%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL602^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:14:26 AM UTC 2026
% Result : Theorem 1.56s 0.55s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 37
% Syntax : Number of formulae : 372 ( 34 unt; 0 typ; 29 def)
% Number of atoms : 4234 ( 783 equ; 0 cnn)
% Maximal formula atoms : 10 ( 11 avg)
% Number of connectives : 4544 ( 372 ~; 959 |; 106 &;2641 @)
% ( 33 <=>; 226 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 185 ( 185 >; 0 *; 0 +; 0 <<)
% Number of symbols : 109 ( 105 usr; 48 con; 0-4 aty)
% ( 206 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 715 ( 0 sgn 320 !; 7 ?; 715 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_21,type,
pair_rel: $i > $i > $i > $i > $o ).
thf(func_def_22,type,
id_rel: ( $i > $o ) > $i > $i > $o ).
thf(func_def_23,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_25,type,
restrict_rel_domain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
rel_diagonal: $i > $i > $o ).
thf(func_def_27,type,
rel_composition: ( $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_28,type,
reflexive: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
irreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
symmetric: ( $i > $i > $o ) > $o ).
thf(func_def_31,type,
transitive: ( $i > $i > $o ) > $o ).
thf(func_def_32,type,
equiv_rel: ( $i > $i > $o ) > $o ).
thf(func_def_33,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_34,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_35,type,
rel_inverse: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_36,type,
equiv_classes: ( $i > $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_37,type,
restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_38,type,
rel_field: ( $i > $i > $o ) > $i > $o ).
thf(func_def_39,type,
well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_40,type,
upwards_well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vIMP: $o > $o > $o ).
thf(func_def_43,type,
vAND: $o > $o > $o ).
thf(func_def_44,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_49,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
vNOT: $o > $o ).
thf(func_def_53,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_54,type,
vIFF: $o > $o > $o ).
thf(func_def_55,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_57,type,
sK0: $i > $i > $o ).
thf(func_def_58,type,
sK1: $i > $o ).
thf(func_def_59,type,
sK2: ( $i > $o ) > $i > $i ).
thf(func_def_60,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_77,type,
sK20: ( $i > $o ) > $i > $i ).
thf(func_def_78,type,
sK21: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f24,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= reflexive ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',reflexive) ).
thf(f27,axiom,
( transitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $i,X2: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',transitive) ).
thf(f37,conjecture,
! [X0: $i > $i > $o] :
( ( ( transitive @ X0 )
& ( reflexive @ X0 ) )
<=> ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
& ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f38,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( transitive @ X0 )
& ( reflexive @ X0 ) )
<=> ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
& ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( transitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f40,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f43,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f44,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f47,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f48,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
~ ! [X0: $i > $i > $o] :
( ( ( transitive @ X0 )
& ( reflexive @ X0 ) )
<=> ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
& ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f50,plain,
~ ! [X0: $i > $i > $o] :
( ! [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true )
& ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
= $true ) )
<=> ( ( ( transitive @ X0 )
= $true )
& ( ( reflexive @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f68,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f69,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f70,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f76,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f77,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f79,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= reflexive ),
inference(rectify,[],[f24]) ).
thf(f80,plain,
( reflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f106,plain,
? [X0: $i > $i > $o] :
( ( ( ( transitive @ X0 )
= $true )
& ( ( reflexive @ X0 )
= $true ) )
<~> ! [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true )
& ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f50]) ).
thf(f107,plain,
? [X0: $i > $i > $o] :
( ( ? [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
!= $true )
| ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
!= $true ) )
| ( ( transitive @ X0 )
!= $true )
| ( ( reflexive @ X0 )
!= $true ) )
& ( ! [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true )
& ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
= $true ) )
| ( ( ( transitive @ X0 )
= $true )
& ( ( reflexive @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f106]) ).
thf(f108,plain,
? [X0: $i > $i > $o] :
( ( ? [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
!= $true )
| ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
!= $true ) )
| ( ( transitive @ X0 )
!= $true )
| ( ( reflexive @ X0 )
!= $true ) )
& ( ! [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true )
& ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
= $true ) )
| ( ( ( transitive @ X0 )
= $true )
& ( ( reflexive @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f107]) ).
thf(f109,plain,
? [X0: $i > $i > $o] :
( ( ? [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
!= $true )
| ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
!= $true ) )
| ( ( transitive @ X0 )
!= $true )
| ( ( reflexive @ X0 )
!= $true ) )
& ( ! [X2: $i > $o] :
( ( $true
= ( mvalid @ ( mimpl @ ( mbox @ X0 @ X2 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X2 ) ) ) ) )
& ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X2 ) @ X2 ) )
= $true ) )
| ( ( ( transitive @ X0 )
= $true )
& ( ( reflexive @ X0 )
= $true ) ) ) ),
inference(rectify,[],[f108]) ).
thf(f110,plain,
( ( ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ sK1 ) ) ) ) )
| ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ sK1 ) ) )
| ( ( transitive @ sK0 )
!= $true )
| ( $true
!= ( reflexive @ sK0 ) ) )
& ( ! [X2: $i > $o] :
( ( $true
= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X2 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ X2 ) ) ) ) )
& ( $true
= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X2 ) @ X2 ) ) ) )
| ( ( ( transitive @ sK0 )
= $true )
& ( $true
= ( reflexive @ sK0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f109]) ).
thf(f112,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f113,plain,
( reflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f116,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f117,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f118,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f119,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f121,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f123,plain,
! [X2: $i > $o] :
( ( $true
= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X2 ) @ X2 ) ) )
| ( $true
= ( reflexive @ sK0 ) ) ),
inference(cnf_transformation,[],[f110]) ).
thf(f126,plain,
! [X2: $i > $o] :
( ( $true
= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X2 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ X2 ) ) ) ) )
| ( ( transitive @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f110]) ).
thf(f127,plain,
( ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ sK1 ) ) ) ) )
| ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ sK1 ) ) )
| ( ( transitive @ sK0 )
!= $true )
| ( $true
!= ( reflexive @ sK0 ) ) ),
inference(cnf_transformation,[],[f110]) ).
thf(f133,plain,
( mimpl
= ( ^ [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,[],[f118,f119,f117]) ).
thf(f135,plain,
( ( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ sK1 )
@ sK1 ) ) )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 )
!= $true )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ sK1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ sK1 ) ) ) )
!= $true )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f127,f121,f133,f116,f116,f116,f121,f133,f116,f112,f113]) ).
thf(f136,plain,
! [X2: $i > $o] :
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 )
= $true )
| ( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ X2 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ X2 ) ) ) ) ) ),
inference(definition_unfolding,[],[f126,f121,f133,f116,f116,f116,f112]) ).
thf(f139,plain,
! [X2: $i > $o] :
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ sK0
@ X2 )
@ X2 ) )
= $true )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f123,f121,f133,f116,f113]) ).
thf(f140,plain,
! [X2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) )
| ( X2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
! [X2: $i > $o,X3: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) )
| ( X2 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f140]) ).
thf(f142,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) )
| ( X2 @ Y0 ) )
@ X4 )
= $true )
| ( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f141]) ).
thf(f143,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( sK0 @ X3 @ X3 )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) )
| ( X2 @ X4 ) ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( sK0 @ X3 @ X3 )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) )
| ( ( X2 @ X4 )
= $true ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( X2 @ X4 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) )
| ( ( sK0 @ X3 @ X3 )
= $true ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( sK0 @ X3 @ X3 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) )
@ ( sK2 @ X2 @ X4 ) ) ) ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f147,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( X2 @ X4 )
= $true )
| ( ( sK0 @ X3 @ X3 )
= $true )
| ( ( ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) )
=> ( X2 @ ( sK2 @ X2 @ X4 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( $false
= ( X2 @ ( sK2 @ X2 @ X4 ) ) )
| ( ( sK0 @ X3 @ X3 )
= $true )
| ( ( X2 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( sK0 @ X3 @ X3 )
= $true )
| ( ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) )
= $true )
| ( ( X2 @ X4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f147]) ).
thf(f167,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
!= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( sK1 @ Y0 ) ) )
!= $true )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f135]) ).
thf(f168,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK4 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( sK1 @ Y0 ) ) )
!= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
!= $true )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
!= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( sK1 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
!= $true )
| ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) )
@ sK6 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( sK1 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) ) )
@ sK6 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK7 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) )
| ( sK1 @ Y0 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( sK1 @ sK5 ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK8 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK8 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK8 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f180,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK8 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK8 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( ( sK0 @ sK6 @ X2 )
=> ( sK1 @ X2 ) ) )
| ( ( ( sK0 @ sK5 @ X1 )
=> ( sK1 @ X1 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) )
=> ( sK0 @ Y0 @ sK8 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK0 @ sK5 @ X1 )
=> ( sK1 @ X1 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) )
=> ( sK0 @ Y0 @ sK8 ) ) )
= $false )
| ( $false
= ( sK0 @ sK6 @ X2 ) )
| ( $true
= ( sK1 @ X2 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK0 @ sK6 @ X2 ) )
| ( $true
= ( sK1 @ X2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) )
=> ( sK0 @ Y0 @ sK8 ) ) )
= $false )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) )
=> ( sK0 @ Y0 @ sK8 ) )
@ sK9 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( sK1 @ X2 ) )
| ( $false
= ( sK0 @ sK6 @ X2 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK0 @ sK6 @ X2 ) )
| ( $true
= ( sK1 @ X2 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( ( ( ( sK0 @ sK9 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) )
=> ( sK0 @ sK9 @ sK8 ) )
= $false )
| ( $false
= ( sK0 @ sK5 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK1 @ X2 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK6 @ X2 ) )
| ( $false
= ( sK0 @ sK9 @ sK8 ) ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( sK0 @ sK9 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK1 @ X2 ) )
| ( $false
= ( sK0 @ sK6 @ X2 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f189,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK1 @ X2 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK6 @ X2 ) )
| ( $true
= ( sK0 @ sK4 @ sK8 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK1 @ X2 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK6 @ X2 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f188]) ).
thf(f191,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK10 ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ sK5 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f192,plain,
! [X1: $i] :
( ( ( ( sK0 @ sK5 @ X1 )
=> ( sK1 @ X1 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) )
=> ( sK0 @ Y0 @ sK8 ) ) )
= $false )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ( sK0 @ sK6 @ sK10 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) )
=> ( sK0 @ Y0 @ sK8 ) ) )
= $false )
| ( $false
= ( ( sK0 @ sK6 @ sK10 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( $false
= ( ( sK0 @ sK6 @ sK10 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) )
=> ( sK0 @ Y0 @ sK8 ) )
@ sK11 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) )
=> ( sK0 @ Y0 @ sK8 ) )
@ sK11 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( ( sK0 @ sK6 @ sK10 )
= $true )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) )
=> ( sK0 @ Y0 @ sK8 ) )
@ sK11 ) ) ),
inference(imp_proxy_clausification,[],[f194]) ).
thf(f197,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ( ( sK0 @ sK11 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) )
=> ( sK0 @ sK11 @ sK8 ) ) )
| ( ( sK0 @ sK6 @ sK10 )
= $true )
| ( $false
= ( sK0 @ sK5 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( ( sK0 @ sK6 @ sK10 )
= $true )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK11 @ sK8 ) ) ),
inference(imp_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK11 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) ) )
| ( $true
= ( sK1 @ X1 ) )
| ( ( sK0 @ sK6 @ sK10 )
= $true )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f197]) ).
thf(f200,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( ( sK0 @ sK6 @ sK10 )
= $true )
| ( $true
= ( sK0 @ sK4 @ sK8 ) ) ),
inference(and_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( ( sK0 @ sK6 @ sK10 )
= $true )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK11 @ sK4 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f199]) ).
thf(f202,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) )
@ sK12 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) )
=> ( sK0 @ Y0 @ sK8 ) )
@ sK11 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f195]) ).
thf(f203,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK11 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) )
=> ( sK0 @ sK11 @ sK8 ) ) )
| ( $false
= ( ( sK0 @ sK10 @ sK12 )
=> ( sK1 @ sK12 ) ) ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( $false
= ( ( sK0 @ sK10 @ sK12 )
=> ( sK1 @ sK12 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK0 @ sK11 @ sK8 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( ( sK0 @ sK11 @ sK4 )
& ( sK0 @ sK4 @ sK8 ) ) )
| ( $false
= ( ( sK0 @ sK10 @ sK12 )
=> ( sK1 @ sK12 ) ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f206,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( $true
= ( sK0 @ sK4 @ sK8 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ( sK0 @ sK10 @ sK12 )
=> ( sK1 @ sK12 ) ) ) ),
inference(and_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ( sK0 @ sK10 @ sK12 )
=> ( sK1 @ sK12 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f205]) ).
thf(f208,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK1 @ sK12 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $true
= ( sK0 @ sK11 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK11 @ sK4 ) )
| ( $true
= ( sK0 @ sK10 @ sK12 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f207]) ).
thf(f210,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK1 @ sK12 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK8 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f206]) ).
thf(f211,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK10 @ sK12 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK8 ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f206]) ).
thf(f212,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK11 @ sK8 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK1 @ sK12 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f204]) ).
thf(f213,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK10 @ sK12 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK0 @ sK11 @ sK8 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f204]) ).
thf(f214,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f215,plain,
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f216,plain,
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f217,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK13 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK13 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK13 ) )
=> ( sK0 @ Y0 @ sK13 ) ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( ( sK0 @ sK6 @ X1 )
=> ( sK1 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK6 @ X1 )
=> ( sK1 @ X1 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK13 ) )
=> ( sK0 @ Y0 @ sK13 ) )
@ sK14 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X1: $i] :
( ( ( sK0 @ sK6 @ X1 )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK13 ) )
=> ( sK0 @ Y0 @ sK13 ) )
@ sK14 )
= $false ) ),
inference(imp_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK6 @ X1 )
= $false )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ( ( sK0 @ sK14 @ sK4 )
& ( sK0 @ sK4 @ sK13 ) )
=> ( sK0 @ sK14 @ sK13 ) ) )
| ( $true
= ( sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f221]) ).
thf(f223,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( ( sK0 @ sK6 @ X1 )
= $false )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK14 @ sK13 ) ) ),
inference(imp_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK6 @ X1 )
= $false )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( $true
= ( ( sK0 @ sK14 @ sK4 )
& ( sK0 @ sK4 @ sK13 ) ) ) ),
inference(imp_proxy_clausification,[],[f222]) ).
thf(f225,plain,
! [X1: $i] :
( ( ( sK0 @ sK6 @ X1 )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK4 @ sK13 )
= $true )
| ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X1: $i] :
( ( $true
= ( sK1 @ X1 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( sK0 @ sK14 @ sK4 ) )
| ( ( sK0 @ sK6 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f224]) ).
thf(f227,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK15 )
= $false )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f214]) ).
thf(f228,plain,
( ( ( ^ [Y0: $i] :
( ( sK0 @ sK6 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK16 )
= $false )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK4 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK15 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f227]) ).
thf(f229,plain,
( ( $false
= ( ( sK0 @ sK6 @ sK16 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK16 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK15 ) )
=> ( sK0 @ Y0 @ sK15 ) ) )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f228]) ).
thf(f230,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK16 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK15 ) )
=> ( sK0 @ Y0 @ sK15 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( ( sK0 @ sK6 @ sK16 )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK15 ) )
=> ( sK0 @ Y0 @ sK15 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f229]) ).
thf(f232,plain,
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK15 ) )
=> ( sK0 @ Y0 @ sK15 ) )
@ sK17 ) )
| ( ( sK0 @ sK6 @ sK16 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f231]) ).
thf(f233,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ( ( sK0 @ sK17 @ sK4 )
& ( sK0 @ sK4 @ sK15 ) )
=> ( sK0 @ sK17 @ sK15 ) ) )
| ( ( sK0 @ sK6 @ sK16 )
= $true ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( ( sK0 @ sK17 @ sK15 )
= $false )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK6 @ sK16 )
= $true ) ),
inference(imp_proxy_clausification,[],[f233]) ).
thf(f235,plain,
( ( ( sK0 @ sK6 @ sK16 )
= $true )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( ( sK0 @ sK17 @ sK4 )
& ( sK0 @ sK4 @ sK15 ) ) ) ),
inference(imp_proxy_clausification,[],[f233]) ).
thf(f236,plain,
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $true
= ( sK0 @ sK4 @ sK15 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK6 @ sK16 )
= $true ) ),
inference(and_proxy_clausification,[],[f235]) ).
thf(f237,plain,
( ( ( sK0 @ sK6 @ sK16 )
= $true )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( sK0 @ sK17 @ sK4 )
= $true ) ),
inference(and_proxy_clausification,[],[f235]) ).
thf(f238,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK16 @ Y0 )
=> ( sK1 @ Y0 ) )
@ sK18 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK15 ) )
=> ( sK0 @ Y0 @ sK15 ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f230]) ).
thf(f239,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK16 @ Y0 )
=> ( sK1 @ Y0 ) )
@ sK18 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ sK4 @ sK15 ) )
=> ( sK0 @ Y0 @ sK15 ) )
@ sK19 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f238]) ).
thf(f240,plain,
( ( $false
= ( ( ( sK0 @ sK19 @ sK4 )
& ( sK0 @ sK4 @ sK15 ) )
=> ( sK0 @ sK19 @ sK15 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ( sK0 @ sK16 @ sK18 )
=> ( sK1 @ sK18 ) ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(beta-eta_normalization,[],[f239]) ).
thf(f241,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ( sK0 @ sK16 @ sK18 )
=> ( sK1 @ sK18 ) ) )
| ( $false
= ( sK0 @ sK19 @ sK15 ) ) ),
inference(imp_proxy_clausification,[],[f240]) ).
thf(f242,plain,
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( ( sK0 @ sK16 @ sK18 )
=> ( sK1 @ sK18 ) ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK19 @ sK4 )
& ( sK0 @ sK4 @ sK15 ) ) ) ),
inference(imp_proxy_clausification,[],[f240]) ).
thf(f243,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK1 @ sK18 ) )
| ( $true
= ( ( sK0 @ sK19 @ sK4 )
& ( sK0 @ sK4 @ sK15 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f242]) ).
thf(f244,plain,
( ( $true
= ( ( sK0 @ sK19 @ sK4 )
& ( sK0 @ sK4 @ sK15 ) ) )
| ( $true
= ( sK0 @ sK16 @ sK18 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f242]) ).
thf(f245,plain,
( ( $true
= ( sK0 @ sK16 @ sK18 ) )
| ( $true
= ( sK0 @ sK4 @ sK15 ) )
| ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK16 @ sK18 ) )
| ( $true
= ( sK0 @ sK19 @ sK4 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f244]) ).
thf(f247,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK4 @ sK15 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK1 @ sK18 ) ) ),
inference(and_proxy_clausification,[],[f243]) ).
thf(f248,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK1 @ sK18 ) )
| ( $true
= ( sK0 @ sK19 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f243]) ).
thf(f249,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK19 @ sK15 ) )
| ( $false
= ( sK1 @ sK18 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f241]) ).
thf(f250,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ( $false
= ( sK0 @ sK19 @ sK15 ) )
| ( $true
= ( sK0 @ sK16 @ sK18 ) ) ),
inference(imp_proxy_clausification,[],[f241]) ).
thf(f251,plain,
! [X2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( X2 @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f252,plain,
! [X2: $i > $o,X3: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( X2 @ Y2 ) ) ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( X2 @ Y2 ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X3 )
& ( sK0 @ X3 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f253]) ).
thf(f255,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X3 )
& ( sK0 @ X3 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X3 )
& ( sK0 @ X3 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X3 )
& ( sK0 @ X3 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ X5 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i > $o,X3: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X3 )
& ( sK0 @ X3 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ X5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) )
@ X6 )
= $true ) ),
inference(pi_proxy_clausification,[],[f257]) ).
thf(f259,plain,
! [X2: $i > $o,X3: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) )
@ ( sK20 @ X2 @ X4 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X3 )
& ( sK0 @ X3 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ X5 ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) )
@ X6 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i > $o,X3: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ( sK0 @ X4 @ X6 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) )
| ( $false
= ( ( sK0 @ X4 @ ( sK20 @ X2 @ X4 ) )
=> ( X2 @ ( sK20 @ X2 @ X4 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X5 ) )
=> ( sK0 @ Y0 @ X5 ) ) ) ) ),
inference(beta-eta_normalization,[],[f259]) ).
thf(f261,plain,
! [X2: $i > $o,X3: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X5 ) )
=> ( sK0 @ Y0 @ X5 ) ) ) )
| ( $false
= ( ( sK0 @ X4 @ ( sK20 @ X2 @ X4 ) )
=> ( X2 @ ( sK20 @ X2 @ X4 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X2: $i > $o,X3: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $false
= ( ( sK0 @ X4 @ ( sK20 @ X2 @ X4 ) )
=> ( X2 @ ( sK20 @ X2 @ X4 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X5 ) )
=> ( sK0 @ Y0 @ X5 ) ) ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) )
@ X7 )
= $true ) ),
inference(pi_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X2: $i > $o,X3: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) )
@ X7 )
= $true )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( X2 @ ( sK20 @ X2 @ X4 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X5 ) )
=> ( sK0 @ Y0 @ X5 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X2: $i > $o,X3: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) )
@ X7 )
= $true )
| ( $true
= ( sK0 @ X4 @ ( sK20 @ X2 @ X4 ) ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X5 ) )
=> ( sK0 @ Y0 @ X5 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f262]) ).
thf(f265,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( sK0 @ X4 @ ( sK20 @ X2 @ X4 ) ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X5 ) )
=> ( sK0 @ Y0 @ X5 ) )
@ X8 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) )
@ X7 )
= $true ) ),
inference(pi_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( sK0 @ X4 @ ( sK20 @ X2 @ X4 ) ) )
| ( $true
= ( ( sK0 @ X6 @ X7 )
=> ( X2 @ X7 ) ) )
| ( ( ( ( sK0 @ X8 @ X3 )
& ( sK0 @ X3 @ X5 ) )
=> ( sK0 @ X8 @ X5 ) )
= $true )
| ( $false
= ( sK0 @ X4 @ X6 ) ) ),
inference(beta-eta_normalization,[],[f265]) ).
thf(f267,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $true
= ( X2 @ X7 ) )
| ( $false
= ( sK0 @ X6 @ X7 ) )
| ( $true
= ( sK0 @ X4 @ ( sK20 @ X2 @ X4 ) ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( ( ( ( sK0 @ X8 @ X3 )
& ( sK0 @ X3 @ X5 ) )
=> ( sK0 @ X8 @ X5 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( sK0 @ X8 @ X5 )
= $true )
| ( $false
= ( sK0 @ X6 @ X7 ) )
| ( $true
= ( X2 @ X7 ) )
| ( ( ( sK0 @ X8 @ X3 )
& ( sK0 @ X3 @ X5 ) )
= $false )
| ( $true
= ( sK0 @ X4 @ ( sK20 @ X2 @ X4 ) ) )
| ( $false
= ( sK0 @ X4 @ X6 ) ) ),
inference(imp_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( sK0 @ X8 @ X3 )
= $false )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( ( sK0 @ X8 @ X5 )
= $true )
| ( $true
= ( X2 @ X7 ) )
| ( $false
= ( sK0 @ X3 @ X5 ) )
| ( $true
= ( sK0 @ X4 @ ( sK20 @ X2 @ X4 ) ) )
| ( $false
= ( sK0 @ X6 @ X7 ) ) ),
inference(and_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X5 ) )
=> ( sK0 @ Y0 @ X5 ) )
@ X8 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK0 @ X6 @ Y0 )
=> ( X2 @ Y0 ) )
@ X7 )
= $true )
| ( $false
= ( X2 @ ( sK20 @ X2 @ X4 ) ) )
| ( $false
= ( sK0 @ X4 @ X6 ) ) ),
inference(pi_proxy_clausification,[],[f263]) ).
thf(f271,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( X2 @ ( sK20 @ X2 @ X4 ) ) )
| ( $true
= ( ( sK0 @ X6 @ X7 )
=> ( X2 @ X7 ) ) )
| ( ( ( ( sK0 @ X8 @ X3 )
& ( sK0 @ X3 @ X5 ) )
=> ( sK0 @ X8 @ X5 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f270]) ).
thf(f272,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( $false
= ( X2 @ ( sK20 @ X2 @ X4 ) ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( sK0 @ X6 @ X7 ) )
| ( ( ( ( sK0 @ X8 @ X3 )
& ( sK0 @ X3 @ X5 ) )
=> ( sK0 @ X8 @ X5 ) )
= $true )
| ( $true
= ( X2 @ X7 ) ) ),
inference(imp_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( sK0 @ X8 @ X5 )
= $true )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( ( ( sK0 @ X8 @ X3 )
& ( sK0 @ X3 @ X5 ) )
= $false )
| ( $false
= ( X2 @ ( sK20 @ X2 @ X4 ) ) )
| ( $false
= ( sK0 @ X6 @ X7 ) )
| ( $true
= ( X2 @ X7 ) ) ),
inference(imp_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X2: $i > $o,X3: $i,X8: $i,X6: $i,X7: $i,X4: $i,X5: $i] :
( ( ( sK0 @ X8 @ X3 )
= $false )
| ( $true
= ( X2 @ X7 ) )
| ( ( sK0 @ X8 @ X5 )
= $true )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( X2 @ ( sK20 @ X2 @ X4 ) ) )
| ( $false
= ( sK0 @ X3 @ X5 ) )
| ( $false
= ( sK0 @ X6 @ X7 ) ) ),
inference(and_proxy_clausification,[],[f273]) ).
thf(f294,definition,
( spl22_1
<=> ! [X4: $i,X2: $i > $o] :
( ( ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) )
= $true )
| ( ( X2 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
thf(f295,plain,
( ! [X2: $i > $o,X4: $i] :
( ( ( sK0 @ X4 @ ( sK2 @ X2 @ X4 ) )
= $true )
| ( ( X2 @ X4 )
= $true ) )
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f294]) ).
thf(f297,definition,
( spl22_2
<=> ! [X3: $i] :
( ( sK0 @ X3 @ X3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl22_2])],[avatar_definition]) ).
thf(f298,plain,
( ! [X3: $i] :
( ( sK0 @ X3 @ X3 )
= $true )
| ~ spl22_2 ),
inference(avatar_component_clause,[],[f297]) ).
thf(f299,plain,
( spl22_1
| spl22_2 ),
inference(avatar_split_clause,[],[f149,f297,f294]) ).
thf(f301,definition,
( spl22_3
<=> ! [X4: $i,X2: $i > $o] :
( ( $false
= ( X2 @ ( sK2 @ X2 @ X4 ) ) )
| ( ( X2 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition]) ).
thf(f302,plain,
( ! [X2: $i > $o,X4: $i] :
( ( $false
= ( X2 @ ( sK2 @ X2 @ X4 ) ) )
| ( ( X2 @ X4 )
= $true ) )
| ~ spl22_3 ),
inference(avatar_component_clause,[],[f301]) ).
thf(f303,plain,
( spl22_3
| spl22_2 ),
inference(avatar_split_clause,[],[f148,f297,f301]) ).
thf(f313,definition,
( spl22_6
<=> ! [X2: $i] :
( ( $true
= ( sK1 @ X2 ) )
| ( $false
= ( sK0 @ sK6 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl22_6])],[avatar_definition]) ).
thf(f314,plain,
( ! [X2: $i] :
( ( $false
= ( sK0 @ sK6 @ X2 ) )
| ( $true
= ( sK1 @ X2 ) ) )
| ~ spl22_6 ),
inference(avatar_component_clause,[],[f313]) ).
thf(f316,definition,
( spl22_7
<=> ( $true
= ( sK0 @ sK9 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_7])],[avatar_definition]) ).
thf(f318,plain,
( ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ~ spl22_7 ),
inference(avatar_component_clause,[],[f316]) ).
thf(f320,definition,
( spl22_8
<=> ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_8])],[avatar_definition]) ).
thf(f322,plain,
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ~ spl22_8 ),
inference(avatar_component_clause,[],[f320]) ).
thf(f324,definition,
( spl22_9
<=> ! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl22_9])],[avatar_definition]) ).
thf(f325,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK1 @ X1 ) ) )
| ~ spl22_9 ),
inference(avatar_component_clause,[],[f324]) ).
thf(f326,plain,
( spl22_6
| spl22_7
| spl22_8
| spl22_9 ),
inference(avatar_split_clause,[],[f190,f324,f320,f316,f313]) ).
thf(f328,definition,
( spl22_10
<=> ( $true
= ( sK0 @ sK4 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_10])],[avatar_definition]) ).
thf(f330,plain,
( ( $true
= ( sK0 @ sK4 @ sK8 ) )
| ~ spl22_10 ),
inference(avatar_component_clause,[],[f328]) ).
thf(f331,plain,
( spl22_6
| spl22_9
| spl22_8
| spl22_10 ),
inference(avatar_split_clause,[],[f189,f328,f320,f324,f313]) ).
thf(f333,definition,
( spl22_11
<=> ( $false
= ( sK0 @ sK9 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_11])],[avatar_definition]) ).
thf(f335,plain,
( ( $false
= ( sK0 @ sK9 @ sK8 ) )
| ~ spl22_11 ),
inference(avatar_component_clause,[],[f333]) ).
thf(f336,plain,
( spl22_6
| spl22_9
| spl22_8
| spl22_11 ),
inference(avatar_split_clause,[],[f187,f333,f320,f324,f313]) ).
thf(f338,definition,
( spl22_12
<=> ( $true
= ( sK0 @ sK11 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_12])],[avatar_definition]) ).
thf(f340,plain,
( ( $true
= ( sK0 @ sK11 @ sK4 ) )
| ~ spl22_12 ),
inference(avatar_component_clause,[],[f338]) ).
thf(f342,definition,
( spl22_13
<=> ( ( sK0 @ sK6 @ sK10 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl22_13])],[avatar_definition]) ).
thf(f344,plain,
( ( ( sK0 @ sK6 @ sK10 )
= $true )
| ~ spl22_13 ),
inference(avatar_component_clause,[],[f342]) ).
thf(f345,plain,
( spl22_12
| spl22_13
| spl22_8
| spl22_9 ),
inference(avatar_split_clause,[],[f201,f324,f320,f342,f338]) ).
thf(f346,plain,
( spl22_8
| spl22_10
| spl22_9
| spl22_13 ),
inference(avatar_split_clause,[],[f200,f342,f324,f328,f320]) ).
thf(f348,definition,
( spl22_14
<=> ( $false
= ( sK0 @ sK11 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_14])],[avatar_definition]) ).
thf(f350,plain,
( ( $false
= ( sK0 @ sK11 @ sK8 ) )
| ~ spl22_14 ),
inference(avatar_component_clause,[],[f348]) ).
thf(f351,plain,
( spl22_8
| spl22_13
| spl22_14
| spl22_9 ),
inference(avatar_split_clause,[],[f198,f324,f348,f342,f320]) ).
thf(f353,definition,
( spl22_15
<=> ( $true
= ( sK0 @ sK10 @ sK12 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_15])],[avatar_definition]) ).
thf(f355,plain,
( ( $true
= ( sK0 @ sK10 @ sK12 ) )
| ~ spl22_15 ),
inference(avatar_component_clause,[],[f353]) ).
thf(f356,plain,
( spl22_8
| spl22_9
| spl22_15
| spl22_12 ),
inference(avatar_split_clause,[],[f209,f338,f353,f324,f320]) ).
thf(f358,definition,
( spl22_16
<=> ( $false
= ( sK1 @ sK12 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_16])],[avatar_definition]) ).
thf(f360,plain,
( ( $false
= ( sK1 @ sK12 ) )
| ~ spl22_16 ),
inference(avatar_component_clause,[],[f358]) ).
thf(f361,plain,
( spl22_9
| spl22_8
| spl22_12
| spl22_16 ),
inference(avatar_split_clause,[],[f208,f358,f338,f320,f324]) ).
thf(f362,plain,
( spl22_9
| spl22_8
| spl22_15
| spl22_10 ),
inference(avatar_split_clause,[],[f211,f328,f353,f320,f324]) ).
thf(f363,plain,
( spl22_10
| spl22_8
| spl22_9
| spl22_16 ),
inference(avatar_split_clause,[],[f210,f358,f324,f320,f328]) ).
thf(f364,plain,
( spl22_15
| spl22_14
| spl22_8
| spl22_9 ),
inference(avatar_split_clause,[],[f213,f324,f320,f348,f353]) ).
thf(f365,plain,
( spl22_16
| spl22_8
| spl22_14
| spl22_9 ),
inference(avatar_split_clause,[],[f212,f324,f348,f320,f358]) ).
thf(f367,definition,
( spl22_17
<=> ( $false
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_17])],[avatar_definition]) ).
thf(f369,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl22_17 ),
inference(avatar_component_clause,[],[f367]) ).
thf(f371,definition,
( spl22_18
<=> ( $true
= ( sK0 @ sK14 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_18])],[avatar_definition]) ).
thf(f373,plain,
( ( $true
= ( sK0 @ sK14 @ sK4 ) )
| ~ spl22_18 ),
inference(avatar_component_clause,[],[f371]) ).
thf(f374,plain,
( spl22_8
| spl22_6
| spl22_17
| spl22_18 ),
inference(avatar_split_clause,[],[f226,f371,f367,f313,f320]) ).
thf(f376,definition,
( spl22_19
<=> ( ( sK0 @ sK4 @ sK13 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl22_19])],[avatar_definition]) ).
thf(f378,plain,
( ( ( sK0 @ sK4 @ sK13 )
= $true )
| ~ spl22_19 ),
inference(avatar_component_clause,[],[f376]) ).
thf(f379,plain,
( spl22_17
| spl22_8
| spl22_6
| spl22_19 ),
inference(avatar_split_clause,[],[f225,f376,f313,f320,f367]) ).
thf(f381,definition,
( spl22_20
<=> ( $false
= ( sK0 @ sK14 @ sK13 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_20])],[avatar_definition]) ).
thf(f383,plain,
( ( $false
= ( sK0 @ sK14 @ sK13 ) )
| ~ spl22_20 ),
inference(avatar_component_clause,[],[f381]) ).
thf(f384,plain,
( spl22_17
| spl22_6
| spl22_20
| spl22_8 ),
inference(avatar_split_clause,[],[f223,f320,f381,f313,f367]) ).
thf(f386,definition,
( spl22_21
<=> ( ( sK0 @ sK6 @ sK16 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl22_21])],[avatar_definition]) ).
thf(f388,plain,
( ( ( sK0 @ sK6 @ sK16 )
= $true )
| ~ spl22_21 ),
inference(avatar_component_clause,[],[f386]) ).
thf(f390,definition,
( spl22_22
<=> ( ( sK0 @ sK17 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl22_22])],[avatar_definition]) ).
thf(f392,plain,
( ( ( sK0 @ sK17 @ sK4 )
= $true )
| ~ spl22_22 ),
inference(avatar_component_clause,[],[f390]) ).
thf(f393,plain,
( spl22_21
| spl22_22
| spl22_17
| spl22_8 ),
inference(avatar_split_clause,[],[f237,f320,f367,f390,f386]) ).
thf(f395,definition,
( spl22_23
<=> ( $true
= ( sK0 @ sK4 @ sK15 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_23])],[avatar_definition]) ).
thf(f397,plain,
( ( $true
= ( sK0 @ sK4 @ sK15 ) )
| ~ spl22_23 ),
inference(avatar_component_clause,[],[f395]) ).
thf(f398,plain,
( spl22_21
| spl22_23
| spl22_17
| spl22_8 ),
inference(avatar_split_clause,[],[f236,f320,f367,f395,f386]) ).
thf(f400,definition,
( spl22_24
<=> ( ( sK0 @ sK17 @ sK15 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl22_24])],[avatar_definition]) ).
thf(f402,plain,
( ( ( sK0 @ sK17 @ sK15 )
= $false )
| ~ spl22_24 ),
inference(avatar_component_clause,[],[f400]) ).
thf(f403,plain,
( spl22_24
| spl22_8
| spl22_17
| spl22_21 ),
inference(avatar_split_clause,[],[f234,f386,f367,f320,f400]) ).
thf(f405,definition,
( spl22_25
<=> ( $true
= ( sK0 @ sK19 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_25])],[avatar_definition]) ).
thf(f407,plain,
( ( $true
= ( sK0 @ sK19 @ sK4 ) )
| ~ spl22_25 ),
inference(avatar_component_clause,[],[f405]) ).
thf(f409,definition,
( spl22_26
<=> ( $true
= ( sK0 @ sK16 @ sK18 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_26])],[avatar_definition]) ).
thf(f411,plain,
( ( $true
= ( sK0 @ sK16 @ sK18 ) )
| ~ spl22_26 ),
inference(avatar_component_clause,[],[f409]) ).
thf(f412,plain,
( spl22_17
| spl22_25
| spl22_26
| spl22_8 ),
inference(avatar_split_clause,[],[f246,f320,f409,f405,f367]) ).
thf(f413,plain,
( spl22_23
| spl22_26
| spl22_17
| spl22_8 ),
inference(avatar_split_clause,[],[f245,f320,f367,f409,f395]) ).
thf(f415,definition,
( spl22_27
<=> ( $false
= ( sK1 @ sK18 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_27])],[avatar_definition]) ).
thf(f417,plain,
( ( $false
= ( sK1 @ sK18 ) )
| ~ spl22_27 ),
inference(avatar_component_clause,[],[f415]) ).
thf(f418,plain,
( spl22_8
| spl22_25
| spl22_27
| spl22_17 ),
inference(avatar_split_clause,[],[f248,f367,f415,f405,f320]) ).
thf(f419,plain,
( spl22_8
| spl22_17
| spl22_23
| spl22_27 ),
inference(avatar_split_clause,[],[f247,f415,f395,f367,f320]) ).
thf(f421,definition,
( spl22_28
<=> ( $false
= ( sK0 @ sK19 @ sK15 ) ) ),
introduced(definition,[new_symbols(definition,[spl22_28])],[avatar_definition]) ).
thf(f423,plain,
( ( $false
= ( sK0 @ sK19 @ sK15 ) )
| ~ spl22_28 ),
inference(avatar_component_clause,[],[f421]) ).
thf(f424,plain,
( spl22_8
| spl22_26
| spl22_17
| spl22_28 ),
inference(avatar_split_clause,[],[f250,f421,f367,f409,f320]) ).
thf(f425,plain,
( spl22_8
| spl22_28
| spl22_17
| spl22_27 ),
inference(avatar_split_clause,[],[f249,f415,f367,f421,f320]) ).
thf(f427,definition,
( spl22_29
<=> ! [X5: $i,X8: $i,X3: $i] :
( ( ( sK0 @ X8 @ X3 )
= $false )
| ( $false
= ( sK0 @ X3 @ X5 ) )
| ( ( sK0 @ X8 @ X5 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl22_29])],[avatar_definition]) ).
thf(f428,plain,
( ! [X3: $i,X8: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X5 ) )
| ( ( sK0 @ X8 @ X3 )
= $false )
| ( ( sK0 @ X8 @ X5 )
= $true ) )
| ~ spl22_29 ),
inference(avatar_component_clause,[],[f427]) ).
thf(f430,definition,
( spl22_30
<=> ! [X4: $i,X7: $i,X6: $i,X2: $i > $o] :
( ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( sK0 @ X6 @ X7 ) )
| ( $true
= ( sK0 @ X4 @ ( sK20 @ X2 @ X4 ) ) )
| ( $true
= ( X2 @ X7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl22_30])],[avatar_definition]) ).
thf(f431,plain,
( ! [X2: $i > $o,X6: $i,X7: $i,X4: $i] :
( ( $true
= ( sK0 @ X4 @ ( sK20 @ X2 @ X4 ) ) )
| ( $true
= ( X2 @ X7 ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( sK0 @ X6 @ X7 ) ) )
| ~ spl22_30 ),
inference(avatar_component_clause,[],[f430]) ).
thf(f432,plain,
( spl22_29
| spl22_30 ),
inference(avatar_split_clause,[],[f269,f430,f427]) ).
thf(f434,definition,
( spl22_31
<=> ! [X4: $i,X7: $i,X6: $i,X2: $i > $o] :
( ( $true
= ( X2 @ X7 ) )
| ( $false
= ( sK0 @ X6 @ X7 ) )
| ( $false
= ( X2 @ ( sK20 @ X2 @ X4 ) ) )
| ( $false
= ( sK0 @ X4 @ X6 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl22_31])],[avatar_definition]) ).
thf(f435,plain,
( ! [X2: $i > $o,X6: $i,X7: $i,X4: $i] :
( ( $false
= ( X2 @ ( sK20 @ X2 @ X4 ) ) )
| ( $true
= ( X2 @ X7 ) )
| ( $false
= ( sK0 @ X4 @ X6 ) )
| ( $false
= ( sK0 @ X6 @ X7 ) ) )
| ~ spl22_31 ),
inference(avatar_component_clause,[],[f434]) ).
thf(f436,plain,
( spl22_29
| spl22_31 ),
inference(avatar_split_clause,[],[f274,f434,f427]) ).
thf(f453,plain,
( ( $false = $true )
| ~ spl22_2
| ~ spl22_8 ),
inference(forward_demodulation,[],[f322,f298]) ).
thf(f454,plain,
( $false
| ~ spl22_2
| ~ spl22_8 ),
inference(trivial_inequality_removal,[],[f453]) ).
thf(f455,plain,
( ~ spl22_2
| ~ spl22_8 ),
inference(avatar_contradiction_clause,[],[f454]) ).
thf(f470,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ( $false = $true )
| ~ spl22_2
| ~ spl22_9 ),
inference(superposition,[],[f298,f325]) ).
thf(f472,plain,
( ( $true
= ( sK1 @ sK5 ) )
| ~ spl22_2
| ~ spl22_9 ),
inference(trivial_inequality_removal,[],[f470]) ).
thf(f477,plain,
( ( $false = $true )
| ~ spl22_2
| ~ spl22_9
| ~ spl22_17 ),
inference(forward_demodulation,[],[f472,f369]) ).
thf(f478,plain,
( $false
| ~ spl22_2
| ~ spl22_9
| ~ spl22_17 ),
inference(trivial_inequality_removal,[],[f477]) ).
thf(f479,plain,
( ~ spl22_2
| ~ spl22_9
| ~ spl22_17 ),
inference(avatar_contradiction_clause,[],[f478]) ).
thf(f480,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $true
= ( sK0 @ X0 @ sK8 ) ) )
| ~ spl22_10
| ~ spl22_29 ),
inference(superposition,[],[f330,f428]) ).
thf(f482,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ sK8 ) )
| ( $false
= ( sK0 @ X0 @ sK4 ) ) )
| ~ spl22_10
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f480]) ).
thf(f501,plain,
( ( $false
= ( sK0 @ sK11 @ sK4 ) )
| ( $false = $true )
| ~ spl22_10
| ~ spl22_14
| ~ spl22_29 ),
inference(superposition,[],[f350,f482]) ).
thf(f505,plain,
( ( $false
= ( sK0 @ sK11 @ sK4 ) )
| ~ spl22_10
| ~ spl22_14
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f501]) ).
thf(f533,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK10 ) )
| ( $true
= ( sK0 @ X0 @ sK12 ) )
| ( $false = $true ) )
| ~ spl22_15
| ~ spl22_29 ),
inference(superposition,[],[f428,f355]) ).
thf(f534,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ sK12 ) )
| ( $false
= ( sK0 @ X0 @ sK10 ) ) )
| ~ spl22_15
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f533]) ).
thf(f551,plain,
( ( $true
= ( sK1 @ sK12 ) )
| ( $false = $true )
| ( $false
= ( sK0 @ sK6 @ sK10 ) )
| ~ spl22_6
| ~ spl22_15
| ~ spl22_29 ),
inference(superposition,[],[f534,f314]) ).
thf(f556,plain,
( ( $false
= ( sK0 @ sK6 @ sK10 ) )
| ( $true
= ( sK1 @ sK12 ) )
| ~ spl22_6
| ~ spl22_15
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f551]) ).
thf(f560,plain,
( ( $true
= ( sK1 @ sK12 ) )
| ( $false = $true )
| ~ spl22_6
| ~ spl22_13
| ~ spl22_15
| ~ spl22_29 ),
inference(forward_demodulation,[],[f556,f344]) ).
thf(f561,plain,
( ( $true
= ( sK1 @ sK12 ) )
| ~ spl22_6
| ~ spl22_13
| ~ spl22_15
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f560]) ).
thf(f562,plain,
( ( $false = $true )
| ~ spl22_6
| ~ spl22_13
| ~ spl22_15
| ~ spl22_16
| ~ spl22_29 ),
inference(forward_demodulation,[],[f561,f360]) ).
thf(f563,plain,
( $false
| ~ spl22_6
| ~ spl22_13
| ~ spl22_15
| ~ spl22_16
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f562]) ).
thf(f564,plain,
( ~ spl22_6
| ~ spl22_13
| ~ spl22_15
| ~ spl22_16
| ~ spl22_29 ),
inference(avatar_contradiction_clause,[],[f563]) ).
thf(f604,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK16 )
= $false )
| ( $true
= ( sK0 @ X0 @ sK18 ) )
| ( $false = $true ) )
| ~ spl22_26
| ~ spl22_29 ),
inference(superposition,[],[f428,f411]) ).
thf(f605,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ sK18 ) )
| ( ( sK0 @ X0 @ sK16 )
= $false ) )
| ~ spl22_26
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f604]) ).
thf(f626,plain,
( ( ( sK1 @ sK18 )
= $true )
| ( $false = $true )
| ( ( sK0 @ sK6 @ sK16 )
= $false )
| ~ spl22_6
| ~ spl22_26
| ~ spl22_29 ),
inference(superposition,[],[f314,f605]) ).
thf(f629,plain,
( ( ( sK0 @ sK6 @ sK16 )
= $false )
| ( ( sK1 @ sK18 )
= $true )
| ~ spl22_6
| ~ spl22_26
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f626]) ).
thf(f635,plain,
( ( ( sK1 @ sK18 )
= $true )
| ( $false = $true )
| ~ spl22_6
| ~ spl22_21
| ~ spl22_26
| ~ spl22_29 ),
inference(forward_demodulation,[],[f629,f388]) ).
thf(f636,plain,
( ( ( sK1 @ sK18 )
= $true )
| ~ spl22_6
| ~ spl22_21
| ~ spl22_26
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f635]) ).
thf(f641,plain,
( ( $false = $true )
| ~ spl22_6
| ~ spl22_21
| ~ spl22_26
| ~ spl22_27
| ~ spl22_29 ),
inference(forward_demodulation,[],[f636,f417]) ).
thf(f642,plain,
( $false
| ~ spl22_6
| ~ spl22_21
| ~ spl22_26
| ~ spl22_27
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f641]) ).
thf(f643,plain,
( ~ spl22_6
| ~ spl22_21
| ~ spl22_26
| ~ spl22_27
| ~ spl22_29 ),
inference(avatar_contradiction_clause,[],[f642]) ).
thf(f644,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $false = $true )
| ( $true
= ( sK0 @ X0 @ sK15 ) ) )
| ~ spl22_23
| ~ spl22_29 ),
inference(superposition,[],[f397,f428]) ).
thf(f646,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ sK15 ) )
| ( $false
= ( sK0 @ X0 @ sK4 ) ) )
| ~ spl22_23
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f644]) ).
thf(f664,plain,
( ( $false
= ( sK0 @ sK19 @ sK4 ) )
| ( $false = $true )
| ~ spl22_23
| ~ spl22_28
| ~ spl22_29 ),
inference(superposition,[],[f423,f646]) ).
thf(f667,plain,
( ( $false
= ( sK0 @ sK19 @ sK4 ) )
| ~ spl22_23
| ~ spl22_28
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f664]) ).
thf(f688,plain,
( ( $false = $true )
| ~ spl22_23
| ~ spl22_25
| ~ spl22_28
| ~ spl22_29 ),
inference(superposition,[],[f667,f407]) ).
thf(f693,plain,
( $false
| ~ spl22_23
| ~ spl22_25
| ~ spl22_28
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f688]) ).
thf(f694,plain,
( ~ spl22_23
| ~ spl22_25
| ~ spl22_28
| ~ spl22_29 ),
inference(avatar_contradiction_clause,[],[f693]) ).
thf(f722,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK17 @ sK4 ) )
| ~ spl22_23
| ~ spl22_24
| ~ spl22_29 ),
inference(superposition,[],[f402,f646]) ).
thf(f725,plain,
( ( $false
= ( sK0 @ sK17 @ sK4 ) )
| ~ spl22_23
| ~ spl22_24
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f722]) ).
thf(f749,plain,
( ( $false = $true )
| ~ spl22_22
| ~ spl22_23
| ~ spl22_24
| ~ spl22_29 ),
inference(superposition,[],[f725,f392]) ).
thf(f754,plain,
( $false
| ~ spl22_22
| ~ spl22_23
| ~ spl22_24
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f749]) ).
thf(f755,plain,
( ~ spl22_22
| ~ spl22_23
| ~ spl22_24
| ~ spl22_29 ),
inference(avatar_contradiction_clause,[],[f754]) ).
thf(f774,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ X0 ) )
| ( $true
= ( sK0 @ X0 @ X0 ) )
| ( $false = $true ) )
| ~ spl22_1
| ~ spl22_3 ),
inference(superposition,[],[f302,f295]) ).
thf(f778,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ X0 ) )
| ( $false = $true ) )
| ~ spl22_1
| ~ spl22_3 ),
inference(duplicate_literal_removal,[],[f774]) ).
thf(f779,plain,
( ! [X0: $i] :
( $true
= ( sK0 @ X0 @ X0 ) )
| ~ spl22_1
| ~ spl22_3 ),
inference(trivial_inequality_removal,[],[f778]) ).
thf(f785,plain,
( spl22_2
| ~ spl22_1
| ~ spl22_3 ),
inference(avatar_split_clause,[],[f779,f301,f294,f297]) ).
thf(f884,plain,
( ( $false = $true )
| ~ spl22_10
| ~ spl22_12
| ~ spl22_14
| ~ spl22_29 ),
inference(superposition,[],[f505,f340]) ).
thf(f890,plain,
( $false
| ~ spl22_10
| ~ spl22_12
| ~ spl22_14
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f884]) ).
thf(f891,plain,
( ~ spl22_10
| ~ spl22_12
| ~ spl22_14
| ~ spl22_29 ),
inference(avatar_contradiction_clause,[],[f890]) ).
thf(f1059,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $false = $true )
| ( $true
= ( sK0 @ X0 @ sK13 ) ) )
| ~ spl22_19
| ~ spl22_29 ),
inference(superposition,[],[f428,f378]) ).
thf(f1060,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ sK13 ) )
| ( $false
= ( sK0 @ X0 @ sK4 ) ) )
| ~ spl22_19
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f1059]) ).
thf(f1942,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK14 @ sK4 ) )
| ~ spl22_19
| ~ spl22_20
| ~ spl22_29 ),
inference(superposition,[],[f1060,f383]) ).
thf(f1957,plain,
( ( $false
= ( sK0 @ sK14 @ sK4 ) )
| ~ spl22_19
| ~ spl22_20
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f1942]) ).
thf(f1970,plain,
( ( $false = $true )
| ~ spl22_18
| ~ spl22_19
| ~ spl22_20
| ~ spl22_29 ),
inference(superposition,[],[f1957,f373]) ).
thf(f1980,plain,
( $false
| ~ spl22_18
| ~ spl22_19
| ~ spl22_20
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f1970]) ).
thf(f1981,plain,
( ~ spl22_18
| ~ spl22_19
| ~ spl22_20
| ~ spl22_29 ),
inference(avatar_contradiction_clause,[],[f1980]) ).
thf(f1990,plain,
( ( $false
= ( sK0 @ sK9 @ sK4 ) )
| ( $false = $true )
| ~ spl22_10
| ~ spl22_11
| ~ spl22_29 ),
inference(superposition,[],[f482,f335]) ).
thf(f1995,plain,
( ( $false
= ( sK0 @ sK9 @ sK4 ) )
| ~ spl22_10
| ~ spl22_11
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f1990]) ).
thf(f2067,plain,
( ( $false = $true )
| ~ spl22_7
| ~ spl22_10
| ~ spl22_11
| ~ spl22_29 ),
inference(superposition,[],[f318,f1995]) ).
thf(f2074,plain,
( $false
| ~ spl22_7
| ~ spl22_10
| ~ spl22_11
| ~ spl22_29 ),
inference(trivial_inequality_removal,[],[f2067]) ).
thf(f2075,plain,
( ~ spl22_7
| ~ spl22_10
| ~ spl22_11
| ~ spl22_29 ),
inference(avatar_contradiction_clause,[],[f2074]) ).
thf(f2091,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( sK20
@ ^ [Y0: $i] : ( Y0 != X0 )
@ X1 )
= X0 )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl22_31 ),
inference(leibniz_equality_elimination,[],[f435]) ).
thf(f2146,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X4 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( sK0 @ X1 @ X0 )
= $true )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != X0 )
@ X2 ) )
| ( ( sK0 @ X3 @ X2 )
= $false )
| ( $false
= ( sK0 @ X1 @ X4 ) ) )
| ~ spl22_30
| ~ spl22_31 ),
inference(superposition,[],[f431,f2091]) ).
thf(f2148,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X1 @ X4 ) )
| ( ( X2 != X0 )
= $true )
| ( ( sK0 @ X1 @ X0 )
= $true )
| ( ( sK0 @ X3 @ X2 )
= $false )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) ) )
| ~ spl22_30
| ~ spl22_31 ),
inference(beta-eta_normalization,[],[f2146]) ).
thf(f2149,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X1 @ X0 )
= $true )
| ( $false
= ( X2 = X0 ) )
| ( $false
= ( sK0 @ X4 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( sK0 @ X3 @ X2 )
= $false )
| ( $false
= ( sK0 @ X1 @ X4 ) ) )
| ~ spl22_30
| ~ spl22_31 ),
inference(not_proxy_clausification,[],[f2148]) ).
thf(f2150,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X4 @ X0 ) )
| ( ( sK0 @ X3 @ X2 )
= $false )
| ( ( sK0 @ X1 @ X0 )
= $true )
| ( $false
= ( sK0 @ X1 @ X4 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( X0 != X2 ) )
| ~ spl22_30
| ~ spl22_31 ),
inference(equality_proxy_clausification,[],[f2149]) ).
thf(f2662,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( X1 != X1 )
| ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) ) )
| ~ spl22_30
| ~ spl22_31 ),
inference(equality_factoring,[],[f2150]) ).
thf(f2669,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false != $false )
| ( X1 != X1 )
| ( $false
= ( sK0 @ X2 @ X0 ) ) )
| ~ spl22_30
| ~ spl22_31 ),
inference(duplicate_literal_removal,[],[f2662]) ).
thf(f2670,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) ) )
| ~ spl22_30
| ~ spl22_31 ),
inference(trivial_inequality_removal,[],[f2669]) ).
thf(f2703,plain,
( spl22_29
| ~ spl22_30
| ~ spl22_31 ),
inference(avatar_split_clause,[],[f2670,f434,f430,f427]) ).
cnf(s1,plain,
( spl22_1
| spl22_2 ),
inference(sat_conversion,[],[f299]) ).
cnf(s2,plain,
( spl22_2
| spl22_3 ),
inference(sat_conversion,[],[f303]) ).
cnf(s5,plain,
( spl22_6
| spl22_7
| spl22_8
| spl22_9 ),
inference(sat_conversion,[],[f326]) ).
cnf(s6,plain,
( spl22_6
| spl22_8
| spl22_9
| spl22_10 ),
inference(sat_conversion,[],[f331]) ).
cnf(s7,plain,
( spl22_6
| spl22_8
| spl22_9
| spl22_11 ),
inference(sat_conversion,[],[f336]) ).
cnf(s8,plain,
( spl22_8
| spl22_9
| spl22_12
| spl22_13 ),
inference(sat_conversion,[],[f345]) ).
cnf(s9,plain,
( spl22_8
| spl22_9
| spl22_10
| spl22_13 ),
inference(sat_conversion,[],[f346]) ).
cnf(s10,plain,
( spl22_8
| spl22_9
| spl22_13
| spl22_14 ),
inference(sat_conversion,[],[f351]) ).
cnf(s11,plain,
( spl22_8
| spl22_9
| spl22_12
| spl22_15 ),
inference(sat_conversion,[],[f356]) ).
cnf(s12,plain,
( spl22_8
| spl22_9
| spl22_12
| spl22_16 ),
inference(sat_conversion,[],[f361]) ).
cnf(s13,plain,
( spl22_8
| spl22_9
| spl22_10
| spl22_15 ),
inference(sat_conversion,[],[f362]) ).
cnf(s14,plain,
( spl22_8
| spl22_9
| spl22_10
| spl22_16 ),
inference(sat_conversion,[],[f363]) ).
cnf(s15,plain,
( spl22_8
| spl22_9
| spl22_14
| spl22_15 ),
inference(sat_conversion,[],[f364]) ).
cnf(s16,plain,
( spl22_8
| spl22_9
| spl22_14
| spl22_16 ),
inference(sat_conversion,[],[f365]) ).
cnf(s17,plain,
( spl22_6
| spl22_8
| spl22_17
| spl22_18 ),
inference(sat_conversion,[],[f374]) ).
cnf(s18,plain,
( spl22_6
| spl22_8
| spl22_17
| spl22_19 ),
inference(sat_conversion,[],[f379]) ).
cnf(s19,plain,
( spl22_6
| spl22_8
| spl22_17
| spl22_20 ),
inference(sat_conversion,[],[f384]) ).
cnf(s20,plain,
( spl22_8
| spl22_17
| spl22_21
| spl22_22 ),
inference(sat_conversion,[],[f393]) ).
cnf(s21,plain,
( spl22_8
| spl22_17
| spl22_21
| spl22_23 ),
inference(sat_conversion,[],[f398]) ).
cnf(s22,plain,
( spl22_8
| spl22_17
| spl22_21
| spl22_24 ),
inference(sat_conversion,[],[f403]) ).
cnf(s23,plain,
( spl22_8
| spl22_17
| spl22_25
| spl22_26 ),
inference(sat_conversion,[],[f412]) ).
cnf(s24,plain,
( spl22_8
| spl22_17
| spl22_23
| spl22_26 ),
inference(sat_conversion,[],[f413]) ).
cnf(s25,plain,
( spl22_8
| spl22_17
| spl22_25
| spl22_27 ),
inference(sat_conversion,[],[f418]) ).
cnf(s26,plain,
( spl22_8
| spl22_17
| spl22_23
| spl22_27 ),
inference(sat_conversion,[],[f419]) ).
cnf(s27,plain,
( spl22_8
| spl22_17
| spl22_26
| spl22_28 ),
inference(sat_conversion,[],[f424]) ).
cnf(s28,plain,
( spl22_8
| spl22_17
| spl22_27
| spl22_28 ),
inference(sat_conversion,[],[f425]) ).
cnf(s29,plain,
( spl22_29
| spl22_30 ),
inference(sat_conversion,[],[f432]) ).
cnf(s30,plain,
( spl22_29
| spl22_31 ),
inference(sat_conversion,[],[f436]) ).
cnf(s33,plain,
( ~ spl22_2
| ~ spl22_8 ),
inference(sat_conversion,[],[f455]) ).
cnf(s36,plain,
( ~ spl22_2
| ~ spl22_9
| ~ spl22_17 ),
inference(sat_conversion,[],[f479]) ).
cnf(s39,plain,
( ~ spl22_6
| ~ spl22_13
| ~ spl22_15
| ~ spl22_16
| ~ spl22_29 ),
inference(sat_conversion,[],[f564]) ).
cnf(s44,plain,
( ~ spl22_6
| ~ spl22_21
| ~ spl22_26
| ~ spl22_27
| ~ spl22_29 ),
inference(sat_conversion,[],[f643]) ).
cnf(s50,plain,
( ~ spl22_23
| ~ spl22_25
| ~ spl22_28
| ~ spl22_29 ),
inference(sat_conversion,[],[f694]) ).
cnf(s52,plain,
( ~ spl22_22
| ~ spl22_23
| ~ spl22_24
| ~ spl22_29 ),
inference(sat_conversion,[],[f755]) ).
cnf(s53,plain,
( ~ spl22_1
| spl22_2
| ~ spl22_3 ),
inference(sat_conversion,[],[f785]) ).
cnf(s60,plain,
( ~ spl22_10
| ~ spl22_12
| ~ spl22_14
| ~ spl22_29 ),
inference(sat_conversion,[],[f891]) ).
cnf(s72,plain,
( ~ spl22_18
| ~ spl22_19
| ~ spl22_20
| ~ spl22_29 ),
inference(sat_conversion,[],[f1981]) ).
cnf(s76,plain,
( ~ spl22_7
| ~ spl22_10
| ~ spl22_11
| ~ spl22_29 ),
inference(sat_conversion,[],[f2075]) ).
cnf(s124,plain,
( spl22_29
| ~ spl22_30
| ~ spl22_31 ),
inference(sat_conversion,[],[f2703]) ).
cnf(s125,plain,
spl22_29,
inference(rat,[],[s124,s29,s30]) ).
cnf(s126,plain,
( spl22_17
| spl22_6
| spl22_8 ),
inference(rat,[],[s72,s17,s18,s19,s125]) ).
cnf(s127,plain,
( spl22_9
| spl22_6
| spl22_8 ),
inference(rat,[],[s76,s5,s6,s7,s125]) ).
cnf(s128,plain,
( spl22_6
| ~ spl22_2 ),
inference(rat,[],[s127,s36,s126,s33]) ).
cnf(s129,plain,
( spl22_21
| spl22_17
| spl22_8 ),
inference(rat,[],[s52,s20,s21,s22,s125]) ).
cnf(s130,plain,
( spl22_25
| spl22_17
| ~ spl22_2 ),
inference(rat,[],[s44,s23,s25,s128,s129,s33,s125]) ).
cnf(s131,plain,
( spl22_27
| ~ spl22_25
| spl22_17
| spl22_8 ),
inference(rat,[],[s50,s26,s28,s125]) ).
cnf(s132,plain,
( spl22_17
| ~ spl22_2 ),
inference(rat,[],[s50,s24,s27,s44,s131,s130,s129,s33,s128,s125]) ).
cnf(s133,plain,
( spl22_10
| ~ spl22_2 ),
inference(rat,[],[s39,s9,s13,s14,s33,s128,s36,s132,s125]) ).
cnf(s134,plain,
( spl22_13
| ~ spl22_2 ),
inference(rat,[],[s60,s8,s10,s33,s36,s132,s133,s125]) ).
cnf(s135,plain,
( spl22_12
| ~ spl22_2 ),
inference(rat,[],[s39,s11,s12,s33,s128,s36,s132,s134,s125]) ).
cnf(s136,plain,
~ spl22_2,
inference(rat,[],[s39,s15,s16,s60,s135,s134,s133,s36,s132,s128,s33,s125]) ).
cnf(s139,plain,
spl22_3,
inference(rat,[],[s2,s136]) ).
cnf(s140,plain,
spl22_1,
inference(rat,[],[s1,s136]) ).
cnf(s141,plain,
$false,
inference(rat,[],[s53,s136,s140,s139]) ).
thf(f2704,plain,
$false,
inference(avatar_sat_refutation,[],[s141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL602^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.19 % Computer : n004.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Sep 29 09:19:07 UTC 2026
% 0.06/0.20 % CPUTime :
% 0.06/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.40 % (1044721)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.40 % (1044726)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3582060693:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.18/0.40 % (1044727)lrs+10_16_si=on:nwc=1.5:random_seed=2005545381:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.18/0.40 % (1044728)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1833783021:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.18/0.40 % (1044729)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3727707624:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.18/0.40 % (1044730)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=85119956:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.18/0.40 % (1044728)Instruction limit reached!
% 0.18/0.40 % (1044728)------------------------------
% 0.18/0.40 % (1044728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.40 % (1044728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.40 % (1044728)CaDiCaL version: 2.1.3
% 0.18/0.40 % (1044728)Termination reason: Instruction limit
% 0.18/0.40 % (1044728)Termination phase: Property scanning
% 0.18/0.40 % (1044728)Time elapsed: 0.003 s
% 0.18/0.40 % (1044728)Peak memory usage: 10 MB
% 0.18/0.40 % (1044728)Instructions burned: 6 (million)
% 0.18/0.40 % (1044727)Instruction limit reached!
% 0.18/0.40 % (1044727)------------------------------
% 0.18/0.40 % (1044727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.40 % (1044727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.40 % (1044727)CaDiCaL version: 2.1.3
% 0.18/0.40 % (1044727)Termination reason: Instruction limit
% 0.18/0.40 % (1044727)Termination phase: Saturation
% 0.18/0.40 % (1044727)Time elapsed: 0.010 s
% 0.18/0.40 % (1044727)Peak memory usage: 12 MB
% 0.18/0.40 % (1044727)Instructions burned: 18 (million)
% 0.18/0.40 % (1044732)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.18/0.40 % (1044732)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.18/0.40 % (1044731)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1308560510:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.18/0.40 % (1044732)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2910213472:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.18/0.40 % (1044730)Instruction limit reached!
% 0.18/0.40 % (1044730)------------------------------
% 0.18/0.40 % (1044730)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.40 % (1044730)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.40 % (1044730)CaDiCaL version: 2.1.3
% 0.18/0.40 % (1044730)Termination reason: Instruction limit
% 0.18/0.40 % (1044730)Termination phase: Saturation
% 0.18/0.40 % (1044730)Time elapsed: 0.015 s
% 0.18/0.40 % (1044730)Peak memory usage: 12 MB
% 0.18/0.40 % (1044730)Instructions burned: 24 (million)
% 0.18/0.40 % (1044726)Instruction limit reached!
% 0.18/0.40 % (1044726)------------------------------
% 0.18/0.40 % (1044726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.40 % (1044726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.40 % (1044726)CaDiCaL version: 2.1.3
% 0.18/0.40 % (1044726)Termination reason: Instruction limit
% 0.18/0.40 % (1044726)Termination phase: Saturation
% 0.18/0.40 % (1044726)Time elapsed: 0.025 s
% 0.18/0.40 % (1044726)Peak memory usage: 13 MB
% 0.18/0.40 % (1044726)Instructions burned: 88 (million)
% 0.18/0.40 % (1044744)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=584042652:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.18/0.40 % (1044744)Instruction limit reached!
% 0.18/0.40 % (1044744)------------------------------
% 0.18/0.40 % (1044744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.42 % (1044744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.42 % (1044744)CaDiCaL version: 2.1.3
% 0.87/0.42 % (1044744)Termination reason: Instruction limit
% 0.87/0.42 % (1044744)Termination phase: shuffling
% 0.87/0.42 % (1044744)Time elapsed: 0.002 s
% 0.87/0.42 % (1044744)Peak memory usage: 9 MB
% 0.87/0.42 % (1044744)Instructions burned: 2 (million)
% 0.87/0.42 % (1044752)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3656077706:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.87/0.42 % (1044746)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2671849669:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.87/0.42 % (1044746)Instruction limit reached!
% 0.87/0.42 % (1044746)------------------------------
% 0.87/0.42 % (1044746)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.42 % (1044746)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.42 % (1044746)CaDiCaL version: 2.1.3
% 0.87/0.42 % (1044746)Termination reason: Instruction limit
% 0.87/0.42 % (1044746)Termination phase: Property scanning
% 0.87/0.42 % (1044746)Time elapsed: 0.003 s
% 0.87/0.42 % (1044746)Peak memory usage: 10 MB
% 0.87/0.42 % (1044746)Instructions burned: 6 (million)
% 0.87/0.42 % (1044752)Instruction limit reached!
% 0.87/0.42 % (1044752)------------------------------
% 0.87/0.42 % (1044752)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.42 % (1044752)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.42 % (1044752)CaDiCaL version: 2.1.3
% 0.87/0.42 % (1044752)Termination reason: Instruction limit
% 0.87/0.42 % (1044752)Termination phase: Saturation
% 0.87/0.42 % (1044752)Time elapsed: 0.004 s
% 0.87/0.42 % (1044752)Peak memory usage: 11 MB
% 0.87/0.42 % (1044752)Instructions burned: 15 (million)
% 0.87/0.42 % (1044751)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.87/0.42 % (1044751)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1536362551:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.87/0.42 % (1044751)Instruction limit reached!
% 0.87/0.42 % (1044751)------------------------------
% 0.87/0.42 % (1044751)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.42 % (1044751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.42 % (1044751)CaDiCaL version: 2.1.3
% 0.87/0.42 % (1044751)Termination reason: Instruction limit
% 0.87/0.42 % (1044751)Termination phase: Saturation
% 0.87/0.42 % (1044751)Time elapsed: 0.004 s
% 0.87/0.42 % (1044751)Peak memory usage: 11 MB
% 0.87/0.42 % (1044751)Instructions burned: 8 (million)
% 0.87/0.42 % (1044757)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.87/0.42 % (1044757)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.87/0.42 % (1044731)Instruction limit reached!
% 0.87/0.42 % (1044731)------------------------------
% 0.87/0.42 % (1044731)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.42 % (1044731)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.42 % (1044731)CaDiCaL version: 2.1.3
% 0.87/0.42 % (1044731)Termination reason: Instruction limit
% 0.87/0.42 % (1044731)Termination phase: Saturation
% 0.87/0.42 % (1044731)Time elapsed: 0.036 s
% 0.87/0.42 % (1044731)Peak memory usage: 12 MB
% 0.87/0.42 % (1044731)Instructions burned: 77 (million)
% 0.87/0.42 % (1044762)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2405189986:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.87/0.42 % (1044757)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1506671351:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.87/0.42 % (1044763)lrs+10_1_si=on:cs=on:random_seed=3607191831:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.87/0.42 % (1044767)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.87/0.46 % (1044767)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3275619165:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.87/0.46 % (1044767)Instruction limit reached!
% 0.87/0.46 % (1044767)------------------------------
% 0.87/0.46 % (1044767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.46 % (1044767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.46 % (1044767)CaDiCaL version: 2.1.3
% 0.87/0.46 % (1044767)Termination reason: Instruction limit
% 0.87/0.46 % (1044767)Termination phase: Saturation
% 0.87/0.46 % (1044767)Time elapsed: 0.003 s
% 0.87/0.46 % (1044767)Peak memory usage: 10 MB
% 0.87/0.46 % (1044767)Instructions burned: 7 (million)
% 0.87/0.46 % (1044763)Instruction limit reached!
% 0.87/0.46 % (1044763)------------------------------
% 0.87/0.46 % (1044763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.46 % (1044763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.46 % (1044763)CaDiCaL version: 2.1.3
% 0.87/0.46 % (1044763)Termination reason: Instruction limit
% 0.87/0.46 % (1044763)Termination phase: Saturation
% 0.87/0.46 % (1044763)Time elapsed: 0.013 s
% 0.87/0.46 % (1044763)Peak memory usage: 12 MB
% 0.87/0.46 % (1044763)Instructions burned: 9 (million)
% 0.87/0.46 % (1044768)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=995780088:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.87/0.46 % (1044757)Instruction limit reached!
% 0.87/0.46 % (1044757)------------------------------
% 0.87/0.46 % (1044757)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.46 % (1044757)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.46 % (1044757)CaDiCaL version: 2.1.3
% 0.87/0.46 % (1044757)Termination reason: Instruction limit
% 0.87/0.46 % (1044757)Termination phase: Saturation
% 0.87/0.46 % (1044757)Time elapsed: 0.023 s
% 0.87/0.46 % (1044757)Peak memory usage: 12 MB
% 0.87/0.46 % (1044757)Instructions burned: 28 (million)
% 0.87/0.46 % (1044768)Refutation not found, incomplete strategy
% 0.87/0.46 % (1044768)------------------------------
% 0.87/0.46 % (1044768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.46 % (1044768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.46 % (1044768)CaDiCaL version: 2.1.3
% 0.87/0.46 % (1044768)Termination reason: Refutation not found, incomplete strategy
% 0.87/0.46 % (1044768)Time elapsed: 0.007 s
% 0.87/0.46 % (1044768)Peak memory usage: 12 MB
% 0.87/0.46 % (1044768)Instructions burned: 12 (million)
% 0.87/0.46 % (1044768)------------------------------
% 0.87/0.46 % (1044768)------------------------------
% 0.87/0.46 % (1044776)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=903565212:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.87/0.46 % (1044776)Instruction limit reached!
% 0.87/0.46 % (1044776)------------------------------
% 0.87/0.46 % (1044776)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.46 % (1044776)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.46 % (1044776)CaDiCaL version: 2.1.3
% 0.87/0.46 % (1044776)Termination reason: Instruction limit
% 0.87/0.46 % (1044776)Termination phase: Saturation
% 0.87/0.46 % (1044776)Time elapsed: 0.004 s
% 0.87/0.46 % (1044776)Peak memory usage: 12 MB
% 0.87/0.46 % (1044776)Instructions burned: 15 (million)
% 0.87/0.46 % (1044775)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=308614898:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.87/0.46 % (1044773)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4009361243:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.87/0.46 % (1044762)Instruction limit reached!
% 0.87/0.46 % (1044762)------------------------------
% 0.87/0.46 % (1044762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.46 % (1044762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.46 % (1044762)CaDiCaL version: 2.1.3
% 0.87/0.46 % (1044762)Termination reason: Instruction limit
% 0.87/0.49 % (1044762)Termination phase: Saturation
% 0.87/0.49 % (1044762)Time elapsed: 0.052 s
% 0.87/0.49 % (1044762)Peak memory usage: 12 MB
% 0.87/0.49 % (1044762)Instructions burned: 87 (million)
% 0.87/0.49 % (1044777)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2191270424:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.87/0.49 % (1044775)Instruction limit reached!
% 0.87/0.49 % (1044775)------------------------------
% 0.87/0.49 % (1044775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.49 % (1044775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.49 % (1044775)CaDiCaL version: 2.1.3
% 0.87/0.49 % (1044775)Termination reason: Instruction limit
% 0.87/0.49 % (1044775)Termination phase: Saturation
% 0.87/0.49 % (1044775)Time elapsed: 0.015 s
% 0.87/0.49 % (1044775)Peak memory usage: 12 MB
% 0.87/0.49 % (1044775)Instructions burned: 26 (million)
% 0.87/0.49 % (1044773)Refutation not found, incomplete strategy
% 0.87/0.49 % (1044773)------------------------------
% 0.87/0.49 % (1044773)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.49 % (1044773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.49 % (1044773)CaDiCaL version: 2.1.3
% 0.87/0.49 % (1044773)Termination reason: Refutation not found, incomplete strategy
% 0.87/0.49 % (1044773)Time elapsed: 0.010 s
% 0.87/0.49 % (1044773)Peak memory usage: 12 MB
% 0.87/0.49 % (1044773)Instructions burned: 13 (million)
% 0.87/0.49 % (1044773)------------------------------
% 0.87/0.49 % (1044773)------------------------------
% 0.87/0.49 % (1044732)Instruction limit reached!
% 0.87/0.49 % (1044732)------------------------------
% 0.87/0.49 % (1044732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.49 % (1044732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.49 % (1044732)CaDiCaL version: 2.1.3
% 0.87/0.49 % (1044732)Termination reason: Instruction limit
% 0.87/0.49 % (1044732)Termination phase: Saturation
% 0.87/0.49 % (1044732)Time elapsed: 0.098 s
% 0.87/0.49 % (1044732)Peak memory usage: 13 MB
% 0.87/0.49 % (1044732)Instructions burned: 157 (million)
% 0.87/0.49 % (1044793)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2273778861:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.87/0.49 % (1044788)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2695725243:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.87/0.49 % (1044793)Instruction limit reached!
% 0.87/0.49 % (1044793)------------------------------
% 0.87/0.49 % (1044793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.49 % (1044793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.49 % (1044793)CaDiCaL version: 2.1.3
% 0.87/0.49 % (1044793)Termination reason: Instruction limit
% 0.87/0.49 % (1044793)Termination phase: Property scanning
% 0.87/0.49 % (1044793)Time elapsed: 0.001 s
% 0.87/0.49 % (1044793)Peak memory usage: 10 MB
% 0.87/0.49 % (1044793)Instructions burned: 4 (million)
% 0.87/0.49 % (1044788)Instruction limit reached!
% 0.87/0.49 % (1044788)------------------------------
% 0.87/0.49 % (1044788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.49 % (1044788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.49 % (1044788)CaDiCaL version: 2.1.3
% 0.87/0.49 % (1044788)Termination reason: Instruction limit
% 0.87/0.49 % (1044788)Termination phase: Saturation
% 0.87/0.49 % (1044788)Time elapsed: 0.007 s
% 0.87/0.49 % (1044788)Peak memory usage: 12 MB
% 0.87/0.49 % (1044788)Instructions burned: 15 (million)
% 0.87/0.49 % (1044800)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.87/0.49 % (1044800)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.87/0.49 % (1044800)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3558953805:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.87/0.49 % (1044795)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3489685586:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.56/0.54 % (1044796)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=3178257636:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.56/0.54 % (1044800)Instruction limit reached!
% 1.56/0.54 % (1044800)------------------------------
% 1.56/0.54 % (1044800)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.54 % (1044800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.54 % (1044800)CaDiCaL version: 2.1.3
% 1.56/0.54 % (1044800)Termination reason: Instruction limit
% 1.56/0.54 % (1044800)Termination phase: Saturation
% 1.56/0.54 % (1044800)Time elapsed: 0.004 s
% 1.56/0.54 % (1044800)Peak memory usage: 12 MB
% 1.56/0.54 % (1044800)Instructions burned: 15 (million)
% 1.56/0.54 % (1044797)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3924830893:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.56/0.54 % (1044801)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.56/0.54 % (1044806)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=613365371:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.56/0.54 % (1044801)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3430495152:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.56/0.54 % (1044795)Instruction limit reached!
% 1.56/0.54 % (1044795)------------------------------
% 1.56/0.54 % (1044795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.54 % (1044795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.54 % (1044795)CaDiCaL version: 2.1.3
% 1.56/0.54 % (1044795)Termination reason: Instruction limit
% 1.56/0.54 % (1044795)Termination phase: Saturation
% 1.56/0.54 % (1044795)Time elapsed: 0.013 s
% 1.56/0.54 % (1044795)Peak memory usage: 12 MB
% 1.56/0.54 % (1044795)Instructions burned: 26 (million)
% 1.56/0.54 % (1044796)Instruction limit reached!
% 1.56/0.54 % (1044796)------------------------------
% 1.56/0.54 % (1044796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.54 % (1044796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.54 % (1044796)CaDiCaL version: 2.1.3
% 1.56/0.54 % (1044796)Termination reason: Instruction limit
% 1.56/0.54 % (1044796)Termination phase: Saturation
% 1.56/0.54 % (1044796)Time elapsed: 0.012 s
% 1.56/0.54 % (1044796)Peak memory usage: 11 MB
% 1.56/0.54 % (1044796)Instructions burned: 24 (million)
% 1.56/0.54 % (1044801)Instruction limit reached!
% 1.56/0.54 % (1044801)------------------------------
% 1.56/0.54 % (1044801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.54 % (1044801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.54 % (1044801)CaDiCaL version: 2.1.3
% 1.56/0.54 % (1044801)Termination reason: Instruction limit
% 1.56/0.54 % (1044801)Termination phase: Function definition elimination
% 1.56/0.54 % (1044801)Time elapsed: 0.004 s
% 1.56/0.54 % (1044801)Peak memory usage: 10 MB
% 1.56/0.54 % (1044801)Instructions burned: 8 (million)
% 1.56/0.54 % (1044806)Instruction limit reached!
% 1.56/0.54 % (1044806)------------------------------
% 1.56/0.54 % (1044806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.54 % (1044806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.54 % (1044806)CaDiCaL version: 2.1.3
% 1.56/0.54 % (1044806)Termination reason: Instruction limit
% 1.56/0.54 % (1044806)Termination phase: Saturation
% 1.56/0.54 % (1044806)Time elapsed: 0.008 s
% 1.56/0.54 % (1044806)Peak memory usage: 12 MB
% 1.56/0.54 % (1044806)Instructions burned: 31 (million)
% 1.56/0.54 % (1044812)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=811608860:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.56/0.54 % (1044809)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=1632804740:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.56/0.54 % (1044810)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=582964740:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.56/0.55 % (1044809)Instruction limit reached!
% 1.56/0.55 % (1044809)------------------------------
% 1.56/0.55 % (1044809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.55 % (1044809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.55 % (1044809)CaDiCaL version: 2.1.3
% 1.56/0.55 % (1044809)Termination reason: Instruction limit
% 1.56/0.55 % (1044809)Termination phase: Function definition elimination
% 1.56/0.55 % (1044809)Time elapsed: 0.003 s
% 1.56/0.55 % (1044809)Peak memory usage: 10 MB
% 1.56/0.55 % (1044809)Instructions burned: 7 (million)
% 1.56/0.55 % (1044811)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1124948327:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.56/0.55 % (1044797)Instruction limit reached!
% 1.56/0.55 % (1044797)------------------------------
% 1.56/0.55 % (1044797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.55 % (1044797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.55 % (1044797)CaDiCaL version: 2.1.3
% 1.56/0.55 % (1044797)Termination reason: Instruction limit
% 1.56/0.55 % (1044797)Termination phase: Saturation
% 1.56/0.55 % (1044797)Time elapsed: 0.034 s
% 1.56/0.55 % (1044797)Peak memory usage: 12 MB
% 1.56/0.55 % (1044797)Instructions burned: 60 (million)
% 1.56/0.55 % (1044810)Instruction limit reached!
% 1.56/0.55 % (1044810)------------------------------
% 1.56/0.55 % (1044810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.55 % (1044810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.55 % (1044810)CaDiCaL version: 2.1.3
% 1.56/0.55 % (1044810)Termination reason: Instruction limit
% 1.56/0.55 % (1044810)Termination phase: Saturation
% 1.56/0.55 % (1044810)Time elapsed: 0.010 s
% 1.56/0.55 % (1044810)Peak memory usage: 11 MB
% 1.56/0.55 % (1044810)Instructions burned: 23 (million)
% 1.56/0.55 % (1044811)Instruction limit reached!
% 1.56/0.55 % (1044811)------------------------------
% 1.56/0.55 % (1044811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.55 % (1044811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.55 % (1044811)CaDiCaL version: 2.1.3
% 1.56/0.55 % (1044811)Termination reason: Instruction limit
% 1.56/0.55 % (1044811)Termination phase: Saturation
% 1.56/0.55 % (1044811)Time elapsed: 0.011 s
% 1.56/0.55 % (1044811)Peak memory usage: 12 MB
% 1.56/0.55 % (1044811)Instructions burned: 20 (million)
% 1.56/0.55 % (1044812)Refutation not found, incomplete strategy
% 1.56/0.55 % (1044812)------------------------------
% 1.56/0.55 % (1044812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.55 % (1044812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.55 % (1044812)CaDiCaL version: 2.1.3
% 1.56/0.55 % (1044812)Termination reason: Refutation not found, incomplete strategy
% 1.56/0.55 % (1044812)Time elapsed: 0.022 s
% 1.56/0.55 % (1044812)Peak memory usage: 12 MB
% 1.56/0.55 % (1044812)Instructions burned: 83 (million)
% 1.56/0.55 % (1044812)------------------------------
% 1.56/0.55 % (1044812)------------------------------
% 1.56/0.55 % (1044817)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=571575185:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 1.56/0.55 % (1044818)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2131173743:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 1.56/0.55 % (1044819)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1630006304:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 1.56/0.55 % (1044820)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.56/0.55 % (1044822)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1108245334:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 1.56/0.55 % (1044820)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2996781148:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 1.56/0.55 % (1044818)Refutation not found, incomplete strategy
% 1.56/0.55 % (1044818)------------------------------
% 1.56/0.55 % (1044818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.55 % (1044818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.55 % (1044818)CaDiCaL version: 2.1.3
% 1.56/0.55 % (1044818)Termination reason: Refutation not found, incomplete strategy
% 1.56/0.55 % (1044818)Time elapsed: 0.008 s
% 1.56/0.55 % (1044818)Peak memory usage: 12 MB
% 1.56/0.55 % (1044818)Instructions burned: 14 (million)
% 1.56/0.55 % (1044818)------------------------------
% 1.56/0.55 % (1044818)------------------------------
% 1.56/0.55 % (1044820)Instruction limit reached!
% 1.56/0.55 % (1044820)------------------------------
% 1.56/0.55 % (1044820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.55 % (1044820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.55 % (1044820)CaDiCaL version: 2.1.3
% 1.56/0.55 % (1044820)Termination reason: Instruction limit
% 1.56/0.55 % (1044820)Termination phase: Saturation
% 1.56/0.55 % (1044820)Time elapsed: 0.004 s
% 1.56/0.55 % (1044820)Peak memory usage: 11 MB
% 1.56/0.55 % (1044820)Instructions burned: 8 (million)
% 1.56/0.55 % (1044828)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 1.56/0.55 % (1044819)Instruction limit reached!
% 1.56/0.55 % (1044819)------------------------------
% 1.56/0.55 % (1044819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.55 % (1044819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.55 % (1044819)CaDiCaL version: 2.1.3
% 1.56/0.55 % (1044819)Termination reason: Instruction limit
% 1.56/0.55 % (1044819)Termination phase: Saturation
% 1.56/0.55 % (1044819)Time elapsed: 0.025 s
% 1.56/0.55 % (1044819)Peak memory usage: 12 MB
% 1.56/0.55 % (1044819)Instructions burned: 43 (million)
% 1.56/0.55 % (1044827)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=421195680:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 1.56/0.55 % (1044828)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=1268374359:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 1.56/0.55 % (1044828)Instruction limit reached!
% 1.56/0.55 % (1044828)------------------------------
% 1.56/0.55 % (1044828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.55 % (1044828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.55 % (1044828)CaDiCaL version: 2.1.3
% 1.56/0.55 % (1044828)Termination reason: Instruction limit
% 1.56/0.55 % (1044828)Termination phase: Property scanning
% 1.56/0.55 % (1044828)Time elapsed: 0.003 s
% 1.56/0.55 % (1044828)Peak memory usage: 10 MB
% 1.56/0.55 % (1044828)Instructions burned: 6 (million)
% 1.56/0.55 % (1044822)Instruction limit reached!
% 1.56/0.55 % (1044822)------------------------------
% 1.56/0.55 % (1044822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.55 % (1044822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.55 % (1044822)CaDiCaL version: 2.1.3
% 1.56/0.55 % (1044822)Termination reason: Instruction limit
% 1.56/0.55 % (1044822)Termination phase: Saturation
% 1.56/0.55 % (1044822)Time elapsed: 0.039 s
% 1.56/0.55 % (1044822)Peak memory usage: 12 MB
% 1.56/0.55 % (1044822)Instructions burned: 182 (million)
% 1.56/0.55 % (1044830)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=1637187101:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 1.56/0.55 % (1044832)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=433482897:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 1.56/0.55 % (1044833)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3480760496:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 1.56/0.55 % (1044777) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1044721-1044777"...
% 1.56/0.55 % (1044830)Instruction limit reached!
% 1.56/0.55 % (1044830)------------------------------
% 1.56/0.55 % (1044830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.55 % (1044830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.55 % (1044830)CaDiCaL version: 2.1.3
% 1.56/0.55 % (1044830)Termination reason: Instruction limit
% 1.56/0.55 % (1044830)Termination phase: Saturation
% 1.56/0.55 % (1044830)Time elapsed: 0.012 s
% 1.56/0.55 % (1044830)Peak memory usage: 12 MB
% 1.56/0.55 % (1044830)Instructions burned: 23 (million)
% 1.56/0.55 % (1044832)Instruction limit reached!
% 1.56/0.55 % (1044832)------------------------------
% 1.56/0.55 % (1044832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.55 % (1044832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.55 % (1044832)CaDiCaL version: 2.1.3
% 1.56/0.55 % (1044832)Termination reason: Instruction limit
% 1.56/0.55 % (1044832)Termination phase: Saturation
% 1.56/0.55 % (1044832)Time elapsed: 0.011 s
% 1.56/0.55 % (1044832)Peak memory usage: 13 MB
% 1.56/0.55 % (1044832)Instructions burned: 20 (million)
% 1.56/0.55 % (1044777)...printing done.
% 1.56/0.55 % (1044777)Refutation found. Thanks to Tanya!
% 1.56/0.55 % SZS status Theorem for theBenchmark
% 1.56/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 1.56/0.56 % (1044777)------------------------------
% 1.56/0.56 % (1044777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.56/0.56 % (1044777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.56/0.56 % (1044777)CaDiCaL version: 2.1.3
% 1.56/0.56 % (1044777)Termination reason: Refutation
% 1.56/0.56 % (1044777)Time elapsed: 0.151 s
% 1.56/0.56 % (1044777)Peak memory usage: 13 MB
% 1.56/0.56 % (1044777)Instructions burned: 314 (million)
% 1.56/0.56 % (1044721)Success in time 0.304 s
% 1.56/0.56 % Vampire exiting
%------------------------------------------------------------------------------