%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO445^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 08:49:59 AM UTC 2026
% Result : Theorem 1.02s 0.42s
% Output : Refutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 34
% Syntax : Number of formulae : 397 ( 73 unt; 0 typ; 21 def)
% Number of atoms : 4183 ( 782 equ; 0 cnn)
% Maximal formula atoms : 12 ( 10 avg)
% Number of connectives : 5129 ( 983 ~;1201 |; 13 &;2671 @)
% ( 21 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 130 ( 130 >; 0 *; 0 +; 0 <<)
% Number of symbols : 85 ( 81 usr; 32 con; 0-4 aty)
% ( 218 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 709 ( 0 sgn 252 !; 0 ?; 709 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: 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,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $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,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
sK2: $i > $i ).
thf(func_def_56,type,
sK4: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mequiv @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f41,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f42,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f44,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f45,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f46,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f48,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f64,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f65,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f68,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f69,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f82,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f83,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f90,plain,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f91,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f90]) ).
thf(f92,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f95,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f96,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f98,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f97]) ).
thf(f99,plain,
~ ( mvalid @ ( mequiv @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f100,plain,
( ( mvalid @ ( mequiv @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( ( mvalid @ ( mequiv @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) ) )
!= $true ),
inference(flattening,[],[f100]) ).
thf(f104,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f105,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f106,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f107,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f109,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f120,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f122,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f129,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f133,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f134,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f136,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f96]) ).
thf(f137,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f138,plain,
( ( mvalid @ ( mequiv @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f141,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f106,f104,f105,f104,f104]) ).
thf(f142,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f107,f105,f104]) ).
thf(f144,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f109,f141,f142,f142]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f134,f104,f133,f104]) ).
thf(f152,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f136,f122]) ).
thf(f153,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f137,f120]) ).
thf(f154,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ p
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) ) ) ),
inference(definition_unfolding,[],[f138,f129,f144,f105,f133,f150,f133,f105,f150]) ).
thf(f155,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( $false
= ( ~ ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( q @ sK1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( q @ sK1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( q @ sK1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( q @ sK1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( q @ sK1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( ~ ( q @ sK1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f180,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X1 @ ( sK2 @ X1 ) )
| ~ ( q @ ( sK2 @ X1 ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( q @ ( sK2 @ X1 ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X1 @ ( sK2 @ X1 ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK2 @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ ( sK2 @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f189,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( q @ sK1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f190,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( q @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( q @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK2 @ X1 ) ) )
| ( $true
= ( q @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X1 @ ( sK2 @ X1 ) )
| ~ ( q @ ( sK2 @ X1 ) ) ) )
| ( $true
= ( q @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( q @ ( sK2 @ X1 ) ) ) )
| ( $true
= ( q @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X1 @ ( sK2 @ X1 ) ) ) )
| ( $true
= ( q @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f196,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK2 @ X1 ) ) )
| ( $true
= ( q @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ ( sK2 @ X1 ) ) )
| ( $true
= ( q @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f198,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| ( p @ sK3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $true
= ( ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| ( p @ sK3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| ( p @ sK3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| ( p @ sK3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| ( p @ sK3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( $false
= ( ( p @ sK3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f206,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X1 @ ( sK4 @ X1 ) )
| ~ ( q @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( ( $false
= ( ~ ( q @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X1 @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f208]) ).
thf(f211,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( ( $true
= ( q @ ( sK4 @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f209]) ).
thf(f213,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f221,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f213]) ).
thf(f222,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( p @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X1 @ ( sK4 @ X1 ) )
| ~ ( q @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK3 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(beta-eta_normalization,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( q @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK3 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X1 @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK3 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f227,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK3 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK4 @ X1 ) ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK4 @ X1 ) ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ ( sK4 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK3 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f232,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ ( sK4 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ ( sK4 @ X1 ) ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ ( sK4 @ X1 ) ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f233]) ).
thf(f235,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f236,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f237,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f236]) ).
thf(f238,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f237]) ).
thf(f239,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f238]) ).
thf(f240,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f238]) ).
thf(f241,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f240]) ).
thf(f242,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f241]) ).
thf(f243,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f242]) ).
thf(f244,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 )
| ( p @ sK5 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ~ ( q @ sK6 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f245]) ).
thf(f247,plain,
! [X1: $i] :
( ( $false
= ( p @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ~ ( q @ sK6 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ~ ( q @ sK6 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f246]) ).
thf(f249,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ~ ( q @ sK6 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( q @ sK6 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f249]) ).
thf(f252,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( q @ sK6 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f250]) ).
thf(f256,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( q @ sK6 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( q @ sK6 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X1: $i] :
( ( $false
= ( p @ sK5 ) )
| ( $false
= ( ~ ( q @ sK6 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f247]) ).
thf(f259,plain,
! [X1: $i] :
( ( $false
= ( p @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f247]) ).
thf(f260,plain,
! [X1: $i] :
( ( $false
= ( p @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X1: $i] :
( ( $false
= ( p @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X1: $i] :
( ( $false
= ( p @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X1: $i] :
( ( $false
= ( p @ sK5 ) )
| ( $true
= ( q @ sK6 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f258]) ).
thf(f264,plain,
! [X1: $i] :
( ( $false
= ( p @ sK5 ) )
| ( $true
= ( q @ sK6 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X1: $i] :
( ( $false
= ( p @ sK5 ) )
| ( $true
= ( q @ sK6 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f264]) ).
thf(f266,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f239]) ).
thf(f267,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 )
| ( p @ sK5 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 )
| ( p @ sK7 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f266]) ).
thf(f268,plain,
( ( $false
= ( p @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 )
| ( p @ sK7 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f267]) ).
thf(f269,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 )
| ( p @ sK7 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f267]) ).
thf(f270,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 )
| ( p @ sK7 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f269]) ).
thf(f271,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ( p @ sK7 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f270]) ).
thf(f272,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f270]) ).
thf(f273,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK7 ) ) ),
inference(not_proxy_clausification,[],[f272]) ).
thf(f275,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( p @ sK7 ) ) ),
inference(or_proxy_clausification,[],[f271]) ).
thf(f282,plain,
( ( $false
= ( p @ sK5 ) )
| ( $false
= ( ( p @ sK7 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f268]) ).
thf(f283,plain,
( ( $false
= ( p @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f268]) ).
thf(f284,plain,
( ( $false
= ( p @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK7 ) ) ),
inference(not_proxy_clausification,[],[f283]) ).
thf(f286,plain,
( ( $false
= ( p @ sK5 ) )
| ( $false
= ( p @ sK7 ) ) ),
inference(or_proxy_clausification,[],[f282]) ).
thf(f293,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f235]) ).
thf(f294,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f293]) ).
thf(f295,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f294]) ).
thf(f296,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f295]) ).
thf(f297,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f295]) ).
thf(f298,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f298]) ).
thf(f300,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f299]) ).
thf(f301,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK8 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK8 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f301]) ).
thf(f303,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK8 )
| ~ ( q @ sK8 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f302]) ).
thf(f304,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK8 )
| ~ ( q @ sK8 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK8 )
| ~ ( q @ sK8 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( ~ ( q @ sK8 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f305]) ).
thf(f307,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK8 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f305]) ).
thf(f308,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f307]) ).
thf(f309,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f308]) ).
thf(f310,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f309]) ).
thf(f311,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f310]) ).
thf(f312,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( q @ sK8 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f306]) ).
thf(f313,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( q @ sK8 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( q @ sK8 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( q @ sK8 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f314]) ).
thf(f316,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ sK9 ) ) ),
inference(sigma_proxy_clausification,[],[f296]) ).
thf(f317,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK9 )
| ( p @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK9 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f316]) ).
thf(f318,plain,
! [X1: $i] :
( ( $true
= ( ~ ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK9 )
| ( p @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK9 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f317]) ).
thf(f319,plain,
! [X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK9 )
| ( p @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK9 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f318]) ).
thf(f320,plain,
! [X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( ( p @ sK9 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK9 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f319]) ).
thf(f321,plain,
! [X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK9 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f319]) ).
thf(f322,plain,
! [X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK9 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK9 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f322]) ).
thf(f324,plain,
! [X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK9 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f320]) ).
thf(f325,plain,
! [X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ sK9 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f320]) ).
thf(f326,plain,
! [X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ sK9 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK9 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f324]) ).
thf(f328,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK9 @ Y0 )
| ~ ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f327]) ).
thf(f329,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK9 @ Y0 )
| ~ ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f328]) ).
thf(f330,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK9 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f329]) ).
thf(f331,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $true
= ( ~ ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK9 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f330]) ).
thf(f332,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK9 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f331]) ).
thf(f333,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK9 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f332]) ).
thf(f334,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f335,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f334]) ).
thf(f336,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f335]) ).
thf(f337,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f336]) ).
thf(f338,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f337]) ).
thf(f339,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f338]) ).
thf(f340,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f341,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f340]) ).
thf(f342,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f341]) ).
thf(f343,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f343]) ).
thf(f345,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f345]) ).
thf(f347,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) ) )
| ( $true
= ( rel_s5 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f346]) ).
thf(f348,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( $true
= ( rel_s5 @ X3 @ X1 ) )
| ( $false
= ( rel_s5 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f347]) ).
thf(f353,definition,
( spl10_1
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
thf(f354,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f353]) ).
thf(f356,definition,
( spl10_2
<=> ( $true
= ( rel_s5 @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f358,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f356]) ).
thf(f360,definition,
( spl10_3
<=> ! [X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK2 @ X1 ) ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f361,plain,
( ! [X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK2 @ X1 ) ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f360]) ).
thf(f362,plain,
( spl10_1
| spl10_2
| spl10_3 ),
inference(avatar_split_clause,[],[f187,f360,f356,f353]) ).
thf(f364,definition,
( spl10_4
<=> ! [X1: $i] :
( ( $true
= ( q @ ( sK2 @ X1 ) ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f365,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( q @ ( sK2 @ X1 ) ) ) )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f364]) ).
thf(f366,plain,
( spl10_1
| spl10_2
| spl10_4 ),
inference(avatar_split_clause,[],[f188,f364,f356,f353]) ).
thf(f368,definition,
( spl10_5
<=> ( $true
= ( q @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
thf(f370,plain,
( ( $true
= ( q @ sK1 ) )
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f368]) ).
thf(f371,plain,
( spl10_1
| spl10_5
| spl10_3 ),
inference(avatar_split_clause,[],[f196,f360,f368,f353]) ).
thf(f372,plain,
( spl10_1
| spl10_5
| spl10_4 ),
inference(avatar_split_clause,[],[f197,f364,f368,f353]) ).
thf(f374,definition,
( spl10_6
<=> ( $true
= ( rel_s5 @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
thf(f376,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f374]) ).
thf(f378,definition,
( spl10_7
<=> ! [X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f379,plain,
( ! [X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f378]) ).
thf(f380,plain,
( spl10_6
| spl10_7 ),
inference(avatar_split_clause,[],[f211,f378,f374]) ).
thf(f382,definition,
( spl10_8
<=> ! [X1: $i] :
( ( $true
= ( q @ ( sK4 @ X1 ) ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
thf(f383,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( q @ ( sK4 @ X1 ) ) ) )
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f382]) ).
thf(f384,plain,
( spl10_6
| spl10_8 ),
inference(avatar_split_clause,[],[f212,f382,f374]) ).
thf(f392,definition,
( spl10_10
<=> ! [X2: $i] :
( ( $false
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
thf(f393,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s5 @ sK3 @ X2 ) )
| ( $false
= ( q @ X2 ) ) )
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f392]) ).
thf(f394,plain,
( spl10_10
| spl10_7 ),
inference(avatar_split_clause,[],[f230,f378,f392]) ).
thf(f395,plain,
( spl10_10
| spl10_8 ),
inference(avatar_split_clause,[],[f234,f382,f392]) ).
thf(f397,definition,
( spl10_11
<=> ( $true
= ( rel_s5 @ sK0 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
thf(f399,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f397]) ).
thf(f401,definition,
( spl10_12
<=> ( $true
= ( rel_s5 @ sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
thf(f403,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ~ spl10_12 ),
inference(avatar_component_clause,[],[f401]) ).
thf(f404,plain,
( spl10_1
| spl10_11
| spl10_12 ),
inference(avatar_split_clause,[],[f254,f401,f397,f353]) ).
thf(f406,definition,
( spl10_13
<=> ( $true
= ( q @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_13])],[avatar_definition]) ).
thf(f408,plain,
( ( $true
= ( q @ sK6 ) )
| ~ spl10_13 ),
inference(avatar_component_clause,[],[f406]) ).
thf(f409,plain,
( spl10_1
| spl10_13
| spl10_12 ),
inference(avatar_split_clause,[],[f257,f401,f406,f353]) ).
thf(f411,definition,
( spl10_14
<=> ( $false
= ( p @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition]) ).
thf(f413,plain,
( ( $false
= ( p @ sK5 ) )
| ~ spl10_14 ),
inference(avatar_component_clause,[],[f411]) ).
thf(f414,plain,
( spl10_1
| spl10_11
| spl10_14 ),
inference(avatar_split_clause,[],[f262,f411,f397,f353]) ).
thf(f415,plain,
( spl10_1
| spl10_13
| spl10_14 ),
inference(avatar_split_clause,[],[f265,f411,f406,f353]) ).
thf(f417,definition,
( spl10_15
<=> ( $true
= ( rel_s5 @ sK0 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_15])],[avatar_definition]) ).
thf(f419,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK7 ) )
| ~ spl10_15 ),
inference(avatar_component_clause,[],[f417]) ).
thf(f420,plain,
( spl10_15
| spl10_12 ),
inference(avatar_split_clause,[],[f273,f401,f417]) ).
thf(f422,definition,
( spl10_16
<=> ( $false
= ( p @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_16])],[avatar_definition]) ).
thf(f424,plain,
( ( $false
= ( p @ sK7 ) )
| ~ spl10_16 ),
inference(avatar_component_clause,[],[f422]) ).
thf(f425,plain,
( spl10_16
| spl10_12 ),
inference(avatar_split_clause,[],[f275,f401,f422]) ).
thf(f430,plain,
( spl10_15
| spl10_14 ),
inference(avatar_split_clause,[],[f284,f411,f417]) ).
thf(f431,plain,
( spl10_16
| spl10_14 ),
inference(avatar_split_clause,[],[f286,f411,f422]) ).
thf(f434,definition,
( spl10_18
<=> ( $true
= ( rel_s5 @ sK0 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_18])],[avatar_definition]) ).
thf(f436,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ~ spl10_18 ),
inference(avatar_component_clause,[],[f434]) ).
thf(f438,definition,
( spl10_19
<=> ! [X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_19])],[avatar_definition]) ).
thf(f439,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( q @ X1 ) ) )
| ~ spl10_19 ),
inference(avatar_component_clause,[],[f438]) ).
thf(f440,plain,
( spl10_1
| spl10_18
| spl10_19 ),
inference(avatar_split_clause,[],[f311,f438,f434,f353]) ).
thf(f442,definition,
( spl10_20
<=> ( $true
= ( q @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_20])],[avatar_definition]) ).
thf(f444,plain,
( ( $true
= ( q @ sK8 ) )
| ~ spl10_20 ),
inference(avatar_component_clause,[],[f442]) ).
thf(f445,plain,
( spl10_1
| spl10_20
| spl10_19 ),
inference(avatar_split_clause,[],[f315,f438,f442,f353]) ).
thf(f447,definition,
( spl10_21
<=> ( $true
= ( rel_s5 @ sK0 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_21])],[avatar_definition]) ).
thf(f449,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK9 ) )
| ~ spl10_21 ),
inference(avatar_component_clause,[],[f447]) ).
thf(f450,plain,
( spl10_21
| spl10_19 ),
inference(avatar_split_clause,[],[f323,f438,f447]) ).
thf(f452,definition,
( spl10_22
<=> ( $false
= ( p @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_22])],[avatar_definition]) ).
thf(f454,plain,
( ( $false
= ( p @ sK9 ) )
| ~ spl10_22 ),
inference(avatar_component_clause,[],[f452]) ).
thf(f455,plain,
( spl10_22
| spl10_19 ),
inference(avatar_split_clause,[],[f326,f438,f452]) ).
thf(f457,definition,
( spl10_23
<=> ! [X2: $i] :
( ( $false
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK9 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_23])],[avatar_definition]) ).
thf(f458,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s5 @ sK9 @ X2 ) )
| ( $false
= ( q @ X2 ) ) )
| ~ spl10_23 ),
inference(avatar_component_clause,[],[f457]) ).
thf(f459,plain,
( spl10_23
| spl10_19 ),
inference(avatar_split_clause,[],[f333,f438,f457]) ).
thf(f460,plain,
( ( $true = $false )
| ( $true
= ( p @ sK5 ) )
| ~ spl10_1
| ~ spl10_12 ),
inference(constrained_superposition,[],[f354,f403]) ).
thf(f463,plain,
( ( $true
= ( p @ sK5 ) )
| ~ spl10_1
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f460]) ).
thf(f467,plain,
( ( $true = $false )
| ~ spl10_1
| ~ spl10_12
| ~ spl10_14 ),
inference(forward_demodulation,[],[f463,f413]) ).
thf(f468,plain,
( $false
| ~ spl10_1
| ~ spl10_12
| ~ spl10_14 ),
inference(trivial_inequality_removal,[],[f467]) ).
thf(f469,plain,
( ~ spl10_1
| ~ spl10_12
| ~ spl10_14 ),
inference(avatar_contradiction_clause,[],[f468]) ).
thf(f483,plain,
( ( $true = $false )
| ( $true
= ( p @ sK7 ) )
| ~ spl10_1
| ~ spl10_15 ),
inference(constrained_superposition,[],[f419,f354]) ).
thf(f486,plain,
( ( $true
= ( p @ sK7 ) )
| ~ spl10_1
| ~ spl10_15 ),
inference(trivial_inequality_removal,[],[f483]) ).
thf(f490,plain,
( ( $true = $false )
| ~ spl10_1
| ~ spl10_15
| ~ spl10_16 ),
inference(forward_demodulation,[],[f486,f424]) ).
thf(f491,plain,
( $false
| ~ spl10_1
| ~ spl10_15
| ~ spl10_16 ),
inference(trivial_inequality_removal,[],[f490]) ).
thf(f492,plain,
( ~ spl10_1
| ~ spl10_15
| ~ spl10_16 ),
inference(avatar_contradiction_clause,[],[f491]) ).
thf(f505,plain,
( ( $true = $false )
| ( $true
= ( p @ sK5 ) )
| ( $true
= ( q @ ( sK2 @ sK5 ) ) )
| ~ spl10_4
| ~ spl10_12 ),
inference(constrained_superposition,[],[f403,f365]) ).
thf(f506,plain,
( ( $true
= ( p @ sK5 ) )
| ( $true
= ( q @ ( sK2 @ sK5 ) ) )
| ~ spl10_4
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f505]) ).
thf(f509,plain,
( ( $true = $false )
| ( $true
= ( q @ ( sK2 @ sK5 ) ) )
| ~ spl10_4
| ~ spl10_12
| ~ spl10_14 ),
inference(forward_demodulation,[],[f506,f413]) ).
thf(f510,plain,
( ( $true
= ( q @ ( sK2 @ sK5 ) ) )
| ~ spl10_4
| ~ spl10_12
| ~ spl10_14 ),
inference(trivial_inequality_removal,[],[f509]) ).
thf(f784,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ X0 @ X2 ) ) ),
inference(constrained_superposition,[],[f339,f348]) ).
thf(f788,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK5 @ X0 ) )
| ( $true
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl10_12 ),
inference(constrained_superposition,[],[f403,f348]) ).
thf(f797,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK5 @ X0 ) )
| ( $true
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f788]) ).
thf(f801,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f784]) ).
thf(f859,plain,
( ( $true = $false )
| ( $true
= ( p @ sK5 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ ( sK2 @ sK5 ) ) )
| ~ spl10_3
| ~ spl10_12 ),
inference(constrained_superposition,[],[f361,f797]) ).
thf(f864,plain,
( ( $true
= ( p @ sK5 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ ( sK2 @ sK5 ) ) )
| ~ spl10_3
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f859]) ).
thf(f877,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ ( sK2 @ sK5 ) ) )
| ~ spl10_3
| ~ spl10_12
| ~ spl10_14 ),
inference(forward_demodulation,[],[f864,f413]) ).
thf(f878,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ ( sK2 @ sK5 ) ) )
| ~ spl10_3
| ~ spl10_12
| ~ spl10_14 ),
inference(trivial_inequality_removal,[],[f877]) ).
thf(f885,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK0 @ ( sK2 @ sK5 ) ) )
| ~ spl10_3
| ~ spl10_12
| ~ spl10_14 ),
inference(forward_demodulation,[],[f878,f403]) ).
thf(f886,plain,
( ( $true
= ( rel_s5 @ sK0 @ ( sK2 @ sK5 ) ) )
| ~ spl10_3
| ~ spl10_12
| ~ spl10_14 ),
inference(trivial_inequality_removal,[],[f885]) ).
thf(f998,plain,
( ( $true = $false )
| ( $true
= ( p @ sK9 ) )
| ( $true
= ( q @ ( sK4 @ sK9 ) ) )
| ~ spl10_8
| ~ spl10_21 ),
inference(constrained_superposition,[],[f383,f449]) ).
thf(f1007,plain,
( ( $true
= ( p @ sK9 ) )
| ( $true
= ( q @ ( sK4 @ sK9 ) ) )
| ~ spl10_8
| ~ spl10_21 ),
inference(trivial_inequality_removal,[],[f998]) ).
thf(f1015,plain,
( ( $true = $false )
| ( $true
= ( q @ ( sK4 @ sK9 ) ) )
| ~ spl10_8
| ~ spl10_21
| ~ spl10_22 ),
inference(forward_demodulation,[],[f1007,f454]) ).
thf(f1016,plain,
( ( $true
= ( q @ ( sK4 @ sK9 ) ) )
| ~ spl10_8
| ~ spl10_21
| ~ spl10_22 ),
inference(trivial_inequality_removal,[],[f1015]) ).
thf(f1156,plain,
( ( $true = $false )
| ( $true
= ( p @ sK9 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK9 ) )
| ( $false
= ( q @ ( sK4 @ sK9 ) ) )
| ~ spl10_7
| ~ spl10_23 ),
inference(constrained_superposition,[],[f379,f458]) ).
thf(f1159,plain,
( ( $true
= ( p @ sK9 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK9 ) )
| ( $false
= ( q @ ( sK4 @ sK9 ) ) )
| ~ spl10_7
| ~ spl10_23 ),
inference(trivial_inequality_removal,[],[f1156]) ).
thf(f1171,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK9 ) )
| ( $false
= ( q @ ( sK4 @ sK9 ) ) )
| ~ spl10_7
| ~ spl10_22
| ~ spl10_23 ),
inference(forward_demodulation,[],[f1159,f454]) ).
thf(f1172,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK9 ) )
| ( $false
= ( q @ ( sK4 @ sK9 ) ) )
| ~ spl10_7
| ~ spl10_22
| ~ spl10_23 ),
inference(trivial_inequality_removal,[],[f1171]) ).
thf(f1179,plain,
( ( $true = $false )
| ( $false
= ( q @ ( sK4 @ sK9 ) ) )
| ~ spl10_7
| ~ spl10_21
| ~ spl10_22
| ~ spl10_23 ),
inference(forward_demodulation,[],[f1172,f449]) ).
thf(f1180,plain,
( ( $false
= ( q @ ( sK4 @ sK9 ) ) )
| ~ spl10_7
| ~ spl10_21
| ~ spl10_22
| ~ spl10_23 ),
inference(trivial_inequality_removal,[],[f1179]) ).
thf(f1191,plain,
( ( $true = $false )
| ~ spl10_7
| ~ spl10_8
| ~ spl10_21
| ~ spl10_22
| ~ spl10_23 ),
inference(constrained_superposition,[],[f1180,f1016]) ).
thf(f1197,plain,
( $false
| ~ spl10_7
| ~ spl10_8
| ~ spl10_21
| ~ spl10_22
| ~ spl10_23 ),
inference(trivial_inequality_removal,[],[f1191]) ).
thf(f1198,plain,
( ~ spl10_7
| ~ spl10_8
| ~ spl10_21
| ~ spl10_22
| ~ spl10_23 ),
inference(avatar_contradiction_clause,[],[f1197]) ).
thf(f1321,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK3 ) ) )
| ~ spl10_6 ),
inference(constrained_superposition,[],[f801,f376]) ).
thf(f1322,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK3 ) ) )
| ~ spl10_6 ),
inference(trivial_inequality_removal,[],[f1321]) ).
thf(f1384,plain,
( ( $true = $false )
| ( $false
= ( q @ sK1 ) )
| ~ spl10_2
| ~ spl10_19 ),
inference(constrained_superposition,[],[f358,f439]) ).
thf(f1389,plain,
( ( $false
= ( q @ sK1 ) )
| ~ spl10_2
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f1384]) ).
thf(f1534,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_5
| ~ spl10_19 ),
inference(constrained_superposition,[],[f1389,f370]) ).
thf(f1540,plain,
( $false
| ~ spl10_2
| ~ spl10_5
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f1534]) ).
thf(f1541,plain,
( ~ spl10_2
| ~ spl10_5
| ~ spl10_19 ),
inference(avatar_contradiction_clause,[],[f1540]) ).
thf(f1707,plain,
( ( $true = $false )
| ( $false
= ( q @ ( sK2 @ sK5 ) ) )
| ~ spl10_3
| ~ spl10_12
| ~ spl10_14
| ~ spl10_19 ),
inference(constrained_superposition,[],[f439,f886]) ).
thf(f1722,plain,
( ( $false
= ( q @ ( sK2 @ sK5 ) ) )
| ~ spl10_3
| ~ spl10_12
| ~ spl10_14
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f1707]) ).
thf(f1731,plain,
( ( $true = $false )
| ~ spl10_3
| ~ spl10_4
| ~ spl10_12
| ~ spl10_14
| ~ spl10_19 ),
inference(constrained_superposition,[],[f1722,f510]) ).
thf(f1737,plain,
( $false
| ~ spl10_3
| ~ spl10_4
| ~ spl10_12
| ~ spl10_14
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f1731]) ).
thf(f1738,plain,
( ~ spl10_3
| ~ spl10_4
| ~ spl10_12
| ~ spl10_14
| ~ spl10_19 ),
inference(avatar_contradiction_clause,[],[f1737]) ).
thf(f1927,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( q @ X0 ) ) )
| ~ spl10_10 ),
inference(constrained_superposition,[],[f339,f393]) ).
thf(f1936,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( q @ X0 ) ) )
| ~ spl10_10 ),
inference(trivial_inequality_removal,[],[f1927]) ).
thf(f2057,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK8 @ sK3 ) )
| ~ spl10_6
| ~ spl10_18 ),
inference(constrained_superposition,[],[f436,f1322]) ).
thf(f2082,plain,
( ( $true
= ( rel_s5 @ sK8 @ sK3 ) )
| ~ spl10_6
| ~ spl10_18 ),
inference(trivial_inequality_removal,[],[f2057]) ).
thf(f2166,plain,
( ( $true = $false )
| ( $false
= ( q @ sK8 ) )
| ~ spl10_6
| ~ spl10_10
| ~ spl10_18 ),
inference(constrained_superposition,[],[f1936,f2082]) ).
thf(f2167,plain,
( ( $false
= ( q @ sK8 ) )
| ~ spl10_6
| ~ spl10_10
| ~ spl10_18 ),
inference(trivial_inequality_removal,[],[f2166]) ).
thf(f2183,plain,
( ( $true = $false )
| ~ spl10_6
| ~ spl10_10
| ~ spl10_18
| ~ spl10_20 ),
inference(constrained_superposition,[],[f2167,f444]) ).
thf(f2189,plain,
( $false
| ~ spl10_6
| ~ spl10_10
| ~ spl10_18
| ~ spl10_20 ),
inference(trivial_inequality_removal,[],[f2183]) ).
thf(f2190,plain,
( ~ spl10_6
| ~ spl10_10
| ~ spl10_18
| ~ spl10_20 ),
inference(avatar_contradiction_clause,[],[f2189]) ).
thf(f2756,plain,
( ( $true = $false )
| ( $false
= ( q @ sK6 ) )
| ~ spl10_11
| ~ spl10_19 ),
inference(constrained_superposition,[],[f399,f439]) ).
thf(f2760,plain,
( ( $false
= ( q @ sK6 ) )
| ~ spl10_11
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f2756]) ).
thf(f2776,plain,
( ( $true = $false )
| ~ spl10_11
| ~ spl10_13
| ~ spl10_19 ),
inference(constrained_superposition,[],[f2760,f408]) ).
thf(f2782,plain,
( $false
| ~ spl10_11
| ~ spl10_13
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f2776]) ).
thf(f2783,plain,
( ~ spl10_11
| ~ spl10_13
| ~ spl10_19 ),
inference(avatar_contradiction_clause,[],[f2782]) ).
cnf(s1,plain,
( spl10_1
| spl10_2
| spl10_3 ),
inference(sat_conversion,[],[f362]) ).
cnf(s2,plain,
( spl10_1
| spl10_2
| spl10_4 ),
inference(sat_conversion,[],[f366]) ).
cnf(s3,plain,
( spl10_1
| spl10_3
| spl10_5 ),
inference(sat_conversion,[],[f371]) ).
cnf(s4,plain,
( spl10_1
| spl10_4
| spl10_5 ),
inference(sat_conversion,[],[f372]) ).
cnf(s5,plain,
( spl10_6
| spl10_7 ),
inference(sat_conversion,[],[f380]) ).
cnf(s6,plain,
( spl10_6
| spl10_8 ),
inference(sat_conversion,[],[f384]) ).
cnf(s9,plain,
( spl10_7
| spl10_10 ),
inference(sat_conversion,[],[f394]) ).
cnf(s10,plain,
( spl10_8
| spl10_10 ),
inference(sat_conversion,[],[f395]) ).
cnf(s11,plain,
( spl10_1
| spl10_11
| spl10_12 ),
inference(sat_conversion,[],[f404]) ).
cnf(s12,plain,
( spl10_1
| spl10_12
| spl10_13 ),
inference(sat_conversion,[],[f409]) ).
cnf(s13,plain,
( spl10_1
| spl10_11
| spl10_14 ),
inference(sat_conversion,[],[f414]) ).
cnf(s14,plain,
( spl10_1
| spl10_13
| spl10_14 ),
inference(sat_conversion,[],[f415]) ).
cnf(s15,plain,
( spl10_12
| spl10_15 ),
inference(sat_conversion,[],[f420]) ).
cnf(s16,plain,
( spl10_12
| spl10_16 ),
inference(sat_conversion,[],[f425]) ).
cnf(s18,plain,
( spl10_14
| spl10_15 ),
inference(sat_conversion,[],[f430]) ).
cnf(s19,plain,
( spl10_14
| spl10_16 ),
inference(sat_conversion,[],[f431]) ).
cnf(s21,plain,
( spl10_1
| spl10_18
| spl10_19 ),
inference(sat_conversion,[],[f440]) ).
cnf(s22,plain,
( spl10_1
| spl10_19
| spl10_20 ),
inference(sat_conversion,[],[f445]) ).
cnf(s23,plain,
( spl10_19
| spl10_21 ),
inference(sat_conversion,[],[f450]) ).
cnf(s24,plain,
( spl10_19
| spl10_22 ),
inference(sat_conversion,[],[f455]) ).
cnf(s25,plain,
( spl10_19
| spl10_23 ),
inference(sat_conversion,[],[f459]) ).
cnf(s27,plain,
( ~ spl10_1
| ~ spl10_12
| ~ spl10_14 ),
inference(sat_conversion,[],[f469]) ).
cnf(s29,plain,
( ~ spl10_1
| ~ spl10_15
| ~ spl10_16 ),
inference(sat_conversion,[],[f492]) ).
cnf(s65,plain,
( ~ spl10_7
| ~ spl10_8
| ~ spl10_21
| ~ spl10_22
| ~ spl10_23 ),
inference(sat_conversion,[],[f1198]) ).
cnf(s67,plain,
( ~ spl10_2
| ~ spl10_5
| ~ spl10_19 ),
inference(sat_conversion,[],[f1541]) ).
cnf(s93,plain,
( ~ spl10_3
| ~ spl10_4
| ~ spl10_12
| ~ spl10_14
| ~ spl10_19 ),
inference(sat_conversion,[],[f1738]) ).
cnf(s95,plain,
( ~ spl10_6
| ~ spl10_10
| ~ spl10_18
| ~ spl10_20 ),
inference(sat_conversion,[],[f2190]) ).
cnf(s187,plain,
( ~ spl10_11
| ~ spl10_13
| ~ spl10_19 ),
inference(sat_conversion,[],[f2783]) ).
cnf(s188,plain,
( spl10_19
| spl10_6 ),
inference(rat,[],[s65,s23,s24,s25,s6,s5]) ).
cnf(s189,plain,
( spl10_11
| ~ spl10_19
| spl10_2
| spl10_1 ),
inference(rat,[],[s93,s11,s13,s2,s1]) ).
cnf(s190,plain,
( ~ spl10_19
| spl10_2
| spl10_1 ),
inference(rat,[],[s93,s12,s14,s187,s189,s2,s1]) ).
cnf(s191,plain,
( spl10_19
| spl10_1 ),
inference(rat,[],[s65,s9,s10,s95,s188,s21,s22,s23,s24,s25]) ).
cnf(s192,plain,
( spl10_11
| spl10_1 ),
inference(rat,[],[s93,s11,s13,s4,s3,s67,s190,s191]) ).
cnf(s193,plain,
( ~ spl10_19
| spl10_1 ),
inference(rat,[],[s93,s12,s14,s187,s192,s3,s4,s67,s190]) ).
cnf(s194,plain,
spl10_1,
inference(rat,[],[s193,s191]) ).
cnf(s195,plain,
spl10_14,
inference(rat,[],[s29,s18,s19,s194]) ).
cnf(s196,plain,
~ spl10_12,
inference(rat,[],[s27,s194,s195]) ).
cnf(s198,plain,
spl10_16,
inference(rat,[],[s16,s196]) ).
cnf(s199,plain,
spl10_15,
inference(rat,[],[s15,s196]) ).
cnf(s200,plain,
$false,
inference(rat,[],[s29,s194,s198,s199]) ).
thf(f2784,plain,
$false,
inference(avatar_sat_refutation,[],[s200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO445^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n005.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 16:51:46 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.02/0.42 % (1917519)Will run a generic schedule for satisfiability detection.
% 1.02/0.42 % (1917527)% WARNING: option uhcvi not known.
% 1.02/0.42 % (1917526)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=747400042_2999 on theBenchmark for (2999ds/0Mi)
% 1.02/0.42 % Exception at run slice level
% 1.02/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.02/0.42 % (1917529)dis+10_1_sil=32000:sp=arity:random_seed=2644157342:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.02/0.42 % (1917530)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1457225648:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.02/0.42 % (1917531)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2529464876:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.02/0.42 % (1917528)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=269108312:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.02/0.42 % (1917527)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4164768559:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.02/0.42 % (1917530)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.02/0.42 % (1917527)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.02/0.42 % (1917527)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.02/0.42 % (1917544)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3512044028:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.02/0.42 % (1917532)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1705885359:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.02/0.42 % Exception at run slice level
% 1.02/0.42 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.02/0.42 % (1917551)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=923015490:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.02/0.42 % (1917529)Instruction limit reached!
% 1.02/0.42 % (1917529)------------------------------
% 1.02/0.42 % (1917529)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.42 % (1917529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.42 % (1917529)CaDiCaL version: 2.1.3
% 1.02/0.42 % (1917529)Termination reason: Instruction limit
% 1.02/0.42 % (1917529)Termination phase: Saturation
% 1.02/0.42 % (1917529)Time elapsed: 0.047 s
% 1.02/0.42 % (1917529)Peak memory usage: 12 MB
% 1.02/0.42 % (1917529)Instructions burned: 104 (million)
% 1.02/0.42 % (1917530)Instruction limit reached!
% 1.02/0.42 % (1917530)------------------------------
% 1.02/0.42 % (1917530)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.42 % (1917530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.42 % (1917530)CaDiCaL version: 2.1.3
% 1.02/0.42 % (1917530)Termination reason: Instruction limit
% 1.02/0.42 % (1917530)Termination phase: Saturation
% 1.02/0.42 % (1917530)Time elapsed: 0.053 s
% 1.02/0.42 % (1917530)Peak memory usage: 12 MB
% 1.02/0.42 % (1917530)Instructions burned: 117 (million)
% 1.02/0.42 % (1917531)Instruction limit reached!
% 1.02/0.42 % (1917531)------------------------------
% 1.02/0.42 % (1917531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.42 % (1917531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.42 % (1917531)CaDiCaL version: 2.1.3
% 1.02/0.42 % (1917531)Termination reason: Instruction limit
% 1.02/0.42 % (1917531)Termination phase: Saturation
% 1.02/0.42 % (1917531)Time elapsed: 0.058 s
% 1.02/0.42 % (1917531)Peak memory usage: 12 MB
% 1.02/0.42 % (1917531)Instructions burned: 131 (million)
% 1.02/0.42 % (1917554)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3987490735:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.02/0.42 % (1917554)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.02/0.42 % (1917554)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.02/0.42 % (1917555)ott-21_1_sil=16000:fs=off:random_seed=3357190071:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.02/0.42 % (1917556)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2431522777:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 1.02/0.42 % (1917551)Instruction limit reached!
% 1.02/0.42 % (1917551)------------------------------
% 1.02/0.42 % (1917551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.42 % (1917551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.42 % (1917551)CaDiCaL version: 2.1.3
% 1.02/0.42 % (1917551)Termination reason: Instruction limit
% 1.02/0.42 % (1917551)Termination phase: Saturation
% 1.02/0.42 % (1917551)Time elapsed: 0.089 s
% 1.02/0.42 % (1917551)Peak memory usage: 12 MB
% 1.02/0.42 % (1917551)Instructions burned: 131 (million)
% 1.02/0.42 % (1917554) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1917519-1917554"...
% 1.02/0.42 % (1917532)Instruction limit reached!
% 1.02/0.42 % (1917532)------------------------------
% 1.02/0.42 % (1917532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.42 % (1917532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.42 % (1917532)CaDiCaL version: 2.1.3
% 1.02/0.42 % (1917532)Termination reason: Instruction limit
% 1.02/0.42 % (1917532)Termination phase: Saturation
% 1.02/0.42 % (1917532)Time elapsed: 0.129 s
% 1.02/0.42 % (1917532)Peak memory usage: 12 MB
% 1.02/0.42 % (1917532)Instructions burned: 161 (million)
% 1.02/0.42 % (1917560)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3840914811:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.02/0.42 % (1917554)...printing done.
% 1.02/0.42 % (1917554)Refutation found. Thanks to Tanya!
% 1.02/0.42 % SZS status Theorem for theBenchmark
% 1.02/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 1.02/0.42 % (1917554)------------------------------
% 1.02/0.42 % (1917554)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.02/0.42 % (1917554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.02/0.42 % (1917554)CaDiCaL version: 2.1.3
% 1.02/0.42 % (1917554)Termination reason: Refutation
% 1.02/0.42 % (1917554)Time elapsed: 0.081 s
% 1.02/0.42 % (1917554)Peak memory usage: 13 MB
% 1.02/0.42 % (1917554)Instructions burned: 165 (million)
% 1.02/0.42 % (1917519)Success in time 0.191 s
% 1.02/0.42 % Vampire exiting
%------------------------------------------------------------------------------