%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO446^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:49:59 AM UTC 2026
% Result : Theorem 0.63s 0.30s
% Output : Refutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 29
% Syntax : Number of formulae : 385 ( 86 unt; 0 typ; 14 def)
% Number of atoms : 4037 ( 713 equ; 0 cnn)
% Maximal formula atoms : 12 ( 10 avg)
% Number of connectives : 5924 (1693 ~;1147 |; 13 &;2761 @)
% ( 14 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 156 ( 156 >; 0 *; 0 +; 0 <<)
% Number of symbols : 75 ( 71 usr; 24 con; 0-4 aty)
% ( 274 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 791 ( 0 sgn 243 !; 0 ?; 791 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f34,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mequiv @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f41,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f42,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f44,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f45,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f46,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f48,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f62,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f63,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f64,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f65,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f68,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f69,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f82,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f83,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f90,plain,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f91,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f90]) ).
thf(f92,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f93,plain,
mreflexive @ rel_s5,
inference(rectify,[],[f34]) ).
thf(f94,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f93]) ).
thf(f95,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f96,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f98,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f97]) ).
thf(f99,plain,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f100,plain,
( ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) )
!= $true ),
inference(flattening,[],[f100]) ).
thf(f104,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f105,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f106,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f107,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f109,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f119,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f120,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f122,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f129,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f133,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f134,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f135,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f94]) ).
thf(f136,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f96]) ).
thf(f137,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f138,plain,
( ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f141,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f106,f104,f105,f104,f104]) ).
thf(f142,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f107,f105,f104]) ).
thf(f144,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f109,f141,f142,f142]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f134,f104,f133,f104]) ).
thf(f151,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f135,f119]) ).
thf(f152,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f136,f122]) ).
thf(f153,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f137,f120]) ).
thf(f154,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ p
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) ) ),
inference(definition_unfolding,[],[f138,f129,f144,f150,f141,f150,f141,f150,f150]) ).
thf(f155,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ( p @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ( p @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ( p @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ( p @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( $false
= ( ~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $true
= ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $false
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( p @ sK1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ~ ( ~ ( p @ sK2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
( ( $false
= ( ~ ( p @ sK1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ~ ( ~ ( p @ sK2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ~ ( ~ ( p @ sK2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f179,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ~ ( ~ ( p @ sK2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( ~ ~ ( ~ ( p @ sK2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( ~ ( p @ sK2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f184,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( p @ sK2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f186,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( p @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f187,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f196,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ~ ( ~ ( p @ sK2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f197,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( ~ ~ ( ~ ( p @ sK2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f199,plain,
( ( $true
= ( p @ sK1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
( ( $true
= ( p @ sK1 ) )
| ( $true
= ( ~ ( ~ ( p @ sK2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f201,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( ~ ( p @ sK2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f203,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( ~ ( p @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f204,plain,
( ( $true
= ( p @ sK1 ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f213,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f214,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f215,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( p @ sK1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f220]) ).
thf(f222,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( p @ sK1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( q @ X1 ) )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ sK1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f232,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ sK1 ) )
| ( $true
= ( ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( q @ X1 ) )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f238,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f239,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f238]) ).
thf(f240,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f239]) ).
thf(f241,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f240]) ).
thf(f242,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f241]) ).
thf(f243,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f241]) ).
thf(f244,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f243]) ).
thf(f245,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f245]) ).
thf(f247,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 )
| ~ ( q @ sK5 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ~ ~ ( ~ ( p @ sK6 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f246]) ).
thf(f248,plain,
( ( $false
= ( ~ ( q @ sK5 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ~ ~ ( ~ ( p @ sK6 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f247]) ).
thf(f249,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ~ ~ ( ~ ( p @ sK6 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f247]) ).
thf(f250,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ~ ~ ( ~ ( p @ sK6 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f249]) ).
thf(f251,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ~ ~ ( ~ ( p @ sK6 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f250]) ).
thf(f252,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f250]) ).
thf(f253,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f252]) ).
thf(f254,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( ~ ( ~ ( p @ sK6 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f251]) ).
thf(f255,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( p @ sK6 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f254]) ).
thf(f256,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f255]) ).
thf(f259,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f256]) ).
thf(f260,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f259]) ).
thf(f261,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f260]) ).
thf(f262,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK6 @ sK7 )
| ~ ( q @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f261]) ).
thf(f263,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( q @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f262]) ).
thf(f264,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK6 @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f262]) ).
thf(f265,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( rel_s5 @ sK6 @ sK7 ) ) ),
inference(not_proxy_clausification,[],[f264]) ).
thf(f266,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( q @ sK7 ) ) ),
inference(not_proxy_clausification,[],[f263]) ).
thf(f267,plain,
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ~ ~ ( ~ ( p @ sK6 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f248]) ).
thf(f268,plain,
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( ~ ~ ( ~ ( p @ sK6 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f267]) ).
thf(f269,plain,
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f267]) ).
thf(f270,plain,
( ( $true
= ( q @ sK5 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f269]) ).
thf(f271,plain,
( ( $true
= ( q @ sK5 ) )
| ( $true
= ( ~ ( ~ ( p @ sK6 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f268]) ).
thf(f272,plain,
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( ~ ( p @ sK6 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f271]) ).
thf(f273,plain,
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f272]) ).
thf(f276,plain,
( ( $true
= ( q @ sK5 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f273]) ).
thf(f277,plain,
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f278,plain,
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f277]) ).
thf(f279,plain,
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK6 @ sK8 )
| ~ ( q @ sK8 ) ) ) ),
inference(beta-eta_normalization,[],[f278]) ).
thf(f280,plain,
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( ~ ( q @ sK8 ) ) ) ),
inference(or_proxy_clausification,[],[f279]) ).
thf(f281,plain,
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( ~ ( rel_s5 @ sK6 @ sK8 ) ) ) ),
inference(or_proxy_clausification,[],[f279]) ).
thf(f282,plain,
( ( $true
= ( q @ sK5 ) )
| ( $true
= ( rel_s5 @ sK6 @ sK8 ) ) ),
inference(not_proxy_clausification,[],[f281]) ).
thf(f283,plain,
( ( $true
= ( q @ sK5 ) )
| ( $true
= ( q @ sK8 ) ) ),
inference(not_proxy_clausification,[],[f280]) ).
thf(f284,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f242]) ).
thf(f285,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f284]) ).
thf(f286,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f287,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f288]) ).
thf(f290,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f290]) ).
thf(f292,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 )
| ~ ( q @ sK5 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f291]) ).
thf(f293,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( q @ sK5 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f292]) ).
thf(f294,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f292]) ).
thf(f295,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f294]) ).
thf(f296,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f295]) ).
thf(f297,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f296]) ).
thf(f298,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( q @ X1 ) )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f298]) ).
thf(f300,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f299]) ).
thf(f301,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ sK5 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f293]) ).
thf(f303,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ sK5 ) )
| ( $true
= ( ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( q @ X1 ) )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f305]) ).
thf(f307,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f306]) ).
thf(f308,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ sK5 ) )
| ( $false
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f307]) ).
thf(f309,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f310,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f309]) ).
thf(f311,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f310]) ).
thf(f312,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f311]) ).
thf(f359,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f312]) ).
thf(f360,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f360]) ).
thf(f362,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f361]) ).
thf(f363,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f362]) ).
thf(f364,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f363]) ).
thf(f365,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f364]) ).
thf(f366,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f365]) ).
thf(f367,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ~ ( ~ ( p @ X1 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f366]) ).
thf(f368,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ~ ( ~ ( p @ X1 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f367]) ).
thf(f369,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f368]) ).
thf(f370,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f369]) ).
thf(f371,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f370]) ).
thf(f372,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f371]) ).
thf(f373,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f372]) ).
thf(f374,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ X4 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f373]) ).
thf(f375,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ X4 ) )
| ( $true
= ( ~ ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f374]) ).
thf(f376,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ X4 ) )
| ( $false
= ( q @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f375]) ).
thf(f377,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ X4 ) )
| ( $false
= ( q @ X2 ) )
| ( $true
= ( ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f376]) ).
thf(f378,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ X4 ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( p @ X3 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f377]) ).
thf(f379,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ X4 ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f378]) ).
thf(f380,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ X4 ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f379]) ).
thf(f381,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ X4 ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f380]) ).
thf(f382,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ X4 ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f381]) ).
thf(f383,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X4 )
| ~ ( q @ X4 ) ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f382]) ).
thf(f384,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( q @ X4 ) ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X3 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f383]) ).
thf(f385,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( q @ X4 ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X3 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f384]) ).
thf(f386,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( q @ X4 ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X3 ) )
| ( $false
= ( rel_s5 @ X1 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f385]) ).
thf(f387,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f388,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f387]) ).
thf(f389,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f388]) ).
thf(f390,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f389]) ).
thf(f391,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f390]) ).
thf(f392,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f391]) ).
thf(f393,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f394,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f393]) ).
thf(f395,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f394]) ).
thf(f396,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f395]) ).
thf(f397,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f396]) ).
thf(f398,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f397]) ).
thf(f399,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f398]) ).
thf(f400,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) ) )
| ( $true
= ( rel_s5 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f399]) ).
thf(f401,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( $true
= ( rel_s5 @ X3 @ X1 ) )
| ( $false
= ( rel_s5 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f400]) ).
thf(f402,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f403,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f402]) ).
thf(f404,plain,
! [X1: $i] :
( $true
= ( rel_s5 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f403]) ).
thf(f406,definition,
( spl11_1
<=> ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
thf(f408,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f406]) ).
thf(f410,definition,
( spl11_2
<=> ( $true
= ( rel_s5 @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f412,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f410]) ).
thf(f413,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f182,f410,f406]) ).
thf(f415,definition,
( spl11_3
<=> ( $true
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
thf(f417,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f415]) ).
thf(f418,plain,
( spl11_3
| spl11_2 ),
inference(avatar_split_clause,[],[f187,f410,f415]) ).
thf(f430,definition,
( spl11_6
<=> ( $true
= ( p @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
thf(f432,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f430]) ).
thf(f433,plain,
( spl11_1
| spl11_6 ),
inference(avatar_split_clause,[],[f199,f430,f406]) ).
thf(f434,plain,
( spl11_3
| spl11_6 ),
inference(avatar_split_clause,[],[f204,f430,f415]) ).
thf(f446,definition,
( spl11_9
<=> ! [X2: $i] :
( ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
thf(f447,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $false
= ( p @ X2 ) ) )
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f446]) ).
thf(f449,definition,
( spl11_10
<=> ! [X1: $i] :
( ( $false
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
thf(f450,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( q @ X1 ) ) )
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f449]) ).
thf(f451,plain,
( spl11_9
| spl11_10
| spl11_2 ),
inference(avatar_split_clause,[],[f230,f410,f449,f446]) ).
thf(f452,plain,
( spl11_9
| spl11_10
| spl11_6 ),
inference(avatar_split_clause,[],[f237,f430,f449,f446]) ).
thf(f454,definition,
( spl11_11
<=> ( $true
= ( rel_s5 @ sK0 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
thf(f456,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f454]) ).
thf(f458,definition,
( spl11_12
<=> ( $true
= ( rel_s5 @ sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
thf(f460,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f458]) ).
thf(f461,plain,
( spl11_11
| spl11_12 ),
inference(avatar_split_clause,[],[f253,f458,f454]) ).
thf(f468,definition,
( spl11_14
<=> ( $true
= ( rel_s5 @ sK6 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
thf(f470,plain,
( ( $true
= ( rel_s5 @ sK6 @ sK7 ) )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f468]) ).
thf(f471,plain,
( spl11_14
| spl11_12 ),
inference(avatar_split_clause,[],[f265,f458,f468]) ).
thf(f473,definition,
( spl11_15
<=> ( $true
= ( q @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
thf(f475,plain,
( ( $true
= ( q @ sK7 ) )
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f473]) ).
thf(f476,plain,
( spl11_15
| spl11_12 ),
inference(avatar_split_clause,[],[f266,f458,f473]) ).
thf(f478,definition,
( spl11_16
<=> ( $true
= ( q @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_16])],[avatar_definition]) ).
thf(f480,plain,
( ( $true
= ( q @ sK5 ) )
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f478]) ).
thf(f481,plain,
( spl11_11
| spl11_16 ),
inference(avatar_split_clause,[],[f270,f478,f454]) ).
thf(f484,definition,
( spl11_17
<=> ( $true
= ( rel_s5 @ sK6 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_17])],[avatar_definition]) ).
thf(f486,plain,
( ( $true
= ( rel_s5 @ sK6 @ sK8 ) )
| ~ spl11_17 ),
inference(avatar_component_clause,[],[f484]) ).
thf(f487,plain,
( spl11_17
| spl11_16 ),
inference(avatar_split_clause,[],[f282,f478,f484]) ).
thf(f489,definition,
( spl11_18
<=> ( $true
= ( q @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_18])],[avatar_definition]) ).
thf(f491,plain,
( ( $true
= ( q @ sK8 ) )
| ~ spl11_18 ),
inference(avatar_component_clause,[],[f489]) ).
thf(f492,plain,
( spl11_18
| spl11_16 ),
inference(avatar_split_clause,[],[f283,f478,f489]) ).
thf(f493,plain,
( spl11_9
| spl11_10
| spl11_12 ),
inference(avatar_split_clause,[],[f301,f458,f449,f446]) ).
thf(f494,plain,
( spl11_9
| spl11_10
| spl11_16 ),
inference(avatar_split_clause,[],[f308,f478,f449,f446]) ).
thf(f500,definition,
( spl11_20
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_20])],[avatar_definition]) ).
thf(f501,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( p @ X1 ) ) )
| ~ spl11_20 ),
inference(avatar_component_clause,[],[f500]) ).
thf(f518,plain,
( spl11_9
| spl11_10
| spl11_20 ),
inference(avatar_split_clause,[],[f386,f500,f449,f446]) ).
thf(f523,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $false
= ( q @ X0 ) )
| ( $false
= ( p @ sK1 ) ) )
| ~ spl11_2
| ~ spl11_20 ),
inference(constrained_superposition,[],[f412,f501]) ).
thf(f534,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $false
= ( q @ X0 ) )
| ( $false
= ( p @ sK1 ) ) )
| ~ spl11_2
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f523]) ).
thf(f568,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $false
= ( q @ X0 ) ) )
| ~ spl11_2
| ~ spl11_6
| ~ spl11_20 ),
inference(forward_demodulation,[],[f534,f432]) ).
thf(f569,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $false
= ( q @ X0 ) ) )
| ~ spl11_2
| ~ spl11_6
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f568]) ).
thf(f632,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK1 @ sK0 ) )
| ~ spl11_2 ),
inference(constrained_superposition,[],[f412,f392]) ).
thf(f647,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK0 ) )
| ~ spl11_2 ),
inference(trivial_inequality_removal,[],[f632]) ).
thf(f710,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $true
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) ) ),
inference(constrained_superposition,[],[f392,f401]) ).
thf(f713,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK5 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl11_12 ),
inference(constrained_superposition,[],[f460,f401]) ).
thf(f721,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ X0 @ X2 ) ) ),
inference(constrained_superposition,[],[f392,f401]) ).
thf(f740,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f721]) ).
thf(f748,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK5 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl11_12 ),
inference(trivial_inequality_removal,[],[f713]) ).
thf(f751,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $true
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f710]) ).
thf(f812,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl11_2 ),
inference(constrained_superposition,[],[f412,f740]) ).
thf(f842,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl11_2 ),
inference(trivial_inequality_removal,[],[f812]) ).
thf(f955,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK1 @ sK0 ) )
| ( $false
= ( q @ sK5 ) )
| ~ spl11_2
| ~ spl11_6
| ~ spl11_12
| ~ spl11_20 ),
inference(constrained_superposition,[],[f748,f569]) ).
thf(f980,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK0 ) )
| ( $false
= ( q @ sK5 ) )
| ~ spl11_2
| ~ spl11_6
| ~ spl11_12
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f955]) ).
thf(f994,plain,
( ( $true = $false )
| ( $false
= ( q @ sK5 ) )
| ~ spl11_2
| ~ spl11_6
| ~ spl11_12
| ~ spl11_20 ),
inference(forward_demodulation,[],[f980,f647]) ).
thf(f995,plain,
( ( $false
= ( q @ sK5 ) )
| ~ spl11_2
| ~ spl11_6
| ~ spl11_12
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f994]) ).
thf(f998,plain,
( ( $true = $false )
| ~ spl11_2
| ~ spl11_6
| ~ spl11_12
| ~ spl11_16
| ~ spl11_20 ),
inference(constrained_superposition,[],[f995,f480]) ).
thf(f1004,plain,
( $false
| ~ spl11_2
| ~ spl11_6
| ~ spl11_12
| ~ spl11_16
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f998]) ).
thf(f1005,plain,
( ~ spl11_2
| ~ spl11_6
| ~ spl11_12
| ~ spl11_16
| ~ spl11_20 ),
inference(avatar_contradiction_clause,[],[f1004]) ).
thf(f1090,plain,
( ( $true = $false )
| ( $false
= ( q @ sK5 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl11_10
| ~ spl11_12 ),
inference(constrained_superposition,[],[f450,f748]) ).
thf(f1115,plain,
( ( $false
= ( q @ sK5 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl11_10
| ~ spl11_12 ),
inference(trivial_inequality_removal,[],[f1090]) ).
thf(f1122,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl11_10
| ~ spl11_12
| ~ spl11_16 ),
inference(forward_demodulation,[],[f1115,f480]) ).
thf(f1123,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl11_10
| ~ spl11_12
| ~ spl11_16 ),
inference(trivial_inequality_removal,[],[f1122]) ).
thf(f1124,plain,
( ( $true = $false )
| ~ spl11_10
| ~ spl11_12
| ~ spl11_16 ),
inference(forward_demodulation,[],[f1123,f404]) ).
thf(f1125,plain,
( $false
| ~ spl11_10
| ~ spl11_12
| ~ spl11_16 ),
inference(trivial_inequality_removal,[],[f1124]) ).
thf(f1126,plain,
( ~ spl11_10
| ~ spl11_12
| ~ spl11_16 ),
inference(avatar_contradiction_clause,[],[f1125]) ).
thf(f1148,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK6 @ X0 ) )
| ( $true
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl11_11 ),
inference(constrained_superposition,[],[f401,f456]) ).
thf(f1155,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK6 @ X0 ) )
| ( $true
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f1148]) ).
thf(f4605,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ~ spl11_11
| ~ spl11_17 ),
inference(constrained_superposition,[],[f486,f1155]) ).
thf(f4610,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ~ spl11_11
| ~ spl11_17 ),
inference(trivial_inequality_removal,[],[f4605]) ).
thf(f4682,plain,
( ( $true = $false )
| ( $false
= ( q @ sK8 ) )
| ~ spl11_10
| ~ spl11_11
| ~ spl11_17 ),
inference(constrained_superposition,[],[f450,f4610]) ).
thf(f4683,plain,
( ( $false
= ( q @ sK8 ) )
| ~ spl11_10
| ~ spl11_11
| ~ spl11_17 ),
inference(trivial_inequality_removal,[],[f4682]) ).
thf(f4711,plain,
( ( $true = $false )
| ~ spl11_10
| ~ spl11_11
| ~ spl11_17
| ~ spl11_18 ),
inference(constrained_superposition,[],[f4683,f491]) ).
thf(f4717,plain,
( $false
| ~ spl11_10
| ~ spl11_11
| ~ spl11_17
| ~ spl11_18 ),
inference(trivial_inequality_removal,[],[f4711]) ).
thf(f4718,plain,
( ~ spl11_10
| ~ spl11_11
| ~ spl11_17
| ~ spl11_18 ),
inference(avatar_contradiction_clause,[],[f4717]) ).
thf(f4726,plain,
( ( $true = $false )
| ( $false
= ( p @ sK1 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl11_2
| ~ spl11_9 ),
inference(constrained_superposition,[],[f447,f842]) ).
thf(f4793,plain,
( ( $false
= ( p @ sK1 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl11_2
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f4726]) ).
thf(f4833,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl11_2
| ~ spl11_6
| ~ spl11_9 ),
inference(forward_demodulation,[],[f4793,f432]) ).
thf(f4834,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl11_2
| ~ spl11_6
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f4833]) ).
thf(f4846,plain,
( ( $true = $false )
| ~ spl11_2
| ~ spl11_6
| ~ spl11_9 ),
inference(forward_demodulation,[],[f4834,f404]) ).
thf(f4847,plain,
( $false
| ~ spl11_2
| ~ spl11_6
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f4846]) ).
thf(f4848,plain,
( ~ spl11_2
| ~ spl11_6
| ~ spl11_9 ),
inference(avatar_contradiction_clause,[],[f4847]) ).
thf(f5362,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ sK6 ) )
| ( $true
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl11_11 ),
inference(constrained_superposition,[],[f751,f456]) ).
thf(f5371,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK6 ) )
| ( $true
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f5362]) ).
thf(f5533,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK7 @ sK6 ) )
| ~ spl11_14 ),
inference(constrained_superposition,[],[f392,f470]) ).
thf(f5556,plain,
( ( $true
= ( rel_s5 @ sK7 @ sK6 ) )
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f5533]) ).
thf(f6456,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK0 @ sK7 ) )
| ~ spl11_11
| ~ spl11_14 ),
inference(constrained_superposition,[],[f5556,f5371]) ).
thf(f6499,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK7 ) )
| ~ spl11_11
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f6456]) ).
thf(f6626,plain,
( ( $true = $false )
| ( $false
= ( q @ sK7 ) )
| ~ spl11_10
| ~ spl11_11
| ~ spl11_14 ),
inference(constrained_superposition,[],[f450,f6499]) ).
thf(f6629,plain,
( ( $false
= ( q @ sK7 ) )
| ~ spl11_10
| ~ spl11_11
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f6626]) ).
thf(f6656,plain,
( ( $true = $false )
| ~ spl11_10
| ~ spl11_11
| ~ spl11_14
| ~ spl11_15 ),
inference(constrained_superposition,[],[f6629,f475]) ).
thf(f6662,plain,
( $false
| ~ spl11_10
| ~ spl11_11
| ~ spl11_14
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f6656]) ).
thf(f6663,plain,
( ~ spl11_10
| ~ spl11_11
| ~ spl11_14
| ~ spl11_15 ),
inference(avatar_contradiction_clause,[],[f6662]) ).
thf(f7907,plain,
( ( $true = $false )
| ( $false
= ( p @ sK2 ) )
| ~ spl11_1
| ~ spl11_9 ),
inference(constrained_superposition,[],[f408,f447]) ).
thf(f7910,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl11_1
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f7907]) ).
thf(f7932,plain,
( ( $true = $false )
| ~ spl11_1
| ~ spl11_3
| ~ spl11_9 ),
inference(constrained_superposition,[],[f7910,f417]) ).
thf(f7938,plain,
( $false
| ~ spl11_1
| ~ spl11_3
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f7932]) ).
thf(f7939,plain,
( ~ spl11_1
| ~ spl11_3
| ~ spl11_9 ),
inference(avatar_contradiction_clause,[],[f7938]) ).
cnf(s1,plain,
( spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f413]) ).
cnf(s2,plain,
( spl11_2
| spl11_3 ),
inference(sat_conversion,[],[f418]) ).
cnf(s5,plain,
( spl11_1
| spl11_6 ),
inference(sat_conversion,[],[f433]) ).
cnf(s6,plain,
( spl11_3
| spl11_6 ),
inference(sat_conversion,[],[f434]) ).
cnf(s9,plain,
( spl11_2
| spl11_9
| spl11_10 ),
inference(sat_conversion,[],[f451]) ).
cnf(s10,plain,
( spl11_6
| spl11_9
| spl11_10 ),
inference(sat_conversion,[],[f452]) ).
cnf(s11,plain,
( spl11_11
| spl11_12 ),
inference(sat_conversion,[],[f461]) ).
cnf(s13,plain,
( spl11_12
| spl11_14 ),
inference(sat_conversion,[],[f471]) ).
cnf(s14,plain,
( spl11_12
| spl11_15 ),
inference(sat_conversion,[],[f476]) ).
cnf(s15,plain,
( spl11_11
| spl11_16 ),
inference(sat_conversion,[],[f481]) ).
cnf(s17,plain,
( spl11_16
| spl11_17 ),
inference(sat_conversion,[],[f487]) ).
cnf(s18,plain,
( spl11_16
| spl11_18 ),
inference(sat_conversion,[],[f492]) ).
cnf(s19,plain,
( spl11_9
| spl11_10
| spl11_12 ),
inference(sat_conversion,[],[f493]) ).
cnf(s20,plain,
( spl11_9
| spl11_10
| spl11_16 ),
inference(sat_conversion,[],[f494]) ).
cnf(s25,plain,
( spl11_9
| spl11_10
| spl11_20 ),
inference(sat_conversion,[],[f518]) ).
cnf(s35,plain,
( ~ spl11_2
| ~ spl11_6
| ~ spl11_12
| ~ spl11_16
| ~ spl11_20 ),
inference(sat_conversion,[],[f1005]) ).
cnf(s36,plain,
( ~ spl11_10
| ~ spl11_12
| ~ spl11_16 ),
inference(sat_conversion,[],[f1126]) ).
cnf(s40,plain,
( ~ spl11_10
| ~ spl11_11
| ~ spl11_17
| ~ spl11_18 ),
inference(sat_conversion,[],[f4718]) ).
cnf(s44,plain,
( ~ spl11_2
| ~ spl11_6
| ~ spl11_9 ),
inference(sat_conversion,[],[f4848]) ).
cnf(s71,plain,
( ~ spl11_10
| ~ spl11_11
| ~ spl11_14
| ~ spl11_15 ),
inference(sat_conversion,[],[f6663]) ).
cnf(s111,plain,
( ~ spl11_1
| ~ spl11_3
| ~ spl11_9 ),
inference(sat_conversion,[],[f7939]) ).
cnf(s118,plain,
( spl11_10
| spl11_1 ),
inference(rat,[],[s35,s20,s25,s19,s44,s1,s5]) ).
cnf(s119,plain,
( spl11_16
| ~ spl11_10 ),
inference(rat,[],[s40,s15,s17,s18]) ).
cnf(s120,plain,
( ~ spl11_16
| ~ spl11_10 ),
inference(rat,[],[s71,s11,s13,s14,s36]) ).
cnf(s121,plain,
~ spl11_10,
inference(rat,[],[s120,s119]) ).
cnf(s122,plain,
spl11_1,
inference(rat,[],[s118,s121]) ).
cnf(s123,plain,
~ spl11_9,
inference(rat,[],[s44,s2,s6,s111,s122]) ).
cnf(s124,plain,
spl11_2,
inference(rat,[],[s9,s121,s123]) ).
cnf(s125,plain,
spl11_6,
inference(rat,[],[s10,s121,s123]) ).
cnf(s126,plain,
spl11_20,
inference(rat,[],[s25,s121,s123]) ).
cnf(s127,plain,
spl11_16,
inference(rat,[],[s20,s121,s123]) ).
cnf(s129,plain,
~ spl11_12,
inference(rat,[],[s35,s126,s125,s124,s127]) ).
cnf(s130,plain,
$false,
inference(rat,[],[s19,s121,s123,s129]) ).
thf(f7940,plain,
$false,
inference(avatar_sat_refutation,[],[s130]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO446^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 16:51:34 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.12 Running first-order model finding
% 0.09/0.12 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.63/0.30 % (372062)Will run a generic schedule for satisfiability detection.
% 0.63/0.30 % (372071)% WARNING: option uhcvi not known.
% 0.63/0.30 % (372072)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3202980889:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.63/0.30 % (372070)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3282291791_2999 on theBenchmark for (2999ds/0Mi)
% 0.63/0.30 % (372074)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2204374963:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.63/0.30 % (372071)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1569574073:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.63/0.30 % (372076)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3340172120:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.63/0.30 % (372073)dis+10_1_sil=32000:sp=arity:random_seed=1730192683:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.63/0.30 % (372075)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=724551985:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.63/0.30 % (372074)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.63/0.30 % (372071)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.63/0.30 % Exception at run slice level
% 0.63/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.63/0.30 % (372071)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.63/0.30 % (372084)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1914015155:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.63/0.30 % Exception at run slice level
% 0.63/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.63/0.30 % (372073)Instruction limit reached!
% 0.63/0.30 % (372073)------------------------------
% 0.63/0.30 % (372073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.30 % (372073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.30 % (372073)CaDiCaL version: 2.1.3
% 0.63/0.30 % (372073)Termination reason: Instruction limit
% 0.63/0.30 % (372073)Termination phase: Saturation
% 0.63/0.30 % (372073)Time elapsed: 0.024 s
% 0.63/0.30 % (372073)Peak memory usage: 12 MB
% 0.63/0.30 % (372073)Instructions burned: 103 (million)
% 0.63/0.30 % (372086)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1438310264:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.63/0.30 % (372074)Instruction limit reached!
% 0.63/0.30 % (372074)------------------------------
% 0.63/0.30 % (372074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.30 % (372074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.30 % (372074)CaDiCaL version: 2.1.3
% 0.63/0.30 % (372074)Termination reason: Instruction limit
% 0.63/0.30 % (372074)Termination phase: Saturation
% 0.63/0.30 % (372074)Time elapsed: 0.028 s
% 0.63/0.30 % (372074)Peak memory usage: 12 MB
% 0.63/0.30 % (372074)Instructions burned: 119 (million)
% 0.63/0.30 % (372075)Instruction limit reached!
% 0.63/0.30 % (372075)------------------------------
% 0.63/0.30 % (372075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.30 % (372075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.30 % (372075)CaDiCaL version: 2.1.3
% 0.63/0.30 % (372075)Termination reason: Instruction limit
% 0.63/0.30 % (372075)Termination phase: Saturation
% 0.63/0.30 % (372075)Time elapsed: 0.031 s
% 0.63/0.30 % (372075)Peak memory usage: 12 MB
% 0.63/0.30 % (372075)Instructions burned: 134 (million)
% 0.63/0.30 % (372088)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=920121286:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.63/0.30 % (372088)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.63/0.30 % (372088)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.63/0.30 % (372089)ott-21_1_sil=16000:fs=off:random_seed=1885476409:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.63/0.30 % (372076)Instruction limit reached!
% 0.63/0.30 % (372076)------------------------------
% 0.63/0.30 % (372076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.30 % (372076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.30 % (372076)CaDiCaL version: 2.1.3
% 0.63/0.30 % (372076)Termination reason: Instruction limit
% 0.63/0.30 % (372076)Termination phase: Saturation
% 0.63/0.30 % (372076)Time elapsed: 0.041 s
% 0.63/0.30 % (372076)Peak memory usage: 12 MB
% 0.63/0.30 % (372076)Instructions burned: 161 (million)
% 0.63/0.30 % (372090)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1024006547:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.63/0.30 % (372093)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1560995276:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 0.63/0.30 % Exception at run slice level
% 0.63/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.63/0.30 % (372086)Instruction limit reached!
% 0.63/0.30 % (372086)------------------------------
% 0.63/0.30 % (372086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.30 % (372086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.30 % (372086)CaDiCaL version: 2.1.3
% 0.63/0.30 % (372086)Termination reason: Instruction limit
% 0.63/0.30 % (372086)Termination phase: Saturation
% 0.63/0.30 % (372086)Time elapsed: 0.032 s
% 0.63/0.30 % (372086)Peak memory usage: 12 MB
% 0.63/0.30 % (372086)Instructions burned: 133 (million)
% 0.63/0.30 % (372096)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2364212452:i=1179_2999 on theBenchmark for (2999ds/1179Mi)
% 0.63/0.30 % (372097)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=999012924:i=889:ins=1_2999 on theBenchmark for (2999ds/889Mi)
% 0.63/0.30 % Exception at run slice level
% 0.63/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.63/0.30 % (372089)Instruction limit reached!
% 0.63/0.30 % (372089)------------------------------
% 0.63/0.30 % (372089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.30 % (372089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.30 % (372089)CaDiCaL version: 2.1.3
% 0.63/0.30 % (372089)Termination reason: Instruction limit
% 0.63/0.30 % (372089)Termination phase: Saturation
% 0.63/0.30 % (372089)Time elapsed: 0.041 s
% 0.63/0.30 % (372089)Peak memory usage: 12 MB
% 0.63/0.30 % (372089)Instructions burned: 181 (million)
% 0.63/0.30 % (372100)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=1415303402:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 0.63/0.30 % (372100)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.63/0.30 % (372101)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2293178774:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 0.63/0.30 % (372101)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.63/0.30 % (372088) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-372062-372088"...
% 0.63/0.30 % (372088)...printing done.
% 0.63/0.30 % (372088)Refutation found. Thanks to Tanya!
% 0.63/0.30 % SZS status Theorem for theBenchmark
% 0.63/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.63/0.30 % (372088)------------------------------
% 0.63/0.30 % (372088)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.63/0.30 % (372088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.63/0.30 % (372088)CaDiCaL version: 2.1.3
% 0.63/0.30 % (372088)Termination reason: Refutation
% 0.63/0.30 % (372088)Time elapsed: 0.105 s
% 0.63/0.30 % (372088)Peak memory usage: 14 MB
% 0.63/0.30 % (372088)Instructions burned: 443 (million)
% 0.63/0.30 % (372062)Success in time 0.177 s
% 0.63/0.30 % Vampire exiting
%------------------------------------------------------------------------------