%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL725^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 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 08:15:09 AM UTC 2026
% Result : Theorem 0.87s 0.46s
% Output : Refutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 33
% Syntax : Number of formulae : 414 ( 68 unt; 0 typ; 20 def)
% Number of atoms : 4203 ( 795 equ; 0 cnn)
% Maximal formula atoms : 18 ( 10 avg)
% Number of connectives : 4393 ( 725 ~;1101 |; 21 &;2322 @)
% ( 20 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 95 ( 95 >; 0 *; 0 +; 0 <<)
% Number of symbols : 85 ( 81 usr; 35 con; 0-4 aty)
% ( 182 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 621 ( 0 sgn 244 !; 0 ?; 621 :)
% 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,
phi: $i > $o ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vAND: $o > $o > $o ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
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(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
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(f34,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a1) ).
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 @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f38,negated_conjecture,
~ ( ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) ) ),
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(f46,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f62,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f63,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f62]) ).
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(f93,plain,
mreflexive @ rel_s5,
inference(rectify,[],[f34]) ).
thf(f94,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f93]) ).
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 @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) ) ),
inference(rectify,[],[f38]) ).
thf(f100,plain,
~ ( ( ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) )
= $true )
& ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
= $true )
& ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) )
= $true ) ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( ( ( mvalid @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) )
!= $true )
| ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
!= $true )
| ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) )
!= $true ) ),
inference(ennf_transformation,[],[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(f107,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f119,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
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(f135,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f94]) ).
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 @ ( mimplies @ phi @ ( mbox_s5 @ ( mdia_s5 @ phi ) ) ) )
!= $true )
| ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ ( mbox_s5 @ ( mbox_s5 @ phi ) ) ) )
!= $true )
| ( ( mvalid @ ( mimplies @ ( mbox_s5 @ phi ) @ phi ) )
!= $true ) ),
inference(cnf_transformation,[],[f101]) ).
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(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(f151,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f135,f119]) ).
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] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ phi
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ phi ) ) ) ) )
| ( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ phi ) ) ) ) )
| ( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ phi )
@ phi ) ) ) ),
inference(definition_unfolding,[],[f138,f129,f142,f133,f150,f129,f142,f133,f133,f133,f129,f142,f133]) ).
thf(f155,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( phi @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( phi @ Y2 ) ) ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( phi @ Y2 ) ) ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( phi @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( phi @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( phi @ Y2 ) ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( phi @ Y2 ) ) ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( phi @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( phi @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( phi @ Y2 ) ) ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( phi @ Y2 ) ) ) ) ) )
@ sK1 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( phi @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( phi @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( phi @ Y2 ) ) ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( phi @ Y2 ) ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( phi @ Y0 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( ~ ( phi @ sK0 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ~ ( phi @ sK0 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f162,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 )
| ( phi @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 )
| ( phi @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f180,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK3 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( phi @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f187,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( phi @ Y0 ) )
@ sK4 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f185]) ).
thf(f191,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( phi @ Y0 ) )
@ sK4 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( phi @ Y0 ) )
@ sK4 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ~ ( rel_s5 @ sK3 @ sK4 )
| ( phi @ sK4 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( phi @ sK4 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ~ ( rel_s5 @ sK3 @ sK4 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( rel_s5 @ sK3 @ sK4 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f198,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( phi @ Y0 ) ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK3 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f197]) ).
thf(f200,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f201,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( phi @ Y0 ) )
@ sK5 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f198]) ).
thf(f202,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ~ ( rel_s5 @ sK3 @ sK5 )
| ( phi @ sK5 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( phi @ sK5 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $false
= ( ~ ( rel_s5 @ sK3 @ sK5 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f205,plain,
( ( $true
= ( phi @ sK0 ) )
| ( $true
= ( rel_s5 @ sK3 @ sK5 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f160]) ).
thf(f207,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f209,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(pi_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f213,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 )
| ( phi @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 )
| ( phi @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 )
| ( phi @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 )
| ( phi @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 )
| ( phi @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 )
| ( phi @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f224,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 )
| ( phi @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X3 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 )
| ( phi @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X3 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X3 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X3 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK6 @ X3 )
| ~ ( phi @ X3 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( phi @ X3 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( phi @ X3 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( phi @ X3 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X2 ) )
| ( $false
= ( rel_s5 @ sK6 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f234,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f236,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f234]) ).
thf(f240,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( phi @ X1 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(pi_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X2 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X2 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK6 @ X2 )
| ~ ( phi @ X2 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( phi @ X2 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( phi @ X2 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( phi @ X2 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ sK6 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f247,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK7 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f207]) ).
thf(f248,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK7 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f247]) ).
thf(f249,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK7 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f247]) ).
thf(f250,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK7 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( phi @ Y1 ) ) ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK7 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f252]) ).
thf(f255,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f255]) ).
thf(f258,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f257]) ).
thf(f259,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) )
@ sK8 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f256]) ).
thf(f262,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) )
@ sK8 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) )
@ sK8 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ~ ( rel_s5 @ sK7 @ sK8 )
| ( phi @ sK8 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f263]) ).
thf(f265,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( phi @ sK8 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ~ ( rel_s5 @ sK7 @ sK8 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f264]) ).
thf(f267,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( rel_s5 @ sK7 @ sK8 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f253]) ).
thf(f269,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f269]) ).
thf(f272,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X2 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X2 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X2 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK6 @ X2 )
| ~ ( phi @ X2 ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( phi @ X2 ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f275]) ).
thf(f277,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( phi @ X2 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( phi @ X2 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) )
| ( $false
= ( rel_s5 @ sK6 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f277]) ).
thf(f279,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) )
@ sK9 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f270]) ).
thf(f280,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) )
@ sK9 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f279]) ).
thf(f281,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) )
@ sK9 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK6 @ X2 )
| ~ ( phi @ X2 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK7 @ sK9 )
| ( phi @ sK9 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f281]) ).
thf(f283,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( phi @ X2 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK7 @ sK9 )
| ( phi @ sK9 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( phi @ X2 ) )
| ( $false
= ( ~ ( rel_s5 @ sK7 @ sK9 )
| ( phi @ sK9 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f283]) ).
thf(f285,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( phi @ X2 ) )
| ( $false
= ( phi @ sK9 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f284]) ).
thf(f286,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( phi @ X2 ) )
| ( $false
= ( ~ ( rel_s5 @ sK7 @ sK9 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f284]) ).
thf(f287,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( phi @ X2 ) )
| ( $true
= ( rel_s5 @ sK7 @ sK9 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( phi @ X2 ) )
| ( $true
= ( rel_s5 @ sK7 @ sK9 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) )
| ( $false
= ( rel_s5 @ sK6 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( phi @ X2 ) )
| ( $false
= ( phi @ sK9 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X1 ) )
| ( $false
= ( rel_s5 @ sK6 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f290,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f248]) ).
thf(f291,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f290]) ).
thf(f292,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f290]) ).
thf(f293,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f292]) ).
thf(f294,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f293]) ).
thf(f295,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f293]) ).
thf(f296,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f295]) ).
thf(f297,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) )
@ sK10 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f294]) ).
thf(f298,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ~ ( rel_s5 @ sK7 @ sK10 )
| ( phi @ sK10 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f297]) ).
thf(f299,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( phi @ sK10 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f298]) ).
thf(f300,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ~ ( rel_s5 @ sK7 @ sK10 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f298]) ).
thf(f301,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( rel_s5 @ sK7 @ sK10 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f300]) ).
thf(f302,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f291]) ).
thf(f303,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(pi_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f303]) ).
thf(f306,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f305]) ).
thf(f307,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK6 @ X1 )
| ~ ( phi @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f306]) ).
thf(f308,plain,
! [X1: $i] :
( ( $true
= ( ~ ( phi @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f309,plain,
! [X1: $i] :
( ( $false
= ( phi @ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f308]) ).
thf(f310,plain,
! [X1: $i] :
( ( $false
= ( phi @ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $false
= ( rel_s5 @ sK6 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f309]) ).
thf(f311,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( phi @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( phi @ Y0 ) )
@ sK11 ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f304]) ).
thf(f312,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK6 @ X1 )
| ~ ( phi @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK7 @ sK11 )
| ( phi @ sK11 ) ) )
| ( $false
= ( phi @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f311]) ).
thf(f313,plain,
! [X1: $i] :
( ( $true
= ( ~ ( phi @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK7 @ sK11 )
| ( phi @ sK11 ) ) )
| ( $false
= ( phi @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X1: $i] :
( ( $false
= ( phi @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK7 @ sK11 )
| ( phi @ sK11 ) ) )
| ( $false
= ( phi @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X1: $i] :
( ( $false
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK11 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f314]) ).
thf(f316,plain,
! [X1: $i] :
( ( $false
= ( phi @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK7 @ sK11 ) ) )
| ( $false
= ( phi @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f314]) ).
thf(f317,plain,
! [X1: $i] :
( ( $false
= ( phi @ X1 ) )
| ( $true
= ( rel_s5 @ sK7 @ sK11 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK6 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X1: $i] :
( ( $false
= ( phi @ X1 ) )
| ( $true
= ( rel_s5 @ sK7 @ sK11 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $false
= ( rel_s5 @ sK6 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f317]) ).
thf(f319,plain,
! [X1: $i] :
( ( $false
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK11 ) )
| ( $false
= ( phi @ sK2 ) )
| ( $false
= ( rel_s5 @ sK6 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f315]) ).
thf(f320,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f321,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f320]) ).
thf(f322,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f321]) ).
thf(f323,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f322]) ).
thf(f324,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f323]) ).
thf(f325,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f324]) ).
thf(f326,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(f327,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,[],[f326]) ).
thf(f328,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,[],[f327]) ).
thf(f329,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,[],[f328]) ).
thf(f330,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,[],[f329]) ).
thf(f331,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,[],[f330]) ).
thf(f332,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f331]) ).
thf(f333,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,[],[f332]) ).
thf(f334,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,[],[f333]) ).
thf(f335,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f336,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f335]) ).
thf(f337,plain,
! [X1: $i] :
( $true
= ( rel_s5 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f336]) ).
thf(f339,definition,
( spl12_1
<=> ! [X2: $i] :
( ( $true
= ( phi @ X2 ) )
| ( $false
= ( rel_s5 @ sK2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
thf(f340,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s5 @ sK2 @ X2 ) )
| ( $true
= ( phi @ X2 ) ) )
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f339]) ).
thf(f342,definition,
( spl12_2
<=> ! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
thf(f343,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( phi @ X1 ) ) )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f342]) ).
thf(f345,definition,
( spl12_3
<=> ( $true
= ( phi @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
thf(f347,plain,
( ( $true
= ( phi @ sK0 ) )
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f345]) ).
thf(f348,plain,
( spl12_1
| spl12_2
| spl12_3 ),
inference(avatar_split_clause,[],[f175,f345,f342,f339]) ).
thf(f350,definition,
( spl12_4
<=> ( $false
= ( phi @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
thf(f352,plain,
( ( $false
= ( phi @ sK2 ) )
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f350]) ).
thf(f353,plain,
( spl12_4
| spl12_2
| spl12_3 ),
inference(avatar_split_clause,[],[f178,f345,f342,f350]) ).
thf(f355,definition,
( spl12_5
<=> ( $true
= ( rel_s5 @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
thf(f357,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f355]) ).
thf(f358,plain,
( spl12_1
| spl12_5
| spl12_3 ),
inference(avatar_split_clause,[],[f189,f345,f355,f339]) ).
thf(f360,definition,
( spl12_6
<=> ( $true
= ( rel_s5 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
thf(f362,plain,
( ( $true
= ( rel_s5 @ sK3 @ sK4 ) )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f360]) ).
thf(f363,plain,
( spl12_1
| spl12_6
| spl12_3 ),
inference(avatar_split_clause,[],[f196,f345,f360,f339]) ).
thf(f365,definition,
( spl12_7
<=> ( $false
= ( phi @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
thf(f367,plain,
( ( $false
= ( phi @ sK4 ) )
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f365]) ).
thf(f368,plain,
( spl12_1
| spl12_7
| spl12_3 ),
inference(avatar_split_clause,[],[f194,f345,f365,f339]) ).
thf(f369,plain,
( spl12_4
| spl12_5
| spl12_3 ),
inference(avatar_split_clause,[],[f200,f345,f355,f350]) ).
thf(f371,definition,
( spl12_8
<=> ( $true
= ( rel_s5 @ sK3 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
thf(f373,plain,
( ( $true
= ( rel_s5 @ sK3 @ sK5 ) )
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f371]) ).
thf(f374,plain,
( spl12_4
| spl12_8
| spl12_3 ),
inference(avatar_split_clause,[],[f205,f345,f371,f350]) ).
thf(f376,definition,
( spl12_9
<=> ( $false
= ( phi @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
thf(f378,plain,
( ( $false
= ( phi @ sK5 ) )
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f376]) ).
thf(f379,plain,
( spl12_4
| spl12_9
| spl12_3 ),
inference(avatar_split_clause,[],[f203,f345,f376,f350]) ).
thf(f381,definition,
( spl12_10
<=> ( $true
= ( rel_s5 @ sK0 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
thf(f383,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f381]) ).
thf(f384,plain,
( spl12_1
| spl12_2
| spl12_10 ),
inference(avatar_split_clause,[],[f222,f381,f342,f339]) ).
thf(f386,definition,
( spl12_11
<=> ! [X3: $i] :
( ( $false
= ( phi @ X3 ) )
| ( $false
= ( rel_s5 @ sK6 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
thf(f387,plain,
( ! [X3: $i] :
( ( $false
= ( rel_s5 @ sK6 @ X3 ) )
| ( $false
= ( phi @ X3 ) ) )
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f386]) ).
thf(f388,plain,
( spl12_1
| spl12_2
| spl12_11 ),
inference(avatar_split_clause,[],[f232,f386,f342,f339]) ).
thf(f389,plain,
( spl12_4
| spl12_2
| spl12_10 ),
inference(avatar_split_clause,[],[f238,f381,f342,f350]) ).
thf(f390,plain,
( spl12_4
| spl12_2
| spl12_11 ),
inference(avatar_split_clause,[],[f246,f386,f342,f350]) ).
thf(f392,definition,
( spl12_12
<=> ( $true
= ( rel_s5 @ sK1 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
thf(f394,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK7 ) )
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f392]) ).
thf(f395,plain,
( spl12_1
| spl12_12
| spl12_10 ),
inference(avatar_split_clause,[],[f260,f381,f392,f339]) ).
thf(f397,definition,
( spl12_13
<=> ( $true
= ( rel_s5 @ sK7 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
thf(f399,plain,
( ( $true
= ( rel_s5 @ sK7 @ sK8 ) )
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f397]) ).
thf(f400,plain,
( spl12_1
| spl12_13
| spl12_10 ),
inference(avatar_split_clause,[],[f267,f381,f397,f339]) ).
thf(f402,definition,
( spl12_14
<=> ( $false
= ( phi @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition]) ).
thf(f404,plain,
( ( $false
= ( phi @ sK8 ) )
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f402]) ).
thf(f405,plain,
( spl12_1
| spl12_14
| spl12_10 ),
inference(avatar_split_clause,[],[f265,f381,f402,f339]) ).
thf(f406,plain,
( spl12_1
| spl12_12
| spl12_11 ),
inference(avatar_split_clause,[],[f278,f386,f392,f339]) ).
thf(f408,definition,
( spl12_15
<=> ( $true
= ( rel_s5 @ sK7 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
thf(f410,plain,
( ( $true
= ( rel_s5 @ sK7 @ sK9 ) )
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f408]) ).
thf(f411,plain,
( spl12_1
| spl12_15
| spl12_11 ),
inference(avatar_split_clause,[],[f288,f386,f408,f339]) ).
thf(f413,definition,
( spl12_16
<=> ( $false
= ( phi @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_16])],[avatar_definition]) ).
thf(f415,plain,
( ( $false
= ( phi @ sK9 ) )
| ~ spl12_16 ),
inference(avatar_component_clause,[],[f413]) ).
thf(f416,plain,
( spl12_1
| spl12_16
| spl12_11 ),
inference(avatar_split_clause,[],[f289,f386,f413,f339]) ).
thf(f417,plain,
( spl12_4
| spl12_12
| spl12_10 ),
inference(avatar_split_clause,[],[f296,f381,f392,f350]) ).
thf(f419,definition,
( spl12_17
<=> ( $true
= ( rel_s5 @ sK7 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_17])],[avatar_definition]) ).
thf(f421,plain,
( ( $true
= ( rel_s5 @ sK7 @ sK10 ) )
| ~ spl12_17 ),
inference(avatar_component_clause,[],[f419]) ).
thf(f422,plain,
( spl12_4
| spl12_17
| spl12_10 ),
inference(avatar_split_clause,[],[f301,f381,f419,f350]) ).
thf(f424,definition,
( spl12_18
<=> ( $false
= ( phi @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_18])],[avatar_definition]) ).
thf(f426,plain,
( ( $false
= ( phi @ sK10 ) )
| ~ spl12_18 ),
inference(avatar_component_clause,[],[f424]) ).
thf(f427,plain,
( spl12_4
| spl12_18
| spl12_10 ),
inference(avatar_split_clause,[],[f299,f381,f424,f350]) ).
thf(f428,plain,
( spl12_4
| spl12_12
| spl12_11 ),
inference(avatar_split_clause,[],[f310,f386,f392,f350]) ).
thf(f430,definition,
( spl12_19
<=> ( $true
= ( rel_s5 @ sK7 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_19])],[avatar_definition]) ).
thf(f432,plain,
( ( $true
= ( rel_s5 @ sK7 @ sK11 ) )
| ~ spl12_19 ),
inference(avatar_component_clause,[],[f430]) ).
thf(f433,plain,
( spl12_4
| spl12_19
| spl12_11 ),
inference(avatar_split_clause,[],[f318,f386,f430,f350]) ).
thf(f435,definition,
( spl12_20
<=> ( $false
= ( phi @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_20])],[avatar_definition]) ).
thf(f437,plain,
( ( $false
= ( phi @ sK11 ) )
| ~ spl12_20 ),
inference(avatar_component_clause,[],[f435]) ).
thf(f438,plain,
( spl12_4
| spl12_20
| spl12_11 ),
inference(avatar_split_clause,[],[f319,f386,f435,f350]) ).
thf(f450,plain,
( ( $true = $false )
| ( $true
= ( phi @ sK2 ) )
| ~ spl12_1 ),
inference(constrained_superposition,[],[f337,f340]) ).
thf(f453,plain,
( ( $true
= ( phi @ sK2 ) )
| ~ spl12_1 ),
inference(trivial_inequality_removal,[],[f450]) ).
thf(f457,plain,
( ( $true = $false )
| ~ spl12_1
| ~ spl12_4 ),
inference(forward_demodulation,[],[f453,f352]) ).
thf(f458,plain,
( $false
| ~ spl12_1
| ~ spl12_4 ),
inference(trivial_inequality_removal,[],[f457]) ).
thf(f459,plain,
( ~ spl12_1
| ~ spl12_4 ),
inference(avatar_contradiction_clause,[],[f458]) ).
thf(f477,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK6 @ sK0 ) )
| ~ spl12_10 ),
inference(constrained_superposition,[],[f383,f325]) ).
thf(f484,plain,
( ( $true
= ( rel_s5 @ sK6 @ sK0 ) )
| ~ spl12_10 ),
inference(trivial_inequality_removal,[],[f477]) ).
thf(f494,plain,
( ( $true = $false )
| ( $false
= ( phi @ sK0 ) )
| ~ spl12_10
| ~ spl12_11 ),
inference(constrained_superposition,[],[f387,f484]) ).
thf(f497,plain,
( ( $false
= ( phi @ sK0 ) )
| ~ spl12_10
| ~ spl12_11 ),
inference(trivial_inequality_removal,[],[f494]) ).
thf(f500,plain,
( ( $true = $false )
| ~ spl12_3
| ~ spl12_10
| ~ spl12_11 ),
inference(constrained_superposition,[],[f497,f347]) ).
thf(f506,plain,
( $false
| ~ spl12_3
| ~ spl12_10
| ~ spl12_11 ),
inference(trivial_inequality_removal,[],[f500]) ).
thf(f507,plain,
( ~ spl12_3
| ~ spl12_10
| ~ spl12_11 ),
inference(avatar_contradiction_clause,[],[f506]) ).
thf(f533,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $true
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) ) ),
inference(constrained_superposition,[],[f325,f334]) ).
thf(f543,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK7 @ X0 ) )
| ( $true
= ( rel_s5 @ sK1 @ X0 ) ) )
| ~ spl12_12 ),
inference(constrained_superposition,[],[f394,f334]) ).
thf(f552,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK7 @ X0 ) )
| ( $true
= ( rel_s5 @ sK1 @ X0 ) ) )
| ~ spl12_12 ),
inference(trivial_inequality_removal,[],[f543]) ).
thf(f562,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $true
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f533]) ).
thf(f969,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK1 @ sK11 ) )
| ~ spl12_12
| ~ spl12_19 ),
inference(constrained_superposition,[],[f432,f552]) ).
thf(f970,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK11 ) )
| ~ spl12_12
| ~ spl12_19 ),
inference(trivial_inequality_removal,[],[f969]) ).
thf(f1055,plain,
( ( $true = $false )
| ( $true
= ( phi @ sK11 ) )
| ~ spl12_2
| ~ spl12_12
| ~ spl12_19 ),
inference(constrained_superposition,[],[f970,f343]) ).
thf(f1078,plain,
( ( $true
= ( phi @ sK11 ) )
| ~ spl12_2
| ~ spl12_12
| ~ spl12_19 ),
inference(trivial_inequality_removal,[],[f1055]) ).
thf(f1082,plain,
( ( $true = $false )
| ~ spl12_2
| ~ spl12_12
| ~ spl12_19
| ~ spl12_20 ),
inference(forward_demodulation,[],[f1078,f437]) ).
thf(f1083,plain,
( $false
| ~ spl12_2
| ~ spl12_12
| ~ spl12_19
| ~ spl12_20 ),
inference(trivial_inequality_removal,[],[f1082]) ).
thf(f1084,plain,
( ~ spl12_2
| ~ spl12_12
| ~ spl12_19
| ~ spl12_20 ),
inference(avatar_contradiction_clause,[],[f1083]) ).
thf(f1396,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK4 @ sK3 ) )
| ~ spl12_6 ),
inference(constrained_superposition,[],[f325,f362]) ).
thf(f1413,plain,
( ( $true
= ( rel_s5 @ sK4 @ sK3 ) )
| ~ spl12_6 ),
inference(trivial_inequality_removal,[],[f1396]) ).
thf(f1432,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK5 @ sK3 ) )
| ~ spl12_8 ),
inference(constrained_superposition,[],[f325,f373]) ).
thf(f1449,plain,
( ( $true
= ( rel_s5 @ sK5 @ sK3 ) )
| ~ spl12_8 ),
inference(trivial_inequality_removal,[],[f1432]) ).
thf(f1554,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK1 @ sK8 ) )
| ~ spl12_12
| ~ spl12_13 ),
inference(constrained_superposition,[],[f552,f399]) ).
thf(f1573,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK8 ) )
| ~ spl12_12
| ~ spl12_13 ),
inference(trivial_inequality_removal,[],[f1554]) ).
thf(f1594,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK1 @ sK10 ) )
| ~ spl12_12
| ~ spl12_17 ),
inference(constrained_superposition,[],[f552,f421]) ).
thf(f1613,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK10 ) )
| ~ spl12_12
| ~ spl12_17 ),
inference(trivial_inequality_removal,[],[f1594]) ).
thf(f1768,plain,
( ( $true = $false )
| ( $true
= ( phi @ sK8 ) )
| ~ spl12_2
| ~ spl12_12
| ~ spl12_13 ),
inference(constrained_superposition,[],[f1573,f343]) ).
thf(f1807,plain,
( ( $true
= ( phi @ sK8 ) )
| ~ spl12_2
| ~ spl12_12
| ~ spl12_13 ),
inference(trivial_inequality_removal,[],[f1768]) ).
thf(f1811,plain,
( ( $true = $false )
| ~ spl12_2
| ~ spl12_12
| ~ spl12_13
| ~ spl12_14 ),
inference(forward_demodulation,[],[f1807,f404]) ).
thf(f1812,plain,
( $false
| ~ spl12_2
| ~ spl12_12
| ~ spl12_13
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f1811]) ).
thf(f1813,plain,
( ~ spl12_2
| ~ spl12_12
| ~ spl12_13
| ~ spl12_14 ),
inference(avatar_contradiction_clause,[],[f1812]) ).
thf(f1907,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK1 @ sK9 ) )
| ~ spl12_12
| ~ spl12_15 ),
inference(constrained_superposition,[],[f552,f410]) ).
thf(f1926,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK9 ) )
| ~ spl12_12
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f1907]) ).
thf(f2061,plain,
( ( $true = $false )
| ( $true
= ( phi @ sK9 ) )
| ~ spl12_2
| ~ spl12_12
| ~ spl12_15 ),
inference(constrained_superposition,[],[f1926,f343]) ).
thf(f2100,plain,
( ( $true
= ( phi @ sK9 ) )
| ~ spl12_2
| ~ spl12_12
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f2061]) ).
thf(f2104,plain,
( ( $true = $false )
| ~ spl12_2
| ~ spl12_12
| ~ spl12_15
| ~ spl12_16 ),
inference(forward_demodulation,[],[f2100,f415]) ).
thf(f2105,plain,
( $false
| ~ spl12_2
| ~ spl12_12
| ~ spl12_15
| ~ spl12_16 ),
inference(trivial_inequality_removal,[],[f2104]) ).
thf(f2106,plain,
( ~ spl12_2
| ~ spl12_12
| ~ spl12_15
| ~ spl12_16 ),
inference(avatar_contradiction_clause,[],[f2105]) ).
thf(f2148,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ sK3 ) )
| ( $true
= ( rel_s5 @ sK1 @ X0 ) ) )
| ~ spl12_5 ),
inference(constrained_superposition,[],[f562,f357]) ).
thf(f2149,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK3 ) )
| ( $true
= ( rel_s5 @ sK1 @ X0 ) ) )
| ~ spl12_5 ),
inference(trivial_inequality_removal,[],[f2148]) ).
thf(f3686,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ~ spl12_5
| ~ spl12_6 ),
inference(constrained_superposition,[],[f1413,f2149]) ).
thf(f3687,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( phi @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK3 ) ) )
| ~ spl12_2
| ~ spl12_5 ),
inference(constrained_superposition,[],[f343,f2149]) ).
thf(f3728,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK3 ) )
| ( $true
= ( phi @ X0 ) ) )
| ~ spl12_2
| ~ spl12_5 ),
inference(trivial_inequality_removal,[],[f3687]) ).
thf(f3729,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ~ spl12_5
| ~ spl12_6 ),
inference(trivial_inequality_removal,[],[f3686]) ).
thf(f3839,plain,
( ( $true = $false )
| ( $true
= ( phi @ sK4 ) )
| ~ spl12_2
| ~ spl12_5
| ~ spl12_6 ),
inference(constrained_superposition,[],[f3729,f343]) ).
thf(f3890,plain,
( ( $true
= ( phi @ sK4 ) )
| ~ spl12_2
| ~ spl12_5
| ~ spl12_6 ),
inference(trivial_inequality_removal,[],[f3839]) ).
thf(f3894,plain,
( ( $true = $false )
| ~ spl12_2
| ~ spl12_5
| ~ spl12_6
| ~ spl12_7 ),
inference(forward_demodulation,[],[f3890,f367]) ).
thf(f3895,plain,
( $false
| ~ spl12_2
| ~ spl12_5
| ~ spl12_6
| ~ spl12_7 ),
inference(trivial_inequality_removal,[],[f3894]) ).
thf(f3896,plain,
( ~ spl12_2
| ~ spl12_5
| ~ spl12_6
| ~ spl12_7 ),
inference(avatar_contradiction_clause,[],[f3895]) ).
thf(f4086,plain,
( ( $true = $false )
| ( $true
= ( phi @ sK10 ) )
| ~ spl12_2
| ~ spl12_12
| ~ spl12_17 ),
inference(constrained_superposition,[],[f1613,f343]) ).
thf(f4137,plain,
( ( $true
= ( phi @ sK10 ) )
| ~ spl12_2
| ~ spl12_12
| ~ spl12_17 ),
inference(trivial_inequality_removal,[],[f4086]) ).
thf(f4141,plain,
( ( $true = $false )
| ~ spl12_2
| ~ spl12_12
| ~ spl12_17
| ~ spl12_18 ),
inference(forward_demodulation,[],[f4137,f426]) ).
thf(f4142,plain,
( $false
| ~ spl12_2
| ~ spl12_12
| ~ spl12_17
| ~ spl12_18 ),
inference(trivial_inequality_removal,[],[f4141]) ).
thf(f4143,plain,
( ~ spl12_2
| ~ spl12_12
| ~ spl12_17
| ~ spl12_18 ),
inference(avatar_contradiction_clause,[],[f4142]) ).
thf(f4889,plain,
( ( $true = $false )
| ( $true
= ( phi @ sK5 ) )
| ~ spl12_2
| ~ spl12_5
| ~ spl12_8 ),
inference(constrained_superposition,[],[f3728,f1449]) ).
thf(f4910,plain,
( ( $true
= ( phi @ sK5 ) )
| ~ spl12_2
| ~ spl12_5
| ~ spl12_8 ),
inference(trivial_inequality_removal,[],[f4889]) ).
thf(f4922,plain,
( ( $true = $false )
| ~ spl12_2
| ~ spl12_5
| ~ spl12_8
| ~ spl12_9 ),
inference(forward_demodulation,[],[f4910,f378]) ).
thf(f4923,plain,
( $false
| ~ spl12_2
| ~ spl12_5
| ~ spl12_8
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f4922]) ).
thf(f4924,plain,
( ~ spl12_2
| ~ spl12_5
| ~ spl12_8
| ~ spl12_9 ),
inference(avatar_contradiction_clause,[],[f4923]) ).
cnf(s1,plain,
( spl12_1
| spl12_2
| spl12_3 ),
inference(sat_conversion,[],[f348]) ).
cnf(s2,plain,
( spl12_2
| spl12_3
| spl12_4 ),
inference(sat_conversion,[],[f353]) ).
cnf(s3,plain,
( spl12_1
| spl12_3
| spl12_5 ),
inference(sat_conversion,[],[f358]) ).
cnf(s4,plain,
( spl12_1
| spl12_3
| spl12_6 ),
inference(sat_conversion,[],[f363]) ).
cnf(s5,plain,
( spl12_1
| spl12_3
| spl12_7 ),
inference(sat_conversion,[],[f368]) ).
cnf(s6,plain,
( spl12_3
| spl12_4
| spl12_5 ),
inference(sat_conversion,[],[f369]) ).
cnf(s7,plain,
( spl12_3
| spl12_4
| spl12_8 ),
inference(sat_conversion,[],[f374]) ).
cnf(s8,plain,
( spl12_3
| spl12_4
| spl12_9 ),
inference(sat_conversion,[],[f379]) ).
cnf(s9,plain,
( spl12_1
| spl12_2
| spl12_10 ),
inference(sat_conversion,[],[f384]) ).
cnf(s10,plain,
( spl12_1
| spl12_2
| spl12_11 ),
inference(sat_conversion,[],[f388]) ).
cnf(s11,plain,
( spl12_2
| spl12_4
| spl12_10 ),
inference(sat_conversion,[],[f389]) ).
cnf(s12,plain,
( spl12_2
| spl12_4
| spl12_11 ),
inference(sat_conversion,[],[f390]) ).
cnf(s13,plain,
( spl12_1
| spl12_10
| spl12_12 ),
inference(sat_conversion,[],[f395]) ).
cnf(s14,plain,
( spl12_1
| spl12_10
| spl12_13 ),
inference(sat_conversion,[],[f400]) ).
cnf(s15,plain,
( spl12_1
| spl12_10
| spl12_14 ),
inference(sat_conversion,[],[f405]) ).
cnf(s16,plain,
( spl12_1
| spl12_11
| spl12_12 ),
inference(sat_conversion,[],[f406]) ).
cnf(s17,plain,
( spl12_1
| spl12_11
| spl12_15 ),
inference(sat_conversion,[],[f411]) ).
cnf(s18,plain,
( spl12_1
| spl12_11
| spl12_16 ),
inference(sat_conversion,[],[f416]) ).
cnf(s19,plain,
( spl12_4
| spl12_10
| spl12_12 ),
inference(sat_conversion,[],[f417]) ).
cnf(s20,plain,
( spl12_4
| spl12_10
| spl12_17 ),
inference(sat_conversion,[],[f422]) ).
cnf(s21,plain,
( spl12_4
| spl12_10
| spl12_18 ),
inference(sat_conversion,[],[f427]) ).
cnf(s22,plain,
( spl12_4
| spl12_11
| spl12_12 ),
inference(sat_conversion,[],[f428]) ).
cnf(s23,plain,
( spl12_4
| spl12_11
| spl12_19 ),
inference(sat_conversion,[],[f433]) ).
cnf(s24,plain,
( spl12_4
| spl12_11
| spl12_20 ),
inference(sat_conversion,[],[f438]) ).
cnf(s26,plain,
( ~ spl12_1
| ~ spl12_4 ),
inference(sat_conversion,[],[f459]) ).
cnf(s28,plain,
( ~ spl12_3
| ~ spl12_10
| ~ spl12_11 ),
inference(sat_conversion,[],[f507]) ).
cnf(s38,plain,
( ~ spl12_2
| ~ spl12_12
| ~ spl12_19
| ~ spl12_20 ),
inference(sat_conversion,[],[f1084]) ).
cnf(s44,plain,
( ~ spl12_2
| ~ spl12_12
| ~ spl12_13
| ~ spl12_14 ),
inference(sat_conversion,[],[f1813]) ).
cnf(s52,plain,
( ~ spl12_2
| ~ spl12_12
| ~ spl12_15
| ~ spl12_16 ),
inference(sat_conversion,[],[f2106]) ).
cnf(s54,plain,
( ~ spl12_2
| ~ spl12_5
| ~ spl12_6
| ~ spl12_7 ),
inference(sat_conversion,[],[f3896]) ).
cnf(s56,plain,
( ~ spl12_2
| ~ spl12_12
| ~ spl12_17
| ~ spl12_18 ),
inference(sat_conversion,[],[f4143]) ).
cnf(s63,plain,
( ~ spl12_2
| ~ spl12_5
| ~ spl12_8
| ~ spl12_9 ),
inference(sat_conversion,[],[f4924]) ).
cnf(s64,plain,
( spl12_2
| spl12_1 ),
inference(rat,[],[s28,s1,s9,s10]) ).
cnf(s65,plain,
( spl12_11
| spl12_1 ),
inference(rat,[],[s52,s16,s17,s18,s64]) ).
cnf(s66,plain,
( spl12_10
| spl12_1 ),
inference(rat,[],[s44,s13,s14,s15,s64]) ).
cnf(s67,plain,
spl12_1,
inference(rat,[],[s54,s3,s4,s5,s28,s66,s65,s64]) ).
cnf(s68,plain,
~ spl12_4,
inference(rat,[],[s26,s67]) ).
cnf(s69,plain,
( spl12_11
| ~ spl12_2 ),
inference(rat,[],[s38,s22,s23,s24,s68]) ).
cnf(s70,plain,
( spl12_10
| ~ spl12_2 ),
inference(rat,[],[s56,s19,s20,s21,s68]) ).
cnf(s71,plain,
~ spl12_2,
inference(rat,[],[s63,s6,s8,s7,s28,s70,s69,s68]) ).
cnf(s72,plain,
spl12_11,
inference(rat,[],[s12,s68,s71]) ).
cnf(s73,plain,
spl12_10,
inference(rat,[],[s11,s68,s71]) ).
cnf(s74,plain,
spl12_3,
inference(rat,[],[s2,s68,s71]) ).
cnf(s76,plain,
$false,
inference(rat,[],[s28,s72,s74,s73]) ).
thf(f4925,plain,
$false,
inference(avatar_sat_refutation,[],[s76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL725^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n005.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 09:56:46 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.87/0.46 % (1460164)Will run a generic schedule for satisfiability detection.
% 0.87/0.46 % (1460169)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=362122940_2999 on theBenchmark for (2999ds/0Mi)
% 0.87/0.46 % Exception at run slice level
% 0.87/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.87/0.46 % (1460170)% WARNING: option uhcvi not known.
% 0.87/0.46 % (1460170)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3080361816:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.87/0.46 % (1460171)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2080845511:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.87/0.46 % (1460170)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.87/0.46 % (1460170)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.87/0.46 % (1460177)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1662858520:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.87/0.46 % Exception at run slice level
% 0.87/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.87/0.46 % (1460172)dis+10_1_sil=32000:sp=arity:random_seed=2445666068:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.87/0.46 % (1460173)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1624244304:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.87/0.46 % (1460174)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1308341028:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.87/0.46 % (1460173)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.87/0.46 % (1460181)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3201711344:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.87/0.46 % (1460175)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2475224593:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.87/0.46 % (1460181)Instruction limit reached!
% 0.87/0.46 % (1460181)------------------------------
% 0.87/0.46 % (1460181)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.46 % (1460181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.46 % (1460181)CaDiCaL version: 2.1.3
% 0.87/0.46 % (1460181)Termination reason: Instruction limit
% 0.87/0.46 % (1460181)Termination phase: Saturation
% 0.87/0.46 % (1460181)Time elapsed: 0.030 s
% 0.87/0.46 % (1460181)Peak memory usage: 12 MB
% 0.87/0.46 % (1460181)Instructions burned: 131 (million)
% 0.87/0.46 % (1460187)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=1459326666:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.87/0.46 % (1460187)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.87/0.46 % (1460187)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.87/0.46 % (1460174)Instruction limit reached!
% 0.87/0.46 % (1460174)------------------------------
% 0.87/0.46 % (1460174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.46 % (1460174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.46 % (1460174)CaDiCaL version: 2.1.3
% 0.87/0.46 % (1460174)Termination reason: Instruction limit
% 0.87/0.46 % (1460174)Termination phase: Saturation
% 0.87/0.46 % (1460174)Time elapsed: 0.057 s
% 0.87/0.46 % (1460174)Peak memory usage: 12 MB
% 0.87/0.46 % (1460174)Instructions burned: 132 (million)
% 0.87/0.46 % (1460173)Instruction limit reached!
% 0.87/0.46 % (1460173)------------------------------
% 0.87/0.46 % (1460173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.46 % (1460173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.46 % (1460173)CaDiCaL version: 2.1.3
% 0.87/0.46 % (1460173)Termination reason: Instruction limit
% 0.87/0.46 % (1460173)Termination phase: Saturation
% 0.87/0.46 % (1460173)Time elapsed: 0.072 s
% 0.87/0.46 % (1460173)Peak memory usage: 12 MB
% 0.87/0.46 % (1460173)Instructions burned: 117 (million)
% 0.87/0.46 % (1460189)ott-21_1_sil=16000:fs=off:random_seed=668743082:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.87/0.46 % (1460172)Instruction limit reached!
% 0.87/0.46 % (1460172)------------------------------
% 0.87/0.46 % (1460172)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.46 % (1460172)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.46 % (1460172)CaDiCaL version: 2.1.3
% 0.87/0.46 % (1460172)Termination reason: Instruction limit
% 0.87/0.46 % (1460172)Termination phase: Saturation
% 0.87/0.46 % (1460172)Time elapsed: 0.084 s
% 0.87/0.46 % (1460172)Peak memory usage: 12 MB
% 0.87/0.46 % (1460172)Instructions burned: 103 (million)
% 0.87/0.46 % (1460192)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1664562821:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.87/0.46 % Exception at run slice level
% 0.87/0.46 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.87/0.46 % (1460194)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3353759537:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.87/0.46 % (1460190)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3976874697:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.87/0.46 % (1460187) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1460164-1460187"...
% 0.87/0.46 % (1460175)Instruction limit reached!
% 0.87/0.46 % (1460175)------------------------------
% 0.87/0.46 % (1460175)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.46 % (1460175)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.46 % (1460175)CaDiCaL version: 2.1.3
% 0.87/0.46 % (1460175)Termination reason: Instruction limit
% 0.87/0.46 % (1460175)Termination phase: Saturation
% 0.87/0.46 % (1460175)Time elapsed: 0.135 s
% 0.87/0.46 % (1460175)Peak memory usage: 12 MB
% 0.87/0.46 % (1460175)Instructions burned: 159 (million)
% 0.87/0.46 % (1460187)...printing done.
% 0.87/0.46 % (1460187)Refutation found. Thanks to Tanya!
% 0.87/0.46 % SZS status Theorem for theBenchmark
% 0.87/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.87/0.46 % (1460187)------------------------------
% 0.87/0.46 % (1460187)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.46 % (1460187)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.46 % (1460187)CaDiCaL version: 2.1.3
% 0.87/0.46 % (1460187)Termination reason: Refutation
% 0.87/0.46 % (1460187)Time elapsed: 0.103 s
% 0.87/0.46 % (1460187)Peak memory usage: 14 MB
% 0.87/0.46 % (1460187)Instructions burned: 288 (million)
% 0.87/0.46 % (1460164)Success in time 0.219 s
% 0.87/0.46 % Vampire exiting
%------------------------------------------------------------------------------