%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL600^1 : 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 08:14:25 AM UTC 2026
% Result : Theorem 0.50s 0.41s
% Output : Refutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 25
% Syntax : Number of formulae : 214 ( 38 unt; 0 typ; 18 def)
% Number of atoms : 1676 ( 363 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 2056 ( 188 ~; 375 |; 29 &;1232 @)
% ( 19 <=>; 102 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 208 ( 208 >; 0 *; 0 +; 0 <<)
% Number of symbols : 89 ( 85 usr; 26 con; 0-4 aty)
% ( 110 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 486 ( 0 sgn 193 !; 5 ?; 486 :)
% 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,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_48,type,
vAND: $o > $o > $o ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_52,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_53,type,
vNOT: $o > $o ).
thf(func_def_54,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
vOR: $o > $o > $o ).
thf(func_def_56,type,
vIFF: $o > $o > $o ).
thf(func_def_57,type,
sK0: $i > $i > $o ).
thf(func_def_58,type,
sK1: $i > $o ).
thf(func_def_59,type,
sF2: $o ).
thf(func_def_60,type,
sF3: $o ).
thf(func_def_61,type,
sF4: ( $i > $o ) > $o ).
thf(func_def_62,type,
sK5: $i > ( $i > $o ) > $i ).
thf(func_def_63,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_64,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_65,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_66,type,
sK9: $i > $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] :
( ( X0 @ X2 )
| ( X1 @ 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,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f27,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $i,X2: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
= transitive ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',transitive) ).
thf(f37,conjecture,
! [X0: $i > $i > $o] :
( ( transitive @ X0 )
<=> ! [X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f38,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( transitive @ X0 )
<=> ! [X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f63,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f64,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f68,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f77,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X3 @ X2 ) )
=> ( X0 @ X1 @ X2 ) ) )
= transitive ),
inference(rectify,[],[f27]) ).
thf(f78,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f80,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f81,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f93,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f94,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f93]) ).
thf(f97,plain,
~ ! [X0: $i > $i > $o] :
( ( transitive @ X0 )
<=> ! [X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f98,plain,
~ ! [X0: $i > $i > $o] :
( ( ( transitive @ X0 )
= $true )
<=> ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true ) ),
inference(fool_elimination,[],[f97]) ).
thf(f99,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f100,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f99]) ).
thf(f106,plain,
? [X0: $i > $i > $o] :
( ( ( transitive @ X0 )
= $true )
<~> ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true ) ),
inference(ennf_transformation,[],[f98]) ).
thf(f107,plain,
? [X0: $i > $i > $o] :
( ( ? [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
!= $true )
| ( ( transitive @ X0 )
!= $true ) )
& ( ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true )
| ( ( transitive @ 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 )
| ( ( transitive @ X0 )
!= $true ) )
& ( ! [X2: $i > $o] :
( $true
= ( mvalid @ ( mimpl @ ( mbox @ X0 @ X2 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X2 ) ) ) ) )
| ( ( transitive @ X0 )
= $true ) ) ),
inference(rectify,[],[f107]) ).
thf(f109,plain,
( ( ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ sK1 ) ) ) ) )
| ( $true
!= ( transitive @ sK0 ) ) )
& ( ! [X2: $i > $o] :
( $true
= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X2 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ X2 ) ) ) ) )
| ( $true
= ( transitive @ sK0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f108]) ).
thf(f117,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f119,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f122,plain,
! [X2: $i > $o] :
( ( $true
= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X2 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ X2 ) ) ) ) )
| ( $true
= ( transitive @ sK0 ) ) ),
inference(cnf_transformation,[],[f109]) ).
thf(f123,plain,
( ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ sK0 @ sK1 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ sK1 ) ) ) ) )
| ( $true
!= ( transitive @ sK0 ) ) ),
inference(cnf_transformation,[],[f109]) ).
thf(f129,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f135,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f142,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f144,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f100]) ).
thf(f150,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f117,f135,f144]) ).
thf(f154,plain,
( ( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ 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
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f123,f142,f150,f129,f129,f129,f119]) ).
thf(f155,plain,
! [X2: $i > $o] :
( ( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ 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 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f122,f142,f150,f129,f129,f129,f119]) ).
thf(f156,definition,
( sF2
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ 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 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f157,definition,
( sF3
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f158,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 )
= sF3 ),
inference(reorient_equations,[],[f157]) ).
thf(f159,plain,
( ( $true != sF2 )
| ( $true != sF3 ) ),
inference(definition_folding,[],[f154,f158,f156]) ).
thf(f160,definition,
! [X2: $i > $o] :
( ( sF4 @ X2 )
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ 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 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f161,plain,
! [X2: $i > $o] :
( ( ( sF4 @ X2 )
= $true )
| ( $true = sF3 ) ),
inference(definition_folding,[],[f155,f158,f160]) ).
thf(f163,plain,
! [X2: $i > $o] :
( ( ( sF4 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ 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(iff_proxy_clausification,[],[f160]) ).
thf(f164,plain,
! [X2: $i > $o] :
( ( ( sF4 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( X2 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
! [X2: $i > $o,X3: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( X2 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) )
@ X3 ) )
| ( ( sF4 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i > $o,X3: $i] :
( ( ( sF4 @ X2 )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X2 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X2: $i > $o,X3: $i] :
( ( ( sF4 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) )
@ X4 ) )
| ( ( sF4 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X2 @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) )
@ X4 ) )
| ( ( sF4 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( sF4 @ X2 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X2 @ Y0 ) )
@ ( sK5 @ X3 @ X2 ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X2 @ Y1 ) ) ) )
@ X4 ) ) ),
inference(sigma_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( sF4 @ X2 )
= $false )
| ( $false
= ( ( sK0 @ X3 @ ( sK5 @ X3 @ X2 ) )
=> ( X2 @ ( sK5 @ X3 @ X2 ) ) ) )
| ( $true
= ( ( sK0 @ X3 @ X4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( $false
= ( X2 @ ( sK5 @ X3 @ X2 ) ) )
| ( ( sF4 @ X2 )
= $false )
| ( $true
= ( ( sK0 @ X3 @ X4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( sF4 @ X2 )
= $false )
| ( $true
= ( ( sK0 @ X3 @ X4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) ) )
| ( $true
= ( sK0 @ X3 @ ( sK5 @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f171]) ).
thf(f174,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) )
| ( $true
= ( sK0 @ X3 @ ( sK5 @ X3 @ X2 ) ) )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( ( sF4 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) )
@ X5 ) )
| ( $true
= ( sK0 @ X3 @ ( sK5 @ X3 @ X2 ) ) )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( ( sF4 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( ( sF4 @ X2 )
= $false )
| ( $true
= ( ( sK0 @ X4 @ X5 )
=> ( X2 @ X5 ) ) )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( $true
= ( sK0 @ X3 @ ( sK5 @ X3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( ( sK0 @ X4 @ X5 )
= $false )
| ( $true
= ( sK0 @ X3 @ ( sK5 @ X3 @ X2 ) ) )
| ( ( sF4 @ X2 )
= $false )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( $true
= ( X2 @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i > $o,X3: $i,X4: $i] :
( ( ( sF4 @ X2 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) ) ) )
| ( $false
= ( X2 @ ( sK5 @ X3 @ X2 ) ) )
| ( ( sK0 @ X3 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f179,plain,
! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X4 @ Y0 )
=> ( X2 @ Y0 ) )
@ X5 ) )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( ( sF4 @ X2 )
= $false )
| ( $false
= ( X2 @ ( sK5 @ X3 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( $true
= ( ( sK0 @ X4 @ X5 )
=> ( X2 @ X5 ) ) )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( $false
= ( X2 @ ( sK5 @ X3 @ X2 ) ) )
| ( ( sF4 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( ( sF4 @ X2 )
= $false )
| ( ( sK0 @ X4 @ X5 )
= $false )
| ( $true
= ( X2 @ X5 ) )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( $false
= ( X2 @ ( sK5 @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f180]) ).
thf(f199,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ 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 = sF2 ) ),
inference(iff_proxy_clausification,[],[f156]) ).
thf(f219,plain,
( ( $true = sF2 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f220,plain,
( ( $true = sF2 )
| ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( sK1 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK10 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f219]) ).
thf(f221,plain,
( ( $true = sF2 )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK10 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f220]) ).
thf(f222,plain,
( ( $true = sF2 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f223,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK10 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) ) )
= $false )
| ( $true = sF2 ) ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f224,plain,
( ( ( ^ [Y0: $i] :
( ( sK0 @ sK10 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK1 @ Y1 ) ) ) )
@ sK11 )
= $false )
| ( $true = sF2 ) ),
inference(sigma_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ( $false
= ( ( sK0 @ sK10 @ sK11 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK11 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) )
| ( $true = sF2 ) ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f226,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK11 @ Y0 )
=> ( sK1 @ Y0 ) ) )
= $false )
| ( $true = sF2 ) ),
inference(imp_proxy_clausification,[],[f225]) ).
thf(f227,plain,
( ( $true = sF2 )
| ( $true
= ( sK0 @ sK10 @ sK11 ) ) ),
inference(imp_proxy_clausification,[],[f225]) ).
thf(f228,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK11 @ Y0 )
=> ( sK1 @ Y0 ) )
@ sK12 ) )
| ( $true = sF2 ) ),
inference(sigma_proxy_clausification,[],[f226]) ).
thf(f229,plain,
( ( $true = sF2 )
| ( $false
= ( ( sK0 @ sK11 @ sK12 )
=> ( sK1 @ sK12 ) ) ) ),
inference(beta-eta_normalization,[],[f228]) ).
thf(f230,plain,
( ( $true = sF2 )
| ( ( sK1 @ sK12 )
= $false ) ),
inference(imp_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( ( $true = sF2 )
| ( ( sK0 @ sK11 @ sK12 )
= $true ) ),
inference(imp_proxy_clausification,[],[f229]) ).
thf(f232,plain,
( ( $true = sF2 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f233,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK10 @ Y0 )
=> ( sK1 @ Y0 ) )
@ X1 ) )
| ( $true = sF2 ) ),
inference(pi_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK10 @ X1 )
=> ( sK1 @ X1 ) ) )
| ( $true = sF2 ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
! [X1: $i] :
( ( ( sK0 @ sK10 @ X1 )
= $false )
| ( $true
= ( sK1 @ X1 ) )
| ( $true = sF2 ) ),
inference(imp_proxy_clausification,[],[f234]) ).
thf(f236,plain,
( ( $false = sF3 )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 ) ) ),
inference(iff_proxy_clausification,[],[f158]) ).
thf(f237,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 )
= $false )
| ( $true = sF3 ) ),
inference(iff_proxy_clausification,[],[f158]) ).
thf(f238,plain,
( ( $true = sF3 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f239,plain,
( ( $true = sF3 )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK13 ) ) ),
inference(sigma_proxy_clausification,[],[f238]) ).
thf(f240,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK13 @ Y0 )
& ( sK0 @ Y1 @ sK13 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $true = sF3 ) ),
inference(beta-eta_normalization,[],[f239]) ).
thf(f241,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK13 @ Y0 )
& ( sK0 @ Y1 @ sK13 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK14 ) )
| ( $true = sF3 ) ),
inference(sigma_proxy_clausification,[],[f240]) ).
thf(f242,plain,
( ( $true = sF3 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK13 @ sK14 )
& ( sK0 @ Y0 @ sK13 ) )
=> ( sK0 @ Y0 @ sK14 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f241]) ).
thf(f243,plain,
( ( ( ^ [Y0: $i] :
( ( ( sK0 @ sK13 @ sK14 )
& ( sK0 @ Y0 @ sK13 ) )
=> ( sK0 @ Y0 @ sK14 ) )
@ sK15 )
= $false )
| ( $true = sF3 ) ),
inference(sigma_proxy_clausification,[],[f242]) ).
thf(f244,plain,
( ( $true = sF3 )
| ( $false
= ( ( ( sK0 @ sK13 @ sK14 )
& ( sK0 @ sK15 @ sK13 ) )
=> ( sK0 @ sK15 @ sK14 ) ) ) ),
inference(beta-eta_normalization,[],[f243]) ).
thf(f245,plain,
( ( $false
= ( sK0 @ sK15 @ sK14 ) )
| ( $true = sF3 ) ),
inference(imp_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( ( $true
= ( ( sK0 @ sK13 @ sK14 )
& ( sK0 @ sK15 @ sK13 ) ) )
| ( $true = sF3 ) ),
inference(imp_proxy_clausification,[],[f244]) ).
thf(f247,plain,
( ( ( sK0 @ sK15 @ sK13 )
= $true )
| ( $true = sF3 ) ),
inference(and_proxy_clausification,[],[f246]) ).
thf(f248,plain,
( ( $true
= ( sK0 @ sK13 @ sK14 ) )
| ( $true = sF3 ) ),
inference(and_proxy_clausification,[],[f246]) ).
thf(f249,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) ) )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f250,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true )
| ( $false = sF3 ) ),
inference(pi_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X1: $i] :
( ( $false = sF3 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ Y1 @ X1 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X1: $i] :
( ( $false = sF3 )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ Y1 @ X1 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X1 @ X2 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y0 @ X2 ) ) )
= $true )
| ( $false = sF3 ) ),
inference(beta-eta_normalization,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF3 )
| ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ X1 @ X2 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y0 @ X2 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF3 )
| ( ( ( ( sK0 @ X1 @ X2 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ X3 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X1 @ X2 )
& ( sK0 @ X3 @ X1 ) ) )
| ( $false = sF3 )
| ( ( sK0 @ X3 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false = sF3 )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X3 @ X2 )
= $true ) ),
inference(and_proxy_clausification,[],[f256]) ).
thf(f259,definition,
( spl16_1
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
thf(f263,definition,
( spl16_2
<=> ( $true = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
thf(f264,plain,
( ( $true = sF3 )
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f263]) ).
thf(f266,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(avatar_split_clause,[],[f159,f263,f259]) ).
thf(f280,definition,
( spl16_6
<=> ( $true
= ( sK0 @ sK10 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
thf(f282,plain,
( ( $true
= ( sK0 @ sK10 @ sK11 ) )
| ~ spl16_6 ),
inference(avatar_component_clause,[],[f280]) ).
thf(f283,plain,
( spl16_1
| spl16_6 ),
inference(avatar_split_clause,[],[f227,f280,f259]) ).
thf(f285,definition,
( spl16_7
<=> ( ( sK0 @ sK11 @ sK12 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl16_7])],[avatar_definition]) ).
thf(f287,plain,
( ( ( sK0 @ sK11 @ sK12 )
= $true )
| ~ spl16_7 ),
inference(avatar_component_clause,[],[f285]) ).
thf(f288,plain,
( spl16_7
| spl16_1 ),
inference(avatar_split_clause,[],[f231,f259,f285]) ).
thf(f290,definition,
( spl16_8
<=> ( ( sK1 @ sK12 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl16_8])],[avatar_definition]) ).
thf(f292,plain,
( ( ( sK1 @ sK12 )
= $false )
| ~ spl16_8 ),
inference(avatar_component_clause,[],[f290]) ).
thf(f293,plain,
( spl16_8
| spl16_1 ),
inference(avatar_split_clause,[],[f230,f259,f290]) ).
thf(f295,definition,
( spl16_9
<=> ! [X1: $i] :
( ( ( sK0 @ sK10 @ X1 )
= $false )
| ( $true
= ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_9])],[avatar_definition]) ).
thf(f296,plain,
( ! [X1: $i] :
( ( ( sK0 @ sK10 @ X1 )
= $false )
| ( $true
= ( sK1 @ X1 ) ) )
| ~ spl16_9 ),
inference(avatar_component_clause,[],[f295]) ).
thf(f297,plain,
( spl16_1
| spl16_9 ),
inference(avatar_split_clause,[],[f235,f295,f259]) ).
thf(f299,definition,
( spl16_10
<=> ! [X2: $i > $o] :
( ( sF4 @ X2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition]) ).
thf(f300,plain,
( ! [X2: $i > $o] :
( ( sF4 @ X2 )
= $true )
| ~ spl16_10 ),
inference(avatar_component_clause,[],[f299]) ).
thf(f301,plain,
( spl16_2
| spl16_10 ),
inference(avatar_split_clause,[],[f161,f299,f263]) ).
thf(f303,definition,
( spl16_11
<=> ( $true
= ( sK0 @ sK13 @ sK14 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_11])],[avatar_definition]) ).
thf(f305,plain,
( ( $true
= ( sK0 @ sK13 @ sK14 ) )
| ~ spl16_11 ),
inference(avatar_component_clause,[],[f303]) ).
thf(f306,plain,
( spl16_2
| spl16_11 ),
inference(avatar_split_clause,[],[f248,f303,f263]) ).
thf(f308,definition,
( spl16_12
<=> ( ( sK0 @ sK15 @ sK13 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl16_12])],[avatar_definition]) ).
thf(f310,plain,
( ( ( sK0 @ sK15 @ sK13 )
= $true )
| ~ spl16_12 ),
inference(avatar_component_clause,[],[f308]) ).
thf(f311,plain,
( spl16_12
| spl16_2 ),
inference(avatar_split_clause,[],[f247,f263,f308]) ).
thf(f313,definition,
( spl16_13
<=> ( $false
= ( sK0 @ sK15 @ sK14 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_13])],[avatar_definition]) ).
thf(f315,plain,
( ( $false
= ( sK0 @ sK15 @ sK14 ) )
| ~ spl16_13 ),
inference(avatar_component_clause,[],[f313]) ).
thf(f316,plain,
( spl16_13
| spl16_2 ),
inference(avatar_split_clause,[],[f245,f263,f313]) ).
thf(f318,definition,
( spl16_14
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl16_14])],[avatar_definition]) ).
thf(f320,plain,
( ( $false = sF3 )
| ~ spl16_14 ),
inference(avatar_component_clause,[],[f318]) ).
thf(f322,definition,
( spl16_15
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( ( sK0 @ X3 @ X2 )
= $true )
| ( ( sK0 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl16_15])],[avatar_definition]) ).
thf(f323,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( ( sK0 @ X3 @ X2 )
= $true )
| ( ( sK0 @ X1 @ X2 )
= $false ) )
| ~ spl16_15 ),
inference(avatar_component_clause,[],[f322]) ).
thf(f324,plain,
( spl16_14
| spl16_15 ),
inference(avatar_split_clause,[],[f257,f322,f318]) ).
thf(f325,plain,
( ( $true = $false )
| ~ spl16_2
| ~ spl16_14 ),
inference(forward_demodulation,[],[f320,f264]) ).
thf(f326,plain,
( $false
| ~ spl16_2
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f325]) ).
thf(f327,plain,
( ~ spl16_2
| ~ spl16_14 ),
inference(avatar_contradiction_clause,[],[f326]) ).
thf(f355,plain,
( ! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( $false
= ( X2 @ ( sK5 @ X3 @ X2 ) ) )
| ( $true = $false )
| ( ( sK0 @ X4 @ X5 )
= $false )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( $true
= ( X2 @ X5 ) ) )
| ~ spl16_10 ),
inference(forward_demodulation,[],[f181,f300]) ).
thf(f356,plain,
( ! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( $false
= ( X2 @ ( sK5 @ X3 @ X2 ) ) )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( $true
= ( X2 @ X5 ) )
| ( ( sK0 @ X4 @ X5 )
= $false ) )
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f355]) ).
thf(f367,plain,
( ! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( ( sK0 @ X4 @ X5 )
= $false )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( $true = $false )
| ( $true
= ( sK0 @ X3 @ ( sK5 @ X3 @ X2 ) ) )
| ( $true
= ( X2 @ X5 ) ) )
| ~ spl16_10 ),
inference(forward_demodulation,[],[f177,f300]) ).
thf(f368,plain,
( ! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( $true
= ( sK0 @ X3 @ ( sK5 @ X3 @ X2 ) ) )
| ( $true
= ( X2 @ X5 ) )
| ( ( sK0 @ X4 @ X5 )
= $false )
| ( ( sK0 @ X3 @ X4 )
= $false ) )
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f367]) ).
thf(f373,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( ( sK1 @ ( sK5 @ sK10 @ X0 ) )
= $true )
| ( ( sK0 @ sK10 @ X2 )
= $false )
| ( $true = $false )
| ( ( X0 @ X1 )
= $true ) )
| ~ spl16_9
| ~ spl16_10 ),
inference(constrained_superposition,[],[f296,f368]) ).
thf(f380,plain,
( ! [X2: $i,X0: $i > $o,X1: $i] :
( ( ( sK1 @ ( sK5 @ sK10 @ X0 ) )
= $true )
| ( ( X0 @ X1 )
= $true )
| ( ( sK0 @ sK10 @ X2 )
= $false )
| ( $false
= ( sK0 @ X2 @ X1 ) ) )
| ~ spl16_9
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f373]) ).
thf(f385,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( sK1 @ X0 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( sK0 @ sK10 @ X2 )
= $false )
| ( $true = $false )
| ( ( sK1 @ X3 )
= $true )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( ( sK0 @ sK10 @ X1 )
= $false ) )
| ~ spl16_9
| ~ spl16_10 ),
inference(constrained_superposition,[],[f380,f356]) ).
thf(f390,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $true
= ( sK1 @ X0 ) )
| ( ( sK1 @ X3 )
= $true )
| ( ( sK0 @ sK10 @ X2 )
= $false )
| ( ( sK0 @ sK10 @ X1 )
= $false )
| ( $false
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl16_9
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f385]) ).
thf(f400,definition,
( spl16_18
<=> ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ sK10 @ X0 ) )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( $true
= ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_18])],[avatar_definition]) ).
thf(f401,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ sK10 @ X0 ) )
| ( $true
= ( sK1 @ X1 ) )
| ( ( sK0 @ X0 @ X1 )
= $false ) )
| ~ spl16_18 ),
inference(avatar_component_clause,[],[f400]) ).
thf(f403,plain,
( spl16_18
| spl16_18
| ~ spl16_9
| ~ spl16_10 ),
inference(avatar_split_clause,[],[f390,f299,f295,f400,f400]) ).
thf(f602,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK11 @ X0 )
= $false )
| ( $true = $false )
| ( $true
= ( sK1 @ X0 ) ) )
| ~ spl16_6
| ~ spl16_18 ),
inference(constrained_superposition,[],[f401,f282]) ).
thf(f611,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK11 @ X0 )
= $false )
| ( $true
= ( sK1 @ X0 ) ) )
| ~ spl16_6
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f602]) ).
thf(f614,plain,
( ( $true
= ( sK1 @ sK12 ) )
| ( $true = $false )
| ~ spl16_6
| ~ spl16_7
| ~ spl16_18 ),
inference(constrained_superposition,[],[f611,f287]) ).
thf(f623,plain,
( ( $true
= ( sK1 @ sK12 ) )
| ~ spl16_6
| ~ spl16_7
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f614]) ).
thf(f627,plain,
( ( $true = $false )
| ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_18 ),
inference(forward_demodulation,[],[f623,f292]) ).
thf(f628,plain,
( $false
| ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f627]) ).
thf(f629,plain,
( ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_18 ),
inference(avatar_contradiction_clause,[],[f628]) ).
thf(f641,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ sK10 @ X0 ) )
| ( $true = $false )
| ( ( sK0 @ sK11 @ X0 )
= $false ) )
| ~ spl16_6
| ~ spl16_15 ),
inference(constrained_superposition,[],[f282,f323]) ).
thf(f652,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ sK10 @ X0 ) )
| ( ( sK0 @ sK11 @ X0 )
= $false ) )
| ~ spl16_6
| ~ spl16_15 ),
inference(trivial_inequality_removal,[],[f641]) ).
thf(f683,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK11 @ X0 )
= $false )
| ( $true = $false )
| ( $true
= ( sK1 @ X0 ) ) )
| ~ spl16_6
| ~ spl16_9
| ~ spl16_15 ),
inference(constrained_superposition,[],[f296,f652]) ).
thf(f689,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK11 @ X0 )
= $false )
| ( $true
= ( sK1 @ X0 ) ) )
| ~ spl16_6
| ~ spl16_9
| ~ spl16_15 ),
inference(trivial_inequality_removal,[],[f683]) ).
thf(f697,plain,
( ( $true
= ( sK1 @ sK12 ) )
| ( $true = $false )
| ~ spl16_6
| ~ spl16_7
| ~ spl16_9
| ~ spl16_15 ),
inference(constrained_superposition,[],[f689,f287]) ).
thf(f706,plain,
( ( $true
= ( sK1 @ sK12 ) )
| ~ spl16_6
| ~ spl16_7
| ~ spl16_9
| ~ spl16_15 ),
inference(trivial_inequality_removal,[],[f697]) ).
thf(f720,plain,
( ( $true = $false )
| ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_9
| ~ spl16_15 ),
inference(forward_demodulation,[],[f706,f292]) ).
thf(f721,plain,
( $false
| ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_9
| ~ spl16_15 ),
inference(trivial_inequality_removal,[],[f720]) ).
thf(f722,plain,
( ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_9
| ~ spl16_15 ),
inference(avatar_contradiction_clause,[],[f721]) ).
thf(f857,plain,
( ! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( $true
= ( X2 @ X5 ) )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( ( sK0 @ X4 @ X5 )
= $false )
| ( $false
= ( X2 @ ( sK5 @ X3 @ X2 ) ) )
| ( $true = $false ) )
| ~ spl16_10 ),
inference(forward_demodulation,[],[f181,f300]) ).
thf(f858,plain,
( ! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( $false
= ( X2 @ ( sK5 @ X3 @ X2 ) ) )
| ( ( sK0 @ X4 @ X5 )
= $false )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( $true
= ( X2 @ X5 ) ) )
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f857]) ).
thf(f946,plain,
( ! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( ( sK0 @ X3 @ X4 )
= $false )
| ( ( sK0 @ X4 @ X5 )
= $false )
| ( $true
= ( sK0 @ X3 @ ( sK5 @ X3 @ X2 ) ) )
| ( $true
= ( X2 @ X5 ) )
| ( $true = $false ) )
| ~ spl16_10 ),
inference(forward_demodulation,[],[f177,f300]) ).
thf(f947,plain,
( ! [X2: $i > $o,X3: $i,X4: $i,X5: $i] :
( ( $true
= ( sK0 @ X3 @ ( sK5 @ X3 @ X2 ) ) )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( ( sK0 @ X4 @ X5 )
= $false )
| ( $true
= ( X2 @ X5 ) ) )
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f946]) ).
thf(f957,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X3 @ X4 )
= $false )
| ( $true
= ( sK0 @ X0 @ X4 ) )
| ( ( sK0 @ X0 @ X3 )
= $false )
| ( $true
= ( sK0 @ X0 @ X2 ) )
| ( $true = $false )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X0 @ X1 )
= $false ) )
| ~ spl16_10 ),
inference(constrained_superposition,[],[f947,f858]) ).
thf(f973,plain,
( ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X0 @ X4 ) )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK0 @ X3 @ X4 )
= $false )
| ( $true
= ( sK0 @ X0 @ X2 ) )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X0 @ X3 )
= $false ) )
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f957]) ).
thf(f1061,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ sK15 @ X2 ) )
| ( $false
= ( sK0 @ sK15 @ X0 ) )
| ( $true = $false )
| ( ( sK0 @ X1 @ sK14 )
= $false )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $false
= ( sK0 @ sK15 @ X1 ) ) )
| ~ spl16_10
| ~ spl16_13 ),
inference(constrained_superposition,[],[f973,f315]) ).
thf(f1106,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ sK15 @ X1 ) )
| ( $true
= ( sK0 @ sK15 @ X2 ) )
| ( $false
= ( sK0 @ sK15 @ X0 ) )
| ( ( sK0 @ X1 @ sK14 )
= $false )
| ( $false
= ( sK0 @ X0 @ X2 ) ) )
| ~ spl16_10
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f1061]) ).
thf(f1117,definition,
( spl16_44
<=> ! [X1: $i] :
( ( $false
= ( sK0 @ sK15 @ X1 ) )
| ( ( sK0 @ X1 @ sK14 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl16_44])],[avatar_definition]) ).
thf(f1118,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK15 @ X1 ) )
| ( ( sK0 @ X1 @ sK14 )
= $false ) )
| ~ spl16_44 ),
inference(avatar_component_clause,[],[f1117]) ).
thf(f1120,definition,
( spl16_45
<=> ! [X2: $i,X0: $i] :
( ( $true
= ( sK0 @ sK15 @ X2 ) )
| ( $false
= ( sK0 @ sK15 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_45])],[avatar_definition]) ).
thf(f1121,plain,
( ! [X2: $i,X0: $i] :
( ( $true
= ( sK0 @ sK15 @ X2 ) )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $false
= ( sK0 @ sK15 @ X0 ) ) )
| ~ spl16_45 ),
inference(avatar_component_clause,[],[f1120]) ).
thf(f1144,plain,
( spl16_44
| spl16_45
| ~ spl16_10
| ~ spl16_13 ),
inference(avatar_split_clause,[],[f1106,f313,f299,f1120,f1117]) ).
thf(f1238,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK15 @ X0 ) )
| ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK14 ) ) )
| ~ spl16_13
| ~ spl16_45 ),
inference(constrained_superposition,[],[f1121,f315]) ).
thf(f1253,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK15 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ sK14 ) ) )
| ~ spl16_13
| ~ spl16_45 ),
inference(trivial_inequality_removal,[],[f1238]) ).
thf(f1271,plain,
( spl16_44
| ~ spl16_13
| ~ spl16_45 ),
inference(avatar_split_clause,[],[f1253,f1120,f313,f1117]) ).
thf(f1288,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK13 @ sK14 ) )
| ~ spl16_12
| ~ spl16_44 ),
inference(constrained_superposition,[],[f1118,f310]) ).
thf(f1299,plain,
( ( $false
= ( sK0 @ sK13 @ sK14 ) )
| ~ spl16_12
| ~ spl16_44 ),
inference(trivial_inequality_removal,[],[f1288]) ).
thf(f1314,plain,
( ( $true = $false )
| ~ spl16_11
| ~ spl16_12
| ~ spl16_44 ),
inference(forward_demodulation,[],[f1299,f305]) ).
thf(f1315,plain,
( $false
| ~ spl16_11
| ~ spl16_12
| ~ spl16_44 ),
inference(trivial_inequality_removal,[],[f1314]) ).
thf(f1316,plain,
( ~ spl16_11
| ~ spl16_12
| ~ spl16_44 ),
inference(avatar_contradiction_clause,[],[f1315]) ).
cnf(s1,plain,
( ~ spl16_1
| ~ spl16_2 ),
inference(sat_conversion,[],[f266]) ).
cnf(s4,plain,
( spl16_1
| spl16_6 ),
inference(sat_conversion,[],[f283]) ).
cnf(s5,plain,
( spl16_1
| spl16_7 ),
inference(sat_conversion,[],[f288]) ).
cnf(s6,plain,
( spl16_1
| spl16_8 ),
inference(sat_conversion,[],[f293]) ).
cnf(s7,plain,
( spl16_1
| spl16_9 ),
inference(sat_conversion,[],[f297]) ).
cnf(s8,plain,
( spl16_2
| spl16_10 ),
inference(sat_conversion,[],[f301]) ).
cnf(s9,plain,
( spl16_2
| spl16_11 ),
inference(sat_conversion,[],[f306]) ).
cnf(s10,plain,
( spl16_2
| spl16_12 ),
inference(sat_conversion,[],[f311]) ).
cnf(s11,plain,
( spl16_2
| spl16_13 ),
inference(sat_conversion,[],[f316]) ).
cnf(s12,plain,
( spl16_14
| spl16_15 ),
inference(sat_conversion,[],[f324]) ).
cnf(s13,plain,
( ~ spl16_2
| ~ spl16_14 ),
inference(sat_conversion,[],[f327]) ).
cnf(s17,plain,
( spl16_18
| ~ spl16_10
| ~ spl16_9
| spl16_18 ),
inference(sat_conversion,[],[f403]) ).
cnf(s18,plain,
( ~ spl16_9
| ~ spl16_10
| spl16_18 ),
inference(rat,[],[s17]) ).
cnf(s36,plain,
( ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_18 ),
inference(sat_conversion,[],[f629]) ).
cnf(s42,plain,
( ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_9
| ~ spl16_15 ),
inference(sat_conversion,[],[f722]) ).
cnf(s77,plain,
( ~ spl16_10
| ~ spl16_13
| spl16_44
| spl16_45 ),
inference(sat_conversion,[],[f1144]) ).
cnf(s86,plain,
( ~ spl16_13
| spl16_44
| ~ spl16_45 ),
inference(sat_conversion,[],[f1271]) ).
cnf(s94,plain,
( ~ spl16_11
| ~ spl16_12
| ~ spl16_44 ),
inference(sat_conversion,[],[f1316]) ).
cnf(s98,plain,
( ~ spl16_6
| ~ spl16_7
| ~ spl16_8
| ~ spl16_9 ),
inference(rat,[],[s8,s13,s18,s12,s36,s42]) ).
cnf(s99,plain,
spl16_1,
inference(rat,[],[s98,s4,s5,s6,s7]) ).
cnf(s101,plain,
~ spl16_2,
inference(rat,[],[s1,s99]) ).
cnf(s105,plain,
spl16_13,
inference(rat,[],[s11,s101]) ).
cnf(s106,plain,
spl16_12,
inference(rat,[],[s10,s101]) ).
cnf(s107,plain,
spl16_11,
inference(rat,[],[s9,s101]) ).
cnf(s108,plain,
spl16_10,
inference(rat,[],[s8,s101]) ).
cnf(s109,plain,
~ spl16_44,
inference(rat,[],[s94,s106,s107]) ).
cnf(s110,plain,
~ spl16_45,
inference(rat,[],[s86,s105,s109]) ).
cnf(s111,plain,
$false,
inference(rat,[],[s77,s108,s105,s110,s109]) ).
thf(f1324,plain,
$false,
inference(avatar_sat_refutation,[],[s111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL600^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n004.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 09:14:37 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 Running higher-order theorem proving
% 0.21/0.28 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
% 0.50/0.41 % (1037980)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.50/0.41 % (1037986)lrs+10_16_si=on:nwc=1.5:random_seed=1421995573:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.50/0.41 % (1037985)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=235440327:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.50/0.41 % (1037986)Instruction limit reached!
% 0.50/0.41 % (1037986)------------------------------
% 0.50/0.41 % (1037986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (1037986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (1037986)CaDiCaL version: 2.1.3
% 0.50/0.41 % (1037986)Termination reason: Instruction limit
% 0.50/0.41 % (1037986)Termination phase: Saturation
% 0.50/0.41 % (1037986)Time elapsed: 0.011 s
% 0.50/0.41 % (1037986)Peak memory usage: 12 MB
% 0.50/0.41 % (1037986)Instructions burned: 18 (million)
% 0.50/0.41 % (1037987)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=541601282:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.50/0.41 % (1037987)Instruction limit reached!
% 0.50/0.41 % (1037987)------------------------------
% 0.50/0.41 % (1037987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (1037987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (1037987)CaDiCaL version: 2.1.3
% 0.50/0.41 % (1037987)Termination reason: Instruction limit
% 0.50/0.41 % (1037987)Termination phase: Property scanning
% 0.50/0.41 % (1037987)Time elapsed: 0.003 s
% 0.50/0.41 % (1037987)Peak memory usage: 10 MB
% 0.50/0.41 % (1037987)Instructions burned: 4 (million)
% 0.50/0.41 % (1037991)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.50/0.41 % (1037991)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
% 0.50/0.41 % (1037988)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=2644233772: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)
% 0.50/0.41 % (1037991)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=1888722707:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.50/0.41 % (1037989)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3158515002:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.50/0.41 % (1037985)Instruction limit reached!
% 0.50/0.41 % (1037985)------------------------------
% 0.50/0.41 % (1037985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (1037985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (1037985)CaDiCaL version: 2.1.3
% 0.50/0.41 % (1037985)Termination reason: Instruction limit
% 0.50/0.41 % (1037985)Termination phase: Saturation
% 0.50/0.41 % (1037985)Time elapsed: 0.045 s
% 0.50/0.41 % (1037985)Peak memory usage: 13 MB
% 0.50/0.41 % (1037985)Instructions burned: 89 (million)
% 0.50/0.41 % (1037990)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3032253638:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.50/0.41 % (1037996)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2752814040:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.50/0.41 % (1037989)Instruction limit reached!
% 0.50/0.41 % (1037989)------------------------------
% 0.50/0.41 % (1037989)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (1037989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (1037989)CaDiCaL version: 2.1.3
% 0.50/0.41 % (1037989)Termination reason: Instruction limit
% 0.50/0.41 % (1037989)Termination phase: Saturation
% 0.50/0.41 % (1037989)Time elapsed: 0.024 s
% 0.50/0.41 % (1037989)Peak memory usage: 12 MB
% 0.50/0.41 % (1037989)Instructions burned: 24 (million)
% 0.50/0.41 % (1037996)Instruction limit reached!
% 0.50/0.41 % (1037996)------------------------------
% 0.50/0.41 % (1037996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (1037996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (1037996)CaDiCaL version: 2.1.3
% 0.50/0.41 % (1037996)Termination reason: Instruction limit
% 0.50/0.41 % (1037996)Termination phase: Property scanning
% 0.50/0.41 % (1037996)Time elapsed: 0.005 s
% 0.50/0.41 % (1037996)Peak memory usage: 10 MB
% 0.50/0.41 % (1037996)Instructions burned: 6 (million)
% 0.50/0.41 % (1037991) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1037980-1037991"...
% 0.50/0.41 % (1037995)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2046370356:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.50/0.41 % (1038001)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.50/0.41 % (1037995)Instruction limit reached!
% 0.50/0.41 % (1037995)------------------------------
% 0.50/0.41 % (1037995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (1037995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (1037995)CaDiCaL version: 2.1.3
% 0.50/0.41 % (1037995)Termination reason: Instruction limit
% 0.50/0.41 % (1037995)Termination phase: shuffling
% 0.50/0.41 % (1037995)Time elapsed: 0.002 s
% 0.50/0.41 % (1037995)Peak memory usage: 9 MB
% 0.50/0.41 % (1037995)Instructions burned: 2 (million)
% 0.50/0.41 % (1037991)...printing done.
% 0.50/0.41 % (1037991)Refutation found. Thanks to Tanya!
% 0.50/0.41 % SZS status Theorem for theBenchmark
% 0.50/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.50/0.41 % (1037991)------------------------------
% 0.50/0.41 % (1037991)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.50/0.41 % (1037991)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.50/0.41 % (1037991)CaDiCaL version: 2.1.3
% 0.50/0.41 % (1037991)Termination reason: Refutation
% 0.50/0.41 % (1037991)Time elapsed: 0.053 s
% 0.50/0.41 % (1037991)Peak memory usage: 13 MB
% 0.50/0.41 % (1037991)Instructions burned: 94 (million)
% 0.50/0.41 % (1037980)Success in time 0.116 s
% 0.50/0.41 % Vampire exiting
%------------------------------------------------------------------------------