%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO470^6 : 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 : n017.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 08:50:14 AM UTC 2026
% Result : Theorem 0.64s 0.43s
% Output : Refutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 33
% Syntax : Number of formulae : 277 ( 89 unt; 0 typ; 18 def)
% Number of atoms : 2225 ( 410 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 3087 ( 570 ~; 564 |; 13 &;1713 @)
% ( 18 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 136 ( 136 >; 0 *; 0 +; 0 <<)
% Number of symbols : 80 ( 76 usr; 26 con; 0-4 aty)
% ( 187 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 562 ( 0 sgn 174 !; 0 ?; 562 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vAND: $o > $o > $o ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
sK5: $i > $i ).
thf(func_def_58,type,
sK7: $i > $i ).
thf(func_def_60,type,
sK9: $i > $i ).
thf(func_def_61,type,
sK10: $i > $i ).
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 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ),
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 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ),
inference(rectify,[],[f38]) ).
thf(f100,plain,
( ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) )
!= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) )
!= $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 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) )
!= $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] :
~ ( 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] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) ),
inference(definition_unfolding,[],[f138,f129,f144,f150,f150,f133,f133]) ).
thf(f155,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( $false
= ( ~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
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 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ 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 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f175,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ sK2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f184,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f191,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| ( p @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| ( p @ sK3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ sK3 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f195,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ sK3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f198,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f251,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f201]) ).
thf(f252,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK8 )
| ( p @ sK8 ) ) ) ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
! [X1: $i] :
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK8 )
| ( p @ sK8 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK8 )
| ( p @ sK8 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK8 )
| ( p @ sK8 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK8 )
| ( p @ sK8 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( p @ sK8 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK8 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f256]) ).
thf(f259,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) )
@ ( sK9 @ X2 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) )
@ ( sK9 @ X2 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK9 @ X2 ) )
| ( p @ ( sK9 @ X2 ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f265]) ).
thf(f267,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK9 @ X2 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK9 @ X2 ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f266]) ).
thf(f269,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK9 @ X2 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( p @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f257]) ).
thf(f271,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( p @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f270]) ).
thf(f272,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( p @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( p @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) )
@ ( sK10 @ X2 ) ) )
| ( $false
= ( p @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( p @ Y0 ) )
@ ( sK10 @ X2 ) ) )
| ( $false
= ( p @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK10 @ X2 ) )
| ( p @ ( sK10 @ X2 ) ) ) )
| ( $false
= ( p @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f275]) ).
thf(f277,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK10 @ X2 ) ) )
| ( $false
= ( p @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK10 @ X2 ) ) ) )
| ( $false
= ( p @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f276]) ).
thf(f279,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK10 @ X2 ) ) )
| ( $false
= ( p @ sK8 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f278]) ).
thf(f280,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f281,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f281]) ).
thf(f283,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f283]) ).
thf(f285,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f284]) ).
thf(f286,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(f287,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,[],[f286]) ).
thf(f288,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,[],[f287]) ).
thf(f289,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,[],[f288]) ).
thf(f290,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,[],[f289]) ).
thf(f291,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,[],[f290]) ).
thf(f292,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f291]) ).
thf(f293,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,[],[f292]) ).
thf(f294,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,[],[f293]) ).
thf(f295,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f296,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f295]) ).
thf(f297,plain,
! [X1: $i] :
( $true
= ( rel_s5 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f296]) ).
thf(f299,definition,
( spl11_1
<=> ( $true
= ( rel_s5 @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
thf(f301,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f299]) ).
thf(f303,definition,
( spl11_2
<=> ! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f304,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f303]) ).
thf(f305,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f176,f303,f299]) ).
thf(f307,definition,
( spl11_3
<=> ( $true
= ( rel_s5 @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
thf(f309,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f307]) ).
thf(f310,plain,
( spl11_3
| spl11_2 ),
inference(avatar_split_clause,[],[f184,f303,f307]) ).
thf(f312,definition,
( spl11_4
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f313,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s5 @ sK2 @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f312]) ).
thf(f314,plain,
( spl11_4
| spl11_2 ),
inference(avatar_split_clause,[],[f189,f303,f312]) ).
thf(f316,definition,
( spl11_5
<=> ( $true
= ( rel_s5 @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
thf(f318,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f316]) ).
thf(f319,plain,
( spl11_5
| spl11_2 ),
inference(avatar_split_clause,[],[f196,f303,f316]) ).
thf(f321,definition,
( spl11_6
<=> ( $false
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
thf(f323,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f321]) ).
thf(f324,plain,
( spl11_6
| spl11_2 ),
inference(avatar_split_clause,[],[f197,f303,f321]) ).
thf(f355,definition,
( spl11_14
<=> ( $true
= ( rel_s5 @ sK0 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
thf(f357,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK8 ) )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f355]) ).
thf(f359,definition,
( spl11_15
<=> ! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK9 @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
thf(f360,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK9 @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) )
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f359]) ).
thf(f361,plain,
( spl11_14
| spl11_15 ),
inference(avatar_split_clause,[],[f269,f359,f355]) ).
thf(f363,definition,
( spl11_16
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK9 @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_16])],[avatar_definition]) ).
thf(f364,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK9 @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) )
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f363]) ).
thf(f365,plain,
( spl11_14
| spl11_16 ),
inference(avatar_split_clause,[],[f267,f363,f355]) ).
thf(f367,definition,
( spl11_17
<=> ( $false
= ( p @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_17])],[avatar_definition]) ).
thf(f369,plain,
( ( $false
= ( p @ sK8 ) )
| ~ spl11_17 ),
inference(avatar_component_clause,[],[f367]) ).
thf(f371,definition,
( spl11_18
<=> ! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK10 @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_18])],[avatar_definition]) ).
thf(f372,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK10 @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) )
| ~ spl11_18 ),
inference(avatar_component_clause,[],[f371]) ).
thf(f373,plain,
( spl11_17
| spl11_18 ),
inference(avatar_split_clause,[],[f279,f371,f367]) ).
thf(f375,definition,
( spl11_19
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK10 @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl11_19])],[avatar_definition]) ).
thf(f376,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK10 @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) )
| ~ spl11_19 ),
inference(avatar_component_clause,[],[f375]) ).
thf(f377,plain,
( spl11_17
| spl11_19 ),
inference(avatar_split_clause,[],[f277,f375,f367]) ).
thf(f383,plain,
( ( $true = $false )
| ( $true
= ( p @ sK8 ) )
| ~ spl11_2
| ~ spl11_14 ),
inference(constrained_superposition,[],[f357,f304]) ).
thf(f384,plain,
( ( $true
= ( p @ sK8 ) )
| ~ spl11_2
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f383]) ).
thf(f388,plain,
( ( $true = $false )
| ~ spl11_2
| ~ spl11_14
| ~ spl11_17 ),
inference(constrained_superposition,[],[f384,f369]) ).
thf(f392,plain,
( $false
| ~ spl11_2
| ~ spl11_14
| ~ spl11_17 ),
inference(trivial_inequality_removal,[],[f388]) ).
thf(f393,plain,
( ~ spl11_2
| ~ spl11_14
| ~ spl11_17 ),
inference(avatar_contradiction_clause,[],[f392]) ).
thf(f401,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( p @ ( sK9 @ sK0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl11_2
| ~ spl11_15 ),
inference(constrained_superposition,[],[f304,f360]) ).
thf(f402,plain,
( ! [X0: $i] :
( ( $true
= ( p @ ( sK9 @ sK0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl11_2
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f401]) ).
thf(f409,definition,
( spl11_20
<=> ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_20])],[avatar_definition]) ).
thf(f410,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl11_20 ),
inference(avatar_component_clause,[],[f409]) ).
thf(f412,definition,
( spl11_21
<=> ( $true
= ( p @ ( sK9 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_21])],[avatar_definition]) ).
thf(f414,plain,
( ( $true
= ( p @ ( sK9 @ sK0 ) ) )
| ~ spl11_21 ),
inference(avatar_component_clause,[],[f412]) ).
thf(f498,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) )
| ( $true
= ( p @ ( sK10 @ sK0 ) ) ) )
| ~ spl11_2
| ~ spl11_18 ),
inference(constrained_superposition,[],[f372,f304]) ).
thf(f513,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) )
| ( $true
= ( p @ ( sK10 @ sK0 ) ) ) )
| ~ spl11_2
| ~ spl11_18 ),
inference(trivial_inequality_removal,[],[f498]) ).
thf(f525,definition,
( spl11_26
<=> ( $true
= ( p @ ( sK10 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_26])],[avatar_definition]) ).
thf(f527,plain,
( ( $true
= ( p @ ( sK10 @ sK0 ) ) )
| ~ spl11_26 ),
inference(avatar_component_clause,[],[f525]) ).
thf(f536,plain,
( spl11_20
| spl11_21
| ~ spl11_2
| ~ spl11_15 ),
inference(avatar_split_clause,[],[f402,f359,f303,f412,f409]) ).
thf(f585,plain,
( ( $true = $false )
| ( $true = $false )
| ~ spl11_20 ),
inference(constrained_superposition,[],[f410,f297]) ).
thf(f598,plain,
( ( $true = $false )
| ~ spl11_20 ),
inference(duplicate_literal_removal,[],[f585]) ).
thf(f599,plain,
( $false
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f598]) ).
thf(f600,plain,
~ spl11_20,
inference(avatar_contradiction_clause,[],[f599]) ).
thf(f605,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl11_16
| ~ spl11_21 ),
inference(constrained_superposition,[],[f364,f414]) ).
thf(f606,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl11_16
| ~ spl11_21 ),
inference(trivial_inequality_removal,[],[f605]) ).
thf(f610,plain,
( spl11_20
| ~ spl11_16
| ~ spl11_21 ),
inference(avatar_split_clause,[],[f606,f412,f363,f409]) ).
thf(f794,definition,
( spl11_28
<=> ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_28])],[avatar_definition]) ).
thf(f795,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK2 ) ) )
| ~ spl11_28 ),
inference(avatar_component_clause,[],[f794]) ).
thf(f877,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl11_5 ),
inference(constrained_superposition,[],[f318,f294]) ).
thf(f929,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl11_5 ),
inference(trivial_inequality_removal,[],[f877]) ).
thf(f977,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK2 @ sK0 ) )
| ( $true
= ( p @ sK3 ) )
| ~ spl11_4
| ~ spl11_5 ),
inference(constrained_superposition,[],[f929,f313]) ).
thf(f1001,plain,
( ( $false
= ( rel_s5 @ sK2 @ sK0 ) )
| ( $true
= ( p @ sK3 ) )
| ~ spl11_4
| ~ spl11_5 ),
inference(trivial_inequality_removal,[],[f977]) ).
thf(f1016,definition,
( spl11_31
<=> ( $true
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_31])],[avatar_definition]) ).
thf(f1018,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl11_31 ),
inference(avatar_component_clause,[],[f1016]) ).
thf(f1021,definition,
( spl11_32
<=> ( $false
= ( rel_s5 @ sK2 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_32])],[avatar_definition]) ).
thf(f1023,plain,
( ( $false
= ( rel_s5 @ sK2 @ sK0 ) )
| ~ spl11_32 ),
inference(avatar_component_clause,[],[f1021]) ).
thf(f1040,plain,
( spl11_31
| spl11_32
| ~ spl11_4
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f1001,f316,f312,f1021,f1016]) ).
thf(f1052,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK2 ) )
| ~ spl11_32 ),
inference(constrained_superposition,[],[f285,f1023]) ).
thf(f1055,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK2 ) )
| ~ spl11_32 ),
inference(trivial_inequality_removal,[],[f1052]) ).
thf(f1071,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ sK2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl11_32 ),
inference(constrained_superposition,[],[f294,f1055]) ).
thf(f1072,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl11_32 ),
inference(trivial_inequality_removal,[],[f1071]) ).
thf(f1075,plain,
( spl11_28
| ~ spl11_32 ),
inference(avatar_split_clause,[],[f1072,f1021,f794]) ).
thf(f1186,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl11_3
| ~ spl11_28 ),
inference(constrained_superposition,[],[f309,f795]) ).
thf(f1187,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl11_3
| ~ spl11_28 ),
inference(trivial_inequality_removal,[],[f1186]) ).
thf(f1203,plain,
( ( $true = $false )
| ~ spl11_1
| ~ spl11_3
| ~ spl11_28 ),
inference(constrained_superposition,[],[f1187,f301]) ).
thf(f1213,plain,
( $false
| ~ spl11_1
| ~ spl11_3
| ~ spl11_28 ),
inference(trivial_inequality_removal,[],[f1203]) ).
thf(f1214,plain,
( ~ spl11_1
| ~ spl11_3
| ~ spl11_28 ),
inference(avatar_contradiction_clause,[],[f1213]) ).
thf(f1406,plain,
( ( $true = $false )
| ~ spl11_6
| ~ spl11_31 ),
inference(constrained_superposition,[],[f1018,f323]) ).
thf(f1410,plain,
( $false
| ~ spl11_6
| ~ spl11_31 ),
inference(trivial_inequality_removal,[],[f1406]) ).
thf(f1411,plain,
( ~ spl11_6
| ~ spl11_31 ),
inference(avatar_contradiction_clause,[],[f1410]) ).
thf(f1430,plain,
( spl11_26
| spl11_20
| ~ spl11_2
| ~ spl11_18 ),
inference(avatar_split_clause,[],[f513,f371,f303,f409,f525]) ).
thf(f1458,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl11_19
| ~ spl11_26 ),
inference(constrained_superposition,[],[f376,f527]) ).
thf(f1459,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl11_19
| ~ spl11_26 ),
inference(trivial_inequality_removal,[],[f1458]) ).
thf(f1475,plain,
( spl11_20
| ~ spl11_19
| ~ spl11_26 ),
inference(avatar_split_clause,[],[f1459,f525,f375,f409]) ).
cnf(s1,plain,
( spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f305]) ).
cnf(s2,plain,
( spl11_2
| spl11_3 ),
inference(sat_conversion,[],[f310]) ).
cnf(s3,plain,
( spl11_2
| spl11_4 ),
inference(sat_conversion,[],[f314]) ).
cnf(s4,plain,
( spl11_2
| spl11_5 ),
inference(sat_conversion,[],[f319]) ).
cnf(s5,plain,
( spl11_2
| spl11_6 ),
inference(sat_conversion,[],[f324]) ).
cnf(s12,plain,
( spl11_14
| spl11_15 ),
inference(sat_conversion,[],[f361]) ).
cnf(s13,plain,
( spl11_14
| spl11_16 ),
inference(sat_conversion,[],[f365]) ).
cnf(s14,plain,
( spl11_17
| spl11_18 ),
inference(sat_conversion,[],[f373]) ).
cnf(s15,plain,
( spl11_17
| spl11_19 ),
inference(sat_conversion,[],[f377]) ).
cnf(s17,plain,
( ~ spl11_2
| ~ spl11_14
| ~ spl11_17 ),
inference(sat_conversion,[],[f393]) ).
cnf(s29,plain,
( ~ spl11_2
| ~ spl11_15
| spl11_20
| spl11_21 ),
inference(sat_conversion,[],[f536]) ).
cnf(s31,plain,
~ spl11_20,
inference(sat_conversion,[],[f600]) ).
cnf(s34,plain,
( ~ spl11_16
| spl11_20
| ~ spl11_21 ),
inference(sat_conversion,[],[f610]) ).
cnf(s50,plain,
( ~ spl11_4
| ~ spl11_5
| spl11_31
| spl11_32 ),
inference(sat_conversion,[],[f1040]) ).
cnf(s54,plain,
( spl11_28
| ~ spl11_32 ),
inference(sat_conversion,[],[f1075]) ).
cnf(s69,plain,
( ~ spl11_1
| ~ spl11_3
| ~ spl11_28 ),
inference(sat_conversion,[],[f1214]) ).
cnf(s73,plain,
( ~ spl11_6
| ~ spl11_31 ),
inference(sat_conversion,[],[f1411]) ).
cnf(s77,plain,
( ~ spl11_2
| ~ spl11_18
| spl11_20
| spl11_26 ),
inference(sat_conversion,[],[f1430]) ).
cnf(s82,plain,
( ~ spl11_19
| spl11_20
| ~ spl11_26 ),
inference(sat_conversion,[],[f1475]) ).
cnf(s94,plain,
( ~ spl11_2
| ~ spl11_15
| spl11_21 ),
inference(rat,[],[s29,s31]) ).
cnf(s102,plain,
( spl11_14
| ~ spl11_2 ),
inference(rat,[],[s94,s34,s12,s13,s31]) ).
cnf(s103,plain,
( ~ spl11_14
| ~ spl11_2 ),
inference(rat,[],[s77,s82,s14,s15,s17,s31]) ).
cnf(s104,plain,
~ spl11_2,
inference(rat,[],[s103,s102]) ).
cnf(s105,plain,
spl11_6,
inference(rat,[],[s5,s104]) ).
cnf(s106,plain,
spl11_5,
inference(rat,[],[s4,s104]) ).
cnf(s107,plain,
spl11_4,
inference(rat,[],[s3,s104]) ).
cnf(s108,plain,
spl11_3,
inference(rat,[],[s2,s104]) ).
cnf(s109,plain,
spl11_1,
inference(rat,[],[s1,s104]) ).
cnf(s110,plain,
~ spl11_31,
inference(rat,[],[s73,s105]) ).
cnf(s111,plain,
spl11_32,
inference(rat,[],[s50,s106,s110,s107]) ).
cnf(s112,plain,
~ spl11_28,
inference(rat,[],[s69,s108,s109]) ).
cnf(s113,plain,
$false,
inference(rat,[],[s54,s111,s112]) ).
thf(f1479,plain,
$false,
inference(avatar_sat_refutation,[],[s113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO470^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 % Computer : n017.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 16:58:53 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.29 Running first-order model finding
% 0.24/0.29 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
% 0.64/0.43 % (612092)Will run a generic schedule for satisfiability detection.
% 0.64/0.43 % (612097)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1422657351_2999 on theBenchmark for (2999ds/0Mi)
% 0.64/0.43 % Exception at run slice level
% 0.64/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.64/0.43 % (612103)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3070000210:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.64/0.43 % (612098)% WARNING: option uhcvi not known.
% 0.64/0.43 % (612100)dis+10_1_sil=32000:sp=arity:random_seed=352526520:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.64/0.43 % (612099)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1229620232:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.64/0.43 % (612098)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1058509646:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.64/0.43 % (612101)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3464231325:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.64/0.43 % (612102)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3619821584:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.64/0.43 % (612098)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.64/0.43 % (612098)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.64/0.43 % (612101)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.64/0.43 % (612105)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=996365677:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.64/0.43 % Exception at run slice level
% 0.64/0.43 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.64/0.43 % (612113)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3855051876:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.64/0.43 % (612103) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-612092-612103"...
% 0.64/0.43 % (612100)Instruction limit reached!
% 0.64/0.43 % (612100)------------------------------
% 0.64/0.43 % (612100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.43 % (612100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.43 % (612100)CaDiCaL version: 2.1.3
% 0.64/0.43 % (612100)Termination reason: Instruction limit
% 0.64/0.43 % (612100)Termination phase: Saturation
% 0.64/0.43 % (612100)Time elapsed: 0.084 s
% 0.64/0.43 % (612100)Peak memory usage: 12 MB
% 0.64/0.43 % (612100)Instructions burned: 104 (million)
% 0.64/0.43 % (612113)Instruction limit reached!
% 0.64/0.43 % (612113)------------------------------
% 0.64/0.43 % (612113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.43 % (612113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.43 % (612113)CaDiCaL version: 2.1.3
% 0.64/0.43 % (612113)Termination reason: Instruction limit
% 0.64/0.43 % (612113)Termination phase: Saturation
% 0.64/0.43 % (612113)Time elapsed: 0.059 s
% 0.64/0.43 % (612113)Peak memory usage: 12 MB
% 0.64/0.43 % (612113)Instructions burned: 134 (million)
% 0.64/0.43 % (612101)Instruction limit reached!
% 0.64/0.43 % (612101)------------------------------
% 0.64/0.43 % (612101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.43 % (612101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.43 % (612101)CaDiCaL version: 2.1.3
% 0.64/0.43 % (612101)Termination reason: Instruction limit
% 0.64/0.43 % (612101)Termination phase: Saturation
% 0.64/0.43 % (612101)Time elapsed: 0.093 s
% 0.64/0.43 % (612101)Peak memory usage: 12 MB
% 0.64/0.43 % (612101)Instructions burned: 117 (million)
% 0.64/0.43 % (612103)...printing done.
% 0.64/0.43 % (612103)Refutation found. Thanks to Tanya!
% 0.64/0.43 % SZS status Theorem for theBenchmark
% 0.64/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.64/0.44 % (612103)------------------------------
% 0.64/0.44 % (612103)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.64/0.44 % (612103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.64/0.44 % (612103)CaDiCaL version: 2.1.3
% 0.64/0.44 % (612103)Termination reason: Refutation
% 0.64/0.44 % (612103)Time elapsed: 0.101 s
% 0.64/0.44 % (612103)Peak memory usage: 13 MB
% 0.64/0.44 % (612103)Instructions burned: 121 (million)
% 0.64/0.44 % (612092)Success in time 0.133 s
% 0.64/0.44 % Vampire exiting
%------------------------------------------------------------------------------