%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO443^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:49:58 AM UTC 2026
% Result : Theorem 0.20s 0.36s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 49
% Number of leaves : 26
% Syntax : Number of formulae : 346 ( 73 unt; 0 typ; 14 def)
% Number of atoms : 3227 ( 561 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 3836 ( 708 ~; 946 |; 13 &;1958 @)
% ( 14 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 119 ( 119 >; 0 *; 0 +; 0 <<)
% Number of symbols : 75 ( 71 usr; 24 con; 0-4 aty)
% ( 175 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 541 ( 0 sgn 164 !; 0 ?; 541 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ 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(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(f95,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f96,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f98,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f97]) ).
thf(f99,plain,
~ ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f100,plain,
( ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ 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(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(f136,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f96]) ).
thf(f137,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f138,plain,
( ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ 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(f152,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f136,f122]) ).
thf(f153,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f137,f120]) ).
thf(f154,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ),
inference(definition_unfolding,[],[f138,f129,f144,f133,f105,f104,f133,f105,f133,f104,f133]) ).
thf(f155,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( $false
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $true
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( p @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) )
@ X4 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 )
| ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ( p @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) )
@ X4 ) )
| ( $true
= ( ~ ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) )
@ X4 ) )
| ( $false
= ( p @ X3 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) )
@ X4 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) )
@ X4 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) )
@ X4 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $false
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) )
@ X4 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X2 @ X4 )
| ( q @ X4 ) ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( q @ X4 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X3 ) )
| ( $true
= ( ~ ( rel_s5 @ X2 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( q @ X4 ) )
| ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X3 ) )
| ( $false
= ( rel_s5 @ X2 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f219,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK3 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f220,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f221,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK3 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f223,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| ~ ( p @ sK3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( p @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f226,plain,
! [X1: $i] :
( ( $false
= ( ~ ( p @ sK3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( p @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f225]) ).
thf(f237,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( p @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f226]) ).
thf(f248,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK4 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( p @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f237]) ).
thf(f249,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK4 ) )
| ( $true
= ( ~ ( p @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK4 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK3 @ sK4 )
| ( q @ sK4 ) ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(beta-eta_normalization,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK4 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK3 @ sK4 ) ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f254]) ).
thf(f257,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK3 @ sK4 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK3 @ sK4 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f257]) ).
thf(f259,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK3 @ sK4 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK4 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f255]) ).
thf(f261,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK4 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f260]) ).
thf(f262,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f263,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f264,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f263]) ).
thf(f265,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| ~ ( p @ sK3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 )
| ~ ( p @ sK5 ) ) ) ),
inference(beta-eta_normalization,[],[f264]) ).
thf(f266,plain,
( ( $false
= ( ~ ( p @ sK3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 )
| ~ ( p @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f265]) ).
thf(f267,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 )
| ~ ( p @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f265]) ).
thf(f268,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 )
| ~ ( p @ sK5 ) ) ) ),
inference(not_proxy_clausification,[],[f267]) ).
thf(f269,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $false
= ( ~ ( p @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f268]) ).
thf(f270,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f268]) ).
thf(f271,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f270]) ).
thf(f272,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( p @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f269]) ).
thf(f273,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 )
| ~ ( p @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f266]) ).
thf(f274,plain,
( ( $false
= ( ~ ( p @ sK3 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 )
| ~ ( p @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f266]) ).
thf(f275,plain,
( ( $true
= ( p @ sK3 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 )
| ~ ( p @ sK5 ) ) ) ),
inference(not_proxy_clausification,[],[f274]) ).
thf(f276,plain,
( ( $true
= ( p @ sK3 ) )
| ( $false
= ( ~ ( p @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f275]) ).
thf(f277,plain,
( ( $true
= ( p @ sK3 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f275]) ).
thf(f278,plain,
( ( $true
= ( p @ sK3 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f277]) ).
thf(f279,plain,
( ( $true
= ( p @ sK3 ) )
| ( $true
= ( p @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f280,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 )
| ~ ( p @ sK5 ) ) ) ),
inference(sigma_proxy_clausification,[],[f273]) ).
thf(f281,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $false
= ( ~ ( p @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f280]) ).
thf(f288,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( p @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f281]) ).
thf(f289,plain,
( ( $false
= ( ~ ( rel_s5 @ sK3 @ sK6 )
| ( q @ sK6 ) ) )
| ( $true
= ( p @ sK5 ) ) ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f290,plain,
( ( $false
= ( q @ sK6 ) )
| ( $true
= ( p @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f291,plain,
( ( $false
= ( ~ ( rel_s5 @ sK3 @ sK6 ) ) )
| ( $true
= ( p @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f292,plain,
( ( $true
= ( rel_s5 @ sK3 @ sK6 ) )
| ( $true
= ( p @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f291]) ).
thf(f293,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f262]) ).
thf(f294,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| ~ ( p @ sK3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 )
| ( q @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f293]) ).
thf(f295,plain,
( ( $false
= ( ~ ( p @ sK3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 )
| ( q @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f296,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 )
| ( q @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f297,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 )
| ( q @ sK7 ) ) ) ),
inference(not_proxy_clausification,[],[f296]) ).
thf(f298,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $false
= ( q @ sK7 ) ) ),
inference(or_proxy_clausification,[],[f297]) ).
thf(f299,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f297]) ).
thf(f300,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK7 ) ) ),
inference(not_proxy_clausification,[],[f299]) ).
thf(f301,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 )
| ( q @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f295]) ).
thf(f302,plain,
( ( $false
= ( ~ ( p @ sK3 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 )
| ( q @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f295]) ).
thf(f303,plain,
( ( $true
= ( p @ sK3 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 )
| ( q @ sK7 ) ) ) ),
inference(not_proxy_clausification,[],[f302]) ).
thf(f304,plain,
( ( $true
= ( p @ sK3 ) )
| ( $false
= ( q @ sK7 ) ) ),
inference(or_proxy_clausification,[],[f303]) ).
thf(f305,plain,
( ( $true
= ( p @ sK3 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f303]) ).
thf(f306,plain,
( ( $true
= ( p @ sK3 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK7 ) ) ),
inference(not_proxy_clausification,[],[f305]) ).
thf(f307,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 )
| ( q @ sK7 ) ) ) ),
inference(sigma_proxy_clausification,[],[f301]) ).
thf(f308,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK8 ) )
| ( $false
= ( q @ sK7 ) ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f309,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f310,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ sK8 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK7 ) ) ),
inference(not_proxy_clausification,[],[f309]) ).
thf(f311,plain,
( ( $false
= ( ~ ( rel_s5 @ sK3 @ sK8 )
| ( q @ sK8 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f310]) ).
thf(f312,plain,
( ( $false
= ( q @ sK8 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK7 ) ) ),
inference(or_proxy_clausification,[],[f311]) ).
thf(f313,plain,
( ( $false
= ( ~ ( rel_s5 @ sK3 @ sK8 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK7 ) ) ),
inference(or_proxy_clausification,[],[f311]) ).
thf(f314,plain,
( ( $true
= ( rel_s5 @ sK3 @ sK8 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK7 ) ) ),
inference(not_proxy_clausification,[],[f313]) ).
thf(f315,plain,
( ( $false
= ( ~ ( rel_s5 @ sK3 @ sK8 )
| ( q @ sK8 ) ) )
| ( $false
= ( q @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f308]) ).
thf(f316,plain,
( ( $false
= ( q @ sK8 ) )
| ( $false
= ( q @ sK7 ) ) ),
inference(or_proxy_clausification,[],[f315]) ).
thf(f317,plain,
( ( $false
= ( ~ ( rel_s5 @ sK3 @ sK8 ) ) )
| ( $false
= ( q @ sK7 ) ) ),
inference(or_proxy_clausification,[],[f315]) ).
thf(f318,plain,
( ( $true
= ( rel_s5 @ sK3 @ sK8 ) )
| ( $false
= ( q @ sK7 ) ) ),
inference(not_proxy_clausification,[],[f317]) ).
thf(f319,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f320,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f319]) ).
thf(f321,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f320]) ).
thf(f322,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f322]) ).
thf(f324,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f323]) ).
thf(f325,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(f326,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,[],[f325]) ).
thf(f327,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,[],[f326]) ).
thf(f328,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,[],[f327]) ).
thf(f329,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,[],[f328]) ).
thf(f330,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,[],[f329]) ).
thf(f331,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f330]) ).
thf(f332,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,[],[f331]) ).
thf(f333,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,[],[f332]) ).
thf(f338,definition,
( spl9_1
<=> ( $true
= ( p @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
thf(f340,plain,
( ( $true
= ( p @ sK5 ) )
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f338]) ).
thf(f342,definition,
( spl9_2
<=> ( $true
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
thf(f343,plain,
( ( $true
!= ( p @ sK3 ) )
| spl9_2 ),
inference(avatar_component_clause,[],[f342]) ).
thf(f344,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f342]) ).
thf(f345,plain,
( spl9_1
| spl9_2 ),
inference(avatar_split_clause,[],[f279,f342,f338]) ).
thf(f347,definition,
( spl9_3
<=> ( $false
= ( q @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
thf(f348,plain,
( ( $false
!= ( q @ sK7 ) )
| spl9_3 ),
inference(avatar_component_clause,[],[f347]) ).
thf(f349,plain,
( ( $false
= ( q @ sK7 ) )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f347]) ).
thf(f350,plain,
( spl9_3
| spl9_2 ),
inference(avatar_split_clause,[],[f304,f342,f347]) ).
thf(f352,definition,
( spl9_4
<=> ( $false
= ( q @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f354,plain,
( ( $false
= ( q @ sK8 ) )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f352]) ).
thf(f355,plain,
( spl9_3
| spl9_4 ),
inference(avatar_split_clause,[],[f316,f352,f347]) ).
thf(f357,definition,
( spl9_5
<=> ( $true
= ( rel_s5 @ sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
thf(f358,plain,
( ( $true
!= ( rel_s5 @ sK0 @ sK5 ) )
| spl9_5 ),
inference(avatar_component_clause,[],[f357]) ).
thf(f359,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f357]) ).
thf(f361,definition,
( spl9_6
<=> ( $false
= ( q @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
thf(f363,plain,
( ( $false
= ( q @ sK6 ) )
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f361]) ).
thf(f366,definition,
( spl9_7
<=> ( $true
= ( rel_s5 @ sK0 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
thf(f367,plain,
( ( $true
!= ( rel_s5 @ sK0 @ sK7 ) )
| spl9_7 ),
inference(avatar_component_clause,[],[f366]) ).
thf(f368,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK7 ) )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f366]) ).
thf(f369,plain,
( spl9_7
| spl9_4 ),
inference(avatar_split_clause,[],[f312,f352,f366]) ).
thf(f371,definition,
( spl9_8
<=> ( $true
= ( rel_s5 @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
thf(f372,plain,
( ( $true
!= ( rel_s5 @ sK0 @ sK3 ) )
| spl9_8 ),
inference(avatar_component_clause,[],[f371]) ).
thf(f373,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f371]) ).
thf(f374,plain,
( spl9_7
| spl9_8 ),
inference(avatar_split_clause,[],[f300,f371,f366]) ).
thf(f382,definition,
( spl9_11
<=> ! [X3: $i] :
( ( $false
= ( p @ X3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
thf(f383,plain,
( ! [X3: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X3 ) )
| ( $false
= ( p @ X3 ) ) )
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f382]) ).
thf(f391,definition,
( spl9_14
<=> ! [X4: $i,X2: $i] :
( ( $true
= ( q @ X4 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $false
= ( rel_s5 @ X2 @ X4 ) )
| ( $false
= ( p @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_14])],[avatar_definition]) ).
thf(f392,plain,
( ! [X2: $i,X4: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X2 ) )
| ( $false
= ( rel_s5 @ X2 @ X4 ) )
| ( $true
= ( q @ X4 ) )
| ( $false
= ( p @ X2 ) ) )
| ~ spl9_14 ),
inference(avatar_component_clause,[],[f391]) ).
thf(f394,definition,
( spl9_15
<=> ! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_15])],[avatar_definition]) ).
thf(f395,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl9_15 ),
inference(avatar_component_clause,[],[f394]) ).
thf(f396,plain,
( spl9_11
| spl9_14
| spl9_15 ),
inference(avatar_split_clause,[],[f185,f394,f391,f382]) ).
thf(f447,plain,
( ( $true = $false )
| ( $false
= ( p @ sK5 ) )
| ~ spl9_5
| ~ spl9_11 ),
inference(constrained_superposition,[],[f359,f383]) ).
thf(f450,plain,
( ( $false
= ( p @ sK5 ) )
| ~ spl9_5
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f447]) ).
thf(f453,plain,
( ( $true = $false )
| ~ spl9_1
| ~ spl9_5
| ~ spl9_11 ),
inference(constrained_superposition,[],[f450,f340]) ).
thf(f457,plain,
( $false
| ~ spl9_1
| ~ spl9_5
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f453]) ).
thf(f458,plain,
( ~ spl9_1
| ~ spl9_5
| ~ spl9_11 ),
inference(avatar_contradiction_clause,[],[f457]) ).
thf(f460,plain,
( ( $true = $false )
| ( $true
= ( q @ sK7 ) )
| ~ spl9_7
| ~ spl9_15 ),
inference(constrained_superposition,[],[f395,f368]) ).
thf(f465,plain,
( ( $true
= ( q @ sK7 ) )
| ~ spl9_7
| ~ spl9_15 ),
inference(trivial_inequality_removal,[],[f460]) ).
thf(f470,plain,
( ( $true = $false )
| ~ spl9_3
| ~ spl9_7
| ~ spl9_15 ),
inference(forward_demodulation,[],[f465,f349]) ).
thf(f471,plain,
( $false
| ~ spl9_3
| ~ spl9_7
| ~ spl9_15 ),
inference(trivial_inequality_removal,[],[f470]) ).
thf(f472,plain,
( ~ spl9_3
| ~ spl9_7
| ~ spl9_15 ),
inference(avatar_contradiction_clause,[],[f471]) ).
thf(f503,plain,
( spl9_1
| spl9_6 ),
inference(avatar_split_clause,[],[f290,f361,f338]) ).
thf(f504,plain,
( spl9_1
| spl9_8 ),
inference(avatar_split_clause,[],[f272,f371,f338]) ).
thf(f510,definition,
( spl9_19
<=> ( $true
= ( rel_s5 @ sK3 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_19])],[avatar_definition]) ).
thf(f512,plain,
( ( $true
= ( rel_s5 @ sK3 @ sK6 ) )
| ~ spl9_19 ),
inference(avatar_component_clause,[],[f510]) ).
thf(f513,plain,
( spl9_1
| spl9_19 ),
inference(avatar_split_clause,[],[f292,f510,f338]) ).
thf(f515,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( q @ sK6 ) )
| ( $false
= ( p @ sK3 ) )
| ~ spl9_14
| ~ spl9_19 ),
inference(constrained_superposition,[],[f392,f512]) ).
thf(f516,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( q @ sK6 ) )
| ( $false
= ( p @ sK3 ) )
| ~ spl9_14
| ~ spl9_19 ),
inference(trivial_inequality_removal,[],[f515]) ).
thf(f518,plain,
( ( $true = $false )
| ( $true
= ( q @ sK6 ) )
| ( $false
= ( p @ sK3 ) )
| ~ spl9_8
| ~ spl9_14
| ~ spl9_19 ),
inference(forward_demodulation,[],[f516,f373]) ).
thf(f519,plain,
( ( $true
= ( q @ sK6 ) )
| ( $false
= ( p @ sK3 ) )
| ~ spl9_8
| ~ spl9_14
| ~ spl9_19 ),
inference(trivial_inequality_removal,[],[f518]) ).
thf(f522,plain,
( ( $true = $false )
| ( $false
= ( p @ sK3 ) )
| ~ spl9_6
| ~ spl9_8
| ~ spl9_14
| ~ spl9_19 ),
inference(forward_demodulation,[],[f519,f363]) ).
thf(f523,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl9_6
| ~ spl9_8
| ~ spl9_14
| ~ spl9_19 ),
inference(trivial_inequality_removal,[],[f522]) ).
thf(f526,plain,
( ( $true = $false )
| ~ spl9_2
| ~ spl9_6
| ~ spl9_8
| ~ spl9_14
| ~ spl9_19 ),
inference(constrained_superposition,[],[f523,f344]) ).
thf(f530,plain,
( $false
| ~ spl9_2
| ~ spl9_6
| ~ spl9_8
| ~ spl9_14
| ~ spl9_19 ),
inference(trivial_inequality_removal,[],[f526]) ).
thf(f531,plain,
( ~ spl9_2
| ~ spl9_6
| ~ spl9_8
| ~ spl9_14
| ~ spl9_19 ),
inference(avatar_contradiction_clause,[],[f530]) ).
thf(f535,plain,
( ( $true = $false )
| ( $false
= ( p @ sK3 ) )
| ~ spl9_8
| ~ spl9_11 ),
inference(constrained_superposition,[],[f373,f383]) ).
thf(f540,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl9_8
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f535]) ).
thf(f544,plain,
( ( $true = $false )
| ~ spl9_2
| ~ spl9_8
| ~ spl9_11 ),
inference(constrained_superposition,[],[f540,f344]) ).
thf(f548,plain,
( $false
| ~ spl9_2
| ~ spl9_8
| ~ spl9_11 ),
inference(trivial_inequality_removal,[],[f544]) ).
thf(f549,plain,
( ~ spl9_2
| ~ spl9_8
| ~ spl9_11 ),
inference(avatar_contradiction_clause,[],[f548]) ).
thf(f561,definition,
( spl9_20
<=> ( $false
= ( q @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_20])],[avatar_definition]) ).
thf(f563,plain,
( ( $false
= ( q @ sK4 ) )
| ~ spl9_20 ),
inference(avatar_component_clause,[],[f561]) ).
thf(f564,plain,
( spl9_14
| spl9_20 ),
inference(avatar_split_clause,[],[f261,f561,f391]) ).
thf(f715,definition,
( spl9_23
<=> ( $true
= ( rel_s5 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_23])],[avatar_definition]) ).
thf(f717,plain,
( ( $true
= ( rel_s5 @ sK3 @ sK4 ) )
| ~ spl9_23 ),
inference(avatar_component_clause,[],[f715]) ).
thf(f718,plain,
( spl9_14
| spl9_23 ),
inference(avatar_split_clause,[],[f259,f715,f391]) ).
thf(f811,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_8 ),
inference(constrained_superposition,[],[f373,f333]) ).
thf(f816,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK4 ) )
| ( $false
= ( rel_s5 @ X0 @ sK3 ) ) )
| ~ spl9_23 ),
inference(constrained_superposition,[],[f717,f333]) ).
thf(f841,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK4 ) )
| ( $false
= ( rel_s5 @ X0 @ sK3 ) ) )
| ~ spl9_23 ),
inference(trivial_inequality_removal,[],[f816]) ).
thf(f844,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_8 ),
inference(trivial_inequality_removal,[],[f811]) ).
thf(f870,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( q @ sK4 ) )
| ~ spl9_15
| ~ spl9_23 ),
inference(constrained_superposition,[],[f841,f395]) ).
thf(f885,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( q @ sK4 ) )
| ~ spl9_15
| ~ spl9_23 ),
inference(trivial_inequality_removal,[],[f870]) ).
thf(f888,plain,
( ( $true = $false )
| ( $true
= ( q @ sK4 ) )
| ~ spl9_8
| ~ spl9_15
| ~ spl9_23 ),
inference(forward_demodulation,[],[f885,f373]) ).
thf(f889,plain,
( ( $true
= ( q @ sK4 ) )
| ~ spl9_8
| ~ spl9_15
| ~ spl9_23 ),
inference(trivial_inequality_removal,[],[f888]) ).
thf(f890,plain,
( ( $true = $false )
| ~ spl9_8
| ~ spl9_15
| ~ spl9_20
| ~ spl9_23 ),
inference(forward_demodulation,[],[f889,f563]) ).
thf(f891,plain,
( $false
| ~ spl9_8
| ~ spl9_15
| ~ spl9_20
| ~ spl9_23 ),
inference(trivial_inequality_removal,[],[f890]) ).
thf(f892,plain,
( ~ spl9_8
| ~ spl9_15
| ~ spl9_20
| ~ spl9_23 ),
inference(avatar_contradiction_clause,[],[f891]) ).
thf(f929,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK5 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_5 ),
inference(constrained_superposition,[],[f333,f359]) ).
thf(f930,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK5 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_5 ),
inference(trivial_inequality_removal,[],[f929]) ).
thf(f961,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK3 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_8 ),
inference(constrained_superposition,[],[f324,f844]) ).
thf(f962,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ sK3 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_8 ),
inference(trivial_inequality_removal,[],[f961]) ).
thf(f1275,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ sK3 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_8
| ~ spl9_14 ),
inference(constrained_superposition,[],[f392,f962]) ).
thf(f1288,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ sK3 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_8
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f1275]) ).
thf(f1297,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ sK3 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_8
| ~ spl9_14 ),
inference(forward_demodulation,[],[f1288,f373]) ).
thf(f1298,plain,
( ! [X0: $i] :
( ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ sK3 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_8
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f1297]) ).
thf(f1301,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_2
| ~ spl9_8
| ~ spl9_14 ),
inference(forward_demodulation,[],[f1298,f344]) ).
thf(f1302,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl9_2
| ~ spl9_8
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f1301]) ).
thf(f1359,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl9_2
| ~ spl9_8
| ~ spl9_14 ),
inference(constrained_superposition,[],[f324,f1302]) ).
thf(f1362,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl9_2
| ~ spl9_8
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f1359]) ).
thf(f1374,plain,
( spl9_15
| ~ spl9_2
| ~ spl9_8
| ~ spl9_14 ),
inference(avatar_split_clause,[],[f1362,f391,f371,f342,f394]) ).
thf(f1604,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK5 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_5 ),
inference(constrained_superposition,[],[f324,f930]) ).
thf(f1609,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ sK5 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_5 ),
inference(trivial_inequality_removal,[],[f1604]) ).
thf(f2079,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ sK5 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_5
| ~ spl9_14 ),
inference(constrained_superposition,[],[f392,f1609]) ).
thf(f2104,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ sK5 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ sK5 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_5
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f2079]) ).
thf(f2121,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ sK5 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_5
| ~ spl9_14 ),
inference(forward_demodulation,[],[f2104,f359]) ).
thf(f2122,plain,
( ! [X0: $i] :
( ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ sK5 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_5
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f2121]) ).
thf(f2127,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl9_1
| ~ spl9_5
| ~ spl9_14 ),
inference(forward_demodulation,[],[f2122,f340]) ).
thf(f2128,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl9_1
| ~ spl9_5
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f2127]) ).
thf(f2214,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl9_1
| ~ spl9_5
| ~ spl9_14 ),
inference(constrained_superposition,[],[f324,f2128]) ).
thf(f2219,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl9_1
| ~ spl9_5
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f2214]) ).
thf(f2228,plain,
( spl9_15
| ~ spl9_1
| ~ spl9_5
| ~ spl9_14 ),
inference(avatar_split_clause,[],[f2219,f391,f357,f338,f394]) ).
thf(f2229,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| spl9_8 ),
inference(forward_subsumption_resolution,[],[f271,f372]) ).
thf(f2239,plain,
( $false
| spl9_5
| spl9_8 ),
inference(forward_subsumption_resolution,[],[f2229,f358]) ).
thf(f2240,plain,
( spl9_5
| spl9_8 ),
inference(avatar_contradiction_clause,[],[f2239]) ).
thf(f2241,plain,
( ( $false
= ( q @ sK7 ) )
| spl9_8 ),
inference(forward_subsumption_resolution,[],[f298,f372]) ).
thf(f2247,plain,
( $false
| spl9_3
| spl9_8 ),
inference(forward_subsumption_resolution,[],[f2241,f348]) ).
thf(f2248,plain,
( spl9_3
| spl9_8 ),
inference(avatar_contradiction_clause,[],[f2247]) ).
thf(f2298,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f278,f343]) ).
thf(f2301,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK7 ) )
| spl9_2 ),
inference(forward_subsumption_resolution,[],[f306,f343]) ).
thf(f2309,plain,
( spl9_5
| spl9_2 ),
inference(avatar_split_clause,[],[f2298,f342,f357]) ).
thf(f2310,plain,
( $false
| spl9_2
| spl9_7 ),
inference(forward_subsumption_resolution,[],[f2301,f367]) ).
thf(f2311,plain,
( spl9_2
| spl9_7 ),
inference(avatar_contradiction_clause,[],[f2310]) ).
thf(f2428,plain,
( ( $true
= ( rel_s5 @ sK3 @ sK8 ) )
| spl9_7 ),
inference(forward_subsumption_resolution,[],[f314,f367]) ).
thf(f2431,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( q @ sK8 ) )
| ( $false
= ( p @ sK3 ) )
| spl9_7
| ~ spl9_14 ),
inference(constrained_superposition,[],[f392,f2428]) ).
thf(f2434,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( q @ sK8 ) )
| ( $false
= ( p @ sK3 ) )
| spl9_7
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f2431]) ).
thf(f2437,plain,
( ( $true = $false )
| ( $true
= ( q @ sK8 ) )
| ( $false
= ( p @ sK3 ) )
| spl9_7
| ~ spl9_8
| ~ spl9_14 ),
inference(forward_demodulation,[],[f2434,f373]) ).
thf(f2438,plain,
( ( $true
= ( q @ sK8 ) )
| ( $false
= ( p @ sK3 ) )
| spl9_7
| ~ spl9_8
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f2437]) ).
thf(f2441,plain,
( ( $true = $false )
| ( $false
= ( p @ sK3 ) )
| ~ spl9_4
| spl9_7
| ~ spl9_8
| ~ spl9_14 ),
inference(forward_demodulation,[],[f2438,f354]) ).
thf(f2442,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl9_4
| spl9_7
| ~ spl9_8
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f2441]) ).
thf(f2446,plain,
( ( $true = $false )
| ~ spl9_2
| ~ spl9_4
| spl9_7
| ~ spl9_8
| ~ spl9_14 ),
inference(constrained_superposition,[],[f2442,f344]) ).
thf(f2450,plain,
( $false
| ~ spl9_2
| ~ spl9_4
| spl9_7
| ~ spl9_8
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f2446]) ).
thf(f2451,plain,
( ~ spl9_2
| ~ spl9_4
| spl9_7
| ~ spl9_8
| ~ spl9_14 ),
inference(avatar_contradiction_clause,[],[f2450]) ).
thf(f2471,plain,
( ( $true
= ( rel_s5 @ sK3 @ sK8 ) )
| spl9_3 ),
inference(forward_subsumption_resolution,[],[f318,f348]) ).
thf(f2474,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( q @ sK8 ) )
| ( $false
= ( p @ sK3 ) )
| spl9_3
| ~ spl9_14 ),
inference(constrained_superposition,[],[f392,f2471]) ).
thf(f2477,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK3 ) )
| ( $true
= ( q @ sK8 ) )
| ( $false
= ( p @ sK3 ) )
| spl9_3
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f2474]) ).
thf(f2480,plain,
( ( $true = $false )
| ( $true
= ( q @ sK8 ) )
| ( $false
= ( p @ sK3 ) )
| spl9_3
| ~ spl9_8
| ~ spl9_14 ),
inference(forward_demodulation,[],[f2477,f373]) ).
thf(f2481,plain,
( ( $true
= ( q @ sK8 ) )
| ( $false
= ( p @ sK3 ) )
| spl9_3
| ~ spl9_8
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f2480]) ).
thf(f2484,plain,
( ( $true = $false )
| ( $false
= ( p @ sK3 ) )
| spl9_3
| ~ spl9_4
| ~ spl9_8
| ~ spl9_14 ),
inference(forward_demodulation,[],[f2481,f354]) ).
thf(f2485,plain,
( ( $false
= ( p @ sK3 ) )
| spl9_3
| ~ spl9_4
| ~ spl9_8
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f2484]) ).
thf(f2489,plain,
( ( $true = $false )
| ~ spl9_2
| spl9_3
| ~ spl9_4
| ~ spl9_8
| ~ spl9_14 ),
inference(constrained_superposition,[],[f2485,f344]) ).
thf(f2493,plain,
( $false
| ~ spl9_2
| spl9_3
| ~ spl9_4
| ~ spl9_8
| ~ spl9_14 ),
inference(trivial_inequality_removal,[],[f2489]) ).
thf(f2494,plain,
( ~ spl9_2
| spl9_3
| ~ spl9_4
| ~ spl9_8
| ~ spl9_14 ),
inference(avatar_contradiction_clause,[],[f2493]) ).
cnf(s33,plain,
( spl9_1
| spl9_2 ),
inference(sat_conversion,[],[f345]) ).
cnf(s37,plain,
( spl9_2
| spl9_3 ),
inference(sat_conversion,[],[f350]) ).
cnf(s41,plain,
( spl9_3
| spl9_4 ),
inference(sat_conversion,[],[f355]) ).
cnf(s49,plain,
( spl9_4
| spl9_7 ),
inference(sat_conversion,[],[f369]) ).
cnf(s53,plain,
( spl9_7
| spl9_8 ),
inference(sat_conversion,[],[f374]) ).
cnf(s57,plain,
( spl9_11
| spl9_14
| spl9_15 ),
inference(sat_conversion,[],[f396]) ).
cnf(s91,plain,
( ~ spl9_1
| ~ spl9_5
| ~ spl9_11 ),
inference(sat_conversion,[],[f458]) ).
cnf(s96,plain,
( ~ spl9_3
| ~ spl9_7
| ~ spl9_15 ),
inference(sat_conversion,[],[f472]) ).
cnf(s118,plain,
( spl9_1
| spl9_6 ),
inference(sat_conversion,[],[f503]) ).
cnf(s122,plain,
( spl9_1
| spl9_8 ),
inference(sat_conversion,[],[f504]) ).
cnf(s126,plain,
( spl9_1
| spl9_19 ),
inference(sat_conversion,[],[f513]) ).
cnf(s133,plain,
( ~ spl9_2
| ~ spl9_6
| ~ spl9_8
| ~ spl9_14
| ~ spl9_19 ),
inference(sat_conversion,[],[f531]) ).
cnf(s146,plain,
( ~ spl9_2
| ~ spl9_8
| ~ spl9_11 ),
inference(sat_conversion,[],[f549]) ).
cnf(s163,plain,
( spl9_14
| spl9_20 ),
inference(sat_conversion,[],[f564]) ).
cnf(s211,plain,
( spl9_14
| spl9_23 ),
inference(sat_conversion,[],[f718]) ).
cnf(s277,plain,
( ~ spl9_8
| ~ spl9_15
| ~ spl9_20
| ~ spl9_23 ),
inference(sat_conversion,[],[f892]) ).
cnf(s468,plain,
( ~ spl9_2
| ~ spl9_8
| ~ spl9_14
| spl9_15 ),
inference(sat_conversion,[],[f1374]) ).
cnf(s727,plain,
( ~ spl9_1
| ~ spl9_5
| ~ spl9_14
| spl9_15 ),
inference(sat_conversion,[],[f2228]) ).
cnf(s735,plain,
( spl9_5
| spl9_8 ),
inference(sat_conversion,[],[f2240]) ).
cnf(s749,plain,
( spl9_3
| spl9_8 ),
inference(sat_conversion,[],[f2248]) ).
cnf(s791,plain,
( spl9_2
| spl9_5 ),
inference(sat_conversion,[],[f2309]) ).
cnf(s792,plain,
( spl9_2
| spl9_7 ),
inference(sat_conversion,[],[f2311]) ).
cnf(s846,plain,
( ~ spl9_2
| ~ spl9_4
| spl9_7
| ~ spl9_8
| ~ spl9_14 ),
inference(sat_conversion,[],[f2451]) ).
cnf(s868,plain,
( ~ spl9_2
| spl9_3
| ~ spl9_4
| ~ spl9_8
| ~ spl9_14 ),
inference(sat_conversion,[],[f2494]) ).
cnf(s869,plain,
( ~ spl9_19
| ~ spl9_8
| ~ spl9_2
| ~ spl9_6 ),
inference(rat,[],[s277,s57,s163,s211,s146,s133]) ).
cnf(s870,plain,
spl9_1,
inference(rat,[],[s869,s33,s118,s122,s126]) ).
cnf(s872,plain,
spl9_2,
inference(rat,[],[s57,s727,s91,s96,s37,s791,s792,s870]) ).
cnf(s873,plain,
( spl9_14
| ~ spl9_8 ),
inference(rat,[],[s277,s57,s163,s211,s146,s872]) ).
cnf(s874,plain,
( spl9_7
| ~ spl9_8 ),
inference(rat,[],[s846,s49,s873,s872]) ).
cnf(s875,plain,
( spl9_3
| ~ spl9_14
| ~ spl9_8 ),
inference(rat,[],[s41,s868,s872]) ).
cnf(s876,plain,
( ~ spl9_14
| ~ spl9_8 ),
inference(rat,[],[s875,s96,s874,s468,s872]) ).
cnf(s877,plain,
~ spl9_8,
inference(rat,[],[s876,s873]) ).
cnf(s878,plain,
spl9_3,
inference(rat,[],[s749,s877]) ).
cnf(s879,plain,
spl9_5,
inference(rat,[],[s735,s877]) ).
cnf(s885,plain,
spl9_7,
inference(rat,[],[s53,s877]) ).
cnf(s889,plain,
~ spl9_11,
inference(rat,[],[s91,s870,s879]) ).
cnf(s890,plain,
~ spl9_15,
inference(rat,[],[s96,s878,s885]) ).
cnf(s891,plain,
spl9_14,
inference(rat,[],[s57,s889,s890]) ).
cnf(s893,plain,
$false,
inference(rat,[],[s727,s879,s870,s891,s890]) ).
thf(f2496,plain,
$false,
inference(avatar_sat_refutation,[],[s893]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO443^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n004.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:51:52 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.36 % (1558308)Will run a generic schedule for satisfiability detection.
% 0.20/0.36 % (1558314)% WARNING: option uhcvi not known.
% 0.20/0.36 % (1558314)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2416025914:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.36 % (1558314)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.36 % (1558314)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.36 % (1558316)dis+10_1_sil=32000:sp=arity:random_seed=3266313403:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.36 % (1558313)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2260435295_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.36 % (1558315)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2581782781:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.36 % (1558318)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3312559437:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.36 % (1558317)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3433075822:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.36 % (1558319)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3412785585:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.36 % (1558317)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.36 % Exception at run slice level
% 0.20/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.36 % (1558327)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3022782816:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.36 % Exception at run slice level
% 0.20/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.36 % (1558329)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2098944863:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.36 % (1558316)Instruction limit reached!
% 0.20/0.36 % (1558316)------------------------------
% 0.20/0.36 % (1558316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1558316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1558316)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1558316)Termination reason: Instruction limit
% 0.20/0.36 % (1558316)Termination phase: Saturation
% 0.20/0.36 % (1558316)Time elapsed: 0.047 s
% 0.20/0.36 % (1558316)Peak memory usage: 12 MB
% 0.20/0.36 % (1558316)Instructions burned: 105 (million)
% 0.20/0.36 % (1558317)Instruction limit reached!
% 0.20/0.36 % (1558317)------------------------------
% 0.20/0.36 % (1558317)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1558317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1558317)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1558317)Termination reason: Instruction limit
% 0.20/0.36 % (1558317)Termination phase: Saturation
% 0.20/0.36 % (1558317)Time elapsed: 0.051 s
% 0.20/0.36 % (1558317)Peak memory usage: 12 MB
% 0.20/0.36 % (1558317)Instructions burned: 117 (million)
% 0.20/0.36 % (1558318)Instruction limit reached!
% 0.20/0.36 % (1558318)------------------------------
% 0.20/0.36 % (1558318)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1558318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1558318)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1558318)Termination reason: Instruction limit
% 0.20/0.36 % (1558318)Termination phase: Saturation
% 0.20/0.36 % (1558318)Time elapsed: 0.057 s
% 0.20/0.36 % (1558318)Peak memory usage: 12 MB
% 0.20/0.36 % (1558318)Instructions burned: 132 (million)
% 0.20/0.36 % (1558331)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=1059312992:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.20/0.36 % (1558331)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.36 % (1558331)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.36 % (1558332)ott-21_1_sil=16000:fs=off:random_seed=3586087423:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.20/0.36 % (1558315) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1558308-1558315"...
% 0.20/0.36 % (1558333)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1840259053:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.20/0.36 % (1558319)Instruction limit reached!
% 0.20/0.36 % (1558319)------------------------------
% 0.20/0.36 % (1558319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1558319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1558319)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1558319)Termination reason: Instruction limit
% 0.20/0.36 % (1558319)Termination phase: Saturation
% 0.20/0.36 % (1558319)Time elapsed: 0.075 s
% 0.20/0.36 % (1558319)Peak memory usage: 12 MB
% 0.20/0.36 % (1558319)Instructions burned: 160 (million)
% 0.20/0.36 % (1558315)...printing done.
% 0.20/0.36 % (1558315)Refutation found. Thanks to Tanya!
% 0.20/0.36 % SZS status Theorem for theBenchmark
% 0.20/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.36 % (1558315)------------------------------
% 0.20/0.36 % (1558315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1558315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1558315)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1558315)Termination reason: Refutation
% 0.20/0.36 % (1558315)Time elapsed: 0.083 s
% 0.20/0.36 % (1558315)Peak memory usage: 13 MB
% 0.20/0.36 % (1558315)Instructions burned: 159 (million)
% 0.20/0.36 % (1558308)Success in time 0.121 s
% 0.20/0.36 % Vampire exiting
%------------------------------------------------------------------------------