%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET669^3 : 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 : n008.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 08:23:27 AM UTC 2026
% Result : Theorem 0.22s 0.28s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 33 unt; 0 typ; 2 def)
% Number of atoms : 355 ( 94 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 386 ( 33 ~; 36 |; 17 &; 242 @)
% ( 2 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 65 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 55 usr; 8 con; 0-4 aty)
% ( 14 !!; 20 ??; 0 @@+; 0 @@-)
% Number of variables : 171 ( 33 sgn 34 !; 5 ?; 171 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > ( $i > $o ) > $o ).
thf(func_def_2,type,
is_a: $i > ( $i > $o ) > $o ).
thf(func_def_3,type,
emptyset: $i > $o ).
thf(func_def_4,type,
unord_pair: $i > $i > $i > $o ).
thf(func_def_5,type,
singleton: $i > $i > $o ).
thf(func_def_6,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
excl_union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
intersection: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
setminus: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
complement: ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
disjoint: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_12,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_13,type,
meets: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_14,type,
misses: ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_15,type,
cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_16,type,
pair_rel: $i > $i > $i > $i > $o ).
thf(func_def_17,type,
id_rel: ( $i > $o ) > $i > $i > $o ).
thf(func_def_18,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_20,type,
restrict_rel_domain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_21,type,
rel_diagonal: $i > $i > $o ).
thf(func_def_22,type,
rel_composition: ( $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_23,type,
reflexive: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
irreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
symmetric: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
transitive: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
equiv_rel: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_29,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_30,type,
rel_inverse: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_31,type,
equiv_classes: ( $i > $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_32,type,
restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_33,type,
rel_field: ( $i > $i > $o ) > $i > $o ).
thf(func_def_34,type,
well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_35,type,
upwards_well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_36,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vAND: $o > $o > $o ).
thf(func_def_42,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vNOT: $o > $o ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_48,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_49,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vIFF: $o > $o > $o ).
thf(func_def_52,type,
sK0: $i > $i > $o ).
thf(f12,axiom,
( subset
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',subset) ).
thf(f17,axiom,
( ( ^ [X0: $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 )
& ( X1 = X2 ) ) )
= id_rel ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',id_rel) ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
= sub_rel ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',sub_rel) ).
thf(f28,axiom,
( rel_codomain
= ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',rel_codomain) ).
thf(f29,axiom,
( rel_domain
= ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',rel_domain) ).
thf(f36,conjecture,
! [X0: $i > $i > $o] :
( ( sub_rel
@ ( id_rel
@ ^ [X1: $i] : $true )
@ X0 )
=> ( ( subset
@ ^ [X1: $i] : $true
@ ( rel_domain @ X0 ) )
& ( ( ^ [X1: $i] : $true )
= ( rel_codomain @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f37,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( sub_rel
@ ( id_rel
@ ^ [X1: $i] : $true )
@ X0 )
=> ( ( subset
@ ^ [X1: $i] : $true
@ ( rel_domain @ X0 ) )
& ( ( ^ [X1: $i] : $true )
= ( rel_codomain @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f49,plain,
~ ! [X0: $i > $i > $o] :
( ( sub_rel
@ ( id_rel
@ ^ [X1: $i] : $true )
@ X0 )
=> ( ( subset
@ ^ [X2: $i] : $true
@ ( rel_domain @ X0 ) )
& ( ( ^ [X3: $i] : $true )
= ( rel_codomain @ X0 ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f50,plain,
~ ! [X0: $i > $i > $o] :
( ( $true
= ( sub_rel
@ ( id_rel
@ ^ [Y0: $i] : $true )
@ X0 ) )
=> ( ( ( rel_codomain @ X0 )
= ( ^ [Y0: $i] : $true ) )
& ( $true
= ( subset
@ ^ [Y0: $i] : $true
@ ( rel_domain @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f62,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o] :
! [X2: $i,X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X2 @ X3 ) ) )
= sub_rel ),
inference(rectify,[],[f18]) ).
thf(f63,plain,
( sub_rel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f66,plain,
( ( ^ [X0: $i > $o,X1: $i,X2: $i] :
( ( X0 @ X1 )
& ( X1 = X2 ) ) )
= id_rel ),
inference(rectify,[],[f17]) ).
thf(f67,plain,
( id_rel
= ( ^ [Y0: $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
& ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f80,plain,
( subset
= ( ^ [X0: $i > $o,X1: $i > $o] :
! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f12]) ).
thf(f81,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f86,plain,
( rel_domain
= ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
inference(rectify,[],[f29]) ).
thf(f87,plain,
( rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f99,plain,
( rel_codomain
= ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f100,plain,
( rel_codomain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
? [X0: $i > $i > $o] :
( ( ( ( rel_codomain @ X0 )
!= ( ^ [Y0: $i] : $true ) )
| ( $true
!= ( subset
@ ^ [Y0: $i] : $true
@ ( rel_domain @ X0 ) ) ) )
& ( $true
= ( sub_rel
@ ( id_rel
@ ^ [Y0: $i] : $true )
@ X0 ) ) ),
inference(ennf_transformation,[],[f50]) ).
thf(f102,plain,
( ( ( ( ^ [Y0: $i] : $true )
!= ( rel_codomain @ sK0 ) )
| ( ( subset
@ ^ [Y0: $i] : $true
@ ( rel_domain @ sK0 ) )
!= $true ) )
& ( ( sub_rel
@ ( id_rel
@ ^ [Y0: $i] : $true )
@ sK0 )
= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f101]) ).
thf(f106,plain,
( sub_rel
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f107,plain,
( rel_codomain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f100]) ).
thf(f109,plain,
( id_rel
= ( ^ [Y0: $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
& ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f117,plain,
( rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f126,plain,
( ( sub_rel
@ ( id_rel
@ ^ [Y0: $i] : $true )
@ sK0 )
= $true ),
inference(cnf_transformation,[],[f102]) ).
thf(f127,plain,
( ( ( ^ [Y0: $i] : $true )
!= ( rel_codomain @ sK0 ) )
| ( ( subset
@ ^ [Y0: $i] : $true
@ ( rel_domain @ sK0 ) )
!= $true ) ),
inference(cnf_transformation,[],[f102]) ).
thf(f129,plain,
( subset
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f145,plain,
( ( ( ^ [Y0: $i > $o,Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) )
@ ^ [Y0: $i] : $true
@ ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) )
@ sK0 ) )
!= $true )
| ( ( ^ [Y0: $i] : $true )
!= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f127,f107,f129,f117]) ).
thf(f146,plain,
( $true
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
& ( Y0 @ Y1 ) )
@ ^ [Y0: $i] : $true )
@ sK0 ) ),
inference(definition_unfolding,[],[f126,f106,f109]) ).
thf(f147,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( Y1 = Y0 )
& $true )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( Y1 = Y0 )
& $true )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( Y0 = X1 )
& $true )
=> ( sK0 @ Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( Y0 = X1 )
& $true )
=> ( sK0 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X1: $i] :
( ( ( ( X2 = X1 )
& $true )
=> ( sK0 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $true )
| ( $false
= ( ( X2 = X1 )
& $true ) ) ),
inference(imp_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $true )
| ( $true = $false )
| ( ( X2 = X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $true )
| ( X1 != X2 )
| ( $true = $false ) ),
inference(equality_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $true )
| ( X1 != X2 ) ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f156,plain,
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) ) )
!= ( ^ [Y0: $i] : $true ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( $true
=> ( ?? @ $i @ ( sK0 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f157,plain,
( ( $false
= ( ^ [Y0: $i] :
( $true
=> ( ?? @ $i @ ( sK0 @ Y0 ) ) )
@ sK1 ) )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) ) )
!= ( ^ [Y0: $i] : $true ) ) ),
inference(sigma_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( ( $true
=> ( ?? @ $i @ ( sK0 @ sK1 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) ) )
!= ( ^ [Y0: $i] : $true ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) ) )
!= ( ^ [Y0: $i] : $true ) )
| ( $false
= ( ?? @ $i @ ( sK0 @ sK1 ) ) ) ),
inference(imp_proxy_clausification,[],[f158]) ).
thf(f161,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) ) )
!= ( ^ [Y0: $i] : $true ) ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f163,definition,
( spl2_1
<=> ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) ) )
= ( ^ [Y0: $i] : $true ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f165,plain,
( ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) ) )
!= ( ^ [Y0: $i] : $true ) )
| spl2_1 ),
inference(avatar_component_clause,[],[f163]) ).
thf(f167,definition,
( spl2_2
<=> ! [X1: $i] :
( ( sK0 @ sK1 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f168,plain,
( ! [X1: $i] :
( ( sK0 @ sK1 @ X1 )
= $false )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f167]) ).
thf(f169,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f161,f167,f163]) ).
thf(f170,plain,
( ( ( ^ [Y0: $i] : $true
@ sK3 )
!= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) )
@ sK3 ) )
| spl2_1 ),
inference(negative_extensionality,[],[f165]) ).
thf(f172,plain,
( ( ( ^ [Y0: $i] : $true
@ sK3 )
= $false )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] : ( sK0 @ Y1 @ Y0 ) )
@ sK3 )
= $false )
| spl2_1 ),
inference(xor_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ sK3 ) )
= $false )
| ( $true = $false )
| spl2_1 ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
( ! [X1: $i] :
( ( $true = $false )
| ( ( ^ [Y0: $i] : ( sK0 @ Y0 @ sK3 )
@ X1 )
= $false ) )
| spl2_1 ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] : ( sK0 @ Y0 @ sK3 )
@ X1 )
= $false )
| spl2_1 ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f176,plain,
( ! [X1: $i] :
( ( sK0 @ X1 @ sK3 )
= $false )
| spl2_1 ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f179,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( sK3 != X0 ) )
| spl2_1 ),
inference(constrained_superposition,[],[f176,f155]) ).
thf(f181,plain,
( ! [X0: $i] : ( sK3 != X0 )
| spl2_1 ),
inference(trivial_inequality_removal,[],[f179]) ).
thf(f183,plain,
( $false
| spl2_1 ),
inference(equality_resolution,[],[f181]) ).
thf(f184,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f183]) ).
thf(f186,plain,
( ! [X0: $i] :
( ( sK1 != X0 )
| ( $true = $false ) )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f155,f168]) ).
thf(f187,plain,
( ! [X0: $i] : ( sK1 != X0 )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f186]) ).
thf(f189,plain,
( $false
| ~ spl2_2 ),
inference(equality_resolution,[],[f187]) ).
thf(f190,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f189]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f169]) ).
cnf(s2,plain,
spl2_1,
inference(sat_conversion,[],[f184]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f190]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
thf(f191,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET669^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n008.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:41:09 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.28 % (3168223)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.28 % (3168229)lrs+10_16_si=on:nwc=1.5:random_seed=3893404960:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.28 % (3168229) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3168223-3168229"...
% 0.22/0.28 % (3168229)...printing done.
% 0.22/0.28 % (3168229)Refutation found. Thanks to Tanya!
% 0.22/0.28 % SZS status Theorem for theBenchmark
% 0.22/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.28 % (3168229)------------------------------
% 0.22/0.28 % (3168229)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.28 % (3168229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.28 % (3168229)CaDiCaL version: 2.1.3
% 0.22/0.28 % (3168229)Termination reason: Refutation
% 0.22/0.28 % (3168229)Time elapsed: 0.004 s
% 0.22/0.28 % (3168229)Peak memory usage: 13 MB
% 0.22/0.28 % (3168229)Instructions burned: 12 (million)
% 0.22/0.28 % (3168223)Success in time 0.033 s
% 0.22/0.28 % Vampire exiting
%------------------------------------------------------------------------------