%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET684^3 : 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 : n003.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 08:23:28 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 83 ( 15 unt; 0 typ; 7 def)
% Number of atoms : 497 ( 103 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 670 ( 94 ~; 111 |; 32 &; 406 @)
% ( 11 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 63 usr; 13 con; 0-4 aty)
% ( 0 !!; 15 ??; 0 @@+; 0 @@-)
% Number of variables : 171 ( 0 sgn 91 !; 21 ?; 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_42,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
vAND: $o > $o > $o ).
thf(func_def_45,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vNOT: $o > $o ).
thf(func_def_47,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vIFF: $o > $o > $o ).
thf(func_def_53,type,
sK1: $i > $i > $o ).
thf(func_def_55,type,
sK3: $i > $i > $o ).
thf(func_def_58,type,
sK6: $i > ( $i > $i > $o ) > $i > ( $i > $i > $o ) > $i ).
thf(f22,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i,X3: $i] :
? [X4: $i] :
( ( X1 @ X4 @ X3 )
& ( X0 @ X2 @ X4 ) ) )
= rel_composition ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',rel_composition) ).
thf(f36,conjecture,
! [X2: $i,X1: $i > $i > $o,X3: $i,X0: $i > $i > $o] :
( ( rel_composition @ X0 @ X1 @ X2 @ X3 )
<=> ? [X4: $i] :
( ( X1 @ X4 @ X3 )
& ( X0 @ X2 @ X4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f37,negated_conjecture,
~ ! [X2: $i,X1: $i > $i > $o,X3: $i,X0: $i > $i > $o] :
( ( rel_composition @ X0 @ X1 @ X2 @ X3 )
<=> ? [X4: $i] :
( ( X1 @ X4 @ X3 )
& ( X0 @ X2 @ X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f90,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i,X3: $i] :
? [X4: $i] :
( ( X1 @ X4 @ X3 )
& ( X0 @ X2 @ X4 ) ) )
= rel_composition ),
inference(rectify,[],[f22]) ).
thf(f91,plain,
( rel_composition
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f90]) ).
thf(f97,plain,
~ ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i > $i > $o] :
( ( rel_composition @ X3 @ X1 @ X0 @ X2 )
<=> ? [X4: $i] :
( ( X1 @ X4 @ X2 )
& ( X3 @ X0 @ X4 ) ) ),
inference(rectify,[],[f37]) ).
thf(f98,plain,
~ ! [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i > $i > $o] :
( ? [X4: $i] :
( ( ( X3 @ X0 @ X4 )
= $true )
& ( ( X1 @ X4 @ X2 )
= $true ) )
<=> ( ( rel_composition @ X3 @ X1 @ X0 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f97]) ).
thf(f101,plain,
? [X2: $i,X3: $i > $i > $o,X0: $i,X1: $i > $i > $o] :
( ? [X4: $i] :
( ( ( X3 @ X0 @ X4 )
= $true )
& ( ( X1 @ X4 @ X2 )
= $true ) )
<~> ( ( rel_composition @ X3 @ X1 @ X0 @ X2 )
= $true ) ),
inference(ennf_transformation,[],[f98]) ).
thf(f102,plain,
? [X2: $i,X3: $i > $i > $o,X0: $i,X1: $i > $i > $o] :
( ( ( ( rel_composition @ X3 @ X1 @ X0 @ X2 )
!= $true )
| ! [X4: $i] :
( ( ( X3 @ X0 @ X4 )
!= $true )
| ( ( X1 @ X4 @ X2 )
!= $true ) ) )
& ( ( ( rel_composition @ X3 @ X1 @ X0 @ X2 )
= $true )
| ? [X4: $i] :
( ( ( X3 @ X0 @ X4 )
= $true )
& ( ( X1 @ X4 @ X2 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f101]) ).
thf(f103,plain,
? [X0: $i,X1: $i > $i > $o,X2: $i,X3: $i > $i > $o] :
( ( ( $true
!= ( rel_composition @ X1 @ X3 @ X2 @ X0 ) )
| ! [X4: $i] :
( ( $true
!= ( X1 @ X2 @ X4 ) )
| ( ( X3 @ X4 @ X0 )
!= $true ) ) )
& ( ( $true
= ( rel_composition @ X1 @ X3 @ X2 @ X0 ) )
| ? [X5: $i] :
( ( ( X1 @ X2 @ X5 )
= $true )
& ( ( X3 @ X5 @ X0 )
= $true ) ) ) ),
inference(rectify,[],[f102]) ).
thf(f104,plain,
( ( ( $true
!= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) )
| ! [X4: $i] :
( ( ( sK1 @ sK2 @ X4 )
!= $true )
| ( ( sK3 @ X4 @ sK0 )
!= $true ) ) )
& ( ( $true
= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) )
| ( ( ( sK1 @ sK2 @ sK4 )
= $true )
& ( ( sK3 @ sK4 @ sK0 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X5,sK4)],[f103]) ).
thf(f108,plain,
( ( $true
= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) )
| ( ( sK3 @ sK4 @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f104]) ).
thf(f109,plain,
( ( ( sK1 @ sK2 @ sK4 )
= $true )
| ( $true
= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f104]) ).
thf(f110,plain,
! [X4: $i] :
( ( $true
!= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) )
| ( ( sK3 @ X4 @ sK0 )
!= $true )
| ( ( sK1 @ sK2 @ X4 )
!= $true ) ),
inference(cnf_transformation,[],[f104]) ).
thf(f141,plain,
( rel_composition
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f218,definition,
( spl5_15
<=> ( ( sK1 @ sK2 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_15])],[avatar_definition]) ).
thf(f220,plain,
( ( ( sK1 @ sK2 @ sK4 )
= $true )
| ~ spl5_15 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f222,definition,
( spl5_16
<=> ( $true
= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_16])],[avatar_definition]) ).
thf(f223,plain,
( ( $true
!= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) )
| spl5_16 ),
inference(avatar_component_clause,[],[f222]) ).
thf(f224,plain,
( ( $true
= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) )
| ~ spl5_16 ),
inference(avatar_component_clause,[],[f222]) ).
thf(f225,plain,
( spl5_15
| spl5_16 ),
inference(avatar_split_clause,[],[f109,f222,f218]) ).
thf(f257,definition,
( spl5_23
<=> ! [X4: $i] :
( ( ( sK3 @ X4 @ sK0 )
!= $true )
| ( ( sK1 @ sK2 @ X4 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl5_23])],[avatar_definition]) ).
thf(f258,plain,
( ! [X4: $i] :
( ( ( sK3 @ X4 @ sK0 )
!= $true )
| ( ( sK1 @ sK2 @ X4 )
!= $true ) )
| ~ spl5_23 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f259,plain,
( ~ spl5_16
| spl5_23 ),
inference(avatar_split_clause,[],[f110,f257,f222]) ).
thf(f316,definition,
( spl5_35
<=> ( rel_composition
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_35])],[avatar_definition]) ).
thf(f318,plain,
( ( rel_composition
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) ) ) ) )
| ~ spl5_35 ),
inference(avatar_component_clause,[],[f316]) ).
thf(f319,plain,
spl5_35,
inference(avatar_split_clause,[],[f141,f316]) ).
thf(f326,definition,
( spl5_37
<=> ( ( sK3 @ sK4 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_37])],[avatar_definition]) ).
thf(f328,plain,
( ( ( sK3 @ sK4 @ sK0 )
= $true )
| ~ spl5_37 ),
inference(avatar_component_clause,[],[f326]) ).
thf(f329,plain,
( spl5_37
| spl5_16 ),
inference(avatar_split_clause,[],[f108,f222,f326]) ).
thf(f341,plain,
( ! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) ) )
@ X1 )
= ( rel_composition @ X1 ) )
| ~ spl5_35 ),
inference(argument_congruence,[],[f318]) ).
thf(f342,plain,
( ! [X1: $i > $i > $o] :
( ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( X1 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) ) ) )
= ( rel_composition @ X1 ) )
| ~ spl5_35 ),
inference(beta-eta_normalization,[],[f341]) ).
thf(f345,plain,
( ! [X2: $i > $i > $o,X1: $i > $i > $o] :
( ( rel_composition @ X1 @ X2 )
= ( ^ [Y0: $i > $i > $o,Y1: $i,Y2: $i] :
( ?? @ $i
@ ^ [Y3: $i] :
( ( X1 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) ) )
@ X2 ) )
| ~ spl5_35 ),
inference(argument_congruence,[],[f342]) ).
thf(f346,plain,
( ! [X2: $i > $i > $o,X1: $i > $i > $o] :
( ( ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y0 @ Y2 )
& ( X2 @ Y2 @ Y1 ) ) ) )
= ( rel_composition @ X1 @ X2 ) )
| ~ spl5_35 ),
inference(beta-eta_normalization,[],[f345]) ).
thf(f358,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o] :
( ( ^ [Y0: $i,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( X1 @ Y0 @ Y2 )
& ( X2 @ Y2 @ Y1 ) ) )
@ X3 )
= ( rel_composition @ X1 @ X2 @ X3 ) )
| ~ spl5_35 ),
inference(argument_congruence,[],[f346]) ).
thf(f359,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o] :
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( X1 @ X3 @ Y1 )
& ( X2 @ Y1 @ Y0 ) ) ) )
= ( rel_composition @ X1 @ X2 @ X3 ) )
| ~ spl5_35 ),
inference(beta-eta_normalization,[],[f358]) ).
thf(f360,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o,X4: $i] :
( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( X1 @ X3 @ Y1 )
& ( X2 @ Y1 @ Y0 ) ) )
@ X4 )
= ( rel_composition @ X1 @ X2 @ X3 @ X4 ) )
| ~ spl5_35 ),
inference(argument_congruence,[],[f359]) ).
thf(f361,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o,X4: $i] :
( ( $false
= ( rel_composition @ X1 @ X2 @ X3 @ X4 ) )
| ( ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( X1 @ X3 @ Y1 )
& ( X2 @ Y1 @ Y0 ) ) )
@ X4 )
= $true ) )
| ~ spl5_35 ),
inference(iff_proxy_clausification,[],[f360]) ).
thf(f362,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o,X4: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( X1 @ X3 @ Y1 )
& ( X2 @ Y1 @ Y0 ) ) )
@ X4 ) )
| ( $true
= ( rel_composition @ X1 @ X2 @ X3 @ X4 ) ) )
| ~ spl5_35 ),
inference(iff_proxy_clausification,[],[f360]) ).
thf(f363,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o,X4: $i] :
( ( $true
= ( rel_composition @ X1 @ X2 @ X3 @ X4 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( X1 @ X3 @ Y0 )
& ( X2 @ Y0 @ X4 ) ) ) ) )
| ~ spl5_35 ),
inference(beta-eta_normalization,[],[f362]) ).
thf(f364,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( $true
= ( rel_composition @ X1 @ X2 @ X3 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( X1 @ X3 @ Y0 )
& ( X2 @ Y0 @ X4 ) )
@ X5 ) ) )
| ~ spl5_35 ),
inference(pi_proxy_clausification,[],[f363]) ).
thf(f365,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( ( ( X1 @ X3 @ X5 )
& ( X2 @ X5 @ X4 ) )
= $false )
| ( $true
= ( rel_composition @ X1 @ X2 @ X3 @ X4 ) ) )
| ~ spl5_35 ),
inference(beta-eta_normalization,[],[f364]) ).
thf(f366,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o,X4: $i,X5: $i] :
( ( $true
= ( rel_composition @ X1 @ X2 @ X3 @ X4 ) )
| ( $false
= ( X1 @ X3 @ X5 ) )
| ( $false
= ( X2 @ X5 @ X4 ) ) )
| ~ spl5_35 ),
inference(and_proxy_clausification,[],[f365]) ).
thf(f367,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o,X4: $i] :
( ( $false
= ( rel_composition @ X1 @ X2 @ X3 @ X4 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( X1 @ X3 @ Y0 )
& ( X2 @ Y0 @ X4 ) ) ) ) )
| ~ spl5_35 ),
inference(beta-eta_normalization,[],[f361]) ).
thf(f368,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( X1 @ X3 @ Y0 )
& ( X2 @ Y0 @ X4 ) )
@ ( sK6 @ X3 @ X1 @ X4 @ X2 ) )
= $true )
| ( $false
= ( rel_composition @ X1 @ X2 @ X3 @ X4 ) ) )
| ~ spl5_35 ),
inference(sigma_proxy_clausification,[],[f367]) ).
thf(f369,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o,X4: $i] :
( ( $false
= ( rel_composition @ X1 @ X2 @ X3 @ X4 ) )
| ( $true
= ( ( X1 @ X3 @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) )
& ( X2 @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ X4 ) ) ) )
| ~ spl5_35 ),
inference(beta-eta_normalization,[],[f368]) ).
thf(f370,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o,X4: $i] :
( ( ( X2 @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) @ X4 )
= $true )
| ( $false
= ( rel_composition @ X1 @ X2 @ X3 @ X4 ) ) )
| ~ spl5_35 ),
inference(and_proxy_clausification,[],[f369]) ).
thf(f371,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $i > $o,X4: $i] :
( ( ( X1 @ X3 @ ( sK6 @ X3 @ X1 @ X4 @ X2 ) )
= $true )
| ( $false
= ( rel_composition @ X1 @ X2 @ X3 @ X4 ) ) )
| ~ spl5_35 ),
inference(and_proxy_clausification,[],[f369]) ).
thf(f380,plain,
( ! [X0: $i,X1: $i > $i > $o] :
( ( $true
!= ( sK1 @ sK2 @ ( sK6 @ X0 @ X1 @ sK0 @ sK3 ) ) )
| ( $false
= ( rel_composition @ X1 @ sK3 @ X0 @ sK0 ) )
| ( $true != $true ) )
| ~ spl5_23
| ~ spl5_35 ),
inference(superposition,[],[f258,f370]) ).
thf(f388,plain,
( ! [X0: $i,X1: $i > $i > $o] :
( ( $true
!= ( sK1 @ sK2 @ ( sK6 @ X0 @ X1 @ sK0 @ sK3 ) ) )
| ( $false
= ( rel_composition @ X1 @ sK3 @ X0 @ sK0 ) ) )
| ~ spl5_23
| ~ spl5_35 ),
inference(trivial_inequality_removal,[],[f380]) ).
thf(f426,plain,
( ( $false
= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) )
| ( $true != $true )
| ( $false
= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) )
| ~ spl5_23
| ~ spl5_35 ),
inference(superposition,[],[f388,f371]) ).
thf(f440,plain,
( ( $false
= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) )
| ( $true != $true )
| ~ spl5_23
| ~ spl5_35 ),
inference(duplicate_literal_removal,[],[f426]) ).
thf(f441,plain,
( ( $false
= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) )
| ~ spl5_23
| ~ spl5_35 ),
inference(trivial_inequality_removal,[],[f440]) ).
thf(f450,definition,
( spl5_40
<=> ( $false
= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_40])],[avatar_definition]) ).
thf(f452,plain,
( ( $false
= ( rel_composition @ sK1 @ sK3 @ sK2 @ sK0 ) )
| ~ spl5_40 ),
inference(avatar_component_clause,[],[f450]) ).
thf(f453,plain,
( spl5_40
| ~ spl5_23
| ~ spl5_35 ),
inference(avatar_split_clause,[],[f441,f316,f257,f450]) ).
thf(f486,plain,
( ( $false = $true )
| ~ spl5_16
| ~ spl5_40 ),
inference(superposition,[],[f224,f452]) ).
thf(f490,plain,
( $false
| ~ spl5_16
| ~ spl5_40 ),
inference(trivial_inequality_removal,[],[f486]) ).
thf(f491,plain,
( ~ spl5_16
| ~ spl5_40 ),
inference(avatar_contradiction_clause,[],[f490]) ).
thf(f508,definition,
( spl5_41
<=> ( $false
= ( sK1 @ sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_41])],[avatar_definition]) ).
thf(f510,plain,
( ( $false
= ( sK1 @ sK2 @ sK4 ) )
| ~ spl5_41 ),
inference(avatar_component_clause,[],[f508]) ).
thf(f513,plain,
( ( $false = $true )
| ~ spl5_15
| ~ spl5_41 ),
inference(superposition,[],[f510,f220]) ).
thf(f515,plain,
( $false
| ~ spl5_15
| ~ spl5_41 ),
inference(trivial_inequality_removal,[],[f513]) ).
thf(f516,plain,
( ~ spl5_15
| ~ spl5_41 ),
inference(avatar_contradiction_clause,[],[f515]) ).
thf(f536,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ sK2 @ X0 ) )
| ( $false
= ( sK3 @ X0 @ sK0 ) )
| ( $true != $true ) )
| spl5_16
| ~ spl5_35 ),
inference(superposition,[],[f223,f366]) ).
thf(f537,plain,
( ! [X0: $i] :
( ( $false
= ( sK3 @ X0 @ sK0 ) )
| ( $false
= ( sK1 @ sK2 @ X0 ) ) )
| spl5_16
| ~ spl5_35 ),
inference(trivial_inequality_removal,[],[f536]) ).
thf(f538,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK2 @ sK4 ) )
| spl5_16
| ~ spl5_35
| ~ spl5_37 ),
inference(superposition,[],[f537,f328]) ).
thf(f544,plain,
( ( $false
= ( sK1 @ sK2 @ sK4 ) )
| spl5_16
| ~ spl5_35
| ~ spl5_37 ),
inference(trivial_inequality_removal,[],[f538]) ).
thf(f546,plain,
( spl5_41
| spl5_16
| ~ spl5_35
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f544,f326,f316,f222,f508]) ).
cnf(s15,plain,
( spl5_15
| spl5_16 ),
inference(sat_conversion,[],[f225]) ).
cnf(s22,plain,
( ~ spl5_16
| spl5_23 ),
inference(sat_conversion,[],[f259]) ).
cnf(s34,plain,
spl5_35,
inference(sat_conversion,[],[f319]) ).
cnf(s36,plain,
( spl5_16
| spl5_37 ),
inference(sat_conversion,[],[f329]) ).
cnf(s39,plain,
( ~ spl5_23
| ~ spl5_35
| spl5_40 ),
inference(sat_conversion,[],[f453]) ).
cnf(s41,plain,
( ~ spl5_16
| ~ spl5_40 ),
inference(sat_conversion,[],[f491]) ).
cnf(s46,plain,
( ~ spl5_15
| ~ spl5_41 ),
inference(sat_conversion,[],[f516]) ).
cnf(s48,plain,
( spl5_16
| ~ spl5_35
| ~ spl5_37
| spl5_41 ),
inference(sat_conversion,[],[f546]) ).
cnf(s50,plain,
~ spl5_16,
inference(rat,[],[s39,s22,s41,s34]) ).
cnf(s51,plain,
spl5_37,
inference(rat,[],[s36,s50]) ).
cnf(s52,plain,
spl5_15,
inference(rat,[],[s15,s50]) ).
cnf(s53,plain,
spl5_41,
inference(rat,[],[s48,s50,s34,s51]) ).
cnf(s55,plain,
$false,
inference(rat,[],[s46,s53,s52]) ).
thf(f547,plain,
$false,
inference(avatar_sat_refutation,[],[s55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET684^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n003.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 13:42:28 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 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
% 0.21/0.28 % (2515483)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (2515491)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=733876843: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)
% 0.21/0.28 % (2515494)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (2515494)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
% 0.21/0.28 % (2515490)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1685682646:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (2515492)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2427793276:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (2515488)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1604909233:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (2515489)lrs+10_16_si=on:nwc=1.5:random_seed=337166301:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (2515493)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=193480197:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (2515494)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=4030623856:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (2515490)Instruction limit reached!
% 0.21/0.28 % (2515490)------------------------------
% 0.21/0.28 % (2515490)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (2515490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (2515490)CaDiCaL version: 2.1.3
% 0.21/0.28 % (2515490)Termination reason: Instruction limit
% 0.21/0.28 % (2515490)Termination phase: Property scanning
% 0.21/0.28 % (2515490)Time elapsed: 0.002 s
% 0.21/0.28 % (2515490)Peak memory usage: 10 MB
% 0.21/0.28 % (2515490)Instructions burned: 3 (million)
% 0.21/0.28 % (2515491) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2515483-2515491"...
% 0.21/0.28 % (2515491)...printing done.
% 0.21/0.28 % (2515491)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (2515491)------------------------------
% 0.21/0.29 % (2515491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2515491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2515491)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2515491)Termination reason: Refutation
% 0.21/0.29 % (2515491)Time elapsed: 0.011 s
% 0.21/0.29 % (2515491)Peak memory usage: 13 MB
% 0.21/0.29 % (2515491)Instructions burned: 33 (million)
% 0.21/0.29 % (2515483)Success in time 0.047 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------