%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL873^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:15:12 AM UTC 2026
% Result : Theorem 3.96s 0.94s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 34
% Syntax : Number of formulae : 444 ( 79 unt; 0 typ; 21 def)
% Number of atoms : 5012 ( 953 equ; 0 cnn)
% Maximal formula atoms : 32 ( 11 avg)
% Number of connectives : 6354 ( 795 ~;1433 |; 26 &;3679 @)
% ( 21 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 233 ( 233 >; 0 *; 0 +; 0 <<)
% Number of symbols : 86 ( 82 usr; 34 con; 0-4 aty)
% ( 380 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 1071 ( 0 sgn 422 !; 0 ?;1071 :)
% 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,
ra: $i > $i > $o ).
thf(func_def_33,type,
rb: $i > $i > $o ).
thf(func_def_34,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_37,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vNOT: $o > $o ).
thf(func_def_40,type,
vOR: $o > $o > $o ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vIMP: $o > $o > $o ).
thf(func_def_46,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
sK2: $i > $o ).
thf(func_def_52,type,
sK3: $i > $o ).
thf(func_def_53,type,
sK4: $i > $o ).
thf(func_def_54,type,
sK5: $i > $o ).
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(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f22,axiom,
( meuclidean
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
mreflexive @ ra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(f33,axiom,
mreflexive @ rb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(f36,axiom,
meuclidean @ ra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).
thf(f37,axiom,
meuclidean @ rb,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).
thf(f38,conjecture,
( ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] :
( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ rb @ X1 ) ) ) @ ( mor @ ( mbox @ rb @ X0 ) @ ( mbox @ rb @ X1 ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] :
( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ rb @ X1 ) ) ) @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ ra @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f39,negated_conjecture,
~ ( ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] :
( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ rb @ X1 ) ) ) @ ( mor @ ( mbox @ rb @ X0 ) @ ( mbox @ rb @ X1 ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] :
( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ rb @ X1 ) ) ) @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ ra @ X1 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
thf(f42,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f43,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f45,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f47,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f53,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f54,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f60,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X1 @ X3 )
| ~ ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f61,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f63,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f64,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f71,plain,
( meuclidean
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f72,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f83,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f84,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f91,plain,
mreflexive @ ra,
inference(rectify,[],[f32]) ).
thf(f92,plain,
( ( mreflexive @ ra )
= $true ),
inference(fool_elimination,[],[f91]) ).
thf(f93,plain,
mreflexive @ rb,
inference(rectify,[],[f33]) ).
thf(f94,plain,
( ( mreflexive @ rb )
= $true ),
inference(fool_elimination,[],[f93]) ).
thf(f99,plain,
meuclidean @ ra,
inference(rectify,[],[f36]) ).
thf(f100,plain,
( ( meuclidean @ ra )
= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
meuclidean @ rb,
inference(rectify,[],[f37]) ).
thf(f102,plain,
( ( meuclidean @ rb )
= $true ),
inference(fool_elimination,[],[f101]) ).
thf(f103,plain,
~ ( ( mvalid
@ ( mforall_prop
@ ^ [X0: $i > $o] :
( mforall_prop
@ ^ [X1: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ X0 ) @ ( mbox @ rb @ X1 ) ) ) @ ( mor @ ( mbox @ rb @ X0 ) @ ( mbox @ rb @ X1 ) ) ) ) ) )
& ( mvalid
@ ( mforall_prop
@ ^ [X2: $i > $o] :
( mforall_prop
@ ^ [X3: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ X2 ) @ ( mbox @ rb @ X3 ) ) ) @ ( mor @ ( mbox @ ra @ X2 ) @ ( mbox @ ra @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f104,plain,
~ ( ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) @ ( mor @ ( mbox @ rb @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) ) ) ) )
& ( $true
= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ ra @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f103]) ).
thf(f105,plain,
( ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) @ ( mor @ ( mbox @ rb @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) ) ) ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ ra @ Y1 ) ) ) ) ) ) ) ),
inference(ennf_transformation,[],[f104]) ).
thf(f108,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f109,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f111,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f116,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f121,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( Y0 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f123,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f127,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f133,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f137,plain,
( ( mreflexive @ ra )
= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f138,plain,
( ( mreflexive @ rb )
= $true ),
inference(cnf_transformation,[],[f94]) ).
thf(f141,plain,
( ( meuclidean @ ra )
= $true ),
inference(cnf_transformation,[],[f100]) ).
thf(f142,plain,
( ( meuclidean @ rb )
= $true ),
inference(cnf_transformation,[],[f102]) ).
thf(f143,plain,
( ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ rb @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) @ ( mor @ ( mbox @ rb @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) ) ) ) )
| ( $true
!= ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] :
( mforall_prop
@ ^ [Y1: $i > $o] : ( mimplies @ ( mbox @ ra @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ rb @ Y1 ) ) ) @ ( mor @ ( mbox @ ra @ Y0 ) @ ( mbox @ ra @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f105]) ).
thf(f147,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,[],[f111,f109,f108]) ).
thf(f155,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ ra ) ),
inference(definition_unfolding,[],[f137,f123]) ).
thf(f156,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rb ) ),
inference(definition_unfolding,[],[f138,f123]) ).
thf(f159,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ ra ) ),
inference(definition_unfolding,[],[f141,f127]) ).
thf(f160,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ rb ) ),
inference(definition_unfolding,[],[f142,f127]) ).
thf(f161,plain,
( ( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: ( $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ rb
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ rb
@ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ rb
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ rb
@ Y1 ) ) ) ) ) ) )
| ( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: ( $i > $o ) > $i > $o,Y2: $i] :
( !! @ ( $i > $o )
@ ^ [Y3: $i > $o] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i > $o] :
( ^ [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 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ ra
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ rb
@ Y1 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ ra
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ~ ( Y2 @ Y4 @ Y5 )
| ( Y3 @ Y5 ) ) )
@ ra
@ Y1 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f143,f133,f116,f116,f147,f121,f109,f121,f121,f109,f121,f121,f133,f116,f116,f147,f121,f109,f121,f121,f109,f121,f121]) ).
thf(f162,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y0 @ Y3 )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( ra @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rb @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y0 @ Y3 )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( ra @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rb @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y0 @ Y3 )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( ra @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rb @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y0 @ Y3 )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( ra @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rb @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y0 @ Y3 )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( ra @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rb @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y0 @ Y3 )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( ra @ Y3 @ Y4 )
| ( Y1 @ Y4 ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rb @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y0 @ Y3 )
| ( Y1 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y0 @ Y3 )
| ( Y2 @ Y3 ) ) ) ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ sK0 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ sK0 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ sK0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ sK1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ sK1 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ sK1 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ sK0 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ sK0 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ sK0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) )
@ sK2 ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ sK1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ sK1 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ sK1 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ sK0 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ sK0 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ sK0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ sK1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( ra @ Y2 @ Y3 )
| ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rb @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ sK1 @ Y2 )
| ( Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ sK1 @ Y2 )
| ( Y1 @ Y2 ) ) ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ sK0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ Y1 @ Y2 )
| ( sK2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ sK0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ sK0 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ sK1 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ sK1 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ sK1 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ sK0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ Y1 @ Y2 )
| ( sK2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ sK0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ sK0 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
@ sK4 ) )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ sK1 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ sK1 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ sK1 @ Y1 )
| ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ sK0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ Y1 @ Y2 )
| ( sK2 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ sK0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ sK0 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i > $o] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ sK1 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( ra @ Y1 @ Y2 )
| ( sK3 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rb @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ sK1 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ sK1 @ Y1 )
| ( Y0 @ Y1 ) ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rb @ sK0 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X2 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X2 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X2 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X2 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X2 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X2 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ~ ( ra @ sK1 @ X2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X2 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X2 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X2 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X2 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X2 @ Y0 )
| ( sK5 @ Y0 ) ) ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X2 @ Y0 )
| ( sK5 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X2 @ Y0 )
| ( sK5 @ Y0 ) )
@ X4 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X2 @ Y0 )
| ( sK5 @ Y0 ) )
@ X4 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) )
@ X5 ) )
| ( $true
= ( ~ ( ra @ sK1 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X2 @ Y0 )
| ( sK5 @ Y0 ) )
@ X4 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) )
@ X5 ) )
| ( $false
= ( ra @ sK1 @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X2 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X2 @ Y0 )
| ( sK5 @ Y0 ) )
@ X4 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) )
@ X5 ) )
| ( $false
= ( ra @ sK1 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ X2 @ Y0 )
| ( sK3 @ Y0 ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ~ ( rb @ X1 @ X3 )
| ( sK4 @ X3 ) ) )
| ( $true
= ( ~ ( rb @ X2 @ X4 )
| ( sK5 @ X4 ) ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X5 )
| ( sK2 @ X5 ) ) )
| ( $false
= ( ra @ sK1 @ X2 ) )
| ( $true
= ( ~ ( ra @ X2 @ X6 )
| ( sK3 @ X6 ) ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( ~ ( rb @ X2 @ X4 )
| ( sK5 @ X4 ) ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X5 )
| ( sK2 @ X5 ) ) )
| ( $false
= ( ra @ sK1 @ X2 ) )
| ( $true
= ( ~ ( ra @ X2 @ X6 )
| ( sK3 @ X6 ) ) )
| ( $true
= ( ~ ( rb @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( sK5 @ X4 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X5 )
| ( sK2 @ X5 ) ) )
| ( $false
= ( ra @ sK1 @ X2 ) )
| ( $true
= ( ~ ( ra @ X2 @ X6 )
| ( sK3 @ X6 ) ) )
| ( $true
= ( ~ ( rb @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rb @ X2 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( sK5 @ X4 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X5 ) )
| ( $false
= ( ra @ sK1 @ X2 ) )
| ( $true
= ( ~ ( ra @ X2 @ X6 )
| ( sK3 @ X6 ) ) )
| ( $true
= ( ~ ( rb @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rb @ X2 @ X4 ) ) )
| ( $true
= ( ~ ( ra @ X1 @ X5 ) ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( sK5 @ X4 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X5 ) )
| ( $false
= ( ra @ sK1 @ X2 ) )
| ( $true
= ( sK3 @ X6 ) )
| ( $true
= ( ~ ( rb @ X1 @ X3 ) ) )
| ( $true
= ( ~ ( rb @ X2 @ X4 ) ) )
| ( $true
= ( ~ ( ra @ X1 @ X5 ) ) )
| ( $true
= ( ~ ( ra @ X2 @ X6 ) ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( sK5 @ X4 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X5 ) )
| ( $false
= ( ra @ sK1 @ X2 ) )
| ( $true
= ( sK3 @ X6 ) )
| ( $false
= ( rb @ X1 @ X3 ) )
| ( $true
= ( ~ ( rb @ X2 @ X4 ) ) )
| ( $true
= ( ~ ( ra @ X1 @ X5 ) ) )
| ( $true
= ( ~ ( ra @ X2 @ X6 ) ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( sK5 @ X4 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X5 ) )
| ( $false
= ( ra @ sK1 @ X2 ) )
| ( $true
= ( sK3 @ X6 ) )
| ( $false
= ( rb @ X1 @ X3 ) )
| ( $false
= ( rb @ X2 @ X4 ) )
| ( $true
= ( ~ ( ra @ X1 @ X5 ) ) )
| ( $true
= ( ~ ( ra @ X2 @ X6 ) ) ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( sK5 @ X4 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X5 ) )
| ( $false
= ( ra @ sK1 @ X2 ) )
| ( $true
= ( sK3 @ X6 ) )
| ( $false
= ( rb @ X1 @ X3 ) )
| ( $false
= ( rb @ X2 @ X4 ) )
| ( $false
= ( ra @ X1 @ X5 ) )
| ( $true
= ( ~ ( ra @ X2 @ X6 ) ) ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( $true
= ( sK5 @ X4 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X5 ) )
| ( $false
= ( ra @ sK1 @ X2 ) )
| ( $true
= ( sK3 @ X6 ) )
| ( $false
= ( rb @ X1 @ X3 ) )
| ( $false
= ( rb @ X2 @ X4 ) )
| ( $false
= ( ra @ X1 @ X5 ) )
| ( $false
= ( ra @ X2 @ X6 ) ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f201,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f202,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rb @ sK0 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK6 )
| ( sK3 @ sK6 ) ) ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK6 )
| ( sK3 @ sK6 ) ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK6 )
| ( sK3 @ sK6 ) ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK6 )
| ( sK3 @ sK6 ) ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $false
= ( sK3 @ sK6 ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK6 ) ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ra @ sK1 @ sK6 ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ra @ sK1 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ra @ sK1 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rb @ X1 @ X2 )
| ( sK4 @ X2 ) ) )
| ( $true
= ( ra @ sK1 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f213,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( ra @ sK1 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( ra @ sK1 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( ra @ sK1 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( ra @ sK1 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $false
= ( ra @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $false
= ( sK3 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f218,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $false
= ( sK3 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rb @ X1 @ X2 )
| ( sK4 @ X2 ) ) )
| ( $false
= ( sK3 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $false
= ( sK3 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $false
= ( sK3 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $false
= ( sK3 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $false
= ( sK3 @ sK6 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $false
= ( ra @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK4 @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f200]) ).
thf(f225,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rb @ sK0 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK7 )
| ( sK5 @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f226,plain,
! [X1: $i] :
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK7 )
| ( sK5 @ sK7 ) ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK7 )
| ( sK5 @ sK7 ) ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK7 )
| ( sK5 @ sK7 ) ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $false
= ( sK5 @ sK7 ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK7 ) ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f228]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ra @ sK1 @ sK7 ) )
| ( $true
= ( ~ ( rb @ sK0 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ra @ sK1 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ra @ sK1 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rb @ X1 @ X2 )
| ( sK4 @ X2 ) ) )
| ( $true
= ( ra @ sK1 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( ra @ sK1 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( ra @ sK1 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( ra @ sK1 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $true
= ( ra @ sK1 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $false
= ( ra @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $false
= ( sK5 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f229]) ).
thf(f240,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK4 @ Y0 ) )
@ X2 ) )
| ( $false
= ( sK5 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK2 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rb @ X1 @ X2 )
| ( sK4 @ X2 ) ) )
| ( $false
= ( sK5 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK2 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $false
= ( sK5 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK2 @ X3 ) ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $false
= ( sK5 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $false
= ( sK5 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK4 @ X2 ) )
| ( $false
= ( sK5 @ sK7 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $true
= ( sK2 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $false
= ( ra @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK4 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f247,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK2 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f248,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK2 @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f247]) ).
thf(f249,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK2 @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f248]) ).
thf(f250,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK2 @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f248]) ).
thf(f251,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK2 @ Y0 ) )
@ sK8 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK2 @ Y0 ) )
@ sK8 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rb @ sK0 @ sK8 )
| ( sK2 @ sK8 ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f252]) ).
thf(f254,plain,
! [X1: $i] :
( ( $false
= ( sK2 @ sK8 ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rb @ sK0 @ sK8 ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f253]) ).
thf(f256,plain,
! [X1: $i] :
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X1: $i] :
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X1: $i] :
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f257]) ).
thf(f259,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 )
| ( sK5 @ X2 ) ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f261]) ).
thf(f263,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK3 @ X3 ) ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $false
= ( ra @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f265]) ).
thf(f267,plain,
! [X1: $i] :
( ( $false
= ( sK2 @ sK8 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f254]) ).
thf(f268,plain,
! [X1: $i] :
( ( $false
= ( sK2 @ sK8 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK2 @ sK8 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK2 @ sK8 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK2 @ sK8 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f270]) ).
thf(f272,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK2 @ sK8 ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 )
| ( sK5 @ X2 ) ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f271]) ).
thf(f273,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK2 @ sK8 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK3 @ X3 ) ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK2 @ sK8 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK2 @ sK8 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK2 @ sK8 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $false
= ( ra @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f275]) ).
thf(f277,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK2 @ Y0 ) )
@ sK8 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f249]) ).
thf(f278,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK2 @ Y0 ) )
@ sK8 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f249]) ).
thf(f279,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK2 @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) )
@ sK9 ) ) ),
inference(sigma_proxy_clausification,[],[f278]) ).
thf(f280,plain,
( ( $false
= ( ~ ( rb @ sK0 @ sK8 )
| ( sK2 @ sK8 ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK9 )
| ( sK3 @ sK9 ) ) ) ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f281,plain,
( ( $false
= ( sK2 @ sK8 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK9 )
| ( sK3 @ sK9 ) ) ) ),
inference(or_proxy_clausification,[],[f280]) ).
thf(f282,plain,
( ( $false
= ( ~ ( rb @ sK0 @ sK8 ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK9 )
| ( sK3 @ sK9 ) ) ) ),
inference(or_proxy_clausification,[],[f280]) ).
thf(f283,plain,
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK9 )
| ( sK3 @ sK9 ) ) ) ),
inference(not_proxy_clausification,[],[f282]) ).
thf(f284,plain,
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $false
= ( sK3 @ sK9 ) ) ),
inference(or_proxy_clausification,[],[f283]) ).
thf(f285,plain,
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK9 ) ) ) ),
inference(or_proxy_clausification,[],[f283]) ).
thf(f286,plain,
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $true
= ( ra @ sK1 @ sK9 ) ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f287,plain,
( ( $false
= ( sK2 @ sK8 ) )
| ( $false
= ( sK3 @ sK9 ) ) ),
inference(or_proxy_clausification,[],[f281]) ).
thf(f288,plain,
( ( $false
= ( sK2 @ sK8 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK9 ) ) ) ),
inference(or_proxy_clausification,[],[f281]) ).
thf(f289,plain,
( ( $false
= ( sK2 @ sK8 ) )
| ( $true
= ( ra @ sK1 @ sK9 ) ) ),
inference(not_proxy_clausification,[],[f288]) ).
thf(f290,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK2 @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) )
@ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f277]) ).
thf(f291,plain,
( ( $false
= ( ~ ( rb @ sK0 @ sK8 )
| ( sK2 @ sK8 ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK10 )
| ( sK5 @ sK10 ) ) ) ),
inference(beta-eta_normalization,[],[f290]) ).
thf(f292,plain,
( ( $false
= ( sK2 @ sK8 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK10 )
| ( sK5 @ sK10 ) ) ) ),
inference(or_proxy_clausification,[],[f291]) ).
thf(f293,plain,
( ( $false
= ( ~ ( rb @ sK0 @ sK8 ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK10 )
| ( sK5 @ sK10 ) ) ) ),
inference(or_proxy_clausification,[],[f291]) ).
thf(f294,plain,
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK10 )
| ( sK5 @ sK10 ) ) ) ),
inference(not_proxy_clausification,[],[f293]) ).
thf(f295,plain,
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $false
= ( sK5 @ sK10 ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f296,plain,
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK10 ) ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f297,plain,
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ( $true
= ( ra @ sK1 @ sK10 ) ) ),
inference(not_proxy_clausification,[],[f296]) ).
thf(f298,plain,
( ( $false
= ( sK2 @ sK8 ) )
| ( $false
= ( sK5 @ sK10 ) ) ),
inference(or_proxy_clausification,[],[f292]) ).
thf(f299,plain,
( ( $false
= ( sK2 @ sK8 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK10 ) ) ) ),
inference(or_proxy_clausification,[],[f292]) ).
thf(f300,plain,
( ( $false
= ( sK2 @ sK8 ) )
| ( $true
= ( ra @ sK1 @ sK10 ) ) ),
inference(not_proxy_clausification,[],[f299]) ).
thf(f301,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK11 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f246]) ).
thf(f302,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK11 ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f301]) ).
thf(f303,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK11 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f301]) ).
thf(f304,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK11 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK11 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ra @ Y0 @ Y1 )
| ( sK3 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rb @ Y0 @ Y1 )
| ( sK5 @ Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rb @ sK0 @ sK11 )
| ( sK4 @ sK11 ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f305]) ).
thf(f307,plain,
! [X1: $i] :
( ( $false
= ( sK4 @ sK11 ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f306]) ).
thf(f308,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rb @ sK0 @ sK11 ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f306]) ).
thf(f309,plain,
! [X1: $i] :
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f308]) ).
thf(f310,plain,
! [X1: $i] :
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f309]) ).
thf(f311,plain,
! [X1: $i] :
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f310]) ).
thf(f312,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f311]) ).
thf(f313,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 )
| ( sK5 @ X2 ) ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f314]) ).
thf(f316,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK3 @ X3 ) ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f315]) ).
thf(f317,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f317]) ).
thf(f319,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $false
= ( ra @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f318]) ).
thf(f320,plain,
! [X1: $i] :
( ( $false
= ( sK4 @ sK11 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f321,plain,
! [X1: $i] :
( ( $false
= ( sK4 @ sK11 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) ) ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f320]) ).
thf(f322,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK4 @ sK11 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( ra @ sK1 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK4 @ sK11 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f322]) ).
thf(f324,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK4 @ sK11 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rb @ X1 @ Y0 )
| ( sK5 @ Y0 ) )
@ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ra @ X1 @ Y0 )
| ( sK3 @ Y0 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK4 @ sK11 ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 )
| ( sK5 @ X2 ) ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK3 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f324]) ).
thf(f326,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK4 @ sK11 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 )
| ( sK3 @ X3 ) ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK4 @ sK11 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $true
= ( ~ ( rb @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f326]) ).
thf(f328,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK4 @ sK11 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $true
= ( ~ ( ra @ X1 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f327]) ).
thf(f329,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK4 @ sK11 ) )
| ( $true
= ( sK5 @ X2 ) )
| ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X3 ) )
| ( $false
= ( rb @ X1 @ X2 ) )
| ( $false
= ( ra @ X1 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f328]) ).
thf(f330,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK11 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f302]) ).
thf(f331,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK11 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f302]) ).
thf(f332,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK11 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK3 @ Y0 ) )
@ sK12 ) ) ),
inference(sigma_proxy_clausification,[],[f331]) ).
thf(f333,plain,
( ( $false
= ( ~ ( rb @ sK0 @ sK11 )
| ( sK4 @ sK11 ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK12 )
| ( sK3 @ sK12 ) ) ) ),
inference(beta-eta_normalization,[],[f332]) ).
thf(f334,plain,
( ( $false
= ( sK4 @ sK11 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK12 )
| ( sK3 @ sK12 ) ) ) ),
inference(or_proxy_clausification,[],[f333]) ).
thf(f335,plain,
( ( $false
= ( ~ ( rb @ sK0 @ sK11 ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK12 )
| ( sK3 @ sK12 ) ) ) ),
inference(or_proxy_clausification,[],[f333]) ).
thf(f336,plain,
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK12 )
| ( sK3 @ sK12 ) ) ) ),
inference(not_proxy_clausification,[],[f335]) ).
thf(f337,plain,
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $false
= ( sK3 @ sK12 ) ) ),
inference(or_proxy_clausification,[],[f336]) ).
thf(f338,plain,
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK12 ) ) ) ),
inference(or_proxy_clausification,[],[f336]) ).
thf(f339,plain,
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $true
= ( ra @ sK1 @ sK12 ) ) ),
inference(not_proxy_clausification,[],[f338]) ).
thf(f340,plain,
( ( $false
= ( sK4 @ sK11 ) )
| ( $false
= ( sK3 @ sK12 ) ) ),
inference(or_proxy_clausification,[],[f334]) ).
thf(f341,plain,
( ( $false
= ( sK4 @ sK11 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK12 ) ) ) ),
inference(or_proxy_clausification,[],[f334]) ).
thf(f342,plain,
( ( $false
= ( sK4 @ sK11 ) )
| ( $true
= ( ra @ sK1 @ sK12 ) ) ),
inference(not_proxy_clausification,[],[f341]) ).
thf(f343,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rb @ sK0 @ Y0 )
| ( sK4 @ Y0 ) )
@ sK11 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( ra @ sK1 @ Y0 )
| ( sK5 @ Y0 ) )
@ sK13 ) ) ),
inference(sigma_proxy_clausification,[],[f330]) ).
thf(f344,plain,
( ( $false
= ( ~ ( rb @ sK0 @ sK11 )
| ( sK4 @ sK11 ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK13 )
| ( sK5 @ sK13 ) ) ) ),
inference(beta-eta_normalization,[],[f343]) ).
thf(f345,plain,
( ( $false
= ( sK4 @ sK11 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK13 )
| ( sK5 @ sK13 ) ) ) ),
inference(or_proxy_clausification,[],[f344]) ).
thf(f346,plain,
( ( $false
= ( ~ ( rb @ sK0 @ sK11 ) ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK13 )
| ( sK5 @ sK13 ) ) ) ),
inference(or_proxy_clausification,[],[f344]) ).
thf(f347,plain,
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK13 )
| ( sK5 @ sK13 ) ) ) ),
inference(not_proxy_clausification,[],[f346]) ).
thf(f348,plain,
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $false
= ( sK5 @ sK13 ) ) ),
inference(or_proxy_clausification,[],[f347]) ).
thf(f349,plain,
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK13 ) ) ) ),
inference(or_proxy_clausification,[],[f347]) ).
thf(f350,plain,
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ( $true
= ( ra @ sK1 @ sK13 ) ) ),
inference(not_proxy_clausification,[],[f349]) ).
thf(f351,plain,
( ( $false
= ( sK4 @ sK11 ) )
| ( $false
= ( sK5 @ sK13 ) ) ),
inference(or_proxy_clausification,[],[f345]) ).
thf(f352,plain,
( ( $false
= ( sK4 @ sK11 ) )
| ( $false
= ( ~ ( ra @ sK1 @ sK13 ) ) ) ),
inference(or_proxy_clausification,[],[f345]) ).
thf(f353,plain,
( ( $false
= ( sK4 @ sK11 ) )
| ( $true
= ( ra @ sK1 @ sK13 ) ) ),
inference(not_proxy_clausification,[],[f352]) ).
thf(f354,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rb @ Y2 @ Y1 )
& ( rb @ Y2 @ Y0 ) )
=> ( rb @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f355,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rb @ Y2 @ Y1 )
& ( rb @ Y2 @ Y0 ) )
=> ( rb @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f354]) ).
thf(f356,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rb @ Y1 @ Y0 )
& ( rb @ Y1 @ X1 ) )
=> ( rb @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f355]) ).
thf(f357,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rb @ Y1 @ Y0 )
& ( rb @ Y1 @ X1 ) )
=> ( rb @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f356]) ).
thf(f358,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rb @ Y0 @ X2 )
& ( rb @ Y0 @ X1 ) )
=> ( rb @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f357]) ).
thf(f359,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rb @ Y0 @ X2 )
& ( rb @ Y0 @ X1 ) )
=> ( rb @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f358]) ).
thf(f360,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rb @ X3 @ X2 )
& ( rb @ X3 @ X1 ) )
=> ( rb @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f359]) ).
thf(f361,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rb @ X3 @ X2 )
& ( rb @ X3 @ X1 ) ) )
| ( $true
= ( rb @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f360]) ).
thf(f362,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rb @ X3 @ X1 ) )
| ( $true
= ( rb @ X2 @ X1 ) )
| ( $false
= ( rb @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f361]) ).
thf(f363,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ra @ Y2 @ Y1 )
& ( ra @ Y2 @ Y0 ) )
=> ( ra @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f364,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( ra @ Y2 @ Y1 )
& ( ra @ Y2 @ Y0 ) )
=> ( ra @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f363]) ).
thf(f365,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ra @ Y1 @ Y0 )
& ( ra @ Y1 @ X1 ) )
=> ( ra @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f364]) ).
thf(f366,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( ra @ Y1 @ Y0 )
& ( ra @ Y1 @ X1 ) )
=> ( ra @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f365]) ).
thf(f367,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( ra @ Y0 @ X2 )
& ( ra @ Y0 @ X1 ) )
=> ( ra @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f366]) ).
thf(f368,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( ra @ Y0 @ X2 )
& ( ra @ Y0 @ X1 ) )
=> ( ra @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f367]) ).
thf(f369,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( ra @ X3 @ X2 )
& ( ra @ X3 @ X1 ) )
=> ( ra @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f368]) ).
thf(f370,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( ra @ X3 @ X2 )
& ( ra @ X3 @ X1 ) ) )
| ( $true
= ( ra @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f369]) ).
thf(f371,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ra @ X3 @ X1 ) )
| ( $true
= ( ra @ X2 @ X1 ) )
| ( $false
= ( ra @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f370]) ).
thf(f390,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rb @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f391,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rb @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f390]) ).
thf(f392,plain,
! [X1: $i] :
( $true
= ( rb @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f391]) ).
thf(f393,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( ra @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f394,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( ra @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f393]) ).
thf(f395,plain,
! [X1: $i] :
( $true
= ( ra @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f394]) ).
thf(f397,definition,
( spl14_1
<=> ! [X6: $i,X4: $i,X2: $i] :
( ( $true
= ( sK5 @ X4 ) )
| ( $false
= ( ra @ X2 @ X6 ) )
| ( $true
= ( sK3 @ X6 ) )
| ( $false
= ( ra @ sK1 @ X2 ) )
| ( $false
= ( rb @ X2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
thf(f398,plain,
( ! [X2: $i,X6: $i,X4: $i] :
( ( $false
= ( rb @ X2 @ X4 ) )
| ( $false
= ( ra @ X2 @ X6 ) )
| ( $true
= ( sK3 @ X6 ) )
| ( $false
= ( ra @ sK1 @ X2 ) )
| ( $true
= ( sK5 @ X4 ) ) )
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f397]) ).
thf(f400,definition,
( spl14_2
<=> ! [X5: $i,X1: $i,X3: $i] :
( ( $true
= ( sK4 @ X3 ) )
| ( $false
= ( ra @ X1 @ X5 ) )
| ( $true
= ( sK2 @ X5 ) )
| ( $false
= ( rb @ sK0 @ X1 ) )
| ( $false
= ( rb @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
thf(f401,plain,
( ! [X3: $i,X1: $i,X5: $i] :
( ( $false
= ( rb @ sK0 @ X1 ) )
| ( $false
= ( rb @ X1 @ X3 ) )
| ( $false
= ( ra @ X1 @ X5 ) )
| ( $true
= ( sK2 @ X5 ) )
| ( $true
= ( sK4 @ X3 ) ) )
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f400]) ).
thf(f402,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f199,f400,f397]) ).
thf(f404,definition,
( spl14_3
<=> ( $true
= ( ra @ sK1 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
thf(f406,plain,
( ( $true
= ( ra @ sK1 @ sK6 ) )
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f404]) ).
thf(f407,plain,
( spl14_3
| spl14_2 ),
inference(avatar_split_clause,[],[f216,f400,f404]) ).
thf(f409,definition,
( spl14_4
<=> ( $false
= ( sK3 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
thf(f411,plain,
( ( $false
= ( sK3 @ sK6 ) )
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f409]) ).
thf(f412,plain,
( spl14_4
| spl14_2 ),
inference(avatar_split_clause,[],[f223,f400,f409]) ).
thf(f414,definition,
( spl14_5
<=> ( $true
= ( ra @ sK1 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
thf(f416,plain,
( ( $true
= ( ra @ sK1 @ sK7 ) )
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f414]) ).
thf(f417,plain,
( spl14_5
| spl14_2 ),
inference(avatar_split_clause,[],[f238,f400,f414]) ).
thf(f419,definition,
( spl14_6
<=> ( $false
= ( sK5 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
thf(f421,plain,
( ( $false
= ( sK5 @ sK7 ) )
| ~ spl14_6 ),
inference(avatar_component_clause,[],[f419]) ).
thf(f422,plain,
( spl14_6
| spl14_2 ),
inference(avatar_split_clause,[],[f245,f400,f419]) ).
thf(f424,definition,
( spl14_7
<=> ( $true
= ( rb @ sK0 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_7])],[avatar_definition]) ).
thf(f426,plain,
( ( $true
= ( rb @ sK0 @ sK8 ) )
| ~ spl14_7 ),
inference(avatar_component_clause,[],[f424]) ).
thf(f427,plain,
( spl14_1
| spl14_7 ),
inference(avatar_split_clause,[],[f266,f424,f397]) ).
thf(f429,definition,
( spl14_8
<=> ( $false
= ( sK2 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_8])],[avatar_definition]) ).
thf(f431,plain,
( ( $false
= ( sK2 @ sK8 ) )
| ~ spl14_8 ),
inference(avatar_component_clause,[],[f429]) ).
thf(f432,plain,
( spl14_1
| spl14_8 ),
inference(avatar_split_clause,[],[f276,f429,f397]) ).
thf(f434,definition,
( spl14_9
<=> ( $true
= ( ra @ sK1 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_9])],[avatar_definition]) ).
thf(f436,plain,
( ( $true
= ( ra @ sK1 @ sK9 ) )
| ~ spl14_9 ),
inference(avatar_component_clause,[],[f434]) ).
thf(f437,plain,
( spl14_9
| spl14_7 ),
inference(avatar_split_clause,[],[f286,f424,f434]) ).
thf(f439,definition,
( spl14_10
<=> ( $false
= ( sK3 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_10])],[avatar_definition]) ).
thf(f441,plain,
( ( $false
= ( sK3 @ sK9 ) )
| ~ spl14_10 ),
inference(avatar_component_clause,[],[f439]) ).
thf(f442,plain,
( spl14_10
| spl14_7 ),
inference(avatar_split_clause,[],[f284,f424,f439]) ).
thf(f443,plain,
( spl14_9
| spl14_8 ),
inference(avatar_split_clause,[],[f289,f429,f434]) ).
thf(f444,plain,
( spl14_10
| spl14_8 ),
inference(avatar_split_clause,[],[f287,f429,f439]) ).
thf(f446,definition,
( spl14_11
<=> ( $true
= ( ra @ sK1 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition]) ).
thf(f448,plain,
( ( $true
= ( ra @ sK1 @ sK10 ) )
| ~ spl14_11 ),
inference(avatar_component_clause,[],[f446]) ).
thf(f449,plain,
( spl14_11
| spl14_7 ),
inference(avatar_split_clause,[],[f297,f424,f446]) ).
thf(f451,definition,
( spl14_12
<=> ( $false
= ( sK5 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_12])],[avatar_definition]) ).
thf(f453,plain,
( ( $false
= ( sK5 @ sK10 ) )
| ~ spl14_12 ),
inference(avatar_component_clause,[],[f451]) ).
thf(f454,plain,
( spl14_12
| spl14_7 ),
inference(avatar_split_clause,[],[f295,f424,f451]) ).
thf(f455,plain,
( spl14_11
| spl14_8 ),
inference(avatar_split_clause,[],[f300,f429,f446]) ).
thf(f456,plain,
( spl14_12
| spl14_8 ),
inference(avatar_split_clause,[],[f298,f429,f451]) ).
thf(f458,definition,
( spl14_13
<=> ( $true
= ( rb @ sK0 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_13])],[avatar_definition]) ).
thf(f460,plain,
( ( $true
= ( rb @ sK0 @ sK11 ) )
| ~ spl14_13 ),
inference(avatar_component_clause,[],[f458]) ).
thf(f461,plain,
( spl14_1
| spl14_13 ),
inference(avatar_split_clause,[],[f319,f458,f397]) ).
thf(f463,definition,
( spl14_14
<=> ( $false
= ( sK4 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_14])],[avatar_definition]) ).
thf(f465,plain,
( ( $false
= ( sK4 @ sK11 ) )
| ~ spl14_14 ),
inference(avatar_component_clause,[],[f463]) ).
thf(f466,plain,
( spl14_1
| spl14_14 ),
inference(avatar_split_clause,[],[f329,f463,f397]) ).
thf(f468,definition,
( spl14_15
<=> ( $true
= ( ra @ sK1 @ sK12 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
thf(f470,plain,
( ( $true
= ( ra @ sK1 @ sK12 ) )
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f468]) ).
thf(f471,plain,
( spl14_15
| spl14_13 ),
inference(avatar_split_clause,[],[f339,f458,f468]) ).
thf(f473,definition,
( spl14_16
<=> ( $false
= ( sK3 @ sK12 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition]) ).
thf(f475,plain,
( ( $false
= ( sK3 @ sK12 ) )
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f473]) ).
thf(f476,plain,
( spl14_16
| spl14_13 ),
inference(avatar_split_clause,[],[f337,f458,f473]) ).
thf(f477,plain,
( spl14_15
| spl14_14 ),
inference(avatar_split_clause,[],[f342,f463,f468]) ).
thf(f478,plain,
( spl14_16
| spl14_14 ),
inference(avatar_split_clause,[],[f340,f463,f473]) ).
thf(f480,definition,
( spl14_17
<=> ( $true
= ( ra @ sK1 @ sK13 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_17])],[avatar_definition]) ).
thf(f482,plain,
( ( $true
= ( ra @ sK1 @ sK13 ) )
| ~ spl14_17 ),
inference(avatar_component_clause,[],[f480]) ).
thf(f483,plain,
( spl14_17
| spl14_13 ),
inference(avatar_split_clause,[],[f350,f458,f480]) ).
thf(f485,definition,
( spl14_18
<=> ( $false
= ( sK5 @ sK13 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition]) ).
thf(f487,plain,
( ( $false
= ( sK5 @ sK13 ) )
| ~ spl14_18 ),
inference(avatar_component_clause,[],[f485]) ).
thf(f488,plain,
( spl14_18
| spl14_13 ),
inference(avatar_split_clause,[],[f348,f458,f485]) ).
thf(f489,plain,
( spl14_17
| spl14_14 ),
inference(avatar_split_clause,[],[f353,f463,f480]) ).
thf(f490,plain,
( spl14_18
| spl14_14 ),
inference(avatar_split_clause,[],[f351,f463,f485]) ).
thf(f596,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( ra @ X0 @ X1 ) )
| ( $true
= ( sK3 @ X1 ) )
| ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK5 @ X0 ) ) )
| ~ spl14_1 ),
inference(constrained_superposition,[],[f392,f398]) ).
thf(f608,definition,
( spl14_25
<=> ! [X0: $i] :
( ( $false
= ( rb @ sK0 @ X0 ) )
| ( $true
= ( sK4 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_25])],[avatar_definition]) ).
thf(f609,plain,
( ! [X0: $i] :
( ( $false
= ( rb @ sK0 @ X0 ) )
| ( $true
= ( sK4 @ X0 ) ) )
| ~ spl14_25 ),
inference(avatar_component_clause,[],[f608]) ).
thf(f719,definition,
( spl14_30
<=> ! [X0: $i] :
( ( $false
= ( ra @ sK8 @ X0 ) )
| ( $true
= ( sK2 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_30])],[avatar_definition]) ).
thf(f720,plain,
( ! [X0: $i] :
( ( $false
= ( ra @ sK8 @ X0 ) )
| ( $true
= ( sK2 @ X0 ) ) )
| ~ spl14_30 ),
inference(avatar_component_clause,[],[f719]) ).
thf(f815,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rb @ sK0 @ X0 ) )
| ( $false
= ( ra @ X0 @ X2 ) )
| ( $true
= ( sK2 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $false
= ( rb @ X3 @ X1 ) )
| ( $false
= ( rb @ X3 @ X0 ) ) )
| ~ spl14_2 ),
inference(constrained_superposition,[],[f401,f362]) ).
thf(f825,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( rb @ sK0 @ X0 ) )
| ( $false
= ( rb @ X3 @ X1 ) )
| ( $false
= ( rb @ X3 @ X0 ) )
| ( $false
= ( ra @ X0 @ X2 ) )
| ( $true
= ( sK4 @ X1 ) )
| ( $true
= ( sK2 @ X2 ) ) )
| ~ spl14_2 ),
inference(trivial_inequality_removal,[],[f815]) ).
thf(f906,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $true = $false )
| ( $false
= ( rb @ sK0 @ X0 ) )
| ( $false
= ( ra @ sK8 @ X1 ) )
| ( $true
= ( sK4 @ X0 ) )
| ( $true
= ( sK2 @ X1 ) ) )
| ~ spl14_2
| ~ spl14_7 ),
inference(constrained_superposition,[],[f825,f426]) ).
thf(f962,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rb @ sK0 @ X0 ) )
| ( $false
= ( ra @ sK8 @ X1 ) )
| ( $true
= ( sK4 @ X0 ) )
| ( $true
= ( sK2 @ X1 ) ) )
| ~ spl14_2
| ~ spl14_7 ),
inference(duplicate_literal_removal,[],[f906]) ).
thf(f963,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rb @ sK0 @ X0 ) )
| ( $false
= ( ra @ sK8 @ X1 ) )
| ( $true
= ( sK4 @ X0 ) )
| ( $true
= ( sK2 @ X1 ) ) )
| ~ spl14_2
| ~ spl14_7 ),
inference(trivial_inequality_removal,[],[f962]) ).
thf(f991,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( ra @ sK1 @ X0 ) )
| ( $false
= ( ra @ X0 @ X1 ) )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( sK5 @ X0 ) ) )
| ~ spl14_1 ),
inference(trivial_inequality_removal,[],[f596]) ).
thf(f1394,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK3 @ X1 ) )
| ( $true
= ( sK5 @ X0 ) )
| ( $false
= ( ra @ X2 @ X1 ) )
| ( $false
= ( ra @ X2 @ X0 ) ) )
| ~ spl14_1 ),
inference(constrained_superposition,[],[f991,f371]) ).
thf(f1408,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( ra @ sK1 @ X0 ) )
| ( $false
= ( ra @ X2 @ X1 ) )
| ( $false
= ( ra @ X2 @ X0 ) )
| ( $true
= ( sK5 @ X0 ) )
| ( $true
= ( sK3 @ X1 ) ) )
| ~ spl14_1 ),
inference(trivial_inequality_removal,[],[f1394]) ).
thf(f1566,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true = $false )
| ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK5 @ sK7 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_5 ),
inference(constrained_superposition,[],[f1408,f416]) ).
thf(f1569,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true = $false )
| ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK5 @ sK13 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_17 ),
inference(constrained_superposition,[],[f1408,f482]) ).
thf(f1623,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK5 @ sK13 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_17 ),
inference(duplicate_literal_removal,[],[f1569]) ).
thf(f1624,plain,
( ! [X0: $i] :
( ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK5 @ sK13 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f1623]) ).
thf(f1629,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK5 @ sK7 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_5 ),
inference(duplicate_literal_removal,[],[f1566]) ).
thf(f1630,plain,
( ! [X0: $i] :
( ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK5 @ sK7 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_5 ),
inference(trivial_inequality_removal,[],[f1629]) ).
thf(f1657,definition,
( spl14_42
<=> ! [X1: $i] :
( ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_42])],[avatar_definition]) ).
thf(f1658,plain,
( ! [X1: $i] :
( ( $false
= ( ra @ sK1 @ X1 ) )
| ( $true
= ( sK3 @ X1 ) ) )
| ~ spl14_42 ),
inference(avatar_component_clause,[],[f1657]) ).
thf(f1674,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_17
| ~ spl14_18 ),
inference(forward_demodulation,[],[f1624,f487]) ).
thf(f1675,plain,
( ! [X0: $i] :
( ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_17
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f1674]) ).
thf(f1676,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_5
| ~ spl14_6 ),
inference(forward_demodulation,[],[f1630,f421]) ).
thf(f1677,plain,
( ! [X0: $i] :
( ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_5
| ~ spl14_6 ),
inference(trivial_inequality_removal,[],[f1676]) ).
thf(f1691,plain,
( spl14_42
| ~ spl14_1
| ~ spl14_17
| ~ spl14_18 ),
inference(avatar_split_clause,[],[f1675,f485,f480,f397,f1657]) ).
thf(f1692,plain,
( spl14_42
| ~ spl14_1
| ~ spl14_5
| ~ spl14_6 ),
inference(avatar_split_clause,[],[f1677,f419,f414,f397,f1657]) ).
thf(f2257,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK6 ) )
| ~ spl14_3
| ~ spl14_42 ),
inference(constrained_superposition,[],[f1658,f406]) ).
thf(f2259,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK9 ) )
| ~ spl14_9
| ~ spl14_42 ),
inference(constrained_superposition,[],[f1658,f436]) ).
thf(f2260,plain,
( ( $true = $false )
| ( $true
= ( sK3 @ sK12 ) )
| ~ spl14_15
| ~ spl14_42 ),
inference(constrained_superposition,[],[f1658,f470]) ).
thf(f2280,plain,
( ( $true
= ( sK3 @ sK12 ) )
| ~ spl14_15
| ~ spl14_42 ),
inference(trivial_inequality_removal,[],[f2260]) ).
thf(f2281,plain,
( ( $true
= ( sK3 @ sK9 ) )
| ~ spl14_9
| ~ spl14_42 ),
inference(trivial_inequality_removal,[],[f2259]) ).
thf(f2283,plain,
( ( $true
= ( sK3 @ sK6 ) )
| ~ spl14_3
| ~ spl14_42 ),
inference(trivial_inequality_removal,[],[f2257]) ).
thf(f2295,plain,
( ( $true = $false )
| ~ spl14_15
| ~ spl14_16
| ~ spl14_42 ),
inference(forward_demodulation,[],[f2280,f475]) ).
thf(f2296,plain,
( $false
| ~ spl14_15
| ~ spl14_16
| ~ spl14_42 ),
inference(trivial_inequality_removal,[],[f2295]) ).
thf(f2297,plain,
( ~ spl14_15
| ~ spl14_16
| ~ spl14_42 ),
inference(avatar_contradiction_clause,[],[f2296]) ).
thf(f2298,plain,
( ( $true = $false )
| ~ spl14_9
| ~ spl14_10
| ~ spl14_42 ),
inference(forward_demodulation,[],[f2281,f441]) ).
thf(f2299,plain,
( $false
| ~ spl14_9
| ~ spl14_10
| ~ spl14_42 ),
inference(trivial_inequality_removal,[],[f2298]) ).
thf(f2300,plain,
( ~ spl14_9
| ~ spl14_10
| ~ spl14_42 ),
inference(avatar_contradiction_clause,[],[f2299]) ).
thf(f2301,plain,
( ( $true = $false )
| ~ spl14_3
| ~ spl14_4
| ~ spl14_42 ),
inference(forward_demodulation,[],[f2283,f411]) ).
thf(f2302,plain,
( $false
| ~ spl14_3
| ~ spl14_4
| ~ spl14_42 ),
inference(trivial_inequality_removal,[],[f2301]) ).
thf(f2303,plain,
( ~ spl14_3
| ~ spl14_4
| ~ spl14_42 ),
inference(avatar_contradiction_clause,[],[f2302]) ).
thf(f3121,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true = $false )
| ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK5 @ sK10 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_11 ),
inference(constrained_superposition,[],[f1408,f448]) ).
thf(f3127,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK5 @ sK10 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_11 ),
inference(duplicate_literal_removal,[],[f3121]) ).
thf(f3128,plain,
( ! [X0: $i] :
( ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK5 @ sK10 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_11 ),
inference(trivial_inequality_removal,[],[f3127]) ).
thf(f3144,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_11
| ~ spl14_12 ),
inference(forward_demodulation,[],[f3128,f453]) ).
thf(f3145,plain,
( ! [X0: $i] :
( ( $false
= ( ra @ sK1 @ X0 ) )
| ( $true
= ( sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_11
| ~ spl14_12 ),
inference(trivial_inequality_removal,[],[f3144]) ).
thf(f3150,plain,
( spl14_42
| ~ spl14_1
| ~ spl14_11
| ~ spl14_12 ),
inference(avatar_split_clause,[],[f3145,f451,f446,f397,f1657]) ).
thf(f3185,plain,
( spl14_30
| spl14_25
| ~ spl14_2
| ~ spl14_7 ),
inference(avatar_split_clause,[],[f963,f424,f400,f608,f719]) ).
thf(f3191,plain,
( ( $true = $false )
| ( $true
= ( sK4 @ sK11 ) )
| ~ spl14_13
| ~ spl14_25 ),
inference(constrained_superposition,[],[f609,f460]) ).
thf(f3204,plain,
( ( $true
= ( sK4 @ sK11 ) )
| ~ spl14_13
| ~ spl14_25 ),
inference(trivial_inequality_removal,[],[f3191]) ).
thf(f3212,plain,
( ( $true = $false )
| ~ spl14_13
| ~ spl14_14
| ~ spl14_25 ),
inference(forward_demodulation,[],[f3204,f465]) ).
thf(f3213,plain,
( $false
| ~ spl14_13
| ~ spl14_14
| ~ spl14_25 ),
inference(trivial_inequality_removal,[],[f3212]) ).
thf(f3214,plain,
( ~ spl14_13
| ~ spl14_14
| ~ spl14_25 ),
inference(avatar_contradiction_clause,[],[f3213]) ).
thf(f3968,plain,
( ( $true = $false )
| ( $true
= ( sK2 @ sK8 ) )
| ~ spl14_30 ),
inference(constrained_superposition,[],[f720,f395]) ).
thf(f3981,plain,
( ( $true
= ( sK2 @ sK8 ) )
| ~ spl14_30 ),
inference(trivial_inequality_removal,[],[f3968]) ).
thf(f3985,plain,
( ( $true = $false )
| ~ spl14_8
| ~ spl14_30 ),
inference(forward_demodulation,[],[f3981,f431]) ).
thf(f3986,plain,
( $false
| ~ spl14_8
| ~ spl14_30 ),
inference(trivial_inequality_removal,[],[f3985]) ).
thf(f3987,plain,
( ~ spl14_8
| ~ spl14_30 ),
inference(avatar_contradiction_clause,[],[f3986]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f402]) ).
cnf(s2,plain,
( spl14_2
| spl14_3 ),
inference(sat_conversion,[],[f407]) ).
cnf(s3,plain,
( spl14_2
| spl14_4 ),
inference(sat_conversion,[],[f412]) ).
cnf(s4,plain,
( spl14_2
| spl14_5 ),
inference(sat_conversion,[],[f417]) ).
cnf(s5,plain,
( spl14_2
| spl14_6 ),
inference(sat_conversion,[],[f422]) ).
cnf(s6,plain,
( spl14_1
| spl14_7 ),
inference(sat_conversion,[],[f427]) ).
cnf(s7,plain,
( spl14_1
| spl14_8 ),
inference(sat_conversion,[],[f432]) ).
cnf(s8,plain,
( spl14_7
| spl14_9 ),
inference(sat_conversion,[],[f437]) ).
cnf(s9,plain,
( spl14_7
| spl14_10 ),
inference(sat_conversion,[],[f442]) ).
cnf(s10,plain,
( spl14_8
| spl14_9 ),
inference(sat_conversion,[],[f443]) ).
cnf(s11,plain,
( spl14_8
| spl14_10 ),
inference(sat_conversion,[],[f444]) ).
cnf(s12,plain,
( spl14_7
| spl14_11 ),
inference(sat_conversion,[],[f449]) ).
cnf(s13,plain,
( spl14_7
| spl14_12 ),
inference(sat_conversion,[],[f454]) ).
cnf(s14,plain,
( spl14_8
| spl14_11 ),
inference(sat_conversion,[],[f455]) ).
cnf(s15,plain,
( spl14_8
| spl14_12 ),
inference(sat_conversion,[],[f456]) ).
cnf(s16,plain,
( spl14_1
| spl14_13 ),
inference(sat_conversion,[],[f461]) ).
cnf(s17,plain,
( spl14_1
| spl14_14 ),
inference(sat_conversion,[],[f466]) ).
cnf(s18,plain,
( spl14_13
| spl14_15 ),
inference(sat_conversion,[],[f471]) ).
cnf(s19,plain,
( spl14_13
| spl14_16 ),
inference(sat_conversion,[],[f476]) ).
cnf(s20,plain,
( spl14_14
| spl14_15 ),
inference(sat_conversion,[],[f477]) ).
cnf(s21,plain,
( spl14_14
| spl14_16 ),
inference(sat_conversion,[],[f478]) ).
cnf(s22,plain,
( spl14_13
| spl14_17 ),
inference(sat_conversion,[],[f483]) ).
cnf(s23,plain,
( spl14_13
| spl14_18 ),
inference(sat_conversion,[],[f488]) ).
cnf(s24,plain,
( spl14_14
| spl14_17 ),
inference(sat_conversion,[],[f489]) ).
cnf(s25,plain,
( spl14_14
| spl14_18 ),
inference(sat_conversion,[],[f490]) ).
cnf(s98,plain,
( ~ spl14_1
| ~ spl14_17
| ~ spl14_18
| spl14_42 ),
inference(sat_conversion,[],[f1691]) ).
cnf(s99,plain,
( ~ spl14_1
| ~ spl14_5
| ~ spl14_6
| spl14_42 ),
inference(sat_conversion,[],[f1692]) ).
cnf(s114,plain,
( ~ spl14_15
| ~ spl14_16
| ~ spl14_42 ),
inference(sat_conversion,[],[f2297]) ).
cnf(s115,plain,
( ~ spl14_9
| ~ spl14_10
| ~ spl14_42 ),
inference(sat_conversion,[],[f2300]) ).
cnf(s116,plain,
( ~ spl14_3
| ~ spl14_4
| ~ spl14_42 ),
inference(sat_conversion,[],[f2303]) ).
cnf(s125,plain,
( ~ spl14_1
| ~ spl14_11
| ~ spl14_12
| spl14_42 ),
inference(sat_conversion,[],[f3150]) ).
cnf(s129,plain,
( ~ spl14_2
| ~ spl14_7
| spl14_25
| spl14_30 ),
inference(sat_conversion,[],[f3185]) ).
cnf(s132,plain,
( ~ spl14_13
| ~ spl14_14
| ~ spl14_25 ),
inference(sat_conversion,[],[f3214]) ).
cnf(s134,plain,
( ~ spl14_8
| ~ spl14_30 ),
inference(sat_conversion,[],[f3987]) ).
cnf(s135,plain,
spl14_1,
inference(rat,[],[s129,s134,s132,s1,s6,s7,s16,s17]) ).
cnf(s136,plain,
spl14_14,
inference(rat,[],[s114,s98,s20,s21,s24,s25,s135]) ).
cnf(s137,plain,
spl14_13,
inference(rat,[],[s114,s98,s18,s19,s22,s23,s135]) ).
cnf(s138,plain,
~ spl14_25,
inference(rat,[],[s132,s136,s137]) ).
cnf(s139,plain,
spl14_8,
inference(rat,[],[s115,s125,s10,s11,s14,s15,s135]) ).
cnf(s140,plain,
~ spl14_30,
inference(rat,[],[s134,s139]) ).
cnf(s141,plain,
spl14_7,
inference(rat,[],[s115,s125,s8,s9,s12,s13,s135]) ).
cnf(s142,plain,
~ spl14_2,
inference(rat,[],[s129,s138,s140,s141]) ).
cnf(s143,plain,
spl14_6,
inference(rat,[],[s5,s142]) ).
cnf(s144,plain,
spl14_5,
inference(rat,[],[s4,s142]) ).
cnf(s145,plain,
spl14_4,
inference(rat,[],[s3,s142]) ).
cnf(s146,plain,
spl14_3,
inference(rat,[],[s2,s142]) ).
cnf(s147,plain,
spl14_42,
inference(rat,[],[s99,s143,s135,s144]) ).
cnf(s148,plain,
$false,
inference(rat,[],[s116,s147,s146,s145]) ).
thf(f3988,plain,
$false,
inference(avatar_sat_refutation,[],[s148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL873^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n020.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 10:19:49 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 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
% 3.60/0.86 % (876789)Will run a generic schedule for satisfiability detection.
% 3.60/0.86 % (876798)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3289574441:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.60/0.86 % (876798)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.60/0.86 % (876795)% WARNING: option uhcvi not known.
% 3.60/0.86 % (876796)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=245276086:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.60/0.86 % (876794)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=987247805_2999 on theBenchmark for (2999ds/0Mi)
% 3.60/0.86 % (876795)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=866224123:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.60/0.86 % (876797)dis+10_1_sil=32000:sp=arity:random_seed=1766065669:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.60/0.86 % (876795)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.60/0.86 % Exception at run slice level
% 3.60/0.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.60/0.87 % (876795)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.60/0.87 % (876799)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4194112570:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.60/0.87 % (876800)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=807468983:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.60/0.87 % (876798)Instruction limit reached!
% 3.60/0.87 % (876798)------------------------------
% 3.60/0.87 % (876798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.60/0.87 % (876798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/0.87 % (876798)CaDiCaL version: 2.1.3
% 3.60/0.87 % (876798)Termination reason: Instruction limit
% 3.60/0.87 % (876798)Termination phase: Saturation
% 3.60/0.87 % (876798)Time elapsed: 0.029 s
% 3.60/0.87 % (876798)Peak memory usage: 12 MB
% 3.60/0.87 % (876798)Instructions burned: 120 (million)
% 3.60/0.87 % (876806)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2407157015:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.60/0.87 % Exception at run slice level
% 3.60/0.87 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.60/0.87 % (876809)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3237385117:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.60/0.87 % (876811)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=2707078819:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.60/0.87 % (876811)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.60/0.87 % (876811)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.60/0.87 % (876797)Instruction limit reached!
% 3.60/0.87 % (876797)------------------------------
% 3.60/0.87 % (876797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.60/0.87 % (876797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/0.87 % (876797)CaDiCaL version: 2.1.3
% 3.60/0.87 % (876797)Termination reason: Instruction limit
% 3.60/0.87 % (876797)Termination phase: Saturation
% 3.60/0.87 % (876797)Time elapsed: 0.059 s
% 3.60/0.87 % (876797)Peak memory usage: 12 MB
% 3.60/0.87 % (876797)Instructions burned: 104 (million)
% 3.60/0.87 % (876809)Instruction limit reached!
% 3.60/0.87 % (876809)------------------------------
% 3.60/0.87 % (876809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.60/0.87 % (876809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/0.87 % (876809)CaDiCaL version: 2.1.3
% 3.60/0.87 % (876809)Termination reason: Instruction limit
% 3.60/0.87 % (876809)Termination phase: Saturation
% 3.60/0.87 % (876809)Time elapsed: 0.032 s
% 3.60/0.87 % (876809)Peak memory usage: 12 MB
% 3.60/0.87 % (876809)Instructions burned: 136 (million)
% 3.60/0.87 % (876799)Instruction limit reached!
% 3.60/0.87 % (876799)------------------------------
% 3.60/0.87 % (876799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.60/0.87 % (876799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/0.94 % (876799)CaDiCaL version: 2.1.3
% 3.96/0.94 % (876799)Termination reason: Instruction limit
% 3.96/0.94 % (876799)Termination phase: Saturation
% 3.96/0.94 % (876799)Time elapsed: 0.067 s
% 3.96/0.94 % (876799)Peak memory usage: 12 MB
% 3.96/0.94 % (876799)Instructions burned: 131 (million)
% 3.96/0.94 % (876815)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3595461674:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.96/0.94 % (876814)ott-21_1_sil=16000:fs=off:random_seed=1810331476:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.96/0.94 % (876800)Instruction limit reached!
% 3.96/0.94 % (876800)------------------------------
% 3.96/0.94 % (876800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.96/0.94 % (876800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/0.94 % (876800)CaDiCaL version: 2.1.3
% 3.96/0.94 % (876800)Termination reason: Instruction limit
% 3.96/0.94 % (876800)Termination phase: Saturation
% 3.96/0.94 % (876800)Time elapsed: 0.078 s
% 3.96/0.94 % (876800)Peak memory usage: 12 MB
% 3.96/0.94 % (876800)Instructions burned: 161 (million)
% 3.96/0.94 % (876819)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1995874616:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.96/0.94 % (876816)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3770275687:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.96/0.94 % Exception at run slice level
% 3.96/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.96/0.94 % (876822)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=537461792:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.96/0.94 % Exception at run slice level
% 3.96/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.96/0.94 % (876814)Instruction limit reached!
% 3.96/0.94 % (876814)------------------------------
% 3.96/0.94 % (876814)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.96/0.94 % (876814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/0.94 % (876814)CaDiCaL version: 2.1.3
% 3.96/0.94 % (876814)Termination reason: Instruction limit
% 3.96/0.94 % (876814)Termination phase: Saturation
% 3.96/0.94 % (876814)Time elapsed: 0.078 s
% 3.96/0.94 % (876814)Peak memory usage: 12 MB
% 3.96/0.94 % (876814)Instructions burned: 183 (million)
% 3.96/0.94 % (876824)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2446420993:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 3.96/0.94 % (876824)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.96/0.94 % (876825)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=233103938:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 3.96/0.94 % (876825)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.96/0.94 % (876815)Instruction limit reached!
% 3.96/0.94 % (876815)------------------------------
% 3.96/0.94 % (876815)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.96/0.94 % (876815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/0.94 % (876815)CaDiCaL version: 2.1.3
% 3.96/0.94 % (876815)Termination reason: Instruction limit
% 3.96/0.94 % (876815)Termination phase: Saturation
% 3.96/0.94 % (876815)Time elapsed: 0.114 s
% 3.96/0.94 % (876815)Peak memory usage: 13 MB
% 3.96/0.94 % (876815)Instructions burned: 478 (million)
% 3.96/0.94 % (876828)fmb+10_1_sil=64000:random_seed=3857469193:i=22061:nm=2:gsp=on_2997 on theBenchmark for (2997ds/22061Mi)
% 3.96/0.94 % (876828)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.96/0.94 % Exception at run slice level
% 3.96/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.96/0.94 % (876830)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=2576794953:i=9515:nm=5_2997 on theBenchmark for (2997ds/9515Mi)
% 3.96/0.94 % Exception at run slice level
% 3.96/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.96/0.94 % (876832)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=3858017504:fmbsr=1.7:i=920_2997 on theBenchmark for (2997ds/920Mi)
% 3.96/0.94 % Exception at run slice level
% 3.96/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.96/0.94 % (876834)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=91868283:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 3.96/0.94 % (876834)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.96/0.94 % (876811)Instruction limit reached!
% 3.96/0.94 % (876811)------------------------------
% 3.96/0.94 % (876811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.96/0.94 % (876811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/0.94 % (876811)CaDiCaL version: 2.1.3
% 3.96/0.94 % (876811)Termination reason: Instruction limit
% 3.96/0.94 % (876811)Termination phase: Saturation
% 3.96/0.94 % (876811)Time elapsed: 0.305 s
% 3.96/0.94 % (876811)Peak memory usage: 15 MB
% 3.96/0.94 % (876811)Instructions burned: 686 (million)
% 3.96/0.94 % (876836)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=3250370027:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 3.96/0.94 % (876836)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.96/0.94 % (876836)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.96/0.94 % (876819)Instruction limit reached!
% 3.96/0.94 % (876819)------------------------------
% 3.96/0.94 % (876819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.96/0.94 % (876819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/0.94 % (876819)CaDiCaL version: 2.1.3
% 3.96/0.94 % (876819)Termination reason: Instruction limit
% 3.96/0.94 % (876819)Termination phase: Saturation
% 3.96/0.94 % (876819)Time elapsed: 0.308 s
% 3.96/0.94 % (876819)Peak memory usage: 13 MB
% 3.96/0.94 % (876819)Instructions burned: 1179 (million)
% 3.96/0.94 % (876838)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3654725627:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 3.96/0.94 % Exception at run slice level
% 3.96/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.96/0.94 % (876824)Instruction limit reached!
% 3.96/0.94 % (876824)------------------------------
% 3.96/0.94 % (876824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.96/0.94 % (876824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/0.94 % (876824)CaDiCaL version: 2.1.3
% 3.96/0.94 % (876824)Termination reason: Instruction limit
% 3.96/0.94 % (876824)Termination phase: Saturation
% 3.96/0.94 % (876824)Time elapsed: 0.291 s
% 3.96/0.94 % (876824)Peak memory usage: 14 MB
% 3.96/0.94 % (876824)Instructions burned: 693 (million)
% 3.96/0.94 % (876840)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=3417408974:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 3.96/0.94 % Exception at run slice level
% 3.96/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.96/0.94 % (876841)ott-2_1_sil=16000:newcnf=on:random_seed=1784312757:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2995 on theBenchmark for (2995ds/869Mi)
% 3.96/0.94 % (876841)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.96/0.94 % (876843)ott+10_1_sil=32000:tgt=ground:random_seed=1178352387:i=5114:av=off_2994 on theBenchmark for (2994ds/5114Mi)
% 3.96/0.94 % (876825)Instruction limit reached!
% 3.96/0.94 % (876825)------------------------------
% 3.96/0.94 % (876825)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.96/0.94 % (876825)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/0.94 % (876825)CaDiCaL version: 2.1.3
% 3.96/0.94 % (876825)Termination reason: Instruction limit
% 3.96/0.94 % (876825)Termination phase: Saturation
% 3.96/0.94 % (876825)Time elapsed: 0.376 s
% 3.96/0.94 % (876825)Peak memory usage: 14 MB
% 3.96/0.94 % (876825)Instructions burned: 880 (million)
% 3.96/0.94 % (876846)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1449834128:i=54282_2994 on theBenchmark for (2994ds/54282Mi)
% 3.96/0.94 % Exception at run slice level
% 3.96/0.94 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.96/0.94 % (876848)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=3840932144:i=3512:aac=none_2993 on theBenchmark for (2993ds/3512Mi)
% 3.96/0.94 % (876848)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.96/0.94 % (876841) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-876789-876841"...
% 3.96/0.94 % (876841)...printing done.
% 3.96/0.94 % (876841)Refutation found. Thanks to Tanya!
% 3.96/0.94 % SZS status Theorem for theBenchmark
% 3.96/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 3.96/0.95 % (876841)------------------------------
% 3.96/0.95 % (876841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.96/0.95 % (876841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/0.95 % (876841)CaDiCaL version: 2.1.3
% 3.96/0.95 % (876841)Termination reason: Refutation
% 3.96/0.95 % (876841)Time elapsed: 0.192 s
% 3.96/0.95 % (876841)Peak memory usage: 14 MB
% 3.96/0.95 % (876841)Instructions burned: 432 (million)
% 3.96/0.95 % (876789)Success in time 0.711 s
% 3.96/0.95 % Vampire exiting
%------------------------------------------------------------------------------