%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL595^1 : 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 : n006.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 0.35s 0.43s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 13
% Syntax : Number of formulae : 97 ( 30 unt; 0 typ; 6 def)
% Number of atoms : 554 ( 124 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 642 ( 74 ~; 106 |; 3 &; 396 @)
% ( 10 <=>; 22 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 95 ( 95 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 65 usr; 11 con; 0-4 aty)
% ( 30 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 178 ( 0 sgn 61 !; 2 ?; 178 :)
% 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,
r: $i > $i > $o ).
thf(func_def_42,type,
vAND: $o > $o > $o ).
thf(func_def_43,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_49,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_52,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
vIMP: $o > $o > $o ).
thf(func_def_56,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
vIFF: $o > $o > $o ).
thf(func_def_58,type,
sK0: $i > $o ).
thf(func_def_61,type,
sK3: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimpl ),
file('/export/starexec/sandbox/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/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(f24,axiom,
( reflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',reflexive) ).
thf(f37,conjecture,
( ( reflexive @ r )
<=> ! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f38,negated_conjecture,
~ ( ( reflexive @ r )
<=> ! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f46,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f52,plain,
~ ( ( reflexive @ r )
<=> ! [X0: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) ) ),
inference(rectify,[],[f38]) ).
thf(f53,plain,
~ ( ! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) )
= $true )
<=> ( ( reflexive @ r )
= $true ) ),
inference(fool_elimination,[],[f52]) ).
thf(f54,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f55,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f59,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f60,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f65,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f12]) ).
thf(f66,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f84,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f85,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f84]) ).
thf(f100,plain,
( reflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f24]) ).
thf(f101,plain,
( reflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f100]) ).
thf(f106,plain,
( ( ( reflexive @ r )
= $true )
<~> ! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) )
= $true ) ),
inference(ennf_transformation,[],[f53]) ).
thf(f107,plain,
( ( ? [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) )
!= $true )
| ( ( reflexive @ r )
!= $true ) )
& ( ! [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) )
= $true )
| ( ( reflexive @ r )
= $true ) ) ),
inference(nnf_transformation,[],[f106]) ).
thf(f108,plain,
( ( ? [X0: $i > $o] :
( ( mvalid @ ( mimpl @ ( mbox @ r @ X0 ) @ X0 ) )
!= $true )
| ( ( reflexive @ r )
!= $true ) )
& ( ! [X1: $i > $o] :
( $true
= ( mvalid @ ( mimpl @ ( mbox @ r @ X1 ) @ X1 ) ) )
| ( ( reflexive @ r )
= $true ) ) ),
inference(rectify,[],[f107]) ).
thf(f109,plain,
( ( ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ r @ sK0 ) @ sK0 ) ) )
| ( ( reflexive @ r )
!= $true ) )
& ( ! [X1: $i > $o] :
( $true
= ( mvalid @ ( mimpl @ ( mbox @ r @ X1 ) @ X1 ) ) )
| ( ( reflexive @ r )
= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f108]) ).
thf(f117,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f119,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f120,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f132,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f137,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f144,plain,
! [X1: $i > $o] :
( ( $true
= ( mvalid @ ( mimpl @ ( mbox @ r @ X1 ) @ X1 ) ) )
| ( ( reflexive @ r )
= $true ) ),
inference(cnf_transformation,[],[f109]) ).
thf(f145,plain,
( ( $true
!= ( mvalid @ ( mimpl @ ( mbox @ r @ sK0 ) @ sK0 ) ) )
| ( ( reflexive @ r )
!= $true ) ),
inference(cnf_transformation,[],[f109]) ).
thf(f147,plain,
( reflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f150,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f117,f119,f132]) ).
thf(f154,plain,
( ( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ r
@ sK0 )
@ sK0 ) ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ r ) ) ),
inference(definition_unfolding,[],[f145,f120,f150,f137,f147]) ).
thf(f155,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] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ r
@ X1 )
@ X1 ) ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ r ) ) ),
inference(definition_unfolding,[],[f144,f120,f150,f137,f147]) ).
thf(f156,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : ( r @ Y0 @ Y0 ) )
!= $true )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) )
| ( sK0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f157,plain,
( ( $false
= ( ^ [Y0: $i] : ( r @ Y0 @ Y0 )
@ sK1 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) )
| ( sK0 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) )
| ( sK0 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] : ( r @ Y0 @ Y0 )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( ( r @ sK1 @ sK1 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) ) )
| ( sK0 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ( ( r @ sK1 @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ) )
| ( ( r @ sK1 @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f162,plain,
( ( ( r @ sK1 @ sK1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( r @ sK2 @ Y0 )
=> ( sK0 @ Y0 ) )
@ X1 ) )
| ( ( r @ sK1 @ sK1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true
= ( ( r @ sK2 @ X1 )
=> ( sK0 @ X1 ) ) )
| ( ( r @ sK1 @ sK1 )
= $false ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( ( r @ sK1 @ sK1 )
= $false )
| ( $false
= ( r @ sK2 @ X1 ) )
| ( $true
= ( sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] : ( r @ Y0 @ Y0 ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f167,plain,
! [X2: $i,X1: $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( X1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] : ( r @ Y0 @ Y0 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( r @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( X1 @ Y0 ) )
@ X3 )
= $true )
| ( $true
= ( ^ [Y0: $i] : ( r @ Y0 @ Y0 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) )
| ( X1 @ X3 ) ) )
| ( $true
= ( r @ X2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( X1 @ X3 )
= $true )
| ( $true
= ( r @ X2 @ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( r @ X2 @ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( r @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
| ( ( X1 @ X3 )
= $true ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( r @ X2 @ X2 ) )
| ( ( X1 @ X3 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( r @ X3 @ Y0 )
=> ( X1 @ Y0 ) )
@ ( sK3 @ X3 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( ( r @ X3 @ ( sK3 @ X3 @ X1 ) )
=> ( X1 @ ( sK3 @ X3 @ X1 ) ) ) )
| ( ( X1 @ X3 )
= $true )
| ( $true
= ( r @ X2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $true
= ( r @ X2 @ X2 ) )
| ( ( X1 @ ( sK3 @ X3 @ X1 ) )
= $false )
| ( ( X1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( r @ X3 @ ( sK3 @ X3 @ X1 ) )
= $true )
| ( $true
= ( r @ X2 @ X2 ) )
| ( ( X1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f173]) ).
thf(f177,definition,
( spl4_1
<=> ( ( r @ sK1 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f179,plain,
( ( ( r @ sK1 @ sK1 )
= $false )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f177]) ).
thf(f181,definition,
( spl4_2
<=> ! [X1: $i] :
( ( $false
= ( r @ sK2 @ X1 ) )
| ( $true
= ( sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f182,plain,
( ! [X1: $i] :
( ( $false
= ( r @ sK2 @ X1 ) )
| ( $true
= ( sK0 @ X1 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f181]) ).
thf(f183,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f165,f181,f177]) ).
thf(f185,definition,
( spl4_3
<=> ( $false
= ( sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f187,plain,
( ( $false
= ( sK0 @ sK2 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f185]) ).
thf(f188,plain,
( spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f160,f185,f177]) ).
thf(f190,definition,
( spl4_4
<=> ! [X1: $i > $o,X3: $i] :
( ( ( r @ X3 @ ( sK3 @ X3 @ X1 ) )
= $true )
| ( ( X1 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f191,plain,
( ! [X3: $i,X1: $i > $o] :
( ( ( r @ X3 @ ( sK3 @ X3 @ X1 ) )
= $true )
| ( ( X1 @ X3 )
= $true ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f190]) ).
thf(f193,definition,
( spl4_5
<=> ! [X2: $i] :
( $true
= ( r @ X2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f194,plain,
( ! [X2: $i] :
( $true
= ( r @ X2 @ X2 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f193]) ).
thf(f195,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f175,f193,f190]) ).
thf(f197,definition,
( spl4_6
<=> ! [X1: $i > $o,X3: $i] :
( ( ( X1 @ ( sK3 @ X3 @ X1 ) )
= $false )
| ( ( X1 @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f198,plain,
( ! [X3: $i,X1: $i > $o] :
( ( ( X1 @ ( sK3 @ X3 @ X1 ) )
= $false )
| ( ( X1 @ X3 )
= $true ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f199,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f174,f197,f193]) ).
thf(f201,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ( $true = $false )
| ~ spl4_2
| ~ spl4_5 ),
inference(constrained_superposition,[],[f194,f182]) ).
thf(f203,plain,
( ( $true
= ( sK0 @ sK2 ) )
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f201]) ).
thf(f207,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(forward_demodulation,[],[f203,f187]) ).
thf(f208,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f207]) ).
thf(f209,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f208]) ).
thf(f210,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_5 ),
inference(forward_demodulation,[],[f179,f194]) ).
thf(f211,plain,
( $false
| ~ spl4_1
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f210]) ).
thf(f212,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f211]) ).
thf(f222,plain,
( ! [X0: $i] :
( ( $true
= ( r @ X0 @ X0 ) )
| ( $true
= ( r @ X0 @ X0 ) )
| ( $true = $false ) )
| ~ spl4_4
| ~ spl4_6 ),
inference(constrained_superposition,[],[f191,f198]) ).
thf(f224,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( r @ X0 @ X0 ) ) )
| ~ spl4_4
| ~ spl4_6 ),
inference(duplicate_literal_removal,[],[f222]) ).
thf(f225,plain,
( ! [X0: $i] :
( $true
= ( r @ X0 @ X0 ) )
| ~ spl4_4
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f224]) ).
thf(f228,plain,
( spl4_5
| ~ spl4_4
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f225,f197,f190,f193]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f183]) ).
cnf(s2,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f188]) ).
cnf(s3,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f195]) ).
cnf(s4,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f199]) ).
cnf(s6,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f209]) ).
cnf(s7,plain,
( ~ spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f212]) ).
cnf(s8,plain,
( ~ spl4_4
| spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f228]) ).
cnf(s10,plain,
spl4_5,
inference(rat,[],[s8,s3,s4]) ).
cnf(s11,plain,
~ spl4_1,
inference(rat,[],[s7,s10]) ).
cnf(s12,plain,
spl4_3,
inference(rat,[],[s2,s11]) ).
cnf(s13,plain,
spl4_2,
inference(rat,[],[s1,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s6,s10,s12,s13]) ).
thf(f229,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL595^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.30 % Computer : n006.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8046.5625MB
% 0.12/0.30 % OS : Linux 6.8.0-71-generic
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Sep 29 09:12:40 UTC 2026
% 0.14/0.31 % CPUTime :
% 0.14/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.36 Running higher-order theorem proving
% 0.14/0.38 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
% 0.35/0.43 % (453200)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.35/0.43 % (453205)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2407337263:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.35/0.43 % (453205) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-453200-453205"...
% 0.35/0.43 % (453205)...printing done.
% 0.35/0.43 % (453211)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.35/0.43 % (453211)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
% 0.35/0.43 % (453205)Refutation found. Thanks to Tanya!
% 0.35/0.43 % SZS status Theorem for theBenchmark
% 0.35/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.44 % (453205)------------------------------
% 0.35/0.44 % (453205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.44 % (453205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.44 % (453205)CaDiCaL version: 2.1.3
% 0.35/0.44 % (453205)Termination reason: Refutation
% 0.35/0.44 % (453205)Time elapsed: 0.008 s
% 0.35/0.44 % (453205)Peak memory usage: 13 MB
% 0.35/0.44 % (453205)Instructions burned: 15 (million)
% 0.35/0.44 % (453200)Success in time 0.042 s
% 0.35/0.44 % Vampire exiting
%------------------------------------------------------------------------------