%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN741^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 08:42:04 AM UTC 2026
% Result : ContradictoryAxioms 22.83s 3.68s
% Output : Refutation 22.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 76
% Number of leaves : 18
% Syntax : Number of formulae : 411 ( 105 unt; 0 typ; 0 def)
% Number of atoms : 6379 (1588 equ; 0 cnn)
% Maximal formula atoms : 16 ( 15 avg)
% Number of connectives : 8296 (1077 ~;1912 |; 0 &;4908 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 164 ( 164 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 3 con; 0-4 aty)
% ( 399 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1740 ( 797 ^; 943 !; 0 ?;1740 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
qmltpeq: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
mtrue: $i > $o ).
thf(func_def_8,type,
mfalse: $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
exists_in_world: mu > $i > $o ).
thf(func_def_16,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_18,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_33,type,
rel_s4: $i > $i > $o ).
thf(func_def_34,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
v1: $i > $o ).
thf(func_def_37,type,
v3: $i > $o ).
thf(func_def_38,type,
v2: $i > $o ).
thf(func_def_39,type,
v4: $i > $o ).
thf(func_def_40,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_44,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vIMP: $o > $o > $o ).
thf(func_def_52,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_53,type,
vAND: $o > $o > $o ).
thf(func_def_54,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
sK0: $i > mu ).
thf(func_def_57,type,
sK2: $i > $i ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f6,axiom,
( mtrue
= ( ^ [X0: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mtrue) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mreflexive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f33,axiom,
( mdia_s4
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mdia_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f41,axiom,
mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ v1 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat5) ).
thf(f45,axiom,
mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat9) ).
thf(f46,axiom,
mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat10) ).
thf(f51,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat15) ).
thf(f52,axiom,
mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat16) ).
thf(f57,axiom,
mvalid @ ( mor @ v4 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat21) ).
thf(f60,axiom,
mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat24) ).
thf(f61,axiom,
mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v1 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat25) ).
thf(f62,axiom,
mvalid @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',persat26) ).
thf(f67,axiom,
mvalid @ ( mdia_s4 @ mtrue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',deontic1) ).
thf(f71,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f72,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f74,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f79,plain,
( mtrue
= ( ^ [Y0: $i] : $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f94,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f95,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f94]) ).
thf(f114,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f115,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f114]) ).
thf(f122,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f123,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f122]) ).
thf(f124,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f125,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f126,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f125]) ).
thf(f139,plain,
mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ v1 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f140,plain,
( ( mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ v1 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f139]) ).
thf(f147,plain,
mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
inference(rectify,[],[f45]) ).
thf(f148,plain,
( ( mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f147]) ).
thf(f149,plain,
mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
inference(rectify,[],[f46]) ).
thf(f150,plain,
( ( mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f149]) ).
thf(f159,plain,
mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ),
inference(rectify,[],[f51]) ).
thf(f160,plain,
( ( mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f159]) ).
thf(f161,plain,
mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ),
inference(rectify,[],[f52]) ).
thf(f162,plain,
( ( mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f161]) ).
thf(f171,plain,
mvalid @ ( mor @ v4 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ),
inference(rectify,[],[f57]) ).
thf(f172,plain,
( ( mvalid @ ( mor @ v4 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f171]) ).
thf(f177,plain,
mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ),
inference(rectify,[],[f60]) ).
thf(f178,plain,
( ( mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f177]) ).
thf(f179,plain,
mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v1 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ),
inference(rectify,[],[f61]) ).
thf(f180,plain,
( ( mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v1 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f179]) ).
thf(f181,plain,
mvalid @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ),
inference(rectify,[],[f62]) ).
thf(f182,plain,
( ( mvalid @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f181]) ).
thf(f191,plain,
mvalid @ ( mdia_s4 @ mtrue ),
inference(rectify,[],[f67]) ).
thf(f192,plain,
( ( mvalid @ ( mdia_s4 @ mtrue ) )
= $true ),
inference(fool_elimination,[],[f191]) ).
thf(f200,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f201,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f204,plain,
( mtrue
= ( ^ [Y0: $i] : $true ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f216,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f226,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f115]) ).
thf(f230,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f231,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f124]) ).
thf(f232,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f126]) ).
thf(f239,plain,
( ( mvalid @ ( mor @ v1 @ ( mor @ ( mbox_s4 @ v1 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f140]) ).
thf(f243,plain,
( ( mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f148]) ).
thf(f244,plain,
( ( mvalid @ ( mor @ v2 @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f150]) ).
thf(f249,plain,
( ( mvalid @ ( mor @ v3 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v4 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f160]) ).
thf(f250,plain,
( ( mvalid @ ( mor @ v3 @ ( mor @ ( mbox_s4 @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v2 ) ) @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f162]) ).
thf(f255,plain,
( ( mvalid @ ( mor @ v4 @ ( mor @ ( mnot @ v2 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f172]) ).
thf(f258,plain,
( ( mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mnot @ v4 ) @ ( mor @ ( mbox_s4 @ ( mbox_s4 @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f178]) ).
thf(f259,plain,
( ( mvalid @ ( mor @ ( mnot @ v1 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v1 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v3 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f180]) ).
thf(f260,plain,
( ( mvalid @ ( mor @ ( mnot @ v3 ) @ ( mor @ ( mbox_s4 @ ( mnot @ v2 ) ) @ ( mor @ ( mbox_s4 @ ( mnot @ v4 ) ) @ ( mbox_s4 @ ( mbox_s4 @ ( mnot @ v3 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f182]) ).
thf(f265,plain,
( ( mvalid @ ( mdia_s4 @ mtrue ) )
= $true ),
inference(cnf_transformation,[],[f192]) ).
thf(f278,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f231,f200,f230,f200]) ).
thf(f279,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f232,f216]) ).
thf(f285,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v1
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v4 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f239,f226,f201,f201,f230,f201,f230,f230,f230,f230,f200]) ).
thf(f289,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v2
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v3 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v3 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f243,f226,f201,f201,f200,f201,f230,f200,f230,f230,f200]) ).
thf(f290,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v2
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v4 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v4 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v4 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f244,f226,f201,f201,f200,f201,f230,f200,f230,f230,f200]) ).
thf(f295,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v3
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v2 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v4 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f249,f226,f201,f201,f200,f201,f230,f230,f200,f230,f230,f200]) ).
thf(f296,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v3
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v4 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v3 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f250,f226,f201,f201,f230,f201,f230,f230,f230,f230]) ).
thf(f301,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ v4
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v2 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v3 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f255,f226,f201,f201,f200,f201,f230,f230,f230,f230,f200]) ).
thf(f304,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v4 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ v3 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f258,f226,f201,f200,f201,f200,f201,f230,f230,f230,f230,f200]) ).
thf(f305,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v3 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f259,f226,f201,f200,f201,f230,f200,f201,f230,f200,f230,f230,f200]) ).
thf(f306,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v3 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v4 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ v3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f260,f226,f201,f200,f201,f230,f200,f201,f230,f200,f230,f230,f200]) ).
thf(f311,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ^ [Y0: $i] : $true ) ) ),
inference(definition_unfolding,[],[f265,f226,f278,f204]) ).
thf(f317,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ $true ) ) ) ),
inference(beta-eta_normalization,[],[f311]) ).
thf(f318,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ $true ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f317]) ).
thf(f319,plain,
! [X1: $i] :
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ $true ) ) ) ),
inference(beta-eta_normalization,[],[f318]) ).
thf(f320,plain,
! [X1: $i] :
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ $true ) ) ),
inference(not_proxy_clausification,[],[f319]) ).
thf(f321,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ $true )
@ ( sK2 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f320]) ).
thf(f322,plain,
! [X1: $i] :
( $false
= ( ~ ( rel_s4 @ X1 @ ( sK2 @ X1 ) )
| ~ $true ) ),
inference(beta-eta_normalization,[],[f321]) ).
thf(f324,plain,
! [X1: $i] :
( $false
= ( ~ ( rel_s4 @ X1 @ ( sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f322]) ).
thf(f325,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ ( sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f324]) ).
thf(f437,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( v3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v3 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f306]) ).
thf(f438,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( v3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v3 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f437]) ).
thf(f439,plain,
! [X1: $i] :
( $true
= ( ~ ( v3 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f438]) ).
thf(f440,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( v3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f439]) ).
thf(f441,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f440]) ).
thf(f442,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f441]) ).
thf(f443,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f442]) ).
thf(f444,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f443]) ).
thf(f445,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f444]) ).
thf(f446,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f445]) ).
thf(f447,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) ) ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ~ ( v2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ~ ( v4 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f446]) ).
thf(f448,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ~ ( v2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ~ ( v4 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f447]) ).
thf(f449,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ~ ( v2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ~ ( v4 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f448]) ).
thf(f450,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( v2 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ~ ( v4 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f449]) ).
thf(f451,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ~ ( v4 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f450]) ).
thf(f452,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X3 ) )
| ( $true
= ( ~ ( v4 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f451]) ).
thf(f453,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X3 ) )
| ( $false
= ( v4 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f452]) ).
thf(f454,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X3 ) )
| ( $false
= ( v4 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f453]) ).
thf(f455,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X3 ) )
| ( $false
= ( v4 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f454]) ).
thf(f456,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X3 ) )
| ( $false
= ( v4 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f455]) ).
thf(f457,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X5 )
| ~ ( v3 @ X5 ) ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X3 ) )
| ( $false
= ( v4 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f456]) ).
thf(f458,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( v3 @ X5 ) ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X3 ) )
| ( $false
= ( v4 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X5 ) ) ) ),
inference(or_proxy_clausification,[],[f457]) ).
thf(f459,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( v3 @ X5 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X3 ) )
| ( $false
= ( v4 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X5 ) ) ) ),
inference(not_proxy_clausification,[],[f458]) ).
thf(f460,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v4 @ X4 ) )
| ( $false
= ( v2 @ X3 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v3 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f459]) ).
thf(f461,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( v1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f305]) ).
thf(f462,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( v1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v1 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f461]) ).
thf(f463,plain,
! [X1: $i] :
( $true
= ( ~ ( v1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f462]) ).
thf(f464,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( v1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f463]) ).
thf(f465,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( v1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f464]) ).
thf(f466,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( v1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f465]) ).
thf(f467,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( v1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f466]) ).
thf(f468,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f467]) ).
thf(f469,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f468]) ).
thf(f470,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f469]) ).
thf(f471,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) ) ) )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ~ ( v1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ~ ( v3 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f470]) ).
thf(f472,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) ) )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ~ ( v1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ~ ( v3 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f471]) ).
thf(f473,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ~ ( v1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ~ ( v3 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f472]) ).
thf(f474,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( ~ ( v1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ~ ( v3 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f473]) ).
thf(f475,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ~ ( v3 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f474]) ).
thf(f476,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v1 @ X3 ) )
| ( $true
= ( ~ ( v3 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f475]) ).
thf(f477,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v1 @ X3 ) )
| ( $false
= ( v3 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f476]) ).
thf(f478,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v1 @ X3 ) )
| ( $false
= ( v3 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f477]) ).
thf(f479,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v1 @ X3 ) )
| ( $false
= ( v3 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f478]) ).
thf(f480,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X5 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v1 @ X3 ) )
| ( $false
= ( v3 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f479]) ).
thf(f481,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X5 )
| ~ ( v1 @ X5 ) ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v1 @ X3 ) )
| ( $false
= ( v3 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f480]) ).
thf(f482,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( v1 @ X5 ) ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v1 @ X3 ) )
| ( $false
= ( v3 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X5 ) ) ) ),
inference(or_proxy_clausification,[],[f481]) ).
thf(f483,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( v1 @ X5 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v1 @ X3 ) )
| ( $false
= ( v3 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X5 ) ) ) ),
inference(not_proxy_clausification,[],[f482]) ).
thf(f484,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v3 @ X4 ) )
| ( $false
= ( v1 @ X3 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v1 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f483]) ).
thf(f485,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( v1 @ Y0 )
| ~ ( v4 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v3 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v2 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f304]) ).
thf(f486,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( v1 @ Y0 )
| ~ ( v4 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v3 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v2 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f485]) ).
thf(f487,plain,
! [X1: $i] :
( $true
= ( ~ ( v1 @ X1 )
| ~ ( v4 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f486]) ).
thf(f488,plain,
! [X1: $i] :
( ( $true
= ( ~ ( v4 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( v1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f487]) ).
thf(f489,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( v1 @ X1 ) ) )
| ( $true
= ( ~ ( v4 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f488]) ).
thf(f490,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( v1 @ X1 ) ) )
| ( $true
= ( ~ ( v4 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f489]) ).
thf(f491,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( v1 @ X1 ) ) )
| ( $true
= ( ~ ( v4 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f490]) ).
thf(f492,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $true
= ( ~ ( v4 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f491]) ).
thf(f493,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f492]) ).
thf(f494,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f493]) ).
thf(f495,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f494]) ).
thf(f496,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f495]) ).
thf(f497,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f496]) ).
thf(f498,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f497]) ).
thf(f499,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f498]) ).
thf(f500,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f499]) ).
thf(f501,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X4 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f500]) ).
thf(f502,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X4 )
| ~ ( v2 @ X4 ) ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 )
| ( v3 @ X5 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f501]) ).
thf(f503,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( v2 @ X4 ) ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 )
| ( v3 @ X5 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f502]) ).
thf(f504,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( v2 @ X4 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 )
| ( v3 @ X5 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f503]) ).
thf(f505,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( v2 @ X4 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( v3 @ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 ) ) ) ),
inference(or_proxy_clausification,[],[f504]) ).
thf(f506,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( v2 @ X4 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( v3 @ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 ) ) ) ),
inference(not_proxy_clausification,[],[f505]) ).
thf(f507,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X3 @ X5 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( v3 @ X5 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v1 @ X1 ) )
| ( $false
= ( v2 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f506]) ).
thf(f552,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( v4 @ Y0 )
| ~ ( v2 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v3 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f301]) ).
thf(f553,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( v4 @ Y0 )
| ~ ( v2 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v3 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v1 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f552]) ).
thf(f554,plain,
! [X1: $i] :
( $true
= ( ( v4 @ X1 )
| ~ ( v2 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f553]) ).
thf(f555,plain,
! [X1: $i] :
( ( $true
= ( ~ ( v2 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v4 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f554]) ).
thf(f556,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( v2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f555]) ).
thf(f557,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) ) ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( v2 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f556]) ).
thf(f558,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( v2 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f557]) ).
thf(f559,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f558]) ).
thf(f560,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v1 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f559]) ).
thf(f561,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) ) ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f560]) ).
thf(f562,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) ) ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f561]) ).
thf(f563,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f562]) ).
thf(f564,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f563]) ).
thf(f565,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f564]) ).
thf(f566,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f565]) ).
thf(f567,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f566]) ).
thf(f568,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X4 )
| ~ ( v1 @ X4 ) ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 )
| ( v3 @ X5 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f567]) ).
thf(f569,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( v1 @ X4 ) ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 )
| ( v3 @ X5 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f568]) ).
thf(f570,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( v1 @ X4 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 )
| ( v3 @ X5 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f569]) ).
thf(f571,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( v1 @ X4 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( v3 @ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 ) ) ) ),
inference(or_proxy_clausification,[],[f570]) ).
thf(f572,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( v1 @ X4 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( v3 @ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 ) ) ) ),
inference(not_proxy_clausification,[],[f571]) ).
thf(f573,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X3 @ X5 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( v3 @ X5 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f572]) ).
thf(f668,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( v3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v2 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v3 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f296]) ).
thf(f669,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( v3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v2 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v3 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f668]) ).
thf(f670,plain,
! [X1: $i] :
( $true
= ( ( v3 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f669]) ).
thf(f671,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v3 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f670]) ).
thf(f672,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f671]) ).
thf(f673,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) ) ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f672]) ).
thf(f674,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f673]) ).
thf(f675,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f674]) ).
thf(f676,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v3 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v2 @ Y1 ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f675]) ).
thf(f677,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) ) ) ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( v4 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f676]) ).
thf(f678,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) ) ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( v4 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f677]) ).
thf(f679,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( v4 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f678]) ).
thf(f680,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f679]) ).
thf(f681,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f680]) ).
thf(f682,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v2 @ Y0 ) )
@ X6 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(pi_proxy_clausification,[],[f681]) ).
thf(f683,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v2 @ Y0 ) )
@ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f682]) ).
thf(f684,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v2 @ Y0 ) )
@ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f683]) ).
thf(f685,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( v3 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v2 @ Y0 ) )
@ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f684]) ).
thf(f686,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X5 )
| ( v3 @ X5 ) ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X4 @ X6 )
| ( v2 @ X6 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f685]) ).
thf(f687,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( v3 @ X5 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X4 @ X6 )
| ( v2 @ X6 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X5 ) ) ) ),
inference(or_proxy_clausification,[],[f686]) ).
thf(f688,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( v3 @ X5 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( v2 @ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X5 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X4 @ X6 ) ) ) ),
inference(or_proxy_clausification,[],[f687]) ).
thf(f689,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( v3 @ X5 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( v2 @ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $true
= ( ~ ( rel_s4 @ X4 @ X6 ) ) ) ),
inference(not_proxy_clausification,[],[f688]) ).
thf(f690,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X4 @ X6 ) )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( v2 @ X6 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( v3 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f689]) ).
thf(f691,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( v3 @ Y0 )
| ~ ( v2 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v2 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v4 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f295]) ).
thf(f692,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( v3 @ Y0 )
| ~ ( v2 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v2 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v4 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f691]) ).
thf(f693,plain,
! [X1: $i] :
( $true
= ( ( v3 @ X1 )
| ~ ( v2 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f692]) ).
thf(f694,plain,
! [X1: $i] :
( ( $true
= ( ~ ( v2 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v3 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f693]) ).
thf(f695,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( v2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f694]) ).
thf(f696,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( v2 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f695]) ).
thf(f697,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( v2 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f696]) ).
thf(f698,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f697]) ).
thf(f699,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f698]) ).
thf(f700,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) ) ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f699]) ).
thf(f701,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f700]) ).
thf(f702,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f701]) ).
thf(f703,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f702]) ).
thf(f704,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X5 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(pi_proxy_clausification,[],[f703]) ).
thf(f705,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f704]) ).
thf(f706,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X3 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f705]) ).
thf(f707,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X4 )
| ~ ( v4 @ X4 ) ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 )
| ~ ( v2 @ X5 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f706]) ).
thf(f708,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( v4 @ X4 ) ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 )
| ~ ( v2 @ X5 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f707]) ).
thf(f709,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( v4 @ X4 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 )
| ~ ( v2 @ X5 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f708]) ).
thf(f710,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( v4 @ X4 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( v2 @ X5 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 ) ) ) ),
inference(or_proxy_clausification,[],[f709]) ).
thf(f711,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( v4 @ X4 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $false
= ( v2 @ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 ) ) ) ),
inference(not_proxy_clausification,[],[f710]) ).
thf(f712,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( v4 @ X4 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $false
= ( v2 @ X5 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X3 @ X5 ) ) ) ),
inference(not_proxy_clausification,[],[f711]) ).
thf(f713,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X3 @ X5 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v2 @ X5 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v4 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f712]) ).
thf(f789,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( v2 @ Y0 )
| ~ ( v4 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v4 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f290]) ).
thf(f790,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( v2 @ Y0 )
| ~ ( v4 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v4 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f789]) ).
thf(f791,plain,
! [X1: $i] :
( $true
= ( ( v2 @ X1 )
| ~ ( v4 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f790]) ).
thf(f792,plain,
! [X1: $i] :
( ( $true
= ( ~ ( v4 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f791]) ).
thf(f793,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( v4 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f792]) ).
thf(f794,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) ) ) )
| ( $true
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( v4 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f793]) ).
thf(f795,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( v4 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f794]) ).
thf(f796,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f795]) ).
thf(f797,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v4 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f796]) ).
thf(f798,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) ) ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ~ ( v4 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f797]) ).
thf(f799,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) ) ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ~ ( v4 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f798]) ).
thf(f800,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ~ ( v4 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f799]) ).
thf(f801,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( ~ ( v4 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f800]) ).
thf(f802,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f801]) ).
thf(f803,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f802]) ).
thf(f804,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v4 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f803]) ).
thf(f805,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X4 )
| ~ ( v4 @ X4 ) ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f804]) ).
thf(f806,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( v4 @ X4 ) ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f805]) ).
thf(f807,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( v4 @ X4 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f806]) ).
thf(f808,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v4 @ X3 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v4 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f807]) ).
thf(f809,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( v2 @ Y0 )
| ~ ( v3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v3 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f289]) ).
thf(f810,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( v2 @ Y0 )
| ~ ( v3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v3 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f809]) ).
thf(f811,plain,
! [X1: $i] :
( $true
= ( ( v2 @ X1 )
| ~ ( v3 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f810]) ).
thf(f812,plain,
! [X1: $i] :
( ( $true
= ( ~ ( v3 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f811]) ).
thf(f813,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( v3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f812]) ).
thf(f814,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) ) ) )
| ( $true
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f813]) ).
thf(f815,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $true
= ( ~ ( v3 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f814]) ).
thf(f816,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f815]) ).
thf(f817,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v3 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f816]) ).
thf(f818,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) ) ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ~ ( v3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f817]) ).
thf(f819,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) ) ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ~ ( v3 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f818]) ).
thf(f820,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ~ ( v3 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f819]) ).
thf(f821,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( ~ ( v3 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f820]) ).
thf(f822,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v3 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f821]) ).
thf(f823,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v3 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f822]) ).
thf(f824,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v3 @ Y0 ) )
@ X4 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v3 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f823]) ).
thf(f825,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X4 )
| ~ ( v3 @ X4 ) ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v3 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f824]) ).
thf(f826,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( v3 @ X4 ) ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v3 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f825]) ).
thf(f827,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( v3 @ X4 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v3 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f826]) ).
thf(f828,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v3 @ X3 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $true
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f827]) ).
thf(f900,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( v1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v4 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v2 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f285]) ).
thf(f901,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( v1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( v4 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( v2 @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f900]) ).
thf(f902,plain,
! [X1: $i] :
( $true
= ( ( v1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f901]) ).
thf(f903,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f902]) ).
thf(f904,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f903]) ).
thf(f905,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) ) ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f904]) ).
thf(f906,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f905]) ).
thf(f907,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f906]) ).
thf(f908,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( v2 @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( v1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( v4 @ Y1 ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f907]) ).
thf(f909,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( v1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v4 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f908]) ).
thf(f910,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) ) ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( v1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f909]) ).
thf(f911,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 )
| ( v1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f910]) ).
thf(f912,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f911]) ).
thf(f913,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v4 @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f912]) ).
thf(f914,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v4 @ Y0 ) )
@ X6 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(pi_proxy_clausification,[],[f913]) ).
thf(f915,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v4 @ Y0 ) )
@ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f914]) ).
thf(f916,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v4 @ Y0 ) )
@ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f915]) ).
thf(f917,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ~ ( v2 @ Y0 ) )
@ X5 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X4 @ Y0 )
| ( v4 @ Y0 ) )
@ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f916]) ).
thf(f918,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X5 )
| ~ ( v2 @ X5 ) ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X4 @ X6 )
| ( v4 @ X6 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f917]) ).
thf(f919,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( v2 @ X5 ) ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X4 @ X6 )
| ( v4 @ X6 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X5 ) ) ) ),
inference(or_proxy_clausification,[],[f918]) ).
thf(f920,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( v2 @ X5 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( ~ ( rel_s4 @ X4 @ X6 )
| ( v4 @ X6 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X5 ) ) ) ),
inference(not_proxy_clausification,[],[f919]) ).
thf(f921,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( v2 @ X5 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( v4 @ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X5 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X4 @ X6 ) ) ) ),
inference(or_proxy_clausification,[],[f920]) ).
thf(f922,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( v2 @ X5 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( v4 @ X6 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $true
= ( ~ ( rel_s4 @ X4 @ X6 ) ) ) ),
inference(not_proxy_clausification,[],[f921]) ).
thf(f923,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( rel_s4 @ X4 @ X6 ) )
| ( $false
= ( rel_s4 @ X2 @ X5 ) )
| ( $false
= ( rel_s4 @ X1 @ X4 ) )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( v4 @ X6 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( v1 @ X1 ) )
| ( $false
= ( v2 @ X5 ) ) ),
inference(not_proxy_clausification,[],[f922]) ).
thf(f1018,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f1019,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1018]) ).
thf(f1020,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f1019]) ).
thf(f1348,plain,
! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $true
= ( v2 @ X0 ) )
| ( $false
= ( v4 @ X0 ) ) ),
inference(equality_factoring,[],[f808]) ).
thf(f1351,plain,
! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f1348]) ).
thf(f1352,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1351]) ).
thf(f1383,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(forward_demodulation,[],[f1352,f1020]) ).
thf(f1384,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1383]) ).
thf(f1495,plain,
! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v3 @ X0 ) )
| ( $true
= ( v2 @ X0 ) )
| ( $false
= ( v3 @ X0 ) ) ),
inference(equality_factoring,[],[f828]) ).
thf(f1498,plain,
! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v3 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f1495]) ).
thf(f1499,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v3 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1498]) ).
thf(f1536,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v3 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(forward_demodulation,[],[f1499,f1020]) ).
thf(f1537,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v3 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1536]) ).
thf(f1867,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X2 ) )
| ( $false
= ( v3 @ X0 ) )
| ( $false
= ( v3 @ X0 ) ) ),
inference(equality_factoring,[],[f460]) ).
thf(f1872,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X2 ) )
| ( $false
= ( v3 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f1867]) ).
thf(f1873,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X2 ) )
| ( $false
= ( v3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1872]) ).
thf(f1928,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X2 ) )
| ( $false
= ( v3 @ X0 ) ) ),
inference(forward_demodulation,[],[f1873,f1020]) ).
thf(f1929,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X2 ) )
| ( $false
= ( v3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1928]) ).
thf(f1997,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v1 @ X2 ) )
| ( $false
= ( v1 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(equality_factoring,[],[f484]) ).
thf(f2002,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v1 @ X2 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f1997]) ).
thf(f2003,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v1 @ X2 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f2002]) ).
thf(f2062,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v1 @ X2 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(forward_demodulation,[],[f2003,f1020]) ).
thf(f2063,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X2 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v1 @ X2 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f2062]) ).
thf(f2279,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v3 @ X2 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) )
| ( $false
= ( v2 @ X3 ) ) ),
inference(equality_factoring,[],[f507]) ).
thf(f2280,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v3 @ X2 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) )
| ( $false
= ( v2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f2279]) ).
thf(f2913,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v3 @ X2 ) )
| ( $false
= ( v2 @ X0 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X3 ) ) ),
inference(equality_factoring,[],[f573]) ).
thf(f2914,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v3 @ X2 ) )
| ( $false
= ( v2 @ X0 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f2913]) ).
thf(f3232,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v2 @ X0 ) )
| ( $false
= ( v2 @ X0 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v4 @ X2 ) ) ),
inference(equality_factoring,[],[f713]) ).
thf(f3243,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v2 @ X0 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v4 @ X2 ) ) ),
inference(duplicate_literal_removal,[],[f3232]) ).
thf(f3244,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v2 @ X0 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v4 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f3243]) ).
thf(f3320,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v2 @ X0 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v4 @ X2 ) ) ),
inference(forward_demodulation,[],[f3244,f1020]) ).
thf(f3321,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( v2 @ X0 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v4 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f3320]) ).
thf(f4113,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(constrained_superposition,[],[f1020,f1384]) ).
thf(f4129,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v4 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f4113]) ).
thf(f4130,plain,
! [X0: $i] :
( ( $false
= ( v4 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f4129]) ).
thf(f4904,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X3 ) )
| ( $true
= ( v2 @ X2 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $true
= ( v3 @ X0 ) ) ),
inference(equality_factoring,[],[f690]) ).
thf(f4909,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X3 ) )
| ( $true
= ( v2 @ X2 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( v3 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f4904]) ).
thf(f4910,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X3 ) )
| ( $true
= ( v2 @ X2 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( v3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f4909]) ).
thf(f5016,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X3 ) )
| ( $true
= ( v2 @ X2 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( v3 @ X0 ) ) ),
inference(forward_demodulation,[],[f4910,f1020]) ).
thf(f5017,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X3 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( v2 @ X2 ) )
| ( $true
= ( v4 @ X3 ) )
| ( $true
= ( v3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f5016]) ).
thf(f5610,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( v1 @ X2 ) )
| ( $false
= ( v2 @ X1 ) ) ),
inference(equality_factoring,[],[f923]) ).
thf(f5641,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( v1 @ X2 ) )
| ( $false
= ( v2 @ X1 ) ) ),
inference(duplicate_literal_removal,[],[f5610]) ).
thf(f5642,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( v1 @ X3 ) )
| ( $true
= ( v1 @ X2 ) )
| ( $false
= ( v2 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f5641]) ).
thf(f7012,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v3 @ X0 ) )
| ( $false
= ( v3 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(constrained_superposition,[],[f1020,f1537]) ).
thf(f7028,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v3 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f7012]) ).
thf(f7029,plain,
! [X0: $i] :
( ( $false
= ( v3 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f7028]) ).
thf(f7749,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v4 @ ( sK2 @ X0 ) ) )
| ( $false
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X0 ) ) ),
inference(constrained_superposition,[],[f325,f1929]) ).
thf(f7769,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v4 @ ( sK2 @ X0 ) ) )
| ( $false
= ( v2 @ X1 ) )
| ( $false
= ( v3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f7749]) ).
thf(f7860,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v1 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(constrained_superposition,[],[f1020,f2063]) ).
thf(f7901,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f7860]) ).
thf(f7902,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v3 @ X1 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f7901]) ).
thf(f7931,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v3 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(constrained_superposition,[],[f1020,f7902]) ).
thf(f7949,plain,
! [X0: $i] :
( ( $false
= ( v3 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f7931]) ).
thf(f8080,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X1 @ X0 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v4 @ X0 ) ) ),
inference(constrained_superposition,[],[f1020,f3321]) ).
thf(f8102,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X1 @ X0 ) )
| ( $false
= ( v2 @ X1 ) )
| ( $true
= ( v3 @ X1 ) )
| ( $false
= ( v4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f8080]) ).
thf(f9741,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v2 @ X0 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v4 @ ( sK2 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f325,f8102]) ).
thf(f9759,plain,
! [X0: $i] :
( ( $false
= ( v4 @ ( sK2 @ X0 ) ) )
| ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f9741]) ).
thf(f13943,plain,
! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $true
= ( v2 @ X0 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( v3 @ X0 ) ) ),
inference(equality_factoring,[],[f5017]) ).
thf(f13944,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $true
= ( v2 @ X0 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( v3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f13943]) ).
thf(f14019,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v2 @ X0 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( v3 @ X0 ) ) ),
inference(forward_demodulation,[],[f13944,f1020]) ).
thf(f14020,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v2 @ X0 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( v3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f14019]) ).
thf(f14389,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( v2 @ X0 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $true
= ( v3 @ X0 ) ) ),
inference(constrained_superposition,[],[f1020,f14020]) ).
thf(f14413,plain,
! [X0: $i] :
( ( $true
= ( v3 @ X0 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f14389]) ).
thf(f14449,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( v2 @ X0 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(constrained_superposition,[],[f7029,f14413]) ).
thf(f14494,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( v2 @ X0 ) )
| ( $true
= ( v4 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f14449]) ).
thf(f14495,plain,
! [X0: $i] :
( ( $true
= ( v4 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f14494]) ).
thf(f14537,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( v2 @ X0 ) )
| ( $true
= ( v2 @ X0 ) ) ),
inference(constrained_superposition,[],[f4130,f14495]) ).
thf(f14566,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( v2 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f14537]) ).
thf(f14567,plain,
! [X0: $i] :
( $true
= ( v2 @ X0 ) ),
inference(trivial_inequality_removal,[],[f14566]) ).
thf(f14624,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v3 @ X2 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(forward_demodulation,[],[f2280,f14567]) ).
thf(f14625,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( v3 @ X2 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f14624]) ).
thf(f14709,plain,
! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(equality_factoring,[],[f14625]) ).
thf(f14710,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f14709]) ).
thf(f14785,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(forward_demodulation,[],[f14710,f1020]) ).
thf(f14786,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f14785]) ).
thf(f15621,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(constrained_superposition,[],[f325,f14786]) ).
thf(f15643,plain,
! [X0: $i] :
( ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f15621]) ).
thf(f15684,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v1 @ X0 ) )
| ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(constrained_superposition,[],[f7949,f15643]) ).
thf(f15726,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v1 @ X0 ) )
| ( $false
= ( v4 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f15684]) ).
thf(f15727,plain,
! [X0: $i] :
( ( $false
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f15726]) ).
thf(f15773,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v3 @ X2 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X3 ) ) ),
inference(forward_demodulation,[],[f2914,f14567]) ).
thf(f15774,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X1 @ X3 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( v3 @ X2 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f15773]) ).
thf(f15858,plain,
! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X1 ) ) ),
inference(equality_factoring,[],[f15774]) ).
thf(f15859,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f15858]) ).
thf(f15934,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X1 ) ) ),
inference(forward_demodulation,[],[f15859,f1020]) ).
thf(f15935,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v3 @ X0 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f15934]) ).
thf(f16292,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( v3 @ X0 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(constrained_superposition,[],[f1020,f15935]) ).
thf(f16316,plain,
! [X0: $i] :
( ( $true
= ( v3 @ X0 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f16292]) ).
thf(f16356,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v1 @ X0 ) )
| ( $true
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(constrained_superposition,[],[f7949,f16316]) ).
thf(f16397,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v1 @ X0 ) )
| ( $true
= ( v4 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f16356]) ).
thf(f16398,plain,
! [X0: $i] :
( ( $true
= ( v4 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f16397]) ).
thf(f16456,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v1 @ X0 ) )
| ( $false
= ( v1 @ X0 ) ) ),
inference(constrained_superposition,[],[f15727,f16398]) ).
thf(f16489,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v1 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f16456]) ).
thf(f16490,plain,
! [X0: $i] :
( $false
= ( v1 @ X0 ) ),
inference(trivial_inequality_removal,[],[f16489]) ).
thf(f16583,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v4 @ ( sK2 @ X0 ) ) )
| ( $false
= ( v3 @ X0 ) ) ),
inference(forward_demodulation,[],[f7769,f14567]) ).
thf(f16584,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( v4 @ ( sK2 @ X0 ) ) )
| ( $false
= ( v3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f16583]) ).
thf(f16598,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v4 @ ( sK2 @ X0 ) ) )
| ( $false
= ( v3 @ X0 ) ) ),
inference(constrained_superposition,[],[f325,f16584]) ).
thf(f16620,plain,
! [X0: $i] :
( ( $false
= ( v4 @ ( sK2 @ X0 ) ) )
| ( $false
= ( v3 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f16598]) ).
thf(f16713,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( v1 @ X2 ) )
| ( $false
= ( v2 @ X1 ) ) ),
inference(forward_demodulation,[],[f5642,f16490]) ).
thf(f16714,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $true
= ( v1 @ X2 ) )
| ( $false
= ( v2 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f16713]) ).
thf(f16715,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) ) ),
inference(forward_demodulation,[],[f16714,f16490]) ).
thf(f16716,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $true
= ( v4 @ X1 ) )
| ( $false
= ( v2 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f16715]) ).
thf(f16717,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $true
= ( v4 @ X1 ) ) ),
inference(forward_demodulation,[],[f16716,f14567]) ).
thf(f16718,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X2 @ X3 ) )
| ( $false
= ( rel_s4 @ X2 @ X0 ) )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v4 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f16717]) ).
thf(f16816,plain,
! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $true
= ( v4 @ X0 ) ) ),
inference(equality_factoring,[],[f16718]) ).
thf(f16817,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $false
= ( rel_s4 @ X0 @ X0 ) )
| ( $true
= ( v4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f16816]) ).
thf(f16892,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v4 @ X0 ) ) ),
inference(forward_demodulation,[],[f16817,f1020]) ).
thf(f16893,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X0 @ X1 ) )
| ( $true
= ( v4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f16892]) ).
thf(f16913,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( v4 @ X0 ) ) ),
inference(constrained_superposition,[],[f325,f16893]) ).
thf(f16935,plain,
! [X0: $i] :
( $true
= ( v4 @ X0 ) ),
inference(trivial_inequality_removal,[],[f16913]) ).
thf(f16973,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( v3 @ X0 ) ) ),
inference(constrained_superposition,[],[f16620,f16935]) ).
thf(f16975,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v2 @ X0 ) ) ),
inference(constrained_superposition,[],[f9759,f16935]) ).
thf(f17006,plain,
! [X0: $i] :
( ( $true
= ( v3 @ X0 ) )
| ( $false
= ( v2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f16975]) ).
thf(f17008,plain,
! [X0: $i] :
( $false
= ( v3 @ X0 ) ),
inference(trivial_inequality_removal,[],[f16973]) ).
thf(f17053,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( v3 @ X0 ) ) ),
inference(forward_demodulation,[],[f17006,f14567]) ).
thf(f17054,plain,
! [X0: $i] :
( $true
= ( v3 @ X0 ) ),
inference(trivial_inequality_removal,[],[f17053]) ).
thf(f17103,plain,
$true = $false,
inference(forward_demodulation,[],[f17054,f17008]) ).
thf(f17104,plain,
$false,
inference(trivial_inequality_removal,[],[f17103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN741^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.26 % Computer : n013.cluster.edu
% 0.12/0.26 % Model : x86_64 x86_64
% 0.12/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.26 % Memory : 8046.5625MB
% 0.12/0.26 % OS : Linux 6.8.0-71-generic
% 0.12/0.26 % CPULimit : 300
% 0.12/0.26 % WCLimit : 300
% 0.12/0.26 % DateTime : Tue Sep 29 16:18:51 UTC 2026
% 0.12/0.26 % CPUTime :
% 0.12/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.26/0.31 Running first-order model finding
% 0.26/0.31 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
% 6.76/1.40 % (2311822)Will run a generic schedule for satisfiability detection.
% 6.76/1.40 % (2311833)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3984738011:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 6.76/1.40 % (2311828)% WARNING: option uhcvi not known.
% 6.76/1.40 % (2311827)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=308735029_2999 on theBenchmark for (2999ds/0Mi)
% 6.76/1.40 % (2311832)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2400793112:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 6.76/1.40 % (2311831)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1982839890:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 6.76/1.40 % (2311830)dis+10_1_sil=32000:sp=arity:random_seed=1359760204:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 6.76/1.40 % (2311828)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4220852616:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 6.76/1.40 % (2311829)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2935895789:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 6.76/1.40 % (2311831)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.76/1.40 % (2311828)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 6.76/1.40 % Exception at run slice level
% 6.76/1.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.76/1.40 % (2311828)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 6.76/1.40 % (2311833)Instruction limit reached!
% 6.76/1.40 % (2311833)------------------------------
% 6.76/1.40 % (2311833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.40 % (2311833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.40 % (2311833)CaDiCaL version: 2.1.3
% 6.76/1.40 % (2311833)Termination reason: Instruction limit
% 6.76/1.40 % (2311833)Termination phase: Saturation
% 6.76/1.40 % (2311833)Time elapsed: 0.070 s
% 6.76/1.40 % (2311833)Peak memory usage: 12 MB
% 6.76/1.40 % (2311833)Instructions burned: 160 (million)
% 6.76/1.40 % (2311841)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3950121202:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 6.76/1.40 % (2311842)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2279606274:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 6.76/1.40 % (2311830)Instruction limit reached!
% 6.76/1.40 % (2311830)------------------------------
% 6.76/1.40 % (2311830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.40 % (2311830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.40 % (2311830)CaDiCaL version: 2.1.3
% 6.76/1.40 % (2311830)Termination reason: Instruction limit
% 6.76/1.40 % (2311830)Termination phase: Saturation
% 6.76/1.40 % (2311830)Time elapsed: 0.082 s
% 6.76/1.40 % (2311830)Peak memory usage: 12 MB
% 6.76/1.40 % (2311830)Instructions burned: 103 (million)
% 6.76/1.40 % Exception at run slice level
% 6.76/1.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 6.76/1.40 % (2311831)Instruction limit reached!
% 6.76/1.40 % (2311831)------------------------------
% 6.76/1.40 % (2311831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.40 % (2311831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.40 % (2311831)CaDiCaL version: 2.1.3
% 6.76/1.40 % (2311831)Termination reason: Instruction limit
% 6.76/1.40 % (2311831)Termination phase: Saturation
% 6.76/1.40 % (2311831)Time elapsed: 0.095 s
% 6.76/1.40 % (2311831)Peak memory usage: 12 MB
% 6.76/1.40 % (2311831)Instructions burned: 116 (million)
% 6.76/1.40 % (2311832)Instruction limit reached!
% 6.76/1.40 % (2311832)------------------------------
% 6.76/1.40 % (2311832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 6.76/1.40 % (2311832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/1.40 % (2311832)CaDiCaL version: 2.1.3
% 6.76/1.40 % (2311832)Termination reason: Instruction limit
% 6.76/1.40 % (2311832)Termination phase: Saturation
% 6.76/1.40 % (2311832)Time elapsed: 0.105 s
% 6.76/1.40 % (2311832)Peak memory usage: 12 MB
% 6.76/1.40 % (2311832)Instructions burned: 131 (million)
% 6.76/1.40 % (2311845)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=3619821315:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 22.83/3.68 % (2311845)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 22.83/3.68 % (2311846)ott-21_1_sil=16000:fs=off:random_seed=1116798956:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 22.83/3.68 % (2311847)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3561677064:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 22.83/3.68 % (2311842)Instruction limit reached!
% 22.83/3.68 % (2311842)------------------------------
% 22.83/3.68 % (2311842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.83/3.68 % (2311842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.83/3.68 % (2311842)CaDiCaL version: 2.1.3
% 22.83/3.68 % (2311842)Termination reason: Instruction limit
% 22.83/3.68 % (2311842)Termination phase: Saturation
% 22.83/3.68 % (2311842)Time elapsed: 0.053 s
% 22.83/3.68 % (2311842)Peak memory usage: 12 MB
% 22.83/3.68 % (2311842)Instructions burned: 131 (million)
% 22.83/3.68 % (2311845)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 22.83/3.68 % (2311849)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=475956876:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 22.83/3.68 % (2311852)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1134613040:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 22.83/3.68 % Exception at run slice level
% 22.83/3.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 22.83/3.68 % (2311856)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=468251276:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 22.83/3.68 % Exception at run slice level
% 22.83/3.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 22.83/3.68 % (2311846)Instruction limit reached!
% 22.83/3.68 % (2311846)------------------------------
% 22.83/3.68 % (2311846)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.83/3.68 % (2311846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.83/3.68 % (2311846)CaDiCaL version: 2.1.3
% 22.83/3.68 % (2311846)Termination reason: Instruction limit
% 22.83/3.68 % (2311846)Termination phase: Saturation
% 22.83/3.68 % (2311846)Time elapsed: 0.141 s
% 22.83/3.68 % (2311846)Peak memory usage: 12 MB
% 22.83/3.68 % (2311846)Instructions burned: 181 (million)
% 22.83/3.68 % (2311859)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2464555884:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 22.83/3.68 % (2311859)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 22.83/3.68 % (2311860)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=4048921966:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 22.83/3.68 % (2311860)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 22.83/3.68 % (2311847)Instruction limit reached!
% 22.83/3.68 % (2311847)------------------------------
% 22.83/3.68 % (2311847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.83/3.68 % (2311847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.83/3.68 % (2311847)CaDiCaL version: 2.1.3
% 22.83/3.68 % (2311847)Termination reason: Instruction limit
% 22.83/3.68 % (2311847)Termination phase: Saturation
% 22.83/3.68 % (2311847)Time elapsed: 0.391 s
% 22.83/3.68 % (2311847)Peak memory usage: 13 MB
% 22.83/3.68 % (2311847)Instructions burned: 478 (million)
% 22.83/3.68 % (2311865)fmb+10_1_sil=64000:random_seed=770853179:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 22.83/3.68 % (2311865)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 22.83/3.68 % Exception at run slice level
% 22.83/3.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 22.83/3.68 % (2311869)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2774861146:i=9515:nm=5_2994 on theBenchmark for (2994ds/9515Mi)
% 22.83/3.68 % Exception at run slice level
% 22.83/3.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 22.83/3.68 % (2311852)Instruction limit reached!
% 22.83/3.68 % (2311852)------------------------------
% 22.83/3.68 % (2311852)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.83/3.68 % (2311852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.83/3.68 % (2311852)CaDiCaL version: 2.1.3
% 22.83/3.68 % (2311852)Termination reason: Instruction limit
% 22.83/3.68 % (2311852)Termination phase: Saturation
% 22.83/3.68 % (2311852)Time elapsed: 0.456 s
% 22.83/3.68 % (2311852)Peak memory usage: 13 MB
% 22.83/3.68 % (2311852)Instructions burned: 1181 (million)
% 22.83/3.68 % (2311872)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2069110864:i=5131_2993 on theBenchmark for (2993ds/5131Mi)
% 22.83/3.68 % (2311872)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 22.83/3.68 % (2311871)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1246757725:fmbsr=1.7:i=920_2993 on theBenchmark for (2993ds/920Mi)
% 22.83/3.68 % (2311845)Instruction limit reached!
% 22.83/3.68 % (2311845)------------------------------
% 22.83/3.68 % (2311845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.83/3.68 % (2311845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.83/3.68 % (2311845)CaDiCaL version: 2.1.3
% 22.83/3.68 % (2311845)Termination reason: Instruction limit
% 22.83/3.68 % (2311845)Termination phase: Saturation
% 22.83/3.68 % (2311845)Time elapsed: 0.543 s
% 22.83/3.68 % (2311845)Peak memory usage: 14 MB
% 22.83/3.68 % (2311845)Instructions burned: 686 (million)
% 22.83/3.68 % Exception at run slice level
% 22.83/3.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 22.83/3.68 % (2311875)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=38324144:i=1472:ins=7:fdi=8:gsp=on_2993 on theBenchmark for (2993ds/1472Mi)
% 22.83/3.68 % (2311876)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3766460291:i=6324_2992 on theBenchmark for (2992ds/6324Mi)
% 22.83/3.68 % (2311875)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 22.83/3.68 % (2311875)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 22.83/3.68 % Exception at run slice level
% 22.83/3.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 22.83/3.68 % (2311879)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=824724273:fmbsr=2.30978:i=2174_2992 on theBenchmark for (2992ds/2174Mi)
% 22.83/3.68 % Exception at run slice level
% 22.83/3.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 22.83/3.68 % (2311859)Instruction limit reached!
% 22.83/3.68 % (2311859)------------------------------
% 22.83/3.68 % (2311859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.83/3.68 % (2311859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.83/3.68 % (2311859)CaDiCaL version: 2.1.3
% 22.83/3.68 % (2311859)Termination reason: Instruction limit
% 22.83/3.68 % (2311859)Termination phase: Saturation
% 22.83/3.68 % (2311859)Time elapsed: 0.513 s
% 22.83/3.68 % (2311859)Peak memory usage: 13 MB
% 22.83/3.68 % (2311859)Instructions burned: 693 (million)
% 22.83/3.68 % (2311881)ott-2_1_sil=16000:newcnf=on:random_seed=2701138810:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2991 on theBenchmark for (2991ds/869Mi)
% 22.83/3.68 % (2311881)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 22.83/3.68 % (2311882)ott+10_1_sil=32000:tgt=ground:random_seed=707498994:i=5114:av=off_2991 on theBenchmark for (2991ds/5114Mi)
% 22.83/3.68 % (2311860)Instruction limit reached!
% 22.83/3.68 % (2311860)------------------------------
% 22.83/3.68 % (2311860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.83/3.68 % (2311860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.83/3.68 % (2311860)CaDiCaL version: 2.1.3
% 22.83/3.68 % (2311860)Termination reason: Instruction limit
% 22.83/3.68 % (2311860)Termination phase: Saturation
% 22.83/3.68 % (2311860)Time elapsed: 0.705 s
% 22.83/3.68 % (2311860)Peak memory usage: 14 MB
% 22.83/3.68 % (2311860)Instructions burned: 880 (million)
% 22.83/3.68 % (2311885)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3219744690:i=54282_2989 on theBenchmark for (2989ds/54282Mi)
% 22.83/3.68 % Exception at run slice level
% 22.83/3.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 22.83/3.68 % (2311887)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=1943098749:i=3512:aac=none_2989 on theBenchmark for (2989ds/3512Mi)
% 22.83/3.68 % (2311887)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 22.83/3.68 % (2311881)Instruction limit reached!
% 22.83/3.68 % (2311881)------------------------------
% 22.83/3.68 % (2311881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.83/3.68 % (2311881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.83/3.68 % (2311881)CaDiCaL version: 2.1.3
% 22.83/3.68 % (2311881)Termination reason: Instruction limit
% 22.83/3.68 % (2311881)Termination phase: Saturation
% 22.83/3.68 % (2311881)Time elapsed: 0.662 s
% 22.83/3.68 % (2311881)Peak memory usage: 13 MB
% 22.83/3.68 % (2311881)Instructions burned: 870 (million)
% 22.83/3.68 % (2311889)dis+21_1_sil=32000:sas=cadical:random_seed=2273321286:i=3773:amm=off_2985 on theBenchmark for (2985ds/3773Mi)
% 22.83/3.68 % (2311875)Instruction limit reached!
% 22.83/3.68 % (2311875)------------------------------
% 22.83/3.68 % (2311875)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.83/3.68 % (2311875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.83/3.68 % (2311875)CaDiCaL version: 2.1.3
% 22.83/3.68 % (2311875)Termination reason: Instruction limit
% 22.83/3.68 % (2311875)Termination phase: Saturation
% 22.83/3.68 % (2311875)Time elapsed: 1.294 s
% 22.83/3.68 % (2311875)Peak memory usage: 18 MB
% 22.83/3.68 % (2311875)Instructions burned: 1472 (million)
% 22.83/3.68 % (2311891)ott+11_1_sil=16000:gs=on:random_seed=2674698008:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2979 on theBenchmark for (2979ds/2251Mi)
% 22.83/3.68 % (2311891)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 22.83/3.68 % (2311872)Instruction limit reached!
% 22.83/3.68 % (2311872)------------------------------
% 22.83/3.68 % (2311872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.83/3.68 % (2311872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.83/3.68 % (2311872)CaDiCaL version: 2.1.3
% 22.83/3.68 % (2311872)Termination reason: Instruction limit
% 22.83/3.68 % (2311872)Termination phase: Saturation
% 22.83/3.68 % (2311872)Time elapsed: 2.045 s
% 22.83/3.68 % (2311872)Peak memory usage: 16 MB
% 22.83/3.68 % (2311872)Instructions burned: 5133 (million)
% 22.83/3.68 % (2311893)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=473743015:fmbsr=1.6:i=67534_2972 on theBenchmark for (2972ds/67534Mi)
% 22.83/3.68 % Exception at run slice level
% 22.83/3.68 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 22.83/3.68 % (2311895)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=205173967:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2972 on theBenchmark for (2972ds/4591Mi)
% 22.83/3.68 % (2311887) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2311822-2311887"...
% 22.83/3.68 % (2311887)...printing done.
% 22.83/3.68 % (2311887)Refutation found. Thanks to Tanya!
% 22.83/3.68 % SZS status ContradictoryAxioms for theBenchmark
% 22.83/3.68 % SZS output start Proof for theBenchmark
% See solution above
% 22.83/3.69 % (2311887)------------------------------
% 22.83/3.69 % (2311887)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 22.83/3.69 % (2311887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 22.83/3.69 % (2311887)CaDiCaL version: 2.1.3
% 22.83/3.69 % (2311887)Termination reason: Refutation
% 22.83/3.69 % (2311887)Time elapsed: 2.243 s
% 22.83/3.69 % (2311887)Peak memory usage: 15 MB
% 22.83/3.69 % (2311887)Instructions burned: 2984 (million)
% 22.83/3.69 % (2311822)Success in time 3.363 s
% 22.83/3.69 % Vampire exiting
%------------------------------------------------------------------------------