(not_proxy_clausification,[],[f978]) ).
thf(f980,plain,
! [X2: $i,X1: $i] :
( ( ( r @ sK47 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( $true
= ( rel_s4 @ sK2 @ sK48 ) ) ),
inference(or_proxy_clausification,[],[f979]) ).
thf(f981,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( $true
= ( rel_s4 @ sK2 @ sK48 ) )
| ( $true
= ( q @ X2 ) )
| ( ( r @ sK47 )
= $false )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f980]) ).
thf(f982,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK48 ) )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( r @ sK47 )
= $false ) ),
inference(not_proxy_clausification,[],[f981]) ).
thf(f983,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( r @ sK47 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( q @ sK48 )
= $false )
| ( $true
= ( q @ X2 ) ) ),
inference(or_proxy_clausification,[],[f976]) ).
thf(f984,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( r @ sK47 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( q @ sK48 )
= $false )
| ( ( rel_s4 @ sK3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f983]) ).
thf(f985,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( r @ sK47 )
= $false )
| ( ( q @ sK48 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) ) ),
inference(or_proxy_clausification,[],[f984]) ).
thf(f986,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( q @ sK48 )
= $false )
| ( ( r @ sK47 )
= $false )
| ( ( rel_s4 @ sK3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f985]) ).
thf(f987,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ sK49 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f956]) ).
thf(f988,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ sK49 )
| ( p @ sK49 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f987]) ).
thf(f989,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( ( p @ sK49 )
= $false ) ),
inference(or_proxy_clausification,[],[f988]) ).
thf(f990,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK49 ) )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f988]) ).
thf(f991,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ sK49 ) )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( ( p @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f990]) ).
thf(f992,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ sK49 ) )
= $false )
| ( ( p @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( ( rel_s4 @ sK3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f991]) ).
thf(f993,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( $true
= ( rel_s4 @ sK2 @ sK49 ) )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f992]) ).
thf(f994,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK49 ) )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f993]) ).
thf(f995,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( rel_s4 @ sK2 @ sK49 ) )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f994]) ).
thf(f996,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( p @ sK49 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f989]) ).
thf(f997,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( p @ sK49 )
= $false )
| ( ( p @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f996]) ).
thf(f998,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( p @ sK49 )
= $false ) ),
inference(or_proxy_clausification,[],[f997]) ).
thf(f999,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( p @ sK49 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f998]) ).
thf(f1000,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( ( ~ ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f951]) ).
thf(f1001,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
= $true )
| ( ( ~ ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f1000]) ).
thf(f1002,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ~ ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f1001]) ).
thf(f1003,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ~ ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f1002]) ).
thf(f1004,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ( ( !! @ $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 )
| ( p @ Y0 ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f1003]) ).
thf(f1005,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f1004]) ).
thf(f1006,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f1004]) ).
thf(f1007,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f1006]) ).
thf(f1008,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f1007]) ).
thf(f1009,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X3 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1008]) ).
thf(f1010,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( r @ Y0 ) )
@ X3 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1009]) ).
thf(f1011,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 )
| ( p @ X4 ) ) )
| ( ( ~ ( rel_s4 @ sK2 @ X3 )
| ( r @ X3 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1010]) ).
thf(f1012,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 )
| ( p @ X4 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ X3 )
| ( r @ X3 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1011]) ).
thf(f1013,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( p @ X4 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ X3 )
| ( r @ X3 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( $true
= ( q @ X2 ) ) ),
inference(or_proxy_clausification,[],[f1012]) ).
thf(f1014,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( q @ X2 ) )
| ( ( p @ X4 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( $true
= ( r @ X3 ) ) ),
inference(or_proxy_clausification,[],[f1013]) ).
thf(f1015,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X4 ) )
| ( $true
= ( r @ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( ( p @ X4 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f1014]) ).
thf(f1016,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( r @ X3 ) )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( p @ X4 )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f1015]) ).
thf(f1017,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( ( p @ X1 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( p @ X4 )
= $true )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( r @ X3 ) )
| ( $false
= ( rel_s4 @ sK2 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f1016]) ).
thf(f1018,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( $true
= ( r @ X3 ) )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( p @ X4 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( ( p @ X1 )
= $true )
| ( $true
= ( q @ X2 ) ) ),
inference(not_proxy_clausification,[],[f1017]) ).
thf(f1019,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( r @ X3 ) )
| ( $false
= ( rel_s4 @ sK2 @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( p @ X4 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f1018]) ).
thf(f1020,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f1005]) ).
thf(f1021,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f1020]) ).
thf(f1022,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X3 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f1021]) ).
thf(f1023,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X4 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f1022]) ).
thf(f1024,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ X4 )
| ( q @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f1023]) ).
thf(f1025,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ X4 )
| ( q @ X4 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1024]) ).
thf(f1026,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X3 ) ) )
| ( $true
= ( p @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 ) ) )
| ( ( q @ X4 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1025]) ).
thf(f1027,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 )
| ( p @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( q @ X4 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 ) ) )
| ( $true
= ( p @ X3 ) ) ),
inference(not_proxy_clausification,[],[f1026]) ).
thf(f1028,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK3 @ X2 )
| ( q @ X2 ) ) )
| ( $true
= ( p @ X3 ) )
| ( ( q @ X4 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( p @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f1027]) ).
thf(f1029,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ~ ( rel_s4 @ sK3 @ X1 ) )
= $true )
| ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( p @ X1 )
= $true )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 ) ) )
| ( ( q @ X4 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f1028]) ).
thf(f1030,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( ( q @ X4 )
= $true )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X3 ) )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK3 @ X2 ) )
= $true )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f1029]) ).
thf(f1031,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK2 @ X4 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) )
| ( $true
= ( p @ X3 ) )
| ( ( q @ X4 )
= $true )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f1030]) ).
thf(f1032,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( p @ X1 )
= $true )
| ( ( q @ X4 )
= $true )
| ( $true
= ( p @ X3 ) )
| ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ sK2 @ X4 ) )
| ( $false
= ( rel_s4 @ sK2 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f1031]) ).
thf(f1073,definition,
( spl50_9
<=> ! [X2: $i] :
( ( ( p @ X2 )
= $true )
| ( ( rel_s4 @ sK2 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl50_9])],[avatar_definition]) ).
thf(f1074,plain,
( ! [X2: $i] :
( ( ( rel_s4 @ sK2 @ X2 )
= $false )
| ( ( p @ X2 )
= $true ) )
| ~ spl50_9 ),
inference(avatar_component_clause,[],[f1073]) ).
thf(f1076,definition,
( spl50_10
<=> ! [X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( r @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl50_10])],[avatar_definition]) ).
thf(f1077,plain,
( ! [X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( ( r @ X1 )
= $true ) )
| ~ spl50_10 ),
inference(avatar_component_clause,[],[f1076]) ).
thf(f1080,definition,
( spl50_11
<=> ! [X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( q @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl50_11])],[avatar_definition]) ).
thf(f1081,plain,
( ! [X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( q @ X1 ) ) )
| ~ spl50_11 ),
inference(avatar_component_clause,[],[f1080]) ).
thf(f1156,definition,
( spl50_26
<=> ( $true
= ( rel_s4 @ sK2 @ sK17 ) ) ),
introduced(definition,[new_symbols(definition,[spl50_26])],[avatar_definition]) ).
thf(f1158,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK17 ) )
| ~ spl50_26 ),
inference(avatar_component_clause,[],[f1156]) ).
thf(f1160,definition,
( spl50_27
<=> ( $true
= ( rel_s4 @ sK2 @ sK16 ) ) ),
introduced(definition,[new_symbols(definition,[spl50_27])],[avatar_definition]) ).
thf(f1162,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK16 ) )
| ~ spl50_27 ),
inference(avatar_component_clause,[],[f1160]) ).
thf(f1164,definition,
( spl50_28
<=> ( ( rel_s4 @ sK3 @ sK14 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl50_28])],[avatar_definition]) ).
thf(f1166,plain,
( ( ( rel_s4 @ sK3 @ sK14 )
= $true )
| ~ spl50_28 ),
inference(avatar_component_clause,[],[f1164]) ).
thf(f1168,definition,
( spl50_29
<=> ( $true
= ( rel_s4 @ sK3 @ sK15 ) ) ),
introduced(definition,[new_symbols(definition,[spl50_29])],[avatar_definition]) ).
thf(f1170,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK15 ) )
| ~ spl50_29 ),
inference(avatar_component_clause,[],[f1168]) ).
thf(f1171,plain,
( spl50_26
| spl50_27
| spl50_28
| spl50_29 ),
inference(avatar_split_clause,[],[f329,f1168,f1164,f1160,f1156]) ).
thf(f1173,definition,
( spl50_30
<=> ( ( r @ sK14 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_30])],[avatar_definition]) ).
thf(f1175,plain,
( ( ( r @ sK14 )
= $false )
| ~ spl50_30 ),
inference(avatar_component_clause,[],[f1173]) ).
thf(f1176,plain,
( spl50_26
| spl50_27
| spl50_29
| spl50_30 ),
inference(avatar_split_clause,[],[f331,f1173,f1168,f1160,f1156]) ).
thf(f1178,definition,
( spl50_31
<=> ( $false
= ( r @ sK16 ) ) ),
introduced(definition,[new_symbols(definition,[spl50_31])],[avatar_definition]) ).
thf(f1180,plain,
( ( $false
= ( r @ sK16 ) )
| ~ spl50_31 ),
inference(avatar_component_clause,[],[f1178]) ).
thf(f1181,plain,
( spl50_31
| spl50_29
| spl50_26
| spl50_28 ),
inference(avatar_split_clause,[],[f336,f1164,f1156,f1168,f1178]) ).
thf(f1182,plain,
( spl50_31
| spl50_29
| spl50_26
| spl50_30 ),
inference(avatar_split_clause,[],[f334,f1173,f1156,f1168,f1178]) ).
thf(f1184,definition,
( spl50_32
<=> ( ( q @ sK17 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_32])],[avatar_definition]) ).
thf(f1186,plain,
( ( ( q @ sK17 )
= $false )
| ~ spl50_32 ),
inference(avatar_component_clause,[],[f1184]) ).
thf(f1187,plain,
( spl50_27
| spl50_32
| spl50_28
| spl50_29 ),
inference(avatar_split_clause,[],[f343,f1168,f1164,f1184,f1160]) ).
thf(f1188,plain,
( spl50_32
| spl50_30
| spl50_29
| spl50_27 ),
inference(avatar_split_clause,[],[f341,f1160,f1168,f1173,f1184]) ).
thf(f1189,plain,
( spl50_32
| spl50_31
| spl50_29
| spl50_28 ),
inference(avatar_split_clause,[],[f347,f1164,f1168,f1178,f1184]) ).
thf(f1190,plain,
( spl50_32
| spl50_29
| spl50_30
| spl50_31 ),
inference(avatar_split_clause,[],[f345,f1178,f1173,f1168,f1184]) ).
thf(f1192,definition,
( spl50_33
<=> ( ( q @ sK15 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_33])],[avatar_definition]) ).
thf(f1194,plain,
( ( ( q @ sK15 )
= $false )
| ~ spl50_33 ),
inference(avatar_component_clause,[],[f1192]) ).
thf(f1195,plain,
( spl50_26
| spl50_33
| spl50_27
| spl50_28 ),
inference(avatar_split_clause,[],[f356,f1164,f1160,f1192,f1156]) ).
thf(f1196,plain,
( spl50_33
| spl50_32
| spl50_28
| spl50_27 ),
inference(avatar_split_clause,[],[f357,f1160,f1164,f1184,f1192]) ).
thf(f1197,plain,
( spl50_33
| spl50_26
| spl50_30
| spl50_27 ),
inference(avatar_split_clause,[],[f361,f1160,f1173,f1156,f1192]) ).
thf(f1198,plain,
( spl50_30
| spl50_27
| spl50_33
| spl50_32 ),
inference(avatar_split_clause,[],[f359,f1184,f1192,f1160,f1173]) ).
thf(f1199,plain,
( spl50_26
| spl50_28
| spl50_31
| spl50_33 ),
inference(avatar_split_clause,[],[f367,f1192,f1178,f1164,f1156]) ).
thf(f1200,plain,
( spl50_26
| spl50_33
| spl50_30
| spl50_31 ),
inference(avatar_split_clause,[],[f368,f1178,f1173,f1192,f1156]) ).
thf(f1201,plain,
( spl50_31
| spl50_32
| spl50_33
| spl50_28 ),
inference(avatar_split_clause,[],[f371,f1164,f1192,f1184,f1178]) ).
thf(f1202,plain,
( spl50_32
| spl50_30
| spl50_33
| spl50_31 ),
inference(avatar_split_clause,[],[f369,f1178,f1192,f1173,f1184]) ).
thf(f1244,definition,
( spl50_40
<=> ( ( rel_s4 @ sK2 @ sK21 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl50_40])],[avatar_definition]) ).
thf(f1246,plain,
( ( ( rel_s4 @ sK2 @ sK21 )
= $true )
| ~ spl50_40 ),
inference(avatar_component_clause,[],[f1244]) ).
thf(f1248,definition,
( spl50_41
<=> ( $true
= ( rel_s4 @ sK3 @ sK22 ) ) ),
introduced(definition,[new_symbols(definition,[spl50_41])],[avatar_definition]) ).
thf(f1250,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK22 ) )
| ~ spl50_41 ),
inference(avatar_component_clause,[],[f1248]) ).
thf(f1251,plain,
( spl50_40
| spl50_41
| spl50_28 ),
inference(avatar_split_clause,[],[f445,f1164,f1248,f1244]) ).
thf(f1253,definition,
( spl50_42
<=> ( ( p @ sK21 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_42])],[avatar_definition]) ).
thf(f1255,plain,
( ( ( p @ sK21 )
= $false )
| ~ spl50_42 ),
inference(avatar_component_clause,[],[f1253]) ).
thf(f1256,plain,
( spl50_41
| spl50_42
| spl50_28 ),
inference(avatar_split_clause,[],[f443,f1164,f1253,f1248]) ).
thf(f1257,plain,
( spl50_40
| spl50_41
| spl50_30 ),
inference(avatar_split_clause,[],[f449,f1173,f1248,f1244]) ).
thf(f1258,plain,
( spl50_41
| spl50_42
| spl50_30 ),
inference(avatar_split_clause,[],[f450,f1173,f1253,f1248]) ).
thf(f1260,definition,
( spl50_43
<=> ( ( q @ sK22 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_43])],[avatar_definition]) ).
thf(f1262,plain,
( ( ( q @ sK22 )
= $false )
| ~ spl50_43 ),
inference(avatar_component_clause,[],[f1260]) ).
thf(f1263,plain,
( spl50_43
| spl50_40
| spl50_28 ),
inference(avatar_split_clause,[],[f456,f1164,f1244,f1260]) ).
thf(f1264,plain,
( spl50_43
| spl50_42
| spl50_28 ),
inference(avatar_split_clause,[],[f454,f1164,f1253,f1260]) ).
thf(f1265,plain,
( spl50_40
| spl50_43
| spl50_30 ),
inference(avatar_split_clause,[],[f459,f1173,f1260,f1244]) ).
thf(f1266,plain,
( spl50_30
| spl50_42
| spl50_43 ),
inference(avatar_split_clause,[],[f457,f1260,f1253,f1173]) ).
thf(f1348,definition,
( spl50_56
<=> ( ( rel_s4 @ sK2 @ sK31 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl50_56])],[avatar_definition]) ).
thf(f1350,plain,
( ( ( rel_s4 @ sK2 @ sK31 )
= $true )
| ~ spl50_56 ),
inference(avatar_component_clause,[],[f1348]) ).
thf(f1352,definition,
( spl50_57
<=> ( $true
= ( rel_s4 @ sK3 @ sK29 ) ) ),
introduced(definition,[new_symbols(definition,[spl50_57])],[avatar_definition]) ).
thf(f1354,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK29 ) )
| ~ spl50_57 ),
inference(avatar_component_clause,[],[f1352]) ).
thf(f1356,definition,
( spl50_58
<=> ( $true
= ( rel_s4 @ sK2 @ sK30 ) ) ),
introduced(definition,[new_symbols(definition,[spl50_58])],[avatar_definition]) ).
thf(f1358,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK30 ) )
| ~ spl50_58 ),
inference(avatar_component_clause,[],[f1356]) ).
thf(f1359,plain,
( spl50_56
| spl50_57
| spl50_58 ),
inference(avatar_split_clause,[],[f597,f1356,f1352,f1348]) ).
thf(f1361,definition,
( spl50_59
<=> ( ( q @ sK31 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_59])],[avatar_definition]) ).
thf(f1363,plain,
( ( ( q @ sK31 )
= $false )
| ~ spl50_59 ),
inference(avatar_component_clause,[],[f1361]) ).
thf(f1364,plain,
( spl50_57
| spl50_58
| spl50_59 ),
inference(avatar_split_clause,[],[f595,f1361,f1356,f1352]) ).
thf(f1366,definition,
( spl50_60
<=> ( ( p @ sK29 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_60])],[avatar_definition]) ).
thf(f1368,plain,
( ( ( p @ sK29 )
= $false )
| ~ spl50_60 ),
inference(avatar_component_clause,[],[f1366]) ).
thf(f1369,plain,
( spl50_58
| spl50_60
| spl50_56 ),
inference(avatar_split_clause,[],[f601,f1348,f1366,f1356]) ).
thf(f1370,plain,
( spl50_59
| spl50_58
| spl50_60 ),
inference(avatar_split_clause,[],[f599,f1366,f1356,f1361]) ).
thf(f1372,definition,
( spl50_61
<=> ( ( r @ sK30 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_61])],[avatar_definition]) ).
thf(f1374,plain,
( ( ( r @ sK30 )
= $false )
| ~ spl50_61 ),
inference(avatar_component_clause,[],[f1372]) ).
thf(f1375,plain,
( spl50_56
| spl50_61
| spl50_57 ),
inference(avatar_split_clause,[],[f607,f1352,f1372,f1348]) ).
thf(f1376,plain,
( spl50_56
| spl50_60
| spl50_61 ),
inference(avatar_split_clause,[],[f605,f1372,f1366,f1348]) ).
thf(f1377,plain,
( spl50_59
| spl50_57
| spl50_61 ),
inference(avatar_split_clause,[],[f610,f1372,f1352,f1361]) ).
thf(f1378,plain,
( spl50_59
| spl50_60
| spl50_61 ),
inference(avatar_split_clause,[],[f608,f1372,f1366,f1361]) ).
thf(f1380,definition,
( spl50_62
<=> ( $true
= ( rel_s4 @ sK2 @ sK32 ) ) ),
introduced(definition,[new_symbols(definition,[spl50_62])],[avatar_definition]) ).
thf(f1382,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK32 ) )
| ~ spl50_62 ),
inference(avatar_component_clause,[],[f1380]) ).
thf(f1383,plain,
( spl50_62
| spl50_57 ),
inference(avatar_split_clause,[],[f619,f1352,f1380]) ).
thf(f1385,definition,
( spl50_63
<=> ( ( p @ sK32 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_63])],[avatar_definition]) ).
thf(f1387,plain,
( ( ( p @ sK32 )
= $false )
| ~ spl50_63 ),
inference(avatar_component_clause,[],[f1385]) ).
thf(f1388,plain,
( spl50_63
| spl50_57 ),
inference(avatar_split_clause,[],[f617,f1352,f1385]) ).
thf(f1389,plain,
( spl50_62
| spl50_60 ),
inference(avatar_split_clause,[],[f622,f1366,f1380]) ).
thf(f1390,plain,
( spl50_60
| spl50_63 ),
inference(avatar_split_clause,[],[f620,f1385,f1366]) ).
thf(f1392,definition,
( spl50_64
<=> ( ( rel_s4 @ sK3 @ sK33 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl50_64])],[avatar_definition]) ).
thf(f1394,plain,
( ( ( rel_s4 @ sK3 @ sK33 )
= $true )
| ~ spl50_64 ),
inference(avatar_component_clause,[],[f1392]) ).
thf(f1396,definition,
( spl50_65
<=> ( $true
= ( rel_s4 @ sK3 @ sK34 ) ) ),
introduced(definition,[new_symbols(definition,[spl50_65])],[avatar_definition]) ).
thf(f1398,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK34 ) )
| ~ spl50_65 ),
inference(avatar_component_clause,[],[f1396]) ).
thf(f1399,plain,
( spl50_64
| spl50_10
| spl50_9
| spl50_65 ),
inference(avatar_split_clause,[],[f650,f1396,f1073,f1076,f1392]) ).
thf(f1401,definition,
( spl50_66
<=> ( ( r @ sK34 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_66])],[avatar_definition]) ).
thf(f1403,plain,
( ( ( r @ sK34 )
= $false )
| ~ spl50_66 ),
inference(avatar_component_clause,[],[f1401]) ).
thf(f1404,plain,
( spl50_10
| spl50_64
| spl50_66
| spl50_9 ),
inference(avatar_split_clause,[],[f653,f1073,f1401,f1392,f1076]) ).
thf(f1406,definition,
( spl50_67
<=> ( ( q @ sK33 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_67])],[avatar_definition]) ).
thf(f1408,plain,
( ( ( q @ sK33 )
= $false )
| ~ spl50_67 ),
inference(avatar_component_clause,[],[f1406]) ).
thf(f1409,plain,
( spl50_10
| spl50_9
| spl50_67
| spl50_65 ),
inference(avatar_split_clause,[],[f659,f1396,f1406,f1073,f1076]) ).
thf(f1410,plain,
( spl50_67
| spl50_10
| spl50_66
| spl50_9 ),
inference(avatar_split_clause,[],[f657,f1073,f1401,f1076,f1406]) ).
thf(f1411,plain,
( spl50_9
| spl50_65
| spl50_64
| spl50_11 ),
inference(avatar_split_clause,[],[f674,f1080,f1392,f1396,f1073]) ).
thf(f1412,plain,
( spl50_11
| spl50_65
| spl50_67
| spl50_9 ),
inference(avatar_split_clause,[],[f677,f1073,f1406,f1396,f1080]) ).
thf(f1413,plain,
( spl50_64
| spl50_9
| spl50_66
| spl50_11 ),
inference(avatar_split_clause,[],[f683,f1080,f1401,f1073,f1392]) ).
thf(f1414,plain,
( spl50_11
| spl50_9
| spl50_67
| spl50_66 ),
inference(avatar_split_clause,[],[f684,f1401,f1406,f1073,f1080]) ).
thf(f1452,definition,
( spl50_75
<=> ( ( rel_s4 @ sK3 @ sK38 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl50_75])],[avatar_definition]) ).
thf(f1454,plain,
( ( ( rel_s4 @ sK3 @ sK38 )
= $true )
| ~ spl50_75 ),
inference(avatar_component_clause,[],[f1452]) ).
thf(f1462,definition,
( spl50_77
<=> ( ( p @ sK38 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_77])],[avatar_definition]) ).
thf(f1464,plain,
( ( ( p @ sK38 )
= $false )
| ~ spl50_77 ),
inference(avatar_component_clause,[],[f1462]) ).
thf(f1468,definition,
( spl50_78
<=> ( $true
= ( rel_s4 @ sK3 @ sK40 ) ) ),
introduced(definition,[new_symbols(definition,[spl50_78])],[avatar_definition]) ).
thf(f1470,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK40 ) )
| ~ spl50_78 ),
inference(avatar_component_clause,[],[f1468]) ).
thf(f1471,plain,
( spl50_9
| spl50_78
| spl50_10
| spl50_75 ),
inference(avatar_split_clause,[],[f790,f1452,f1076,f1468,f1073]) ).
thf(f1473,definition,
( spl50_79
<=> ( ( p @ sK40 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_79])],[avatar_definition]) ).
thf(f1475,plain,
( ( ( p @ sK40 )
= $false )
| ~ spl50_79 ),
inference(avatar_component_clause,[],[f1473]) ).
thf(f1476,plain,
( spl50_79
| spl50_75
| spl50_10
| spl50_9 ),
inference(avatar_split_clause,[],[f791,f1073,f1076,f1452,f1473]) ).
thf(f1477,plain,
( spl50_77
| spl50_78
| spl50_10
| spl50_9 ),
inference(avatar_split_clause,[],[f798,f1073,f1076,f1468,f1462]) ).
thf(f1478,plain,
( spl50_10
| spl50_77
| spl50_79
| spl50_9 ),
inference(avatar_split_clause,[],[f796,f1073,f1473,f1462,f1076]) ).
thf(f1500,definition,
( spl50_84
<=> ( ( rel_s4 @ sK3 @ sK43 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl50_84])],[avatar_definition]) ).
thf(f1502,plain,
( ( ( rel_s4 @ sK3 @ sK43 )
= $true )
| ~ spl50_84 ),
inference(avatar_component_clause,[],[f1500]) ).
thf(f1503,plain,
( spl50_9
| spl50_84
| spl50_11 ),
inference(avatar_split_clause,[],[f839,f1080,f1500,f1073]) ).
thf(f1505,definition,
( spl50_85
<=> ( ( p @ sK43 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_85])],[avatar_definition]) ).
thf(f1507,plain,
( ( ( p @ sK43 )
= $false )
| ~ spl50_85 ),
inference(avatar_component_clause,[],[f1505]) ).
thf(f1508,plain,
( spl50_85
| spl50_11
| spl50_9 ),
inference(avatar_split_clause,[],[f843,f1073,f1080,f1505]) ).
thf(f1510,definition,
( spl50_86
<=> ! [X2: $i] :
( ( ( r @ X2 )
= $true )
| ( ( rel_s4 @ sK3 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl50_86])],[avatar_definition]) ).
thf(f1511,plain,
( ! [X2: $i] :
( ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( ( r @ X2 )
= $true ) )
| ~ spl50_86 ),
inference(avatar_component_clause,[],[f1510]) ).
thf(f1513,definition,
( spl50_87
<=> ! [X1: $i] :
( ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl50_87])],[avatar_definition]) ).
thf(f1514,plain,
( ! [X1: $i] :
( ( ( rel_s4 @ sK3 @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) )
| ~ spl50_87 ),
inference(avatar_component_clause,[],[f1513]) ).
thf(f1517,definition,
( spl50_88
<=> ! [X2: $i] :
( ( $true
= ( q @ X2 ) )
| ( ( rel_s4 @ sK3 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl50_88])],[avatar_definition]) ).
thf(f1518,plain,
( ! [X2: $i] :
( ( ( rel_s4 @ sK3 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) ) )
| ~ spl50_88 ),
inference(avatar_component_clause,[],[f1517]) ).
thf(f1521,definition,
( spl50_89
<=> ( $true
= ( rel_s4 @ sK2 @ sK45 ) ) ),
introduced(definition,[new_symbols(definition,[spl50_89])],[avatar_definition]) ).
thf(f1523,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK45 ) )
| ~ spl50_89 ),
inference(avatar_component_clause,[],[f1521]) ).
thf(f1525,definition,
( spl50_90
<=> ( ( rel_s4 @ sK2 @ sK44 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl50_90])],[avatar_definition]) ).
thf(f1527,plain,
( ( ( rel_s4 @ sK2 @ sK44 )
= $true )
| ~ spl50_90 ),
inference(avatar_component_clause,[],[f1525]) ).
thf(f1528,plain,
( spl50_86
| spl50_89
| spl50_90
| spl50_87 ),
inference(avatar_split_clause,[],[f893,f1513,f1525,f1521,f1510]) ).
thf(f1530,definition,
( spl50_91
<=> ( ( r @ sK44 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_91])],[avatar_definition]) ).
thf(f1532,plain,
( ( ( r @ sK44 )
= $false )
| ~ spl50_91 ),
inference(avatar_component_clause,[],[f1530]) ).
thf(f1533,plain,
( spl50_87
| spl50_86
| spl50_89
| spl50_91 ),
inference(avatar_split_clause,[],[f897,f1530,f1521,f1510,f1513]) ).
thf(f1535,definition,
( spl50_92
<=> ( ( q @ sK45 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_92])],[avatar_definition]) ).
thf(f1537,plain,
( ( ( q @ sK45 )
= $false )
| ~ spl50_92 ),
inference(avatar_component_clause,[],[f1535]) ).
thf(f1538,plain,
( spl50_92
| spl50_90
| spl50_87
| spl50_86 ),
inference(avatar_split_clause,[],[f903,f1510,f1513,f1525,f1535]) ).
thf(f1539,plain,
( spl50_86
| spl50_92
| spl50_91
| spl50_87 ),
inference(avatar_split_clause,[],[f905,f1513,f1530,f1535,f1510]) ).
thf(f1541,definition,
( spl50_93
<=> ( ( rel_s4 @ sK2 @ sK46 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl50_93])],[avatar_definition]) ).
thf(f1543,plain,
( ( ( rel_s4 @ sK2 @ sK46 )
= $true )
| ~ spl50_93 ),
inference(avatar_component_clause,[],[f1541]) ).
thf(f1544,plain,
( spl50_87
| spl50_86
| spl50_93 ),
inference(avatar_split_clause,[],[f914,f1541,f1510,f1513]) ).
thf(f1546,definition,
( spl50_94
<=> ( ( p @ sK46 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_94])],[avatar_definition]) ).
thf(f1548,plain,
( ( ( p @ sK46 )
= $false )
| ~ spl50_94 ),
inference(avatar_component_clause,[],[f1546]) ).
thf(f1549,plain,
( spl50_87
| spl50_86
| spl50_94 ),
inference(avatar_split_clause,[],[f917,f1546,f1510,f1513]) ).
thf(f1550,plain,
( spl50_9
| spl50_10
| spl50_86
| spl50_87 ),
inference(avatar_split_clause,[],[f937,f1513,f1510,f1076,f1073]) ).
thf(f1551,plain,
( spl50_9
| spl50_86
| spl50_11
| spl50_87 ),
inference(avatar_split_clause,[],[f950,f1513,f1080,f1510,f1073]) ).
thf(f1553,definition,
( spl50_95
<=> ( $true
= ( rel_s4 @ sK2 @ sK48 ) ) ),
introduced(definition,[new_symbols(definition,[spl50_95])],[avatar_definition]) ).
thf(f1555,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK48 ) )
| ~ spl50_95 ),
inference(avatar_component_clause,[],[f1553]) ).
thf(f1557,definition,
( spl50_96
<=> ( ( rel_s4 @ sK2 @ sK47 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl50_96])],[avatar_definition]) ).
thf(f1559,plain,
( ( ( rel_s4 @ sK2 @ sK47 )
= $true )
| ~ spl50_96 ),
inference(avatar_component_clause,[],[f1557]) ).
thf(f1560,plain,
( spl50_87
| spl50_95
| spl50_96
| spl50_88 ),
inference(avatar_split_clause,[],[f974,f1517,f1557,f1553,f1513]) ).
thf(f1562,definition,
( spl50_97
<=> ( ( q @ sK48 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_97])],[avatar_definition]) ).
thf(f1564,plain,
( ( ( q @ sK48 )
= $false )
| ~ spl50_97 ),
inference(avatar_component_clause,[],[f1562]) ).
thf(f1565,plain,
( spl50_88
| spl50_96
| spl50_97
| spl50_87 ),
inference(avatar_split_clause,[],[f975,f1513,f1562,f1557,f1517]) ).
thf(f1567,definition,
( spl50_98
<=> ( ( r @ sK47 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_98])],[avatar_definition]) ).
thf(f1569,plain,
( ( ( r @ sK47 )
= $false )
| ~ spl50_98 ),
inference(avatar_component_clause,[],[f1567]) ).
thf(f1570,plain,
( spl50_98
| spl50_87
| spl50_95
| spl50_88 ),
inference(avatar_split_clause,[],[f982,f1517,f1553,f1513,f1567]) ).
thf(f1571,plain,
( spl50_98
| spl50_97
| spl50_87
| spl50_88 ),
inference(avatar_split_clause,[],[f986,f1517,f1513,f1562,f1567]) ).
thf(f1573,definition,
( spl50_99
<=> ( $true
= ( rel_s4 @ sK2 @ sK49 ) ) ),
introduced(definition,[new_symbols(definition,[spl50_99])],[avatar_definition]) ).
thf(f1575,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK49 ) )
| ~ spl50_99 ),
inference(avatar_component_clause,[],[f1573]) ).
thf(f1576,plain,
( spl50_88
| spl50_99
| spl50_87 ),
inference(avatar_split_clause,[],[f995,f1513,f1573,f1517]) ).
thf(f1578,definition,
( spl50_100
<=> ( ( p @ sK49 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl50_100])],[avatar_definition]) ).
thf(f1580,plain,
( ( ( p @ sK49 )
= $false )
| ~ spl50_100 ),
inference(avatar_component_clause,[],[f1578]) ).
thf(f1581,plain,
( spl50_88
| spl50_100
| spl50_87 ),
inference(avatar_split_clause,[],[f999,f1513,f1578,f1517]) ).
thf(f1582,plain,
( spl50_87
| spl50_9
| spl50_88
| spl50_10 ),
inference(avatar_split_clause,[],[f1019,f1076,f1517,f1073,f1513]) ).
thf(f1583,plain,
( spl50_11
| spl50_9
| spl50_88
| spl50_87 ),
inference(avatar_split_clause,[],[f1032,f1513,f1517,f1073,f1080]) ).
thf(f1622,plain,
( ( ( p @ sK29 )
= $true )
| ( $true = $false )
| ~ spl50_57
| ~ spl50_87 ),
inference(constrained_superposition,[],[f1514,f1354]) ).
thf(f1625,plain,
( ( ( p @ sK38 )
= $true )
| ( $true = $false )
| ~ spl50_75
| ~ spl50_87 ),
inference(constrained_superposition,[],[f1514,f1454]) ).
thf(f1637,plain,
( ( ( p @ sK29 )
= $true )
| ~ spl50_57
| ~ spl50_87 ),
inference(trivial_inequality_removal,[],[f1622]) ).
thf(f1638,plain,
( ( ( p @ sK38 )
= $true )
| ~ spl50_75
| ~ spl50_87 ),
inference(trivial_inequality_removal,[],[f1625]) ).
thf(f1653,plain,
( ( $true = $false )
| ~ spl50_57
| ~ spl50_60
| ~ spl50_87 ),
inference(forward_demodulation,[],[f1637,f1368]) ).
thf(f1654,plain,
( $false
| ~ spl50_57
| ~ spl50_60
| ~ spl50_87 ),
inference(trivial_inequality_removal,[],[f1653]) ).
thf(f1655,plain,
( ~ spl50_57
| ~ spl50_60
| ~ spl50_87 ),
inference(avatar_contradiction_clause,[],[f1654]) ).
thf(f1656,plain,
( ( $true = $false )
| ~ spl50_75
| ~ spl50_77
| ~ spl50_87 ),
inference(forward_demodulation,[],[f1638,f1464]) ).
thf(f1657,plain,
( $false
| ~ spl50_75
| ~ spl50_77
| ~ spl50_87 ),
inference(trivial_inequality_removal,[],[f1656]) ).
thf(f1658,plain,
( ~ spl50_75
| ~ spl50_77
| ~ spl50_87 ),
inference(avatar_contradiction_clause,[],[f1657]) ).
thf(f1673,plain,
( ( $true = $false )
| ( $true
= ( p @ sK40 ) )
| ~ spl50_78
| ~ spl50_87 ),
inference(constrained_superposition,[],[f1470,f1514]) ).
thf(f1676,plain,
( ( $true
= ( p @ sK40 ) )
| ~ spl50_78
| ~ spl50_87 ),
inference(trivial_inequality_removal,[],[f1673]) ).
thf(f1680,plain,
( ( $true = $false )
| ~ spl50_78
| ~ spl50_79
| ~ spl50_87 ),
inference(forward_demodulation,[],[f1676,f1475]) ).
thf(f1681,plain,
( $false
| ~ spl50_78
| ~ spl50_79
| ~ spl50_87 ),
inference(trivial_inequality_removal,[],[f1680]) ).
thf(f1682,plain,
( ~ spl50_78
| ~ spl50_79
| ~ spl50_87 ),
inference(avatar_contradiction_clause,[],[f1681]) ).
thf(f1704,plain,
( ( $true
= ( r @ sK30 ) )
| ( $true = $false )
| ~ spl50_10
| ~ spl50_58 ),
inference(constrained_superposition,[],[f1358,f1077]) ).
thf(f1711,plain,
( ( $true
= ( r @ sK30 ) )
| ~ spl50_10
| ~ spl50_58 ),
inference(trivial_inequality_removal,[],[f1704]) ).
thf(f1717,plain,
( ( $true = $false )
| ~ spl50_10
| ~ spl50_58
| ~ spl50_61 ),
inference(forward_demodulation,[],[f1711,f1374]) ).
thf(f1718,plain,
( $false
| ~ spl50_10
| ~ spl50_58
| ~ spl50_61 ),
inference(trivial_inequality_removal,[],[f1717]) ).
thf(f1719,plain,
( ~ spl50_10
| ~ spl50_58
| ~ spl50_61 ),
inference(avatar_contradiction_clause,[],[f1718]) ).
thf(f1723,plain,
( ( $true = $false )
| ( $true
= ( q @ sK31 ) )
| ~ spl50_11
| ~ spl50_56 ),
inference(constrained_superposition,[],[f1081,f1350]) ).
thf(f1727,plain,
( ( $true
= ( q @ sK31 ) )
| ~ spl50_11
| ~ spl50_56 ),
inference(trivial_inequality_removal,[],[f1723]) ).
thf(f1731,plain,
( ( $true = $false )
| ~ spl50_11
| ~ spl50_56
| ~ spl50_59 ),
inference(forward_demodulation,[],[f1727,f1363]) ).
thf(f1732,plain,
( $false
| ~ spl50_11
| ~ spl50_56
| ~ spl50_59 ),
inference(trivial_inequality_removal,[],[f1731]) ).
thf(f1733,plain,
( ~ spl50_11
| ~ spl50_56
| ~ spl50_59 ),
inference(avatar_contradiction_clause,[],[f1732]) ).
thf(f1734,plain,
( ( $true = $false )
| ( $true
= ( p @ sK43 ) )
| ~ spl50_84
| ~ spl50_87 ),
inference(constrained_superposition,[],[f1502,f1514]) ).
thf(f1737,plain,
( ( $true
= ( p @ sK43 ) )
| ~ spl50_84
| ~ spl50_87 ),
inference(trivial_inequality_removal,[],[f1734]) ).
thf(f1741,plain,
( ( $true = $false )
| ~ spl50_84
| ~ spl50_85
| ~ spl50_87 ),
inference(forward_demodulation,[],[f1737,f1507]) ).
thf(f1742,plain,
( $false
| ~ spl50_84
| ~ spl50_85
| ~ spl50_87 ),
inference(trivial_inequality_removal,[],[f1741]) ).
thf(f1743,plain,
( ~ spl50_84
| ~ spl50_85
| ~ spl50_87 ),
inference(avatar_contradiction_clause,[],[f1742]) ).
thf(f1776,plain,
( ( $true = $false )
| ( $true
= ( p @ sK32 ) )
| ~ spl50_9
| ~ spl50_62 ),
inference(constrained_superposition,[],[f1074,f1382]) ).
thf(f1785,plain,
( ( $true
= ( p @ sK32 ) )
| ~ spl50_9
| ~ spl50_62 ),
inference(trivial_inequality_removal,[],[f1776]) ).
thf(f1792,plain,
( ( $true = $false )
| ~ spl50_9
| ~ spl50_62
| ~ spl50_63 ),
inference(forward_demodulation,[],[f1785,f1387]) ).
thf(f1793,plain,
( $false
| ~ spl50_9
| ~ spl50_62
| ~ spl50_63 ),
inference(trivial_inequality_removal,[],[f1792]) ).
thf(f1794,plain,
( ~ spl50_9
| ~ spl50_62
| ~ spl50_63 ),
inference(avatar_contradiction_clause,[],[f1793]) ).
thf(f1795,plain,
( ( $true
= ( p @ sK49 ) )
| ( $true = $false )
| ~ spl50_9
| ~ spl50_99 ),
inference(constrained_superposition,[],[f1575,f1074]) ).
thf(f1802,plain,
( ( $true
= ( p @ sK49 ) )
| ~ spl50_9
| ~ spl50_99 ),
inference(trivial_inequality_removal,[],[f1795]) ).
thf(f1806,plain,
( ( $true = $false )
| ~ spl50_9
| ~ spl50_99
| ~ spl50_100 ),
inference(forward_demodulation,[],[f1802,f1580]) ).
thf(f1807,plain,
( $false
| ~ spl50_9
| ~ spl50_99
| ~ spl50_100 ),
inference(trivial_inequality_removal,[],[f1806]) ).
thf(f1808,plain,
( ~ spl50_9
| ~ spl50_99
| ~ spl50_100 ),
inference(avatar_contradiction_clause,[],[f1807]) ).
thf(f1828,plain,
( ( $true = $false )
| ( $true
= ( r @ sK14 ) )
| ~ spl50_28
| ~ spl50_86 ),
inference(constrained_superposition,[],[f1166,f1511]) ).
thf(f1832,plain,
( ( $true = $false )
| ( ( r @ sK34 )
= $true )
| ~ spl50_65
| ~ spl50_86 ),
inference(constrained_superposition,[],[f1398,f1511]) ).
thf(f1846,plain,
( ( $true
= ( r @ sK14 ) )
| ~ spl50_28
| ~ spl50_86 ),
inference(trivial_inequality_removal,[],[f1828]) ).
thf(f1853,plain,
( ( ( r @ sK34 )
= $true )
| ~ spl50_65
| ~ spl50_86 ),
inference(trivial_inequality_removal,[],[f1832]) ).
thf(f1857,plain,
( ( $true = $false )
| ~ spl50_28
| ~ spl50_30
| ~ spl50_86 ),
inference(forward_demodulation,[],[f1846,f1175]) ).
thf(f1858,plain,
( $false
| ~ spl50_28
| ~ spl50_30
| ~ spl50_86 ),
inference(trivial_inequality_removal,[],[f1857]) ).
thf(f1859,plain,
( ~ spl50_28
| ~ spl50_30
| ~ spl50_86 ),
inference(avatar_contradiction_clause,[],[f1858]) ).
thf(f1869,plain,
( ( $true = $false )
| ~ spl50_65
| ~ spl50_66
| ~ spl50_86 ),
inference(forward_demodulation,[],[f1853,f1403]) ).
thf(f1870,plain,
( $false
| ~ spl50_65
| ~ spl50_66
| ~ spl50_86 ),
inference(trivial_inequality_removal,[],[f1869]) ).
thf(f1871,plain,
( ~ spl50_65
| ~ spl50_66
| ~ spl50_86 ),
inference(avatar_contradiction_clause,[],[f1870]) ).
thf(f1918,plain,
( ( $true = $false )
| ( $true
= ( q @ sK22 ) )
| ~ spl50_41
| ~ spl50_88 ),
inference(constrained_superposition,[],[f1250,f1518]) ).
thf(f1925,plain,
( ( $true
= ( q @ sK22 ) )
| ~ spl50_41
| ~ spl50_88 ),
inference(trivial_inequality_removal,[],[f1918]) ).
thf(f1929,plain,
( ( $true = $false )
| ~ spl50_41
| ~ spl50_43
| ~ spl50_88 ),
inference(forward_demodulation,[],[f1925,f1262]) ).
thf(f1930,plain,
( $false
| ~ spl50_41
| ~ spl50_43
| ~ spl50_88 ),
inference(trivial_inequality_removal,[],[f1929]) ).
thf(f1931,plain,
( ~ spl50_41
| ~ spl50_43
| ~ spl50_88 ),
inference(avatar_contradiction_clause,[],[f1930]) ).
thf(f1934,plain,
( ( $true = $false )
| ( ( p @ sK21 )
= $true )
| ~ spl50_9
| ~ spl50_40 ),
inference(constrained_superposition,[],[f1074,f1246]) ).
thf(f1939,plain,
( ( ( p @ sK21 )
= $true )
| ~ spl50_9
| ~ spl50_40 ),
inference(trivial_inequality_removal,[],[f1934]) ).
thf(f1943,plain,
( ( $true = $false )
| ~ spl50_9
| ~ spl50_40
| ~ spl50_42 ),
inference(forward_demodulation,[],[f1939,f1255]) ).
thf(f1944,plain,
( $false
| ~ spl50_9
| ~ spl50_40
| ~ spl50_42 ),
inference(trivial_inequality_removal,[],[f1943]) ).
thf(f1945,plain,
( ~ spl50_9
| ~ spl50_40
| ~ spl50_42 ),
inference(avatar_contradiction_clause,[],[f1944]) ).
thf(f1949,plain,
( ( ( p @ sK46 )
= $true )
| ( $true = $false )
| ~ spl50_9
| ~ spl50_93 ),
inference(constrained_superposition,[],[f1074,f1543]) ).
thf(f1952,plain,
( ( ( p @ sK46 )
= $true )
| ~ spl50_9
| ~ spl50_93 ),
inference(trivial_inequality_removal,[],[f1949]) ).
thf(f1958,plain,
( ( $true = $false )
| ~ spl50_9
| ~ spl50_93
| ~ spl50_94 ),
inference(forward_demodulation,[],[f1952,f1548]) ).
thf(f1959,plain,
( $false
| ~ spl50_9
| ~ spl50_93
| ~ spl50_94 ),
inference(trivial_inequality_removal,[],[f1958]) ).
thf(f1960,plain,
( ~ spl50_9
| ~ spl50_93
| ~ spl50_94 ),
inference(avatar_contradiction_clause,[],[f1959]) ).
thf(f1978,plain,
( ( $true
= ( q @ sK33 ) )
| ( $true = $false )
| ~ spl50_64
| ~ spl50_88 ),
inference(constrained_superposition,[],[f1394,f1518]) ).
thf(f1981,plain,
( ( $true
= ( q @ sK33 ) )
| ~ spl50_64
| ~ spl50_88 ),
inference(trivial_inequality_removal,[],[f1978]) ).
thf(f1985,plain,
( ( $true = $false )
| ~ spl50_64
| ~ spl50_67
| ~ spl50_88 ),
inference(forward_demodulation,[],[f1981,f1408]) ).
thf(f1986,plain,
( $false
| ~ spl50_64
| ~ spl50_67
| ~ spl50_88 ),
inference(trivial_inequality_removal,[],[f1985]) ).
thf(f1987,plain,
( ~ spl50_64
| ~ spl50_67
| ~ spl50_88 ),
inference(avatar_contradiction_clause,[],[f1986]) ).
thf(f1995,plain,
( ( $true = $false )
| ( $true
= ( q @ sK45 ) )
| ~ spl50_11
| ~ spl50_89 ),
inference(constrained_superposition,[],[f1081,f1523]) ).
thf(f2004,plain,
( ( $true = $false )
| ( $true
= ( q @ sK48 ) )
| ~ spl50_11
| ~ spl50_95 ),
inference(constrained_superposition,[],[f1555,f1081]) ).
thf(f2009,plain,
( ( $true
= ( q @ sK48 ) )
| ~ spl50_11
| ~ spl50_95 ),
inference(trivial_inequality_removal,[],[f2004]) ).
thf(f2015,plain,
( ( $true
= ( q @ sK45 ) )
| ~ spl50_11
| ~ spl50_89 ),
inference(trivial_inequality_removal,[],[f1995]) ).
thf(f2021,plain,
( ( $true = $false )
| ~ spl50_11
| ~ spl50_95
| ~ spl50_97 ),
inference(forward_demodulation,[],[f2009,f1564]) ).
thf(f2022,plain,
( $false
| ~ spl50_11
| ~ spl50_95
| ~ spl50_97 ),
inference(trivial_inequality_removal,[],[f2021]) ).
thf(f2023,plain,
( ~ spl50_11
| ~ spl50_95
| ~ spl50_97 ),
inference(avatar_contradiction_clause,[],[f2022]) ).
thf(f2027,plain,
( ( $true = $false )
| ~ spl50_11
| ~ spl50_89
| ~ spl50_92 ),
inference(forward_demodulation,[],[f2015,f1537]) ).
thf(f2028,plain,
( $false
| ~ spl50_11
| ~ spl50_89
| ~ spl50_92 ),
inference(trivial_inequality_removal,[],[f2027]) ).
thf(f2029,plain,
( ~ spl50_11
| ~ spl50_89
| ~ spl50_92 ),
inference(avatar_contradiction_clause,[],[f2028]) ).
thf(f2059,plain,
( ( ( q @ sK15 )
= $true )
| ( $true = $false )
| ~ spl50_29
| ~ spl50_88 ),
inference(constrained_superposition,[],[f1518,f1170]) ).
thf(f2061,plain,
( ( ( q @ sK15 )
= $true )
| ~ spl50_29
| ~ spl50_88 ),
inference(trivial_inequality_removal,[],[f2059]) ).
thf(f2065,plain,
( ( $true = $false )
| ~ spl50_29
| ~ spl50_33
| ~ spl50_88 ),
inference(forward_demodulation,[],[f2061,f1194]) ).
thf(f2066,plain,
( $false
| ~ spl50_29
| ~ spl50_33
| ~ spl50_88 ),
inference(trivial_inequality_removal,[],[f2065]) ).
thf(f2067,plain,
( ~ spl50_29
| ~ spl50_33
| ~ spl50_88 ),
inference(avatar_contradiction_clause,[],[f2066]) ).
thf(f2072,plain,
( ( $true = $false )
| ( $true
= ( r @ sK16 ) )
| ~ spl50_10
| ~ spl50_27 ),
inference(constrained_superposition,[],[f1077,f1162]) ).
thf(f2076,plain,
( ( $true
= ( r @ sK16 ) )
| ~ spl50_10
| ~ spl50_27 ),
inference(trivial_inequality_removal,[],[f2072]) ).
thf(f2080,plain,
( ( $true = $false )
| ~ spl50_10
| ~ spl50_27
| ~ spl50_31 ),
inference(forward_demodulation,[],[f2076,f1180]) ).
thf(f2081,plain,
( $false
| ~ spl50_10
| ~ spl50_27
| ~ spl50_31 ),
inference(trivial_inequality_removal,[],[f2080]) ).
thf(f2082,plain,
( ~ spl50_10
| ~ spl50_27
| ~ spl50_31 ),
inference(avatar_contradiction_clause,[],[f2081]) ).
thf(f2086,plain,
( ( $true = $false )
| ( $true
= ( q @ sK17 ) )
| ~ spl50_11
| ~ spl50_26 ),
inference(constrained_superposition,[],[f1081,f1158]) ).
thf(f2090,plain,
( ( $true
= ( q @ sK17 ) )
| ~ spl50_11
| ~ spl50_26 ),
inference(trivial_inequality_removal,[],[f2086]) ).
thf(f2095,plain,
( ( $true = $false )
| ~ spl50_11
| ~ spl50_26
| ~ spl50_32 ),
inference(forward_demodulation,[],[f2090,f1186]) ).
thf(f2096,plain,
( $false
| ~ spl50_11
| ~ spl50_26
| ~ spl50_32 ),
inference(trivial_inequality_removal,[],[f2095]) ).
thf(f2097,plain,
( ~ spl50_11
| ~ spl50_26
| ~ spl50_32 ),
inference(avatar_contradiction_clause,[],[f2096]) ).
thf(f2112,plain,
( ( $true
= ( r @ sK47 ) )
| ( $true = $false )
| ~ spl50_10
| ~ spl50_96 ),
inference(constrained_superposition,[],[f1077,f1559]) ).
thf(f2116,plain,
( ( $true
= ( r @ sK47 ) )
| ~ spl50_10
| ~ spl50_96 ),
inference(trivial_inequality_removal,[],[f2112]) ).
thf(f2120,plain,
( ( $true = $false )
| ~ spl50_10
| ~ spl50_96
| ~ spl50_98 ),
inference(forward_demodulation,[],[f2116,f1569]) ).
thf(f2121,plain,
( $false
| ~ spl50_10
| ~ spl50_96
| ~ spl50_98 ),
inference(trivial_inequality_removal,[],[f2120]) ).
thf(f2122,plain,
( ~ spl50_10
| ~ spl50_96
| ~ spl50_98 ),
inference(avatar_contradiction_clause,[],[f2121]) ).
thf(f2188,plain,
( ( ( r @ sK44 )
= $true )
| ( $true = $false )
| ~ spl50_10
| ~ spl50_90 ),
inference(constrained_superposition,[],[f1077,f1527]) ).
thf(f2192,plain,
( ( ( r @ sK44 )
= $true )
| ~ spl50_10
| ~ spl50_90 ),
inference(trivial_inequality_removal,[],[f2188]) ).
thf(f2196,plain,
( ( $true = $false )
| ~ spl50_10
| ~ spl50_90
| ~ spl50_91 ),
inference(forward_demodulation,[],[f2192,f1532]) ).
thf(f2197,plain,
( $false
| ~ spl50_10
| ~ spl50_90
| ~ spl50_91 ),
inference(trivial_inequality_removal,[],[f2196]) ).
thf(f2198,plain,
( ~ spl50_10
| ~ spl50_90
| ~ spl50_91 ),
inference(avatar_contradiction_clause,[],[f2197]) ).
cnf(s26,plain,
( spl50_26
| spl50_27
| spl50_28
| spl50_29 ),
inference(sat_conversion,[],[f1171]) ).
cnf(s27,plain,
( spl50_26
| spl50_27
| spl50_29
| spl50_30 ),
inference(sat_conversion,[],[f1176]) ).
cnf(s28,plain,
( spl50_26
| spl50_28
| spl50_29
| spl50_31 ),
inference(sat_conversion,[],[f1181]) ).
cnf(s29,plain,
( spl50_26
| spl50_29
| spl50_30
| spl50_31 ),
inference(sat_conversion,[],[f1182]) ).
cnf(s30,plain,
( spl50_27
| spl50_28
| spl50_29
| spl50_32 ),
inference(sat_conversion,[],[f1187]) ).
cnf(s31,plain,
( spl50_27
| spl50_29
| spl50_30
| spl50_32 ),
inference(sat_conversion,[],[f1188]) ).
cnf(s32,plain,
( spl50_28
| spl50_29
| spl50_31
| spl50_32 ),
inference(sat_conversion,[],[f1189]) ).
cnf(s33,plain,
( spl50_29
| spl50_30
| spl50_31
| spl50_32 ),
inference(sat_conversion,[],[f1190]) ).
cnf(s34,plain,
( spl50_26
| spl50_27
| spl50_28
| spl50_33 ),
inference(sat_conversion,[],[f1195]) ).
cnf(s35,plain,
( spl50_27
| spl50_28
| spl50_32
| spl50_33 ),
inference(sat_conversion,[],[f1196]) ).
cnf(s36,plain,
( spl50_26
| spl50_27
| spl50_30
| spl50_33 ),
inference(sat_conversion,[],[f1197]) ).
cnf(s37,plain,
( spl50_27
| spl50_30
| spl50_32
| spl50_33 ),
inference(sat_conversion,[],[f1198]) ).
cnf(s38,plain,
( spl50_26
| spl50_28
| spl50_31
| spl50_33 ),
inference(sat_conversion,[],[f1199]) ).
cnf(s39,plain,
( spl50_26
| spl50_30
| spl50_31
| spl50_33 ),
inference(sat_conversion,[],[f1200]) ).
cnf(s40,plain,
( spl50_28
| spl50_31
| spl50_32
| spl50_33 ),
inference(sat_conversion,[],[f1201]) ).
cnf(s41,plain,
( spl50_30
| spl50_31
| spl50_32
| spl50_33 ),
inference(sat_conversion,[],[f1202]) ).
cnf(s58,plain,
( spl50_28
| spl50_40
| spl50_41 ),
inference(sat_conversion,[],[f1251]) ).
cnf(s59,plain,
( spl50_28
| spl50_41
| spl50_42 ),
inference(sat_conversion,[],[f1256]) ).
cnf(s60,plain,
( spl50_30
| spl50_40
| spl50_41 ),
inference(sat_conversion,[],[f1257]) ).
cnf(s61,plain,
( spl50_30
| spl50_41
| spl50_42 ),
inference(sat_conversion,[],[f1258]) ).
cnf(s62,plain,
( spl50_28
| spl50_40
| spl50_43 ),
inference(sat_conversion,[],[f1263]) ).
cnf(s63,plain,
( spl50_28
| spl50_42
| spl50_43 ),
inference(sat_conversion,[],[f1264]) ).
cnf(s64,plain,
( spl50_30
| spl50_40
| spl50_43 ),
inference(sat_conversion,[],[f1265]) ).
cnf(s65,plain,
( spl50_30
| spl50_42
| spl50_43 ),
inference(sat_conversion,[],[f1266]) ).
cnf(s98,plain,
( spl50_56
| spl50_57
| spl50_58 ),
inference(sat_conversion,[],[f1359]) ).
cnf(s99,plain,
( spl50_57
| spl50_58
| spl50_59 ),
inference(sat_conversion,[],[f1364]) ).
cnf(s100,plain,
( spl50_56
| spl50_58
| spl50_60 ),
inference(sat_conversion,[],[f1369]) ).
cnf(s101,plain,
( spl50_58
| spl50_59
| spl50_60 ),
inference(sat_conversion,[],[f1370]) ).
cnf(s102,plain,
( spl50_56
| spl50_57
| spl50_61 ),
inference(sat_conversion,[],[f1375]) ).
cnf(s103,plain,
( spl50_56
| spl50_60
| spl50_61 ),
inference(sat_conversion,[],[f1376]) ).
cnf(s104,plain,
( spl50_57
| spl50_59
| spl50_61 ),
inference(sat_conversion,[],[f1377]) ).
cnf(s105,plain,
( spl50_59
| spl50_60
| spl50_61 ),
inference(sat_conversion,[],[f1378]) ).
cnf(s106,plain,
( spl50_57
| spl50_62 ),
inference(sat_conversion,[],[f1383]) ).
cnf(s107,plain,
( spl50_57
| spl50_63 ),
inference(sat_conversion,[],[f1388]) ).
cnf(s108,plain,
( spl50_60
| spl50_62 ),
inference(sat_conversion,[],[f1389]) ).
cnf(s109,plain,
( spl50_60
| spl50_63 ),
inference(sat_conversion,[],[f1390]) ).
cnf(s110,plain,
( spl50_9
| spl50_10
| spl50_64
| spl50_65 ),
inference(sat_conversion,[],[f1399]) ).
cnf(s111,plain,
( spl50_9
| spl50_10
| spl50_64
| spl50_66 ),
inference(sat_conversion,[],[f1404]) ).
cnf(s112,plain,
( spl50_9
| spl50_10
| spl50_65
| spl50_67 ),
inference(sat_conversion,[],[f1409]) ).
cnf(s113,plain,
( spl50_9
| spl50_10
| spl50_66
| spl50_67 ),
inference(sat_conversion,[],[f1410]) ).
cnf(s114,plain,
( spl50_9
| spl50_11
| spl50_64
| spl50_65 ),
inference(sat_conversion,[],[f1411]) ).
cnf(s115,plain,
( spl50_9
| spl50_11
| spl50_65
| spl50_67 ),
inference(sat_conversion,[],[f1412]) ).
cnf(s116,plain,
( spl50_9
| spl50_11
| spl50_64
| spl50_66 ),
inference(sat_conversion,[],[f1413]) ).
cnf(s117,plain,
( spl50_9
| spl50_11
| spl50_66
| spl50_67 ),
inference(sat_conversion,[],[f1414]) ).
cnf(s130,plain,
( spl50_9
| spl50_10
| spl50_75
| spl50_78 ),
inference(sat_conversion,[],[f1471]) ).
cnf(s131,plain,
( spl50_9
| spl50_10
| spl50_75
| spl50_79 ),
inference(sat_conversion,[],[f1476]) ).
cnf(s132,plain,
( spl50_9
| spl50_10
| spl50_77
| spl50_78 ),
inference(sat_conversion,[],[f1477]) ).
cnf(s133,plain,
( spl50_9
| spl50_10
| spl50_77
| spl50_79 ),
inference(sat_conversion,[],[f1478]) ).
cnf(s138,plain,
( spl50_9
| spl50_11
| spl50_84 ),
inference(sat_conversion,[],[f1503]) ).
cnf(s139,plain,
( spl50_9
| spl50_11
| spl50_85 ),
inference(sat_conversion,[],[f1508]) ).
cnf(s142,plain,
( spl50_86
| spl50_87
| spl50_89
| spl50_90 ),
inference(sat_conversion,[],[f1528]) ).
cnf(s143,plain,
( spl50_86
| spl50_87
| spl50_89
| spl50_91 ),
inference(sat_conversion,[],[f1533]) ).
cnf(s144,plain,
( spl50_86
| spl50_87
| spl50_90
| spl50_92 ),
inference(sat_conversion,[],[f1538]) ).
cnf(s145,plain,
( spl50_86
| spl50_87
| spl50_91
| spl50_92 ),
inference(sat_conversion,[],[f1539]) ).
cnf(s146,plain,
( spl50_86
| spl50_87
| spl50_93 ),
inference(sat_conversion,[],[f1544]) ).
cnf(s147,plain,
( spl50_86
| spl50_87
| spl50_94 ),
inference(sat_conversion,[],[f1549]) ).
cnf(s148,plain,
( spl50_9
| spl50_10
| spl50_86
| spl50_87 ),
inference(sat_conversion,[],[f1550]) ).
cnf(s149,plain,
( spl50_9
| spl50_11
| spl50_86
| spl50_87 ),
inference(sat_conversion,[],[f1551]) ).
cnf(s150,plain,
( spl50_87
| spl50_88
| spl50_95
| spl50_96 ),
inference(sat_conversion,[],[f1560]) ).
cnf(s151,plain,
( spl50_87
| spl50_88
| spl50_96
| spl50_97 ),
inference(sat_conversion,[],[f1565]) ).
cnf(s152,plain,
( spl50_87
| spl50_88
| spl50_95
| spl50_98 ),
inference(sat_conversion,[],[f1570]) ).
cnf(s153,plain,
( spl50_87
| spl50_88
| spl50_97
| spl50_98 ),
inference(sat_conversion,[],[f1571]) ).
cnf(s154,plain,
( spl50_87
| spl50_88
| spl50_99 ),
inference(sat_conversion,[],[f1576]) ).
cnf(s155,plain,
( spl50_87
| spl50_88
| spl50_100 ),
inference(sat_conversion,[],[f1581]) ).
cnf(s156,plain,
( spl50_9
| spl50_10
| spl50_87
| spl50_88 ),
inference(sat_conversion,[],[f1582]) ).
cnf(s157,plain,
( spl50_9
| spl50_11
| spl50_87
| spl50_88 ),
inference(sat_conversion,[],[f1583]) ).
cnf(s165,plain,
( ~ spl50_57
| ~ spl50_60
| ~ spl50_87 ),
inference(sat_conversion,[],[f1655]) ).
cnf(s166,plain,
( ~ spl50_75
| ~ spl50_77
| ~ spl50_87 ),
inference(sat_conversion,[],[f1658]) ).
cnf(s169,plain,
( ~ spl50_78
| ~ spl50_79
| ~ spl50_87 ),
inference(sat_conversion,[],[f1682]) ).
cnf(s171,plain,
( ~ spl50_10
| ~ spl50_58
| ~ spl50_61 ),
inference(sat_conversion,[],[f1719]) ).
cnf(s173,plain,
( ~ spl50_11
| ~ spl50_56
| ~ spl50_59 ),
inference(sat_conversion,[],[f1733]) ).
cnf(s175,plain,
( ~ spl50_84
| ~ spl50_85
| ~ spl50_87 ),
inference(sat_conversion,[],[f1743]) ).
cnf(s181,plain,
( ~ spl50_9
| ~ spl50_62
| ~ spl50_63 ),
inference(sat_conversion,[],[f1794]) ).
cnf(s183,plain,
( ~ spl50_9
| ~ spl50_99
| ~ spl50_100 ),
inference(sat_conversion,[],[f1808]) ).
cnf(s185,plain,
( ~ spl50_28
| ~ spl50_30
| ~ spl50_86 ),
inference(sat_conversion,[],[f1859]) ).
cnf(s189,plain,
( ~ spl50_65
| ~ spl50_66
| ~ spl50_86 ),
inference(sat_conversion,[],[f1871]) ).
cnf(s195,plain,
( ~ spl50_41
| ~ spl50_43
| ~ spl50_88 ),
inference(sat_conversion,[],[f1931]) ).
cnf(s197,plain,
( ~ spl50_9
| ~ spl50_40
| ~ spl50_42 ),
inference(sat_conversion,[],[f1945]) ).
cnf(s199,plain,
( ~ spl50_9
| ~ spl50_93
| ~ spl50_94 ),
inference(sat_conversion,[],[f1960]) ).
cnf(s201,plain,
( ~ spl50_64
| ~ spl50_67
| ~ spl50_88 ),
inference(sat_conversion,[],[f1987]) ).
cnf(s203,plain,
( ~ spl50_11
| ~ spl50_95
| ~ spl50_97 ),
inference(sat_conversion,[],[f2023]) ).
cnf(s205,plain,
( ~ spl50_11
| ~ spl50_89
| ~ spl50_92 ),
inference(sat_conversion,[],[f2029]) ).
cnf(s207,plain,
( ~ spl50_29
| ~ spl50_33
| ~ spl50_88 ),
inference(sat_conversion,[],[f2067]) ).
cnf(s209,plain,
( ~ spl50_10
| ~ spl50_27
| ~ spl50_31 ),
inference(sat_conversion,[],[f2082]) ).
cnf(s211,plain,
( ~ spl50_11
| ~ spl50_26
| ~ spl50_32 ),
inference(sat_conversion,[],[f2097]) ).
cnf(s213,plain,
( ~ spl50_10
| ~ spl50_96
| ~ spl50_98 ),
inference(sat_conversion,[],[f2122]) ).
cnf(s215,plain,
( ~ spl50_10
| ~ spl50_90
| ~ spl50_91 ),
inference(sat_conversion,[],[f2198]) ).
cnf(s217,plain,
( spl50_57
| spl50_56
| ~ spl50_10 ),
inference(rat,[],[s171,s98,s102]) ).
cnf(s218,plain,
( spl50_89
| spl50_86
| spl50_87
| ~ spl50_10 ),
inference(rat,[],[s215,s143,s142]) ).
cnf(s220,plain,
( spl50_95
| spl50_87
| spl50_88
| ~ spl50_10 ),
inference(rat,[],[s213,s150,s152]) ).
cnf(s222,plain,
( spl50_56
| ~ spl50_87
| ~ spl50_10 ),
inference(rat,[],[s171,s100,s103,s165,s217]) ).
cnf(s223,plain,
( spl50_60
| spl50_59
| ~ spl50_10 ),
inference(rat,[],[s171,s105,s101]) ).
cnf(s225,plain,
( spl50_33
| spl50_27
| spl50_26
| ~ spl50_86 ),
inference(rat,[],[s185,s34,s36]) ).
cnf(s227,plain,
( spl50_33
| spl50_31
| spl50_26
| ~ spl50_86 ),
inference(rat,[],[s185,s39,s38]) ).
cnf(s234,plain,
( spl50_87
| ~ spl50_10
| spl50_88 ),
inference(rat,[],[s213,s151,s153,s203,s157,s183,s220,s154,s155]) ).
cnf(s235,plain,
( spl50_11
| spl50_9
| ~ spl50_87 ),
inference(rat,[],[s175,s138,s139]) ).
cnf(s236,plain,
( spl50_59
| ~ spl50_87
| ~ spl50_10 ),
inference(rat,[],[s171,s104,s99,s165,s223]) ).
cnf(s237,plain,
( spl50_57
| ~ spl50_9 ),
inference(rat,[],[s181,s106,s107]) ).
cnf(s238,plain,
( spl50_11
| ~ spl50_87 ),
inference(rat,[],[s181,s108,s109,s165,s237,s235]) ).
cnf(s239,plain,
( ~ spl50_87
| ~ spl50_10 ),
inference(rat,[],[s238,s173,s236,s222]) ).
cnf(s240,plain,
( ~ spl50_10
| spl50_88 ),
inference(rat,[],[s239,s234]) ).
cnf(s241,plain,
( spl50_87
| spl50_10
| spl50_88 ),
inference(rat,[],[s183,s154,s155,s156]) ).
cnf(s242,plain,
( spl50_64
| ~ spl50_86
| spl50_9
| spl50_10 ),
inference(rat,[],[s189,s110,s111]) ).
cnf(s246,plain,
( spl50_75
| spl50_9
| spl50_88 ),
inference(rat,[],[s169,s130,s131,s241,s240]) ).
cnf(s247,plain,
( spl50_9
| spl50_88 ),
inference(rat,[],[s169,s132,s133,s166,s246,s241,s240]) ).
cnf(s248,plain,
( spl50_10
| spl50_88 ),
inference(rat,[],[s181,s108,s109,s165,s237,s247,s241]) ).
cnf(s249,plain,
spl50_88,
inference(rat,[],[s248,s240]) ).
cnf(s250,plain,
( spl50_27
| ~ spl50_11
| ~ spl50_86
| spl50_33 ),
inference(rat,[],[s185,s37,s35,s211,s225]) ).
cnf(s251,plain,
( ~ spl50_11
| ~ spl50_86
| ~ spl50_10
| spl50_33 ),
inference(rat,[],[s185,s41,s40,s211,s227,s209,s250]) ).
cnf(s252,plain,
( spl50_64
| spl50_11
| ~ spl50_86
| spl50_9 ),
inference(rat,[],[s189,s114,s116]) ).
cnf(s253,plain,
( spl50_11
| ~ spl50_86
| spl50_9 ),
inference(rat,[],[s189,s115,s117,s201,s252,s249]) ).
cnf(s254,plain,
( ~ spl50_86
| spl50_9
| ~ spl50_10
| spl50_33 ),
inference(rat,[],[s253,s251]) ).
cnf(s255,plain,
( spl50_9
| ~ spl50_10
| spl50_33 ),
inference(rat,[],[s215,s145,s144,s205,s149,s218,s254,s239]) ).
cnf(s256,plain,
( spl50_40
| spl50_30 ),
inference(rat,[],[s195,s60,s64,s249]) ).
cnf(s258,plain,
( spl50_40
| spl50_28 ),
inference(rat,[],[s195,s58,s62,s249]) ).
cnf(s259,plain,
( spl50_42
| spl50_28 ),
inference(rat,[],[s195,s59,s63,s249]) ).
cnf(s260,plain,
( spl50_28
| ~ spl50_9 ),
inference(rat,[],[s259,s197,s258]) ).
cnf(s261,plain,
( spl50_42
| spl50_30 ),
inference(rat,[],[s195,s61,s65,s249]) ).
cnf(s262,plain,
( spl50_30
| ~ spl50_9 ),
inference(rat,[],[s261,s197,s256]) ).
cnf(s263,plain,
( ~ spl50_10
| spl50_33 ),
inference(rat,[],[s199,s146,s147,s185,s262,s260,s255,s239]) ).
cnf(s264,plain,
( ~ spl50_86
| spl50_9
| spl50_10 ),
inference(rat,[],[s189,s112,s113,s201,s242,s249]) ).
cnf(s266,plain,
( spl50_75
| spl50_9
| spl50_10 ),
inference(rat,[],[s169,s130,s131,s148,s264]) ).
cnf(s267,plain,
( spl50_86
| spl50_9
| spl50_10 ),
inference(rat,[],[s169,s132,s133,s166,s266,s148]) ).
cnf(s268,plain,
( spl50_9
| spl50_10 ),
inference(rat,[],[s267,s264]) ).
cnf(s269,plain,
( spl50_87
| ~ spl50_9 ),
inference(rat,[],[s199,s146,s147,s185,s262,s260]) ).
cnf(s270,plain,
~ spl50_9,
inference(rat,[],[s181,s108,s109,s165,s269,s237]) ).
cnf(s271,plain,
spl50_10,
inference(rat,[],[s268,s270]) ).
cnf(s272,plain,
~ spl50_87,
inference(rat,[],[s239,s271]) ).
cnf(s273,plain,
spl50_33,
inference(rat,[],[s263,s271]) ).
cnf(s274,plain,
~ spl50_29,
inference(rat,[],[s207,s249,s273]) ).
cnf(s277,plain,
( spl50_27
| spl50_30
| ~ spl50_11 ),
inference(rat,[],[s211,s27,s31,s274]) ).
cnf(s278,plain,
( spl50_30
| ~ spl50_11 ),
inference(rat,[],[s211,s33,s29,s209,s277,s271,s274]) ).
cnf(s279,plain,
( spl50_27
| ~ spl50_86 ),
inference(rat,[],[s211,s26,s30,s185,s278,s253,s274,s270]) ).
cnf(s280,plain,
~ spl50_86,
inference(rat,[],[s211,s32,s28,s209,s279,s185,s278,s253,s274,s271,s270]) ).
cnf(s283,plain,
spl50_89,
inference(rat,[],[s218,s271,s272,s280]) ).
cnf(s284,plain,
spl50_11,
inference(rat,[],[s149,s272,s270,s280]) ).
cnf(s286,plain,
~ spl50_92,
inference(rat,[],[s205,s284,s283]) ).
cnf(s288,plain,
spl50_90,
inference(rat,[],[s144,s272,s280,s286]) ).
cnf(s289,plain,
spl50_91,
inference(rat,[],[s145,s280,s272,s286]) ).
cnf(s290,plain,
$false,
inference(rat,[],[s215,s271,s289,s288]) ).
thf(f2199,plain,
$false,
inference(avatar_sat_refutation,[],[s290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN045^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:14:15 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.36 % (2861700)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.36 % (2861708)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2102342668:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.36 % (2861705)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2361697920:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.36 % (2861707)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1407160759:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.36 % (2861709)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2212293840:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.36 % (2861707)Instruction limit reached!
% 0.21/0.36 % (2861707)------------------------------
% 0.21/0.36 % (2861707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2861707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2861707)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2861707)Termination reason: Instruction limit
% 0.21/0.36 % (2861707)Termination phase: Property scanning
% 0.21/0.36 % (2861707)Time elapsed: 0.002 s
% 0.21/0.36 % (2861707)Peak memory usage: 10 MB
% 0.21/0.36 % (2861707)Instructions burned: 4 (million)
% 0.21/0.36 % (2861711)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.36 % (2861711)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.36 % (2861706)lrs+10_16_si=on:nwc=1.5:random_seed=1003310375:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.36 % (2861709)Instruction limit reached!
% 0.21/0.36 % (2861709)------------------------------
% 0.21/0.36 % (2861709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2861709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2861709)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2861709)Termination reason: Instruction limit
% 0.21/0.36 % (2861709)Termination phase: Saturation
% 0.21/0.36 % (2861709)Time elapsed: 0.014 s
% 0.21/0.36 % (2861709)Peak memory usage: 12 MB
% 0.21/0.36 % (2861709)Instructions burned: 25 (million)
% 0.21/0.36 % (2861711)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2243410614:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.36 % (2861710)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=392769041:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.36 % (2861716)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2096555023:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (2861716)Instruction limit reached!
% 0.21/0.36 % (2861716)------------------------------
% 0.21/0.36 % (2861716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2861716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2861716)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2861716)Termination reason: Instruction limit
% 0.21/0.36 % (2861716)Termination phase: Property scanning
% 0.21/0.36 % (2861716)Time elapsed: 0.002 s
% 0.21/0.36 % (2861716)Peak memory usage: 10 MB
% 0.21/0.36 % (2861716)Instructions burned: 4 (million)
% 0.21/0.36 % (2861706)Instruction limit reached!
% 0.21/0.36 % (2861706)------------------------------
% 0.21/0.36 % (2861706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2861706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2861706)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2861706)Termination reason: Instruction limit
% 0.21/0.36 % (2861706)Termination phase: Saturation
% 0.21/0.36 % (2861706)Time elapsed: 0.015 s
% 0.21/0.36 % (2861706)Peak memory usage: 12 MB
% 0.21/0.36 % (2861706)Instructions burned: 18 (million)
% 0.21/0.36 % (2861718)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4148262459:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.36 % (2861718)Instruction limit reached!
% 0.21/0.36 % (2861718)------------------------------
% 0.21/0.36 % (2861718)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2861718)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2861718)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2861718)Termination reason: Instruction limit
% 0.21/0.36 % (2861718)Termination phase: Property scanning
% 0.21/0.36 % (2861718)Time elapsed: 0.002 s
% 0.21/0.36 % (2861718)Peak memory usage: 10 MB
% 0.21/0.36 % (2861718)Instructions burned: 5 (million)
% 0.21/0.36 % (2861705) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2861700-2861705"...
% 0.21/0.36 % (2861722)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.36 % (2861722)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3453261698:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.36 % (2861723)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4183428964:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.36 % (2861722)Instruction limit reached!
% 0.21/0.36 % (2861722)------------------------------
% 0.21/0.36 % (2861722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2861722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2861722)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2861722)Termination reason: Instruction limit
% 0.21/0.36 % (2861722)Termination phase: Function definition elimination
% 0.21/0.36 % (2861722)Time elapsed: 0.003 s
% 0.21/0.36 % (2861722)Peak memory usage: 10 MB
% 0.21/0.36 % (2861722)Instructions burned: 7 (million)
% 0.21/0.36 % (2861725)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.36 % (2861725)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.36 % (2861723)Instruction limit reached!
% 0.21/0.36 % (2861723)------------------------------
% 0.21/0.36 % (2861723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2861723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2861723)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2861723)Termination reason: Instruction limit
% 0.21/0.36 % (2861723)Termination phase: Saturation
% 0.21/0.36 % (2861723)Time elapsed: 0.006 s
% 0.21/0.36 % (2861723)Peak memory usage: 12 MB
% 0.21/0.36 % (2861723)Instructions burned: 13 (million)
% 0.21/0.36 % (2861725)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2098905692:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.36 % (2861710)Instruction limit reached!
% 0.21/0.36 % (2861710)------------------------------
% 0.21/0.36 % (2861710)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2861710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2861710)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2861710)Termination reason: Instruction limit
% 0.21/0.36 % (2861710)Termination phase: Saturation
% 0.21/0.36 % (2861710)Time elapsed: 0.040 s
% 0.21/0.36 % (2861710)Peak memory usage: 13 MB
% 0.21/0.36 % (2861710)Instructions burned: 75 (million)
% 0.21/0.36 % (2861728)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2591158566:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.36 % (2861705)...printing done.
% 0.21/0.36 % (2861725)Instruction limit reached!
% 0.21/0.36 % (2861725)------------------------------
% 0.21/0.36 % (2861725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (2861725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (2861725)CaDiCaL version: 2.1.3
% 0.21/0.36 % (2861725)Termination reason: Instruction limit
% 0.21/0.36 % (2861725)Termination phase: Saturation
% 0.21/0.36 % (2861725)Time elapsed: 0.013 s
% 0.21/0.36 % (2861725)Peak memory usage: 12 MB
% 0.21/0.36 % (2861725)Instructions burned: 29 (million)
% 0.21/0.36 % (2861705)Refutation found. Thanks to Tanya!
% 0.21/0.36 % SZS status Theorem for theBenchmark
% 0.21/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38 % (2861705)------------------------------
% 0.21/0.38 % (2861705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (2861705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (2861705)CaDiCaL version: 2.1.3
% 0.21/0.38 % (2861705)Termination reason: Refutation
% 0.21/0.38 % (2861705)Time elapsed: 0.069 s
% 0.21/0.38 % (2861705)Peak memory usage: 14 MB
% 0.21/0.38 % (2861705)Instructions burned: 146 (million)
% 0.21/0.38 % (2861700)Success in time 0.111 s
% 0.21/0.38 % Vampire exiting
%------------------------------------------------------------------------------