%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL603^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 0.23s 0.33s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 20
% Syntax : Number of formulae : 157 ( 52 unt; 0 typ; 12 def)
% Number of atoms : 1069 ( 264 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 1431 ( 85 ~; 197 |; 28 &; 956 @)
% ( 8 <=>; 74 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 201 ( 201 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 77 usr; 17 con; 0-4 aty)
% ( 83 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 402 ( 0 sgn 157 !; 1 ?; 402 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
vAND: $o > $o > $o ).
thf(func_def_47,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_51,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
vOR: $o > $o > $o ).
thf(func_def_53,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_56,type,
vIFF: $o > $o > $o ).
thf(func_def_57,type,
sK0: $i > $i > $o ).
thf(func_def_58,type,
sF1: $o ).
thf(func_def_59,type,
sF2: $o ).
thf(func_def_60,type,
sF3: ( $i > $o ) > $o ).
thf(func_def_61,type,
sF4: ( $i > $o ) > $o ).
thf(func_def_66,type,
sK9: ( $i > $o ) > $i > $i ).
thf(func_def_67,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_68,type,
sK11: ( $i > $o ) > $i ).
thf(func_def_69,type,
sK12: ( $i > $o ) > $i ).
thf(func_def_70,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_71,type,
sK14: ( $i > $o ) > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimpl ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f24,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= reflexive ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',reflexive) ).
thf(f27,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
= transitive ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',transitive) ).
thf(f37,conjecture,
! [X0: $i > $i > $o] :
( ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
& ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) )
=> ( ( transitive @ X0 )
& ( reflexive @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f38,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
& ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) )
=> ( ( transitive @ X0 )
& ( reflexive @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f41,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f45,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f46,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f49,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f50,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
~ ! [X0: $i > $i > $o] :
( ! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
& ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) ) )
=> ( ( transitive @ X0 )
& ( reflexive @ X0 ) ) ),
inference(rectify,[],[f38]) ).
thf(f52,plain,
~ ! [X0: $i > $i > $o] :
( ! [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
= $true )
& ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true ) )
=> ( ( ( transitive @ X0 )
= $true )
& ( ( reflexive @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f61,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f62,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f71,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f72,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f76,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= reflexive ),
inference(rectify,[],[f24]) ).
thf(f77,plain,
( reflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f102,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
= transitive ),
inference(rectify,[],[f27]) ).
thf(f103,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f102]) ).
thf(f106,plain,
? [X0: $i > $i > $o] :
( ( ( ( reflexive @ X0 )
!= $true )
| ( ( transitive @ X0 )
!= $true ) )
& ! [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ X1 ) )
= $true )
& ( ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
= $true ) ) ),
inference(ennf_transformation,[],[f52]) ).
thf(f107,plain,
( ( ( ( reflexive @ sK0 )
!= $true )
| ( ( transitive @ sK0 )
!= $true ) )
& ! [X1: $i > $o] :
( ( ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X1 ) @ X1 ) )
= $true )
& ( ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X1 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ X1 ) ) ) )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f106]) ).
thf(f110,plain,
( reflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f113,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f114,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f119,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f103]) ).
thf(f124,plain,
! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X1 ) @ ( mbox @ sK0 @ ( mbox @ sK0 @ X1 ) ) ) )
= $true ),
inference(cnf_transformation,[],[f107]) ).
thf(f125,plain,
! [X1: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ sK0 @ X1 ) @ X1 ) )
= $true ),
inference(cnf_transformation,[],[f107]) ).
thf(f126,plain,
( ( ( reflexive @ sK0 )
!= $true )
| ( ( transitive @ sK0 )
!= $true ) ),
inference(cnf_transformation,[],[f107]) ).
thf(f130,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f137,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f139,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f149,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,[],[f113,f139,f114]) ).
thf(f153,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
!= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 )
!= $true ) ),
inference(definition_unfolding,[],[f126,f110,f119]) ).
thf(f154,plain,
! [X1: $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
@ X1 )
@ X1 ) ) ),
inference(definition_unfolding,[],[f125,f137,f149,f130]) ).
thf(f155,plain,
! [X1: $i > $o] :
( ( ^ [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
@ X1 )
@ ( ^ [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
@ X1 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f124,f137,f149,f130,f130,f130]) ).
thf(f156,definition,
( sF1
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f157,definition,
( sF2
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f158,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 )
= sF2 ),
inference(reorient_equations,[],[f157]) ).
thf(f159,plain,
( ( sF1 != $true )
| ( sF2 != $true ) ),
inference(definition_folding,[],[f153,f158,f156]) ).
thf(f160,definition,
! [X1: $i > $o] :
( ( sF3 @ X1 )
= ( ^ [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
@ X1 )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f161,plain,
! [X1: $i > $o] :
( ( sF3 @ X1 )
= $true ),
inference(definition_folding,[],[f154,f160]) ).
thf(f162,definition,
! [X1: $i > $o] :
( ( sF4 @ X1 )
= ( ^ [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
@ X1 )
@ ( ^ [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
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f163,plain,
! [X1: $i > $o] :
( ( sF4 @ X1 )
= $true ),
inference(definition_folding,[],[f155,f162]) ).
thf(f165,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( sF2 = $true ) ),
inference(iff_proxy_clausification,[],[f158]) ).
thf(f166,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y2 @ Y1 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( sF2 = $true ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( ( sF2 = $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y2 @ Y1 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y1 @ sK5 ) ) ) ) )
| ( sF2 = $true ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y1 @ sK5 ) ) )
@ sK6 ) )
| ( sF2 = $true ) ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK6 @ sK5 )
& ( sK0 @ Y0 @ sK6 ) )
=> ( sK0 @ Y0 @ sK5 ) ) )
= $false )
| ( sF2 = $true ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
( ( sF2 = $true )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ sK6 @ sK5 )
& ( sK0 @ Y0 @ sK6 ) )
=> ( sK0 @ Y0 @ sK5 ) )
@ sK7 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( ( ( ( sK0 @ sK6 @ sK5 )
& ( sK0 @ sK7 @ sK6 ) )
=> ( sK0 @ sK7 @ sK5 ) )
= $false )
| ( sF2 = $true ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
( ( ( sK0 @ sK7 @ sK5 )
= $false )
| ( sF2 = $true ) ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( ( ( sK0 @ sK6 @ sK5 )
& ( sK0 @ sK7 @ sK6 ) )
= $true )
| ( sF2 = $true ) ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( ( ( sK0 @ sK7 @ sK6 )
= $true )
| ( sF2 = $true ) ),
inference(and_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( sF2 = $true )
| ( ( sK0 @ sK6 @ sK5 )
= $true ) ),
inference(and_proxy_clausification,[],[f174]) ).
thf(f186,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) )
| ( sF1 = $true ) ),
inference(iff_proxy_clausification,[],[f156]) ).
thf(f191,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f192,plain,
( ( sF1 = $true )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( ( sK0 @ sK8 @ sK8 )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f195,plain,
! [X1: $i > $o] :
( ( ( sF4 @ X1 )
= $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
@ X1 )
@ ( ^ [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
@ X1 ) ) ) )
= $true ) ),
inference(iff_proxy_clausification,[],[f162]) ).
thf(f196,plain,
! [X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) )
= $true )
| ( ( sF4 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X1: $i > $o] :
( ( ( sF4 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK0 @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X1: $i > $o] :
( ( ( sF4 @ X1 )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) )
= $true )
| ( ( sF4 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( sF4 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X3 )
= $true )
| ( ( sF4 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( sF4 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) )
@ ( sK9 @ X1 @ X2 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( ( sK0 @ X2 @ X3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true )
| ( ( ( sK0 @ X2 @ ( sK9 @ X1 @ X2 ) )
=> ( X1 @ ( sK9 @ X1 @ X2 ) ) )
= $false )
| ( ( sF4 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( sF4 @ X1 )
= $false )
| ( ( ( sK0 @ X2 @ ( sK9 @ X1 @ X2 ) )
=> ( X1 @ ( sK9 @ X1 @ X2 ) ) )
= $false )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( X1 @ ( sK9 @ X1 @ X2 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true )
| ( ( sF4 @ X1 )
= $false )
| ( $false
= ( sK0 @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( sF4 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) )
= $true )
| ( ( sK0 @ X2 @ ( sK9 @ X1 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f204]) ).
thf(f207,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) )
@ X4 ) )
| ( ( sK0 @ X2 @ ( sK9 @ X1 @ X2 ) )
= $true )
| ( ( sF4 @ X1 )
= $false )
| ( $false
= ( sK0 @ X2 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( ( sK0 @ X2 @ ( sK9 @ X1 @ X2 ) )
= $true )
| ( ( ( sK0 @ X3 @ X4 )
=> ( X1 @ X4 ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( sF4 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( ( X1 @ X4 )
= $true )
| ( ( sK0 @ X2 @ ( sK9 @ X1 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( ( sF4 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X3 @ Y0 )
=> ( X1 @ Y0 ) )
@ X4 ) )
| ( $false
= ( X1 @ ( sK9 @ X1 @ X2 ) ) )
| ( ( sF4 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f205]) ).
thf(f211,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( ( sK0 @ X3 @ X4 )
=> ( X1 @ X4 ) )
= $true )
| ( ( sF4 @ X1 )
= $false )
| ( $false
= ( X1 @ ( sK9 @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( sF4 @ X1 )
= $false )
| ( $false
= ( X1 @ ( sK9 @ X1 @ X2 ) ) )
| ( ( X1 @ X4 )
= $true )
| ( $false
= ( sK0 @ X3 @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f211]) ).
thf(f231,plain,
! [X1: $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
@ X1 )
@ X1 ) ) )
| ( ( sF3 @ X1 )
= $false ) ),
inference(iff_proxy_clausification,[],[f160]) ).
thf(f232,plain,
! [X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) )
= $true )
| ( ( sF3 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X1: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X2 )
= $true )
| ( ( sF3 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X1: $i > $o] :
( ( ( sF3 @ X1 )
= $false )
| ( $true
= ( ( X1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( ( sF3 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( ( sF3 @ X1 )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X1: $i > $o] :
( ( ( sF3 @ X1 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ X2 @ Y0 )
=> ( X1 @ Y0 ) )
@ ( sK13 @ X1 @ X2 ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( ( sK0 @ X2 @ ( sK13 @ X1 @ X2 ) )
=> ( X1 @ ( sK13 @ X1 @ X2 ) ) ) )
| ( ( X1 @ X2 )
= $true )
| ( ( sF3 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( ( sF3 @ X1 )
= $false )
| ( $false
= ( X1 @ ( sK13 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X1: $i > $o] :
( ( ( sF3 @ X1 )
= $false )
| ( ( X1 @ X2 )
= $true )
| ( ( sK0 @ X2 @ ( sK13 @ X1 @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f251,definition,
( spl15_1
<=> ( ( sK0 @ sK6 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
thf(f253,plain,
( ( ( sK0 @ sK6 @ sK5 )
= $true )
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f251]) ).
thf(f255,definition,
( spl15_2
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
thf(f258,plain,
( spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f176,f255,f251]) ).
thf(f260,definition,
( spl15_3
<=> ( ( sK0 @ sK7 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
thf(f262,plain,
( ( ( sK0 @ sK7 @ sK6 )
= $true )
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f263,plain,
( spl15_2
| spl15_3 ),
inference(avatar_split_clause,[],[f175,f260,f255]) ).
thf(f265,definition,
( spl15_4
<=> ( ( sK0 @ sK7 @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
thf(f267,plain,
( ( ( sK0 @ sK7 @ sK5 )
= $false )
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f268,plain,
( spl15_2
| spl15_4 ),
inference(avatar_split_clause,[],[f173,f265,f255]) ).
thf(f274,definition,
( spl15_6
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( sK0 @ X3 @ X1 )
= $true )
| ( ( sK0 @ X3 @ X2 )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
thf(f275,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X3 @ X2 )
= $false )
| ( ( sK0 @ X3 @ X1 )
= $true )
| ( ( sK0 @ X2 @ X1 )
= $false ) )
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f274]) ).
thf(f278,definition,
( spl15_7
<=> ! [X1: $i] :
( ( sK0 @ X1 @ X1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
thf(f279,plain,
( ! [X1: $i] :
( ( sK0 @ X1 @ X1 )
= $true )
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f278]) ).
thf(f286,definition,
( spl15_9
<=> ( ( sK0 @ sK8 @ sK8 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl15_9])],[avatar_definition]) ).
thf(f288,plain,
( ( ( sK0 @ sK8 @ sK8 )
= $false )
| ~ spl15_9 ),
inference(avatar_component_clause,[],[f286]) ).
thf(f290,definition,
( spl15_10
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl15_10])],[avatar_definition]) ).
thf(f293,plain,
( spl15_9
| spl15_10 ),
inference(avatar_split_clause,[],[f193,f290,f286]) ).
thf(f294,plain,
( ~ spl15_10
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f159,f255,f290]) ).
thf(f313,plain,
( ( $false = $true )
| ~ spl15_7
| ~ spl15_9 ),
inference(forward_demodulation,[],[f288,f279]) ).
thf(f314,plain,
( $false
| ~ spl15_7
| ~ spl15_9 ),
inference(trivial_inequality_removal,[],[f313]) ).
thf(f315,plain,
( ~ spl15_7
| ~ spl15_9 ),
inference(avatar_contradiction_clause,[],[f314]) ).
thf(f334,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK7 @ X0 )
= $true )
| ( $false
= ( sK0 @ sK6 @ X0 ) )
| ( $false = $true ) )
| ~ spl15_3
| ~ spl15_6 ),
inference(constrained_superposition,[],[f275,f262]) ).
thf(f341,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK6 @ X0 ) )
| ( ( sK0 @ sK7 @ X0 )
= $true ) )
| ~ spl15_3
| ~ spl15_6 ),
inference(trivial_inequality_removal,[],[f334]) ).
thf(f348,plain,
( ( $false = $true )
| ( ( sK0 @ sK7 @ sK5 )
= $true )
| ~ spl15_1
| ~ spl15_3
| ~ spl15_6 ),
inference(constrained_superposition,[],[f253,f341]) ).
thf(f351,plain,
( ( ( sK0 @ sK7 @ sK5 )
= $true )
| ~ spl15_1
| ~ spl15_3
| ~ spl15_6 ),
inference(trivial_inequality_removal,[],[f348]) ).
thf(f355,plain,
( ( $false = $true )
| ~ spl15_1
| ~ spl15_3
| ~ spl15_4
| ~ spl15_6 ),
inference(forward_demodulation,[],[f351,f267]) ).
thf(f356,plain,
( $false
| ~ spl15_1
| ~ spl15_3
| ~ spl15_4
| ~ spl15_6 ),
inference(trivial_inequality_removal,[],[f355]) ).
thf(f357,plain,
( ~ spl15_1
| ~ spl15_3
| ~ spl15_4
| ~ spl15_6 ),
inference(avatar_contradiction_clause,[],[f356]) ).
thf(f378,plain,
! [X2: $i,X1: $i > $o] :
( ( $false = $true )
| ( $false
= ( X1 @ ( sK13 @ X1 @ X2 ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(forward_demodulation,[],[f239,f161]) ).
thf(f379,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( X1 @ ( sK13 @ X1 @ X2 ) ) )
| ( ( X1 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f378]) ).
thf(f392,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $true )
| ( $false = $true )
| ( ( sK0 @ X2 @ ( sK13 @ X1 @ X2 ) )
= $true ) ),
inference(forward_demodulation,[],[f240,f161]) ).
thf(f393,plain,
! [X2: $i,X1: $i > $o] :
( ( ( sK0 @ X2 @ ( sK13 @ X1 @ X2 ) )
= $true )
| ( ( X1 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f392]) ).
thf(f399,plain,
! [X0: $i] :
( ( ( sK0 @ X0 @ X0 )
= $true )
| ( $false = $true )
| ( ( sK0 @ X0 @ X0 )
= $true ) ),
inference(constrained_superposition,[],[f393,f379]) ).
thf(f406,plain,
! [X0: $i] :
( ( $false = $true )
| ( ( sK0 @ X0 @ X0 )
= $true ) ),
inference(duplicate_literal_removal,[],[f399]) ).
thf(f407,plain,
! [X0: $i] :
( ( sK0 @ X0 @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f406]) ).
thf(f422,plain,
spl15_7,
inference(avatar_split_clause,[],[f407,f278]) ).
thf(f431,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( X1 @ ( sK9 @ X1 @ X2 ) ) )
| ( ( X1 @ X4 )
= $true )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f212,f163]) ).
thf(f432,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( X1 @ ( sK9 @ X1 @ X2 ) ) )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( X1 @ X4 )
= $true ) ),
inference(trivial_inequality_removal,[],[f431]) ).
thf(f450,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( sK0 @ X2 @ ( sK9 @ X1 @ X2 ) )
= $true )
| ( ( X1 @ X4 )
= $true )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f209,f163]) ).
thf(f451,plain,
! [X2: $i,X3: $i,X1: $i > $o,X4: $i] :
( ( ( sK0 @ X2 @ ( sK9 @ X1 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( ( X1 @ X4 )
= $true )
| ( $false
= ( sK0 @ X2 @ X3 ) ) ),
inference(trivial_inequality_removal,[],[f450]) ).
thf(f453,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false = $true )
| ( ( sK0 @ X0 @ X4 )
= $true )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X0 @ X2 )
= $true )
| ( $false
= ( sK0 @ X0 @ X3 ) )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f451,f432]) ).
thf(f461,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X3 @ X4 ) )
| ( ( sK0 @ X0 @ X2 )
= $true )
| ( $false
= ( sK0 @ X0 @ X3 ) )
| ( ( sK0 @ X0 @ X4 )
= $true )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( $false
= ( sK0 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f453]) ).
thf(f487,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X0 ) )
| ( ( sK0 @ X2 @ X1 )
= $true )
| ( $false != $false )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( ( sK0 @ X2 @ X1 )
= $true )
| ( $false
= ( sK0 @ X2 @ X0 ) ) ),
inference(equality_factoring,[],[f461]) ).
thf(f503,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false != $false )
| ( ( sK0 @ X2 @ X1 )
= $true ) ),
inference(duplicate_literal_removal,[],[f487]) ).
thf(f504,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $true )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f503]) ).
thf(f505,plain,
spl15_6,
inference(avatar_split_clause,[],[f504,f274]) ).
cnf(s1,plain,
( spl15_1
| spl15_2 ),
inference(sat_conversion,[],[f258]) ).
cnf(s2,plain,
( spl15_2
| spl15_3 ),
inference(sat_conversion,[],[f263]) ).
cnf(s3,plain,
( spl15_2
| spl15_4 ),
inference(sat_conversion,[],[f268]) ).
cnf(s6,plain,
( spl15_9
| spl15_10 ),
inference(sat_conversion,[],[f293]) ).
cnf(s7,plain,
( ~ spl15_2
| ~ spl15_10 ),
inference(sat_conversion,[],[f294]) ).
cnf(s10,plain,
( ~ spl15_7
| ~ spl15_9 ),
inference(sat_conversion,[],[f315]) ).
cnf(s15,plain,
( ~ spl15_1
| ~ spl15_3
| ~ spl15_4
| ~ spl15_6 ),
inference(sat_conversion,[],[f357]) ).
cnf(s16,plain,
spl15_7,
inference(sat_conversion,[],[f422]) ).
cnf(s18,plain,
spl15_6,
inference(sat_conversion,[],[f505]) ).
cnf(s19,plain,
( ~ spl15_1
| ~ spl15_3
| ~ spl15_4 ),
inference(rat,[],[s15,s18]) ).
cnf(s21,plain,
~ spl15_9,
inference(rat,[],[s10,s16]) ).
cnf(s22,plain,
spl15_10,
inference(rat,[],[s6,s21]) ).
cnf(s24,plain,
~ spl15_2,
inference(rat,[],[s7,s22]) ).
cnf(s26,plain,
spl15_4,
inference(rat,[],[s3,s24]) ).
cnf(s27,plain,
spl15_3,
inference(rat,[],[s2,s24]) ).
cnf(s28,plain,
~ spl15_1,
inference(rat,[],[s19,s26,s27]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s1,s24,s28]) ).
thf(f506,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL603^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n007.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 09:14:11 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.33 % (3104148)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.33 % (3104156)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=475076787: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)
% 0.23/0.33 % (3104159)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.33 % (3104159)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
% 0.23/0.33 % (3104153)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=951726188:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.33 % (3104154)lrs+10_16_si=on:nwc=1.5:random_seed=1548025931:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.33 % (3104157)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1443763798:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.33 % (3104155)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2076866236:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.33 % (3104158)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1307461672:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.33 % (3104159)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=3345602973:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.33 % (3104155)Instruction limit reached!
% 0.23/0.33 % (3104155)------------------------------
% 0.23/0.33 % (3104155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (3104155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (3104155)CaDiCaL version: 2.1.3
% 0.23/0.33 % (3104155)Termination reason: Instruction limit
% 0.23/0.33 % (3104155)Termination phase: Property scanning
% 0.23/0.33 % (3104155)Time elapsed: 0.003 s
% 0.23/0.33 % (3104155)Peak memory usage: 10 MB
% 0.23/0.33 % (3104155)Instructions burned: 5 (million)
% 0.23/0.33 % (3104154)Instruction limit reached!
% 0.23/0.33 % (3104154)------------------------------
% 0.23/0.33 % (3104154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (3104154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (3104154)CaDiCaL version: 2.1.3
% 0.23/0.33 % (3104154)Termination reason: Instruction limit
% 0.23/0.33 % (3104154)Termination phase: Saturation
% 0.23/0.33 % (3104154)Time elapsed: 0.010 s
% 0.23/0.33 % (3104154)Peak memory usage: 12 MB
% 0.23/0.33 % (3104154)Instructions burned: 18 (million)
% 0.23/0.33 % (3104157)Instruction limit reached!
% 0.23/0.33 % (3104157)------------------------------
% 0.23/0.33 % (3104157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (3104157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (3104157)CaDiCaL version: 2.1.3
% 0.23/0.33 % (3104157)Termination reason: Instruction limit
% 0.23/0.33 % (3104157)Termination phase: Saturation
% 0.23/0.33 % (3104157)Time elapsed: 0.014 s
% 0.23/0.33 % (3104157)Peak memory usage: 12 MB
% 0.23/0.33 % (3104157)Instructions burned: 25 (million)
% 0.23/0.33 % (3104159) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3104148-3104159"...
% 0.23/0.33 % (3104159)...printing done.
% 0.23/0.33 % (3104159)Refutation found. Thanks to Tanya!
% 0.23/0.33 % SZS status Theorem for theBenchmark
% 0.23/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.33 % (3104159)------------------------------
% 0.23/0.33 % (3104159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (3104159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (3104159)CaDiCaL version: 2.1.3
% 0.23/0.33 % (3104159)Termination reason: Refutation
% 0.23/0.33 % (3104159)Time elapsed: 0.020 s
% 0.23/0.33 % (3104159)Peak memory usage: 13 MB
% 0.23/0.33 % (3104159)Instructions burned: 37 (million)
% 0.23/0.33 % (3104148)Success in time 0.06 s
% 0.23/0.33 % Vampire exiting
%------------------------------------------------------------------------------