%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO449^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:50:00 AM UTC 2026
% Result : Theorem 5.83s 1.10s
% Output : Refutation 5.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 34
% Syntax : Number of formulae : 385 ( 91 unt; 0 typ; 19 def)
% Number of atoms : 3810 ( 717 equ; 0 cnn)
% Maximal formula atoms : 13 ( 9 avg)
% Number of connectives : 4706 ( 901 ~;1121 |; 13 &;2413 @)
% ( 19 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 144 ( 144 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 78 usr; 31 con; 0-4 aty)
% ( 217 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 697 ( 0 sgn 246 !; 0 ?; 697 :)
% 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/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f34,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_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 @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f100,plain,
( ( mvalid @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( ( mvalid @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_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 @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_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] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [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] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $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 )
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [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 )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f138,f129,f133,f144,f133,f142,f150,f133,f142,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 ) ) )
| ( q @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( p @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( q @ Y3 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( p @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( q @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) )
| ( q @ Y2 ) ) ) ) ) ) ) ) ),
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 ) ) )
| ( q @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( p @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( q @ Y3 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( p @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( q @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) )
| ( q @ Y2 ) ) ) ) ) ) )
@ 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 ) ) )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) )
| ( q @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) )
| ( q @ Y1 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
( $false
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f162,plain,
( $true
= ( rel_s5 @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f164,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f173,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ~ ( p @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( q @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( q @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( p @ Y0 ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X3 )
| ( q @ X3 ) ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ X2 @ X4 )
| ~ ( p @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ X2 @ X4 )
| ~ ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $true
= ( ~ ( p @ X4 ) ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ X2 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $false
= ( p @ X4 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ X2 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $false
= ( p @ X4 ) )
| ( $false
= ( rel_s5 @ X1 @ X3 ) )
| ( $true
= ( ~ ( rel_s5 @ X2 @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X3 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $false
= ( p @ X4 ) )
| ( $false
= ( rel_s5 @ X1 @ X3 ) )
| ( $false
= ( rel_s5 @ X2 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f194,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ~ ( p @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ~ ( p @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ~ ( p @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ~ ( p @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ~ ( p @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( p @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f197]) ).
thf(f200,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ( q @ X2 ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( p @ sK2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( p @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( p @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( p @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ( q @ X2 ) ) )
| ( $true
= ( p @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK3 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f206]) ).
thf(f215,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK3 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ sK3 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ( q @ X2 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK2 @ sK3 )
| ( q @ sK3 ) ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(beta-eta_normalization,[],[f216]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $false
= ( ~ ( rel_s5 @ sK2 @ sK3 )
| ( q @ sK3 ) ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $false
= ( q @ sK3 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $false
= ( ~ ( rel_s5 @ sK2 @ sK3 ) ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( rel_s5 @ sK2 @ sK3 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( rel_s5 @ sK2 @ sK3 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $false
= ( q @ sK3 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f224,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) )
@ sK4 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f225,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) )
@ sK4 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f226,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) )
@ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f225]) ).
thf(f276,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( q @ Y0 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f226]) ).
thf(f277,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK4 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( q @ sK4 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK6 )
| ~ ( p @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f276]) ).
thf(f278,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( q @ sK4 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK6 )
| ~ ( p @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f277]) ).
thf(f279,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK4 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK6 )
| ~ ( p @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f277]) ).
thf(f280,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK6 )
| ~ ( p @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f279]) ).
thf(f281,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $false
= ( ~ ( p @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f280]) ).
thf(f282,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f280]) ).
thf(f283,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f282]) ).
thf(f284,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f281]) ).
thf(f285,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $false
= ( ~ ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f281]) ).
thf(f286,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $true
= ( p @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f287,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f284]) ).
thf(f288,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $false
= ( ~ ( rel_s5 @ sK6 @ sK7 )
| ( q @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f287]) ).
thf(f289,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $false
= ( q @ sK7 ) ) ),
inference(or_proxy_clausification,[],[f288]) ).
thf(f290,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $false
= ( ~ ( rel_s5 @ sK6 @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f288]) ).
thf(f291,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $true
= ( rel_s5 @ sK6 @ sK7 ) ) ),
inference(not_proxy_clausification,[],[f290]) ).
thf(f292,plain,
( ( $false
= ( q @ sK4 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK6 )
| ~ ( p @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f278]) ).
thf(f293,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK6 )
| ~ ( p @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f278]) ).
thf(f294,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK6 )
| ~ ( p @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f293]) ).
thf(f295,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK6 )
| ~ ( p @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f294]) ).
thf(f296,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK6 )
| ~ ( p @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f295]) ).
thf(f297,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ~ ( p @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f296]) ).
thf(f298,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f296]) ).
thf(f299,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK8 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f298]) ).
thf(f300,plain,
( ( $false
= ( ~ ( rel_s5 @ sK4 @ sK8 )
| ~ ( p @ sK8 ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK6 ) ) ),
inference(beta-eta_normalization,[],[f299]) ).
thf(f301,plain,
( ( $false
= ( ~ ( p @ sK8 ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK6 ) ) ),
inference(or_proxy_clausification,[],[f300]) ).
thf(f302,plain,
( ( $false
= ( ~ ( rel_s5 @ sK4 @ sK8 ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK6 ) ) ),
inference(or_proxy_clausification,[],[f300]) ).
thf(f303,plain,
( ( $true
= ( rel_s5 @ sK4 @ sK8 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f302]) ).
thf(f304,plain,
( ( $true
= ( p @ sK8 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f301]) ).
thf(f306,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ~ ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f297]) ).
thf(f307,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK8 ) )
| ( $true
= ( p @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f306]) ).
thf(f308,plain,
( ( $false
= ( ~ ( rel_s5 @ sK4 @ sK8 )
| ~ ( p @ sK8 ) ) )
| ( $true
= ( p @ sK6 ) ) ),
inference(beta-eta_normalization,[],[f307]) ).
thf(f309,plain,
( ( $false
= ( ~ ( p @ sK8 ) ) )
| ( $true
= ( p @ sK6 ) ) ),
inference(or_proxy_clausification,[],[f308]) ).
thf(f310,plain,
( ( $false
= ( ~ ( rel_s5 @ sK4 @ sK8 ) ) )
| ( $true
= ( p @ sK6 ) ) ),
inference(or_proxy_clausification,[],[f308]) ).
thf(f311,plain,
( ( $true
= ( rel_s5 @ sK4 @ sK8 ) )
| ( $true
= ( p @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f310]) ).
thf(f312,plain,
( ( $true
= ( p @ sK8 ) )
| ( $true
= ( p @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f309]) ).
thf(f325,plain,
( ( $false
= ( q @ sK4 ) )
| ( $false
= ( ~ ( p @ sK6 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f292]) ).
thf(f326,plain,
( ( $false
= ( q @ sK4 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f292]) ).
thf(f327,plain,
( ( $false
= ( q @ sK4 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f326]) ).
thf(f328,plain,
( ( $false
= ( q @ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f325]) ).
thf(f329,plain,
( ( $false
= ( q @ sK4 ) )
| ( $false
= ( ~ ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f325]) ).
thf(f330,plain,
( ( $false
= ( q @ sK4 ) )
| ( $true
= ( p @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f329]) ).
thf(f331,plain,
( ( $false
= ( q @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK6 @ Y0 )
| ( q @ Y0 ) )
@ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f328]) ).
thf(f332,plain,
( ( $false
= ( q @ sK4 ) )
| ( $false
= ( ~ ( rel_s5 @ sK6 @ sK10 )
| ( q @ sK10 ) ) ) ),
inference(beta-eta_normalization,[],[f331]) ).
thf(f333,plain,
( ( $false
= ( q @ sK4 ) )
| ( $false
= ( q @ sK10 ) ) ),
inference(or_proxy_clausification,[],[f332]) ).
thf(f334,plain,
( ( $false
= ( q @ sK4 ) )
| ( $false
= ( ~ ( rel_s5 @ sK6 @ sK10 ) ) ) ),
inference(or_proxy_clausification,[],[f332]) ).
thf(f335,plain,
( ( $false
= ( q @ sK4 ) )
| ( $true
= ( rel_s5 @ sK6 @ sK10 ) ) ),
inference(not_proxy_clausification,[],[f334]) ).
thf(f336,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f337,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f336]) ).
thf(f338,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f337]) ).
thf(f339,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f338]) ).
thf(f340,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f339]) ).
thf(f341,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f340]) ).
thf(f342,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(f343,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,[],[f342]) ).
thf(f344,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,[],[f343]) ).
thf(f345,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,[],[f344]) ).
thf(f346,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,[],[f345]) ).
thf(f347,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,[],[f346]) ).
thf(f348,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f347]) ).
thf(f349,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,[],[f348]) ).
thf(f350,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,[],[f349]) ).
thf(f351,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f352,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f351]) ).
thf(f353,plain,
! [X1: $i] :
( $true
= ( rel_s5 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f352]) ).
thf(f355,definition,
( spl11_1
<=> ! [X2: $i,X4: $i] :
( ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ X2 @ X4 ) )
| ( $false
= ( p @ X4 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
thf(f356,plain,
( ! [X2: $i,X4: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $false
= ( rel_s5 @ X2 @ X4 ) )
| ( $false
= ( p @ X4 ) )
| ( $true
= ( q @ X2 ) ) )
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f355]) ).
thf(f358,definition,
( spl11_2
<=> ! [X1: $i,X3: $i] :
( ( $true
= ( q @ X3 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ X1 @ X3 ) )
| ( $false
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f359,plain,
( ! [X3: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ X1 @ X3 ) )
| ( $true
= ( q @ X3 ) )
| ( $false
= ( p @ X1 ) ) )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f358]) ).
thf(f360,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f192,f358,f355]) ).
thf(f362,definition,
( spl11_3
<=> ( $true
= ( rel_s5 @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
thf(f364,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f362]) ).
thf(f365,plain,
( spl11_3
| spl11_2 ),
inference(avatar_split_clause,[],[f205,f358,f362]) ).
thf(f367,definition,
( spl11_4
<=> ( $true
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f369,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f367]) ).
thf(f370,plain,
( spl11_4
| spl11_2 ),
inference(avatar_split_clause,[],[f213,f358,f367]) ).
thf(f372,definition,
( spl11_5
<=> ( $true
= ( rel_s5 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
thf(f374,plain,
( ( $true
= ( rel_s5 @ sK2 @ sK3 ) )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f372]) ).
thf(f375,plain,
( spl11_5
| spl11_2 ),
inference(avatar_split_clause,[],[f222,f358,f372]) ).
thf(f377,definition,
( spl11_6
<=> ( $false
= ( q @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
thf(f379,plain,
( ( $false
= ( q @ sK3 ) )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f377]) ).
thf(f380,plain,
( spl11_6
| spl11_2 ),
inference(avatar_split_clause,[],[f223,f358,f377]) ).
thf(f382,definition,
( spl11_7
<=> ( $true
= ( rel_s5 @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
thf(f384,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f382]) ).
thf(f397,definition,
( spl11_10
<=> ( $false
= ( q @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
thf(f399,plain,
( ( $false
= ( q @ sK4 ) )
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f397]) ).
thf(f402,definition,
( spl11_11
<=> ( $true
= ( rel_s5 @ sK1 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
thf(f404,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK6 ) )
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f402]) ).
thf(f405,plain,
( spl11_11
| spl11_7 ),
inference(avatar_split_clause,[],[f283,f382,f402]) ).
thf(f407,definition,
( spl11_12
<=> ( $true
= ( p @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
thf(f409,plain,
( ( $true
= ( p @ sK6 ) )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f407]) ).
thf(f410,plain,
( spl11_12
| spl11_7 ),
inference(avatar_split_clause,[],[f286,f382,f407]) ).
thf(f412,definition,
( spl11_13
<=> ( $true
= ( rel_s5 @ sK6 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition]) ).
thf(f414,plain,
( ( $true
= ( rel_s5 @ sK6 @ sK7 ) )
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f412]) ).
thf(f415,plain,
( spl11_13
| spl11_7 ),
inference(avatar_split_clause,[],[f291,f382,f412]) ).
thf(f417,definition,
( spl11_14
<=> ( $false
= ( q @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
thf(f419,plain,
( ( $false
= ( q @ sK7 ) )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f417]) ).
thf(f420,plain,
( spl11_14
| spl11_7 ),
inference(avatar_split_clause,[],[f289,f382,f417]) ).
thf(f422,definition,
( spl11_15
<=> ( $true
= ( rel_s5 @ sK4 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
thf(f424,plain,
( ( $true
= ( rel_s5 @ sK4 @ sK8 ) )
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f422]) ).
thf(f425,plain,
( spl11_11
| spl11_15 ),
inference(avatar_split_clause,[],[f303,f422,f402]) ).
thf(f427,definition,
( spl11_16
<=> ( $true
= ( p @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_16])],[avatar_definition]) ).
thf(f429,plain,
( ( $true
= ( p @ sK8 ) )
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f427]) ).
thf(f430,plain,
( spl11_11
| spl11_16 ),
inference(avatar_split_clause,[],[f304,f427,f402]) ).
thf(f431,plain,
( spl11_12
| spl11_15 ),
inference(avatar_split_clause,[],[f311,f422,f407]) ).
thf(f432,plain,
( spl11_12
| spl11_16 ),
inference(avatar_split_clause,[],[f312,f427,f407]) ).
thf(f445,plain,
( spl11_11
| spl11_10 ),
inference(avatar_split_clause,[],[f327,f397,f402]) ).
thf(f446,plain,
( spl11_12
| spl11_10 ),
inference(avatar_split_clause,[],[f330,f397,f407]) ).
thf(f448,definition,
( spl11_19
<=> ( $true
= ( rel_s5 @ sK6 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_19])],[avatar_definition]) ).
thf(f450,plain,
( ( $true
= ( rel_s5 @ sK6 @ sK10 ) )
| ~ spl11_19 ),
inference(avatar_component_clause,[],[f448]) ).
thf(f451,plain,
( spl11_19
| spl11_10 ),
inference(avatar_split_clause,[],[f335,f397,f448]) ).
thf(f453,definition,
( spl11_20
<=> ( $false
= ( q @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_20])],[avatar_definition]) ).
thf(f455,plain,
( ( $false
= ( q @ sK10 ) )
| ~ spl11_20 ),
inference(avatar_component_clause,[],[f453]) ).
thf(f456,plain,
( spl11_20
| spl11_10 ),
inference(avatar_split_clause,[],[f333,f397,f453]) ).
thf(f498,definition,
( spl11_25
<=> ( $false
= ( rel_s5 @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_25])],[avatar_definition]) ).
thf(f499,plain,
( ( $false
!= ( rel_s5 @ sK1 @ sK4 ) )
| spl11_25 ),
inference(avatar_component_clause,[],[f498]) ).
thf(f500,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK4 ) )
| ~ spl11_25 ),
inference(avatar_component_clause,[],[f498]) ).
thf(f533,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK1 @ sK6 ) )
| ( $true
= ( q @ sK7 ) )
| ( $false
= ( p @ sK6 ) )
| ~ spl11_2
| ~ spl11_13 ),
inference(constrained_superposition,[],[f359,f414]) ).
thf(f534,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK6 ) )
| ( $true
= ( q @ sK7 ) )
| ( $false
= ( p @ sK6 ) )
| ~ spl11_2
| ~ spl11_13 ),
inference(trivial_inequality_removal,[],[f533]) ).
thf(f538,plain,
( ( $true = $false )
| ( $true
= ( q @ sK7 ) )
| ( $false
= ( p @ sK6 ) )
| ~ spl11_2
| ~ spl11_11
| ~ spl11_13 ),
inference(forward_demodulation,[],[f534,f404]) ).
thf(f539,plain,
( ( $true
= ( q @ sK7 ) )
| ( $false
= ( p @ sK6 ) )
| ~ spl11_2
| ~ spl11_11
| ~ spl11_13 ),
inference(trivial_inequality_removal,[],[f538]) ).
thf(f546,plain,
( ( $true = $false )
| ( $false
= ( p @ sK6 ) )
| ~ spl11_2
| ~ spl11_11
| ~ spl11_13
| ~ spl11_14 ),
inference(forward_demodulation,[],[f539,f419]) ).
thf(f547,plain,
( ( $false
= ( p @ sK6 ) )
| ~ spl11_2
| ~ spl11_11
| ~ spl11_13
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f546]) ).
thf(f560,plain,
( ( $true = $false )
| ~ spl11_2
| ~ spl11_11
| ~ spl11_12
| ~ spl11_13
| ~ spl11_14 ),
inference(constrained_superposition,[],[f547,f409]) ).
thf(f564,plain,
( $false
| ~ spl11_2
| ~ spl11_11
| ~ spl11_12
| ~ spl11_13
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f560]) ).
thf(f565,plain,
( ~ spl11_2
| ~ spl11_11
| ~ spl11_12
| ~ spl11_13
| ~ spl11_14 ),
inference(avatar_contradiction_clause,[],[f564]) ).
thf(f570,plain,
( ( $true = $false )
| ~ spl11_7
| ~ spl11_25 ),
inference(forward_demodulation,[],[f384,f500]) ).
thf(f571,plain,
( $false
| ~ spl11_7
| ~ spl11_25 ),
inference(trivial_inequality_removal,[],[f570]) ).
thf(f572,plain,
( ~ spl11_7
| ~ spl11_25 ),
inference(avatar_contradiction_clause,[],[f571]) ).
thf(f603,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $false
= ( p @ sK8 ) )
| ( $true
= ( q @ sK4 ) )
| ~ spl11_1
| ~ spl11_15 ),
inference(constrained_superposition,[],[f424,f356]) ).
thf(f610,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK4 ) )
| ( $false
= ( p @ sK8 ) )
| ( $true
= ( q @ sK4 ) )
| ~ spl11_1
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f603]) ).
thf(f614,plain,
( ( $false
= ( p @ sK8 ) )
| ( $true
= ( q @ sK4 ) )
| ~ spl11_1
| ~ spl11_15
| spl11_25 ),
inference(forward_subsumption_resolution,[],[f610,f499]) ).
thf(f623,plain,
( ( $true = $false )
| ( $true
= ( q @ sK4 ) )
| ~ spl11_1
| ~ spl11_15
| ~ spl11_16
| spl11_25 ),
inference(forward_demodulation,[],[f614,f429]) ).
thf(f624,plain,
( ( $true
= ( q @ sK4 ) )
| ~ spl11_1
| ~ spl11_15
| ~ spl11_16
| spl11_25 ),
inference(trivial_inequality_removal,[],[f623]) ).
thf(f628,plain,
( ( $true = $false )
| ~ spl11_1
| ~ spl11_10
| ~ spl11_15
| ~ spl11_16
| spl11_25 ),
inference(forward_demodulation,[],[f624,f399]) ).
thf(f629,plain,
( $false
| ~ spl11_1
| ~ spl11_10
| ~ spl11_15
| ~ spl11_16
| spl11_25 ),
inference(trivial_inequality_removal,[],[f628]) ).
thf(f630,plain,
( ~ spl11_1
| ~ spl11_10
| ~ spl11_15
| ~ spl11_16
| spl11_25 ),
inference(avatar_contradiction_clause,[],[f629]) ).
thf(f695,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl11_2 ),
inference(constrained_superposition,[],[f359,f341]) ).
thf(f696,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X0 ) )
| ( $false
= ( rel_s5 @ X1 @ X0 ) ) )
| ~ spl11_2 ),
inference(constrained_superposition,[],[f359,f341]) ).
thf(f698,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $false
= ( p @ X0 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl11_2 ),
inference(trivial_inequality_removal,[],[f696]) ).
thf(f699,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( $false
= ( p @ X0 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl11_2 ),
inference(trivial_inequality_removal,[],[f695]) ).
thf(f824,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK1 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f162,f350]) ).
thf(f826,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK4 ) )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl11_7 ),
inference(constrained_superposition,[],[f384,f350]) ).
thf(f828,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK6 ) )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl11_11 ),
inference(constrained_superposition,[],[f404,f350]) ).
thf(f831,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $false
= ( p @ X0 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) ) )
| ~ spl11_2 ),
inference(constrained_superposition,[],[f698,f350]) ).
thf(f836,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ X0 @ X2 ) ) )
| ~ spl11_2 ),
inference(constrained_superposition,[],[f698,f350]) ).
thf(f840,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,[],[f341,f350]) ).
thf(f843,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,[],[f840]) ).
thf(f846,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ X0 @ X2 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ X1 ) ) )
| ~ spl11_2 ),
inference(trivial_inequality_removal,[],[f836]) ).
thf(f851,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X0 ) ) )
| ~ spl11_2 ),
inference(trivial_inequality_removal,[],[f831]) ).
thf(f854,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK6 ) )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f828]) ).
thf(f856,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK4 ) )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl11_7 ),
inference(trivial_inequality_removal,[],[f826]) ).
thf(f858,plain,
! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK1 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f824]) ).
thf(f946,definition,
( spl11_31
<=> ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( q @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_31])],[avatar_definition]) ).
thf(f947,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl11_31 ),
inference(avatar_component_clause,[],[f946]) ).
thf(f1144,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( q @ sK4 ) )
| ~ spl11_7
| ~ spl11_31 ),
inference(constrained_superposition,[],[f856,f947]) ).
thf(f1194,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( q @ sK4 ) )
| ~ spl11_7
| ~ spl11_31 ),
inference(trivial_inequality_removal,[],[f1144]) ).
thf(f1211,plain,
( ( $true = $false )
| ( $true
= ( q @ sK4 ) )
| ~ spl11_7
| ~ spl11_31 ),
inference(forward_demodulation,[],[f1194,f162]) ).
thf(f1212,plain,
( ( $true
= ( q @ sK4 ) )
| ~ spl11_7
| ~ spl11_31 ),
inference(trivial_inequality_removal,[],[f1211]) ).
thf(f1213,plain,
( ( $true = $false )
| ~ spl11_7
| ~ spl11_10
| ~ spl11_31 ),
inference(forward_demodulation,[],[f1212,f399]) ).
thf(f1214,plain,
( $false
| ~ spl11_7
| ~ spl11_10
| ~ spl11_31 ),
inference(trivial_inequality_removal,[],[f1213]) ).
thf(f1215,plain,
( ~ spl11_7
| ~ spl11_10
| ~ spl11_31 ),
inference(avatar_contradiction_clause,[],[f1214]) ).
thf(f1420,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ sK6 ) ) )
| ~ spl11_2
| ~ spl11_11 ),
inference(constrained_superposition,[],[f846,f404]) ).
thf(f1485,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ sK6 ) ) )
| ~ spl11_2
| ~ spl11_11 ),
inference(duplicate_literal_removal,[],[f1420]) ).
thf(f1486,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ sK6 ) ) )
| ~ spl11_2
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f1485]) ).
thf(f1627,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( $false
= ( p @ X0 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl11_2 ),
inference(constrained_superposition,[],[f699,f858]) ).
thf(f1630,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK0 ) )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X0 ) ) )
| ~ spl11_2 ),
inference(trivial_inequality_removal,[],[f1627]) ).
thf(f1835,plain,
( ! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ X1 ) ) )
| ~ spl11_2 ),
inference(equality_factoring,[],[f851]) ).
thf(f1836,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ X1 ) ) )
| ~ spl11_2 ),
inference(trivial_inequality_removal,[],[f1835]) ).
thf(f2219,definition,
( spl11_38
<=> ! [X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ sK1 ) )
| ( $true
= ( q @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_38])],[avatar_definition]) ).
thf(f2220,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ sK1 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl11_38 ),
inference(avatar_component_clause,[],[f2219]) ).
thf(f2284,plain,
( spl11_1
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f1836,f358,f355]) ).
thf(f2294,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl11_2
| ~ spl11_11
| ~ spl11_12 ),
inference(forward_demodulation,[],[f1486,f409]) ).
thf(f2295,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl11_2
| ~ spl11_11
| ~ spl11_12 ),
inference(trivial_inequality_removal,[],[f2294]) ).
thf(f2355,plain,
( spl11_38
| ~ spl11_2
| ~ spl11_11
| ~ spl11_12 ),
inference(avatar_split_clause,[],[f2295,f407,f402,f358,f2219]) ).
thf(f2383,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ X0 @ X2 ) )
| ( $false
= ( p @ X2 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl11_1 ),
inference(constrained_superposition,[],[f350,f356]) ).
thf(f2410,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ X2 ) )
| ( $false
= ( p @ X2 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl11_1 ),
inference(trivial_inequality_removal,[],[f2383]) ).
thf(f2462,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl11_1 ),
inference(constrained_superposition,[],[f341,f2410]) ).
thf(f2491,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl11_1 ),
inference(trivial_inequality_removal,[],[f2462]) ).
thf(f2792,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f162,f843]) ).
thf(f2903,plain,
! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f2792]) ).
thf(f3903,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK6 @ sK0 ) )
| ( $true
= ( q @ sK10 ) )
| ( $false
= ( p @ sK6 ) )
| ~ spl11_2
| ~ spl11_19 ),
inference(constrained_superposition,[],[f1630,f450]) ).
thf(f3910,plain,
( ( $false
= ( rel_s5 @ sK6 @ sK0 ) )
| ( $true
= ( q @ sK10 ) )
| ( $false
= ( p @ sK6 ) )
| ~ spl11_2
| ~ spl11_19 ),
inference(trivial_inequality_removal,[],[f3903]) ).
thf(f3959,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK6 @ sK0 ) )
| ( $false
= ( p @ sK6 ) )
| ~ spl11_2
| ~ spl11_19
| ~ spl11_20 ),
inference(forward_demodulation,[],[f3910,f455]) ).
thf(f3960,plain,
( ( $false
= ( rel_s5 @ sK6 @ sK0 ) )
| ( $false
= ( p @ sK6 ) )
| ~ spl11_2
| ~ spl11_19
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f3959]) ).
thf(f3991,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK6 @ sK0 ) )
| ~ spl11_2
| ~ spl11_12
| ~ spl11_19
| ~ spl11_20 ),
inference(forward_demodulation,[],[f3960,f409]) ).
thf(f3992,plain,
( ( $false
= ( rel_s5 @ sK6 @ sK0 ) )
| ~ spl11_2
| ~ spl11_12
| ~ spl11_19
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f3991]) ).
thf(f5390,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK6 ) )
| ~ spl11_2
| ~ spl11_12
| ~ spl11_19
| ~ spl11_20 ),
inference(constrained_superposition,[],[f341,f3992]) ).
thf(f5395,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK6 ) )
| ~ spl11_2
| ~ spl11_12
| ~ spl11_19
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f5390]) ).
thf(f5597,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl11_2
| ~ spl11_11
| ~ spl11_12
| ~ spl11_19
| ~ spl11_20 ),
inference(constrained_superposition,[],[f854,f5395]) ).
thf(f5598,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl11_2
| ~ spl11_11
| ~ spl11_12
| ~ spl11_19
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f5597]) ).
thf(f5799,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl11_2
| ~ spl11_11
| ~ spl11_12
| ~ spl11_19
| ~ spl11_20 ),
inference(constrained_superposition,[],[f5598,f858]) ).
thf(f5815,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl11_2
| ~ spl11_11
| ~ spl11_12
| ~ spl11_19
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f5799]) ).
thf(f5829,plain,
( ( $true = $false )
| ~ spl11_2
| ~ spl11_11
| ~ spl11_12
| ~ spl11_19
| ~ spl11_20 ),
inference(forward_demodulation,[],[f5815,f353]) ).
thf(f5830,plain,
( $false
| ~ spl11_2
| ~ spl11_11
| ~ spl11_12
| ~ spl11_19
| ~ spl11_20 ),
inference(trivial_inequality_removal,[],[f5829]) ).
thf(f5831,plain,
( ~ spl11_2
| ~ spl11_11
| ~ spl11_12
| ~ spl11_19
| ~ spl11_20 ),
inference(avatar_contradiction_clause,[],[f5830]) ).
thf(f6658,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( p @ X0 ) )
| ( $true
= ( q @ sK3 ) ) )
| ~ spl11_1
| ~ spl11_5 ),
inference(constrained_superposition,[],[f2491,f374]) ).
thf(f6671,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( p @ X0 ) )
| ( $true
= ( q @ sK3 ) ) )
| ~ spl11_1
| ~ spl11_5 ),
inference(trivial_inequality_removal,[],[f6658]) ).
thf(f6691,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( p @ X0 ) )
| ( $true
= ( q @ sK3 ) ) )
| ~ spl11_1
| ~ spl11_3
| ~ spl11_5 ),
inference(forward_demodulation,[],[f6671,f364]) ).
thf(f6692,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( p @ X0 ) )
| ( $true
= ( q @ sK3 ) ) )
| ~ spl11_1
| ~ spl11_3
| ~ spl11_5 ),
inference(trivial_inequality_removal,[],[f6691]) ).
thf(f6695,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( p @ X0 ) ) )
| ~ spl11_1
| ~ spl11_3
| ~ spl11_5
| ~ spl11_6 ),
inference(forward_demodulation,[],[f6692,f379]) ).
thf(f6696,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( p @ X0 ) ) )
| ~ spl11_1
| ~ spl11_3
| ~ spl11_5
| ~ spl11_6 ),
inference(trivial_inequality_removal,[],[f6695]) ).
thf(f7054,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl11_38 ),
inference(constrained_superposition,[],[f2903,f2220]) ).
thf(f7055,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl11_38 ),
inference(trivial_inequality_removal,[],[f7054]) ).
thf(f7072,plain,
( spl11_31
| ~ spl11_38 ),
inference(avatar_split_clause,[],[f7055,f2219,f946]) ).
thf(f8101,plain,
( ( $true = $false )
| ( $false
= ( p @ sK2 ) )
| ~ spl11_1
| ~ spl11_3
| ~ spl11_5
| ~ spl11_6 ),
inference(constrained_superposition,[],[f374,f6696]) ).
thf(f8102,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl11_1
| ~ spl11_3
| ~ spl11_5
| ~ spl11_6 ),
inference(trivial_inequality_removal,[],[f8101]) ).
thf(f8275,plain,
( ( $true = $false )
| ~ spl11_1
| ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_6 ),
inference(constrained_superposition,[],[f8102,f369]) ).
thf(f8281,plain,
( $false
| ~ spl11_1
| ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_6 ),
inference(trivial_inequality_removal,[],[f8275]) ).
thf(f8282,plain,
( ~ spl11_1
| ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_6 ),
inference(avatar_contradiction_clause,[],[f8281]) ).
cnf(s1,plain,
( spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f360]) ).
cnf(s2,plain,
( spl11_2
| spl11_3 ),
inference(sat_conversion,[],[f365]) ).
cnf(s3,plain,
( spl11_2
| spl11_4 ),
inference(sat_conversion,[],[f370]) ).
cnf(s4,plain,
( spl11_2
| spl11_5 ),
inference(sat_conversion,[],[f375]) ).
cnf(s5,plain,
( spl11_2
| spl11_6 ),
inference(sat_conversion,[],[f380]) ).
cnf(s10,plain,
( spl11_7
| spl11_11 ),
inference(sat_conversion,[],[f405]) ).
cnf(s11,plain,
( spl11_7
| spl11_12 ),
inference(sat_conversion,[],[f410]) ).
cnf(s12,plain,
( spl11_7
| spl11_13 ),
inference(sat_conversion,[],[f415]) ).
cnf(s13,plain,
( spl11_7
| spl11_14 ),
inference(sat_conversion,[],[f420]) ).
cnf(s14,plain,
( spl11_11
| spl11_15 ),
inference(sat_conversion,[],[f425]) ).
cnf(s15,plain,
( spl11_11
| spl11_16 ),
inference(sat_conversion,[],[f430]) ).
cnf(s16,plain,
( spl11_12
| spl11_15 ),
inference(sat_conversion,[],[f431]) ).
cnf(s17,plain,
( spl11_12
| spl11_16 ),
inference(sat_conversion,[],[f432]) ).
cnf(s22,plain,
( spl11_10
| spl11_11 ),
inference(sat_conversion,[],[f445]) ).
cnf(s23,plain,
( spl11_10
| spl11_12 ),
inference(sat_conversion,[],[f446]) ).
cnf(s24,plain,
( spl11_10
| spl11_19 ),
inference(sat_conversion,[],[f451]) ).
cnf(s25,plain,
( spl11_10
| spl11_20 ),
inference(sat_conversion,[],[f456]) ).
cnf(s37,plain,
( ~ spl11_2
| ~ spl11_11
| ~ spl11_12
| ~ spl11_13
| ~ spl11_14 ),
inference(sat_conversion,[],[f565]) ).
cnf(s38,plain,
( ~ spl11_7
| ~ spl11_25 ),
inference(sat_conversion,[],[f572]) ).
cnf(s48,plain,
( ~ spl11_1
| ~ spl11_10
| ~ spl11_15
| ~ spl11_16
| spl11_25 ),
inference(sat_conversion,[],[f630]) ).
cnf(s56,plain,
( ~ spl11_7
| ~ spl11_10
| ~ spl11_31 ),
inference(sat_conversion,[],[f1215]) ).
cnf(s92,plain,
( spl11_1
| ~ spl11_2 ),
inference(sat_conversion,[],[f2284]) ).
cnf(s122,plain,
( ~ spl11_2
| ~ spl11_11
| ~ spl11_12
| spl11_38 ),
inference(sat_conversion,[],[f2355]) ).
cnf(s161,plain,
( ~ spl11_2
| ~ spl11_11
| ~ spl11_12
| ~ spl11_19
| ~ spl11_20 ),
inference(sat_conversion,[],[f5831]) ).
cnf(s168,plain,
( spl11_31
| ~ spl11_38 ),
inference(sat_conversion,[],[f7072]) ).
cnf(s189,plain,
( ~ spl11_1
| ~ spl11_3
| ~ spl11_4
| ~ spl11_5
| ~ spl11_6 ),
inference(sat_conversion,[],[f8282]) ).
cnf(s190,plain,
spl11_1,
inference(rat,[],[s1,s92]) ).
cnf(s191,plain,
spl11_2,
inference(rat,[],[s189,s2,s3,s4,s5,s190]) ).
cnf(s192,plain,
spl11_10,
inference(rat,[],[s161,s22,s23,s24,s25,s191]) ).
cnf(s193,plain,
( spl11_12
| spl11_25 ),
inference(rat,[],[s48,s16,s17,s190,s192]) ).
cnf(s194,plain,
~ spl11_7,
inference(rat,[],[s48,s14,s15,s122,s193,s168,s56,s38,s190,s192,s191]) ).
cnf(s195,plain,
spl11_14,
inference(rat,[],[s13,s194]) ).
cnf(s196,plain,
spl11_13,
inference(rat,[],[s12,s194]) ).
cnf(s197,plain,
spl11_12,
inference(rat,[],[s11,s194]) ).
cnf(s198,plain,
spl11_11,
inference(rat,[],[s10,s194]) ).
cnf(s200,plain,
$false,
inference(rat,[],[s37,s195,s196,s191,s197,s198]) ).
thf(f8283,plain,
$false,
inference(avatar_sat_refutation,[],[s200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO449^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:53:05 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.48/0.84 % (1307248)Will run a generic schedule for satisfiability detection.
% 3.48/0.84 % (1307257)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2427121926:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.48/0.84 % (1307257)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.48/0.84 % (1307254)% WARNING: option uhcvi not known.
% 3.48/0.84 % (1307255)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2727029237:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.48/0.84 % (1307253)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2650299002_2999 on theBenchmark for (2999ds/0Mi)
% 3.48/0.84 % (1307254)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=538622796:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.48/0.84 % (1307256)dis+10_1_sil=32000:sp=arity:random_seed=3999302148:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.48/0.84 % (1307258)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=398602430:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.48/0.84 % (1307254)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.48/0.84 % Exception at run slice level
% 3.48/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.48/0.84 % (1307254)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.48/0.84 % (1307259)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1290737958:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.48/0.84 % (1307257)Instruction limit reached!
% 3.48/0.84 % (1307257)------------------------------
% 3.48/0.84 % (1307257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/0.84 % (1307257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/0.84 % (1307257)CaDiCaL version: 2.1.3
% 3.48/0.84 % (1307257)Termination reason: Instruction limit
% 3.48/0.84 % (1307257)Termination phase: Saturation
% 3.48/0.84 % (1307257)Time elapsed: 0.028 s
% 3.48/0.84 % (1307257)Peak memory usage: 12 MB
% 3.48/0.84 % (1307257)Instructions burned: 117 (million)
% 3.48/0.84 % (1307266)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1897277460:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.48/0.84 % Exception at run slice level
% 3.48/0.84 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.48/0.84 % (1307268)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2246863712:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.48/0.84 % (1307270)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=103799362:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.48/0.84 % (1307256)Instruction limit reached!
% 3.48/0.84 % (1307256)------------------------------
% 3.48/0.84 % (1307256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/0.84 % (1307256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/0.84 % (1307256)CaDiCaL version: 2.1.3
% 3.48/0.84 % (1307256)Termination reason: Instruction limit
% 3.48/0.84 % (1307256)Termination phase: Saturation
% 3.48/0.84 % (1307256)Time elapsed: 0.046 s
% 3.48/0.84 % (1307256)Peak memory usage: 12 MB
% 3.48/0.84 % (1307256)Instructions burned: 103 (million)
% 3.48/0.84 % (1307270)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.48/0.84 % (1307270)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.48/0.84 % (1307258)Instruction limit reached!
% 3.48/0.84 % (1307258)------------------------------
% 3.48/0.84 % (1307258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.48/0.84 % (1307258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.48/0.84 % (1307258)CaDiCaL version: 2.1.3
% 3.48/0.84 % (1307258)Termination reason: Instruction limit
% 3.48/0.84 % (1307258)Termination phase: Saturation
% 3.48/0.84 % (1307258)Time elapsed: 0.059 s
% 3.48/0.84 % (1307258)Peak memory usage: 12 MB
% 3.48/0.84 % (1307258)Instructions burned: 132 (million)
% 3.48/0.84 % (1307268)Instruction limit reached!
% 3.48/0.84 % (1307268)------------------------------
% 3.48/0.84 % (1307268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.83/1.10 % (1307268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.10 % (1307268)CaDiCaL version: 2.1.3
% 5.83/1.10 % (1307268)Termination reason: Instruction limit
% 5.83/1.10 % (1307268)Termination phase: Saturation
% 5.83/1.10 % (1307268)Time elapsed: 0.030 s
% 5.83/1.10 % (1307268)Peak memory usage: 12 MB
% 5.83/1.10 % (1307268)Instructions burned: 132 (million)
% 5.83/1.10 % (1307273)ott-21_1_sil=16000:fs=off:random_seed=2529703011:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 5.83/1.10 % (1307275)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2508776810:fmbsr=1.3:i=865:ins=25_2999 on theBenchmark for (2999ds/865Mi)
% 5.83/1.10 % Exception at run slice level
% 5.83/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.83/1.10 % (1307274)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2556477746:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 5.83/1.10 % (1307278)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3908538086:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 5.83/1.10 % (1307273)Instruction limit reached!
% 5.83/1.10 % (1307273)------------------------------
% 5.83/1.10 % (1307273)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.83/1.10 % (1307273)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.10 % (1307273)CaDiCaL version: 2.1.3
% 5.83/1.10 % (1307273)Termination reason: Instruction limit
% 5.83/1.10 % (1307273)Termination phase: Saturation
% 5.83/1.10 % (1307273)Time elapsed: 0.077 s
% 5.83/1.10 % (1307273)Peak memory usage: 12 MB
% 5.83/1.10 % (1307273)Instructions burned: 180 (million)
% 5.83/1.10 % (1307259)Instruction limit reached!
% 5.83/1.10 % (1307259)------------------------------
% 5.83/1.10 % (1307259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.83/1.10 % (1307259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.10 % (1307259)CaDiCaL version: 2.1.3
% 5.83/1.10 % (1307259)Termination reason: Instruction limit
% 5.83/1.10 % (1307259)Termination phase: Saturation
% 5.83/1.10 % (1307259)Time elapsed: 0.127 s
% 5.83/1.10 % (1307259)Peak memory usage: 12 MB
% 5.83/1.10 % (1307259)Instructions burned: 160 (million)
% 5.83/1.10 % (1307281)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=88101379:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 5.83/1.10 % (1307282)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=1096977312: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)
% 5.83/1.10 % (1307282)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.83/1.10 % Exception at run slice level
% 5.83/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.83/1.10 % (1307285)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2413588476:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 5.83/1.10 % (1307285)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.83/1.10 % (1307274)Instruction limit reached!
% 5.83/1.10 % (1307274)------------------------------
% 5.83/1.10 % (1307274)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.83/1.10 % (1307274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.10 % (1307274)CaDiCaL version: 2.1.3
% 5.83/1.10 % (1307274)Termination reason: Instruction limit
% 5.83/1.10 % (1307274)Termination phase: Saturation
% 5.83/1.10 % (1307274)Time elapsed: 0.222 s
% 5.83/1.10 % (1307274)Peak memory usage: 13 MB
% 5.83/1.10 % (1307274)Instructions burned: 480 (million)
% 5.83/1.10 % (1307304)fmb+10_1_sil=64000:random_seed=499190897:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 5.83/1.10 % (1307304)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.83/1.10 % Exception at run slice level
% 5.83/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.83/1.10 % (1307278)Instruction limit reached!
% 5.83/1.10 % (1307278)------------------------------
% 5.83/1.10 % (1307278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.83/1.10 % (1307278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.10 % (1307278)CaDiCaL version: 2.1.3
% 5.83/1.10 % (1307278)Termination reason: Instruction limit
% 5.83/1.10 % (1307278)Termination phase: Saturation
% 5.83/1.10 % (1307278)Time elapsed: 0.246 s
% 5.83/1.10 % (1307278)Peak memory usage: 13 MB
% 5.83/1.10 % (1307278)Instructions burned: 1183 (million)
% 5.83/1.10 % (1307270)Instruction limit reached!
% 5.83/1.10 % (1307270)------------------------------
% 5.83/1.10 % (1307270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.83/1.10 % (1307270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.10 % (1307270)CaDiCaL version: 2.1.3
% 5.83/1.10 % (1307270)Termination reason: Instruction limit
% 5.83/1.10 % (1307270)Termination phase: Saturation
% 5.83/1.10 % (1307270)Time elapsed: 0.291 s
% 5.83/1.10 % (1307270)Peak memory usage: 15 MB
% 5.83/1.10 % (1307270)Instructions burned: 686 (million)
% 5.83/1.10 % (1307317)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=389884530:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 5.83/1.10 % Exception at run slice level
% 5.83/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.83/1.10 % (1307314)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3206076763:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 5.83/1.10 % Exception at run slice level
% 5.83/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.83/1.10 % (1307326)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3195242006:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 5.83/1.10 % (1307326)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.83/1.10 % (1307326)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.83/1.10 % (1307322)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1558222927:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 5.83/1.10 % (1307322)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.83/1.10 % (1307330)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3364892068:i=6324_2996 on theBenchmark for (2996ds/6324Mi)
% 5.83/1.10 % Exception at run slice level
% 5.83/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.83/1.10 % (1307344)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3910561726:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 5.83/1.10 % Exception at run slice level
% 5.83/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.83/1.10 % (1307361)ott-2_1_sil=16000:newcnf=on:random_seed=2187343176:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2995 on theBenchmark for (2995ds/869Mi)
% 5.83/1.10 % (1307361)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.83/1.10 % (1307282)Instruction limit reached!
% 5.83/1.10 % (1307282)------------------------------
% 5.83/1.10 % (1307282)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.83/1.10 % (1307282)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.10 % (1307282)CaDiCaL version: 2.1.3
% 5.83/1.10 % (1307282)Termination reason: Instruction limit
% 5.83/1.10 % (1307282)Termination phase: Saturation
% 5.83/1.10 % (1307282)Time elapsed: 0.328 s
% 5.83/1.10 % (1307282)Peak memory usage: 14 MB
% 5.83/1.10 % (1307282)Instructions burned: 692 (million)
% 5.83/1.10 % (1307385)ott+10_1_sil=32000:tgt=ground:random_seed=4026702173:i=5114:av=off_2994 on theBenchmark for (2994ds/5114Mi)
% 5.83/1.10 % (1307285)Instruction limit reached!
% 5.83/1.10 % (1307285)------------------------------
% 5.83/1.10 % (1307285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.83/1.10 % (1307285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.10 % (1307285)CaDiCaL version: 2.1.3
% 5.83/1.10 % (1307285)Termination reason: Instruction limit
% 5.83/1.10 % (1307285)Termination phase: Saturation
% 5.83/1.10 % (1307285)Time elapsed: 0.369 s
% 5.83/1.10 % (1307285)Peak memory usage: 13 MB
% 5.83/1.10 % (1307285)Instructions burned: 880 (million)
% 5.83/1.10 % (1307397)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=2956368709:i=54282_2994 on theBenchmark for (2994ds/54282Mi)
% 5.83/1.10 % Exception at run slice level
% 5.83/1.10 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.83/1.10 % (1307406)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2540326649:i=3512:aac=none_2993 on theBenchmark for (2993ds/3512Mi)
% 5.83/1.10 % (1307406)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.83/1.10 % (1307326)Instruction limit reached!
% 5.83/1.10 % (1307326)------------------------------
% 5.83/1.10 % (1307326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.83/1.10 % (1307326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.10 % (1307326)CaDiCaL version: 2.1.3
% 5.83/1.10 % (1307326)Termination reason: Instruction limit
% 5.83/1.10 % (1307326)Termination phase: Saturation
% 5.83/1.10 % (1307326)Time elapsed: 0.394 s
% 5.83/1.10 % (1307326)Peak memory usage: 20 MB
% 5.83/1.10 % (1307326)Instructions burned: 1474 (million)
% 5.83/1.10 % (1307446)dis+21_1_sil=32000:sas=cadical:random_seed=3023436336:i=3773:amm=off_2992 on theBenchmark for (2992ds/3773Mi)
% 5.83/1.10 % (1307361) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1307248-1307361"...
% 5.83/1.10 % (1307361)...printing done.
% 5.83/1.10 % (1307361)Refutation found. Thanks to Tanya!
% 5.83/1.10 % SZS status Theorem for theBenchmark
% 5.83/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 5.83/1.11 % (1307361)------------------------------
% 5.83/1.11 % (1307361)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.83/1.11 % (1307361)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.83/1.11 % (1307361)CaDiCaL version: 2.1.3
% 5.83/1.11 % (1307361)Termination reason: Refutation
% 5.83/1.11 % (1307361)Time elapsed: 0.417 s
% 5.83/1.11 % (1307361)Peak memory usage: 14 MB
% 5.83/1.11 % (1307361)Instructions burned: 806 (million)
% 5.83/1.11 % (1307248)Success in time 0.87 s
% 5.83/1.11 % Vampire exiting
%------------------------------------------------------------------------------