%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO463^6 : 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 : n009.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 08:50:10 AM UTC 2026
% Result : Theorem 0.19s 0.34s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 25
% Syntax : Number of formulae : 250 ( 82 unt; 0 typ; 13 def)
% Number of atoms : 1768 ( 310 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 2251 ( 403 ~; 443 |; 13 &;1247 @)
% ( 13 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 137 ( 137 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 68 usr; 21 con; 0-4 aty)
% ( 110 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 415 ( 0 sgn 104 !; 0 ?; 415 :)
% 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(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(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 @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ 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 @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f100,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ 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 @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ 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] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ 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 ) )
@ 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 > $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 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ) ),
inference(definition_unfolding,[],[f138,f129,f142,f133,f144,f133,f144,f133,f133]) ).
thf(f155,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( !! @ $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 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( !! @ $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 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f160,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $true
= ( ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f172,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( !! @ $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 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f176,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
( $false
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f179,plain,
( $true
= ( rel_s5 @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f181,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f185,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f190,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f188]) ).
thf(f198,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f202,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f205,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f206,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f207,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f209,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK3 )
| ( p @ sK3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( p @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( ( $false
= ( p @ sK3 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK3 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f214,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( $false
= ( p @ sK3 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f212]) ).
thf(f218,plain,
! [X1: $i] :
( ( $false
= ( p @ sK3 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f219,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f207]) ).
thf(f220,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK3 )
| ( p @ sK3 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK4 )
| ( q @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f219]) ).
thf(f221,plain,
( ( $false
= ( p @ sK3 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK4 )
| ( q @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK3 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK4 )
| ( q @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f223,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK4 )
| ( q @ sK4 ) ) ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( $false
= ( q @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f226,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK4 ) ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
( ( $false
= ( p @ sK3 ) )
| ( $false
= ( q @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f228,plain,
( ( $false
= ( p @ sK3 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f229,plain,
( ( $false
= ( p @ sK3 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK4 ) ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f231,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f234]) ).
thf(f236,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(f237,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,[],[f236]) ).
thf(f238,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,[],[f237]) ).
thf(f239,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,[],[f238]) ).
thf(f240,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,[],[f239]) ).
thf(f241,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,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f241]) ).
thf(f243,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,[],[f242]) ).
thf(f244,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,[],[f243]) ).
thf(f249,definition,
( spl5_1
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f250,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f252,definition,
( spl5_2
<=> ! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f253,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f252]) ).
thf(f254,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f196,f252,f249]) ).
thf(f256,definition,
( spl5_3
<=> ( $true
= ( rel_s5 @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f258,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f256]) ).
thf(f259,plain,
( spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f203,f252,f256]) ).
thf(f261,definition,
( spl5_4
<=> ( $false
= ( q @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f263,plain,
( ( $false
= ( q @ sK2 ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f261]) ).
thf(f264,plain,
( spl5_4
| spl5_2 ),
inference(avatar_split_clause,[],[f204,f252,f261]) ).
thf(f266,definition,
( spl5_5
<=> ( $true
= ( rel_s5 @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f268,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f269,plain,
( spl5_1
| spl5_5 ),
inference(avatar_split_clause,[],[f216,f266,f249]) ).
thf(f271,definition,
( spl5_6
<=> ( $false
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f273,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f271]) ).
thf(f274,plain,
( spl5_1
| spl5_6 ),
inference(avatar_split_clause,[],[f218,f271,f249]) ).
thf(f276,definition,
( spl5_7
<=> ( $true
= ( rel_s5 @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
thf(f278,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK4 ) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f276]) ).
thf(f279,plain,
( spl5_7
| spl5_5 ),
inference(avatar_split_clause,[],[f226,f266,f276]) ).
thf(f281,definition,
( spl5_8
<=> ( $false
= ( q @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
thf(f283,plain,
( ( $false
= ( q @ sK4 ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f281]) ).
thf(f284,plain,
( spl5_8
| spl5_5 ),
inference(avatar_split_clause,[],[f224,f266,f281]) ).
thf(f285,plain,
( spl5_7
| spl5_6 ),
inference(avatar_split_clause,[],[f229,f271,f276]) ).
thf(f286,plain,
( spl5_8
| spl5_6 ),
inference(avatar_split_clause,[],[f227,f271,f281]) ).
thf(f287,plain,
( ( $true = $false )
| ( $true
= ( q @ sK3 ) )
| ~ spl5_2
| ~ spl5_5 ),
inference(constrained_superposition,[],[f253,f268]) ).
thf(f488,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $true
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) ) ),
inference(constrained_superposition,[],[f235,f244]) ).
thf(f490,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl5_5 ),
inference(constrained_superposition,[],[f268,f244]) ).
thf(f508,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f490]) ).
thf(f510,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $true
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f488]) ).
thf(f540,plain,
( ( $true = $false )
| ( $true
= ( p @ sK2 ) )
| ~ spl5_1
| ~ spl5_3 ),
inference(constrained_superposition,[],[f250,f258]) ).
thf(f547,plain,
( ( $true = $false )
| ( $true
= ( p @ sK3 ) )
| ~ spl5_1
| ~ spl5_5 ),
inference(constrained_superposition,[],[f268,f250]) ).
thf(f549,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl5_1
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f547]) ).
thf(f560,plain,
( ( $true = $false )
| ~ spl5_1
| ~ spl5_5
| ~ spl5_6 ),
inference(constrained_superposition,[],[f549,f273]) ).
thf(f564,plain,
( $false
| ~ spl5_1
| ~ spl5_5
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f560]) ).
thf(f565,plain,
( ~ spl5_1
| ~ spl5_5
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[],[f564]) ).
thf(f566,plain,
( ( $true
= ( q @ sK3 ) )
| ~ spl5_2
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f287]) ).
thf(f1028,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( p @ sK3 ) )
| ( $false
= ( q @ sK3 ) )
| ~ spl5_5 ),
inference(constrained_superposition,[],[f508,f174]) ).
thf(f1061,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( p @ sK3 ) )
| ( $false
= ( q @ sK3 ) )
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f1028]) ).
thf(f1064,definition,
( spl5_17
<=> ( $false
= ( rel_s5 @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_17])],[avatar_definition]) ).
thf(f1066,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl5_17 ),
inference(avatar_component_clause,[],[f1064]) ).
thf(f1068,definition,
( spl5_18
<=> ( $false
= ( q @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_18])],[avatar_definition]) ).
thf(f1070,plain,
( ( $false
= ( q @ sK3 ) )
| ~ spl5_18 ),
inference(avatar_component_clause,[],[f1068]) ).
thf(f1072,definition,
( spl5_19
<=> ( $true
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_19])],[avatar_definition]) ).
thf(f1074,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl5_19 ),
inference(avatar_component_clause,[],[f1072]) ).
thf(f1076,plain,
( spl5_18
| spl5_19
| spl5_17
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f1061,f266,f1064,f1072,f1068]) ).
thf(f1084,plain,
( ( $true = $false )
| ~ spl5_17 ),
inference(constrained_superposition,[],[f1066,f179]) ).
thf(f1102,plain,
( $false
| ~ spl5_17 ),
inference(trivial_inequality_removal,[],[f1084]) ).
thf(f1103,plain,
~ spl5_17,
inference(avatar_contradiction_clause,[],[f1102]) ).
thf(f1106,plain,
( ( $true = $false )
| ~ spl5_2
| ~ spl5_5
| ~ spl5_18 ),
inference(constrained_superposition,[],[f1070,f566]) ).
thf(f1112,plain,
( $false
| ~ spl5_2
| ~ spl5_5
| ~ spl5_18 ),
inference(trivial_inequality_removal,[],[f1106]) ).
thf(f1113,plain,
( ~ spl5_2
| ~ spl5_5
| ~ spl5_18 ),
inference(avatar_contradiction_clause,[],[f1112]) ).
thf(f1116,plain,
( ( $true = $false )
| ~ spl5_6
| ~ spl5_19 ),
inference(constrained_superposition,[],[f1074,f273]) ).
thf(f1120,plain,
( $false
| ~ spl5_6
| ~ spl5_19 ),
inference(trivial_inequality_removal,[],[f1116]) ).
thf(f1121,plain,
( ~ spl5_6
| ~ spl5_19 ),
inference(avatar_contradiction_clause,[],[f1120]) ).
thf(f1283,plain,
( ( $true = $false )
| ( $true
= ( q @ sK4 ) )
| ~ spl5_2
| ~ spl5_7 ),
inference(constrained_superposition,[],[f253,f278]) ).
thf(f1288,plain,
( ( $true
= ( q @ sK4 ) )
| ~ spl5_2
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f1283]) ).
thf(f1292,plain,
( ( $true = $false )
| ~ spl5_2
| ~ spl5_7
| ~ spl5_8 ),
inference(constrained_superposition,[],[f1288,f283]) ).
thf(f1296,plain,
( $false
| ~ spl5_2
| ~ spl5_7
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f1292]) ).
thf(f1297,plain,
( ~ spl5_2
| ~ spl5_7
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f1296]) ).
thf(f1298,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl5_1
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f540]) ).
thf(f1619,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true
= ( rel_s5 @ sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f179,f510]) ).
thf(f1636,plain,
! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true
= ( rel_s5 @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1619]) ).
thf(f1804,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $true
= ( rel_s5 @ sK0 @ X0 ) ) ),
inference(constrained_superposition,[],[f235,f1636]) ).
thf(f1847,plain,
! [X0: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $true
= ( rel_s5 @ sK0 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1804]) ).
thf(f2001,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f258,f1847]) ).
thf(f2005,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f2001]) ).
thf(f2033,plain,
( ( $true = $false )
| ( $true
= ( q @ sK2 ) )
| ( $false
= ( p @ sK2 ) )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f2005,f170]) ).
thf(f2056,plain,
( ( $true
= ( q @ sK2 ) )
| ( $false
= ( p @ sK2 ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f2033]) ).
thf(f2060,definition,
( spl5_20
<=> ( $false
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_20])],[avatar_definition]) ).
thf(f2062,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl5_20 ),
inference(avatar_component_clause,[],[f2060]) ).
thf(f2064,definition,
( spl5_21
<=> ( $true
= ( q @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_21])],[avatar_definition]) ).
thf(f2066,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl5_21 ),
inference(avatar_component_clause,[],[f2064]) ).
thf(f2068,plain,
( spl5_20
| spl5_21
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f2056,f256,f2064,f2060]) ).
thf(f2069,plain,
( ( $true = $false )
| ~ spl5_1
| ~ spl5_3
| ~ spl5_20 ),
inference(constrained_superposition,[],[f2062,f1298]) ).
thf(f2075,plain,
( $false
| ~ spl5_1
| ~ spl5_3
| ~ spl5_20 ),
inference(trivial_inequality_removal,[],[f2069]) ).
thf(f2076,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_20 ),
inference(avatar_contradiction_clause,[],[f2075]) ).
thf(f2079,plain,
( ( $true = $false )
| ~ spl5_4
| ~ spl5_21 ),
inference(constrained_superposition,[],[f2066,f263]) ).
thf(f2083,plain,
( $false
| ~ spl5_4
| ~ spl5_21 ),
inference(trivial_inequality_removal,[],[f2079]) ).
thf(f2084,plain,
( ~ spl5_4
| ~ spl5_21 ),
inference(avatar_contradiction_clause,[],[f2083]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f254]) ).
cnf(s2,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f259]) ).
cnf(s3,plain,
( spl5_2
| spl5_4 ),
inference(sat_conversion,[],[f264]) ).
cnf(s4,plain,
( spl5_1
| spl5_5 ),
inference(sat_conversion,[],[f269]) ).
cnf(s5,plain,
( spl5_1
| spl5_6 ),
inference(sat_conversion,[],[f274]) ).
cnf(s6,plain,
( spl5_5
| spl5_7 ),
inference(sat_conversion,[],[f279]) ).
cnf(s7,plain,
( spl5_5
| spl5_8 ),
inference(sat_conversion,[],[f284]) ).
cnf(s8,plain,
( spl5_6
| spl5_7 ),
inference(sat_conversion,[],[f285]) ).
cnf(s9,plain,
( spl5_6
| spl5_8 ),
inference(sat_conversion,[],[f286]) ).
cnf(s32,plain,
( ~ spl5_1
| ~ spl5_5
| ~ spl5_6 ),
inference(sat_conversion,[],[f565]) ).
cnf(s40,plain,
( ~ spl5_5
| spl5_17
| spl5_18
| spl5_19 ),
inference(sat_conversion,[],[f1076]) ).
cnf(s42,plain,
~ spl5_17,
inference(sat_conversion,[],[f1103]) ).
cnf(s44,plain,
( ~ spl5_2
| ~ spl5_5
| ~ spl5_18 ),
inference(sat_conversion,[],[f1113]) ).
cnf(s46,plain,
( ~ spl5_6
| ~ spl5_19 ),
inference(sat_conversion,[],[f1121]) ).
cnf(s48,plain,
( ~ spl5_2
| ~ spl5_7
| ~ spl5_8 ),
inference(sat_conversion,[],[f1297]) ).
cnf(s50,plain,
( ~ spl5_3
| spl5_20
| spl5_21 ),
inference(sat_conversion,[],[f2068]) ).
cnf(s52,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_20 ),
inference(sat_conversion,[],[f2076]) ).
cnf(s54,plain,
( ~ spl5_4
| ~ spl5_21 ),
inference(sat_conversion,[],[f2084]) ).
cnf(s55,plain,
( ~ spl5_5
| spl5_18
| spl5_19 ),
inference(rat,[],[s40,s42]) ).
cnf(s57,plain,
spl5_1,
inference(rat,[],[s55,s44,s46,s1,s4,s5]) ).
cnf(s58,plain,
spl5_2,
inference(rat,[],[s50,s52,s54,s2,s3,s57]) ).
cnf(s67,plain,
spl5_6,
inference(rat,[],[s48,s8,s9,s58]) ).
cnf(s69,plain,
~ spl5_5,
inference(rat,[],[s32,s57,s67]) ).
cnf(s70,plain,
spl5_8,
inference(rat,[],[s7,s69]) ).
cnf(s71,plain,
spl5_7,
inference(rat,[],[s6,s69]) ).
cnf(s72,plain,
$false,
inference(rat,[],[s48,s58,s70,s71]) ).
thf(f2085,plain,
$false,
inference(avatar_sat_refutation,[],[s72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO463^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n009.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 16:59:30 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.19/0.34 % (80454)Will run a generic schedule for satisfiability detection.
% 0.19/0.34 % (80463)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1571019153:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.34 % (80463)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.34 % (80460)% WARNING: option uhcvi not known.
% 0.19/0.34 % (80459)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=814513964_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.34 % (80460)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2766416042:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.34 % (80461)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4196978679:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.34 % (80462)dis+10_1_sil=32000:sp=arity:random_seed=3885672354:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.34 % (80464)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=326820086:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.34 % (80465)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1787904106:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.34 % (80460)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.34 % Exception at run slice level
% 0.19/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.34 % (80460)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.34 % (80463)Instruction limit reached!
% 0.19/0.34 % (80463)------------------------------
% 0.19/0.34 % (80463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (80463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (80463)CaDiCaL version: 2.1.3
% 0.19/0.34 % (80463)Termination reason: Instruction limit
% 0.19/0.34 % (80463)Termination phase: Saturation
% 0.19/0.34 % (80463)Time elapsed: 0.035 s
% 0.19/0.34 % (80463)Peak memory usage: 12 MB
% 0.19/0.34 % (80463)Instructions burned: 119 (million)
% 0.19/0.34 % (80473)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3198511:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.34 % Exception at run slice level
% 0.19/0.34 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.34 % (80474)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1967540722:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.34 % (80476)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=1160772438:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.19/0.34 % (80462)Instruction limit reached!
% 0.19/0.34 % (80462)------------------------------
% 0.19/0.34 % (80462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.34 % (80462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.34 % (80462)CaDiCaL version: 2.1.3
% 0.19/0.34 % (80462)Termination reason: Instruction limit
% 0.19/0.34 % (80462)Termination phase: Saturation
% 0.19/0.34 % (80462)Time elapsed: 0.047 s
% 0.19/0.34 % (80462)Peak memory usage: 12 MB
% 0.19/0.34 % (80462)Instructions burned: 104 (million)
% 0.19/0.34 % (80476)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.34 % (80476)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.34 % (80465) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-80454-80465"...
% 0.19/0.34 % (80465)...printing done.
% 0.19/0.34 % (80465)Refutation found. Thanks to Tanya!
% 0.19/0.34 % SZS status Theorem for theBenchmark
% 0.19/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.35 % (80465)------------------------------
% 0.19/0.35 % (80465)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.35 % (80465)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.35 % (80465)CaDiCaL version: 2.1.3
% 0.19/0.35 % (80465)Termination reason: Refutation
% 0.19/0.35 % (80465)Time elapsed: 0.060 s
% 0.19/0.35 % (80465)Peak memory usage: 13 MB
% 0.19/0.35 % (80465)Instructions burned: 119 (million)
% 0.19/0.35 % (80454)Success in time 0.118 s
% 0.19/0.35 % Vampire exiting
%------------------------------------------------------------------------------