%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET680^3 : 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 : n009.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 0.23s 0.32s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of formulae : 89 ( 23 unt; 0 typ; 6 def)
% Number of atoms : 525 ( 119 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 550 ( 97 ~; 88 |; 34 &; 284 @)
% ( 10 <=>; 18 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 63 usr; 14 con; 0-4 aty)
% ( 10 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 115 ( 0 sgn 43 !; 26 ?; 115 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
vNOT: $o > $o ).
thf(func_def_41,type,
vAND: $o > $o > $o ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vIFF: $o > $o > $o ).
thf(func_def_51,type,
vOR: $o > $o > $o ).
thf(func_def_52,type,
sK0: $i > $o ).
thf(func_def_53,type,
sK1: $i > $o ).
thf(func_def_54,type,
sK2: $i > $i > $o ).
thf(f19,axiom,
( is_rel_on
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
! [X3: $i,X4: $i] :
( ( X0 @ X3 @ X4 )
=> ( ( X1 @ X3 )
& ( X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',is_rel_on) ).
thf(f29,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= rel_domain ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^2.ax',rel_domain) ).
thf(f36,conjecture,
! [X0: $i > $i > $o,X2: $i > $o,X1: $i > $o] :
( ( is_rel_on @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( X1 @ X3 )
=> ( ( rel_domain @ X0 @ X3 )
<=> ? [X4: $i] :
( ( X2 @ X4 )
& ( X0 @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f37,negated_conjecture,
~ ! [X0: $i > $i > $o,X2: $i > $o,X1: $i > $o] :
( ( is_rel_on @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( X1 @ X3 )
=> ( ( rel_domain @ X0 @ X3 )
<=> ? [X4: $i] :
( ( X2 @ X4 )
& ( X0 @ X3 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f49,plain,
( is_rel_on
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
! [X3: $i,X4: $i] :
( ( X0 @ X3 @ X4 )
=> ( ( X1 @ X3 )
& ( X2 @ X4 ) ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f50,plain,
( is_rel_on
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 @ Y3 )
=> ( ( Y2 @ Y3 )
& ( Y1 @ Y4 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f69,plain,
~ ! [X0: $i > $i > $o,X1: $i > $o,X2: $i > $o] :
( ( is_rel_on @ X0 @ X2 @ X1 )
=> ! [X3: $i] :
( ( X2 @ X3 )
=> ( ( rel_domain @ X0 @ X3 )
<=> ? [X4: $i] :
( ( X1 @ X4 )
& ( X0 @ X3 @ X4 ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f70,plain,
~ ! [X1: $i > $o,X0: $i > $i > $o,X2: $i > $o] :
( ( $true
= ( is_rel_on @ X0 @ X2 @ X1 ) )
=> ! [X3: $i] :
( ( ( X2 @ X3 )
= $true )
=> ( ( ( rel_domain @ X0 @ X3 )
= $true )
<=> ? [X4: $i] :
( ( ( X1 @ X4 )
= $true )
& ( ( X0 @ X3 @ X4 )
= $true ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f87,plain,
( ( ^ [X0: $i > $i > $o,X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= rel_domain ),
inference(rectify,[],[f29]) ).
thf(f88,plain,
( rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f101,plain,
? [X1: $i > $o,X2: $i > $o,X0: $i > $i > $o] :
( ( $true
= ( is_rel_on @ X0 @ X2 @ X1 ) )
& ? [X3: $i] :
( ( ? [X4: $i] :
( ( ( X1 @ X4 )
= $true )
& ( ( X0 @ X3 @ X4 )
= $true ) )
<~> ( ( rel_domain @ X0 @ X3 )
= $true ) )
& ( ( X2 @ X3 )
= $true ) ) ),
inference(ennf_transformation,[],[f70]) ).
thf(f102,plain,
? [X1: $i > $o,X2: $i > $o,X0: $i > $i > $o] :
( ( $true
= ( is_rel_on @ X0 @ X2 @ X1 ) )
& ? [X3: $i] :
( ( ( ( rel_domain @ X0 @ X3 )
!= $true )
| ! [X4: $i] :
( ( ( X1 @ X4 )
!= $true )
| ( ( X0 @ X3 @ X4 )
!= $true ) ) )
& ( ( ( rel_domain @ X0 @ X3 )
= $true )
| ? [X4: $i] :
( ( ( X1 @ X4 )
= $true )
& ( ( X0 @ X3 @ X4 )
= $true ) ) )
& ( ( X2 @ X3 )
= $true ) ) ),
inference(nnf_transformation,[],[f101]) ).
thf(f103,plain,
? [X1: $i > $o,X2: $i > $o,X0: $i > $i > $o] :
( ( $true
= ( is_rel_on @ X0 @ X2 @ X1 ) )
& ? [X3: $i] :
( ( ( ( rel_domain @ X0 @ X3 )
!= $true )
| ! [X4: $i] :
( ( ( X1 @ X4 )
!= $true )
| ( ( X0 @ X3 @ X4 )
!= $true ) ) )
& ( ( ( rel_domain @ X0 @ X3 )
= $true )
| ? [X4: $i] :
( ( ( X1 @ X4 )
= $true )
& ( ( X0 @ X3 @ X4 )
= $true ) ) )
& ( ( X2 @ X3 )
= $true ) ) ),
inference(flattening,[],[f102]) ).
thf(f104,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $i > $o] :
( ( $true
= ( is_rel_on @ X2 @ X1 @ X0 ) )
& ? [X3: $i] :
( ( ( $true
!= ( rel_domain @ X2 @ X3 ) )
| ! [X4: $i] :
( ( $true
!= ( X0 @ X4 ) )
| ( $true
!= ( X2 @ X3 @ X4 ) ) ) )
& ( ( $true
= ( rel_domain @ X2 @ X3 ) )
| ? [X5: $i] :
( ( $true
= ( X0 @ X5 ) )
& ( $true
= ( X2 @ X3 @ X5 ) ) ) )
& ( ( X1 @ X3 )
= $true ) ) ),
inference(rectify,[],[f103]) ).
thf(f105,plain,
( ( ( is_rel_on @ sK2 @ sK1 @ sK0 )
= $true )
& ( ( $true
!= ( rel_domain @ sK2 @ sK3 ) )
| ! [X4: $i] :
( ( $true
!= ( sK0 @ X4 ) )
| ( $true
!= ( sK2 @ sK3 @ X4 ) ) ) )
& ( ( $true
= ( rel_domain @ sK2 @ sK3 ) )
| ( ( $true
= ( sK0 @ sK4 ) )
& ( $true
= ( sK2 @ sK3 @ sK4 ) ) ) )
& ( $true
= ( sK1 @ sK3 ) ) ),
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)],[f104]) ).
thf(f119,plain,
( rel_domain
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f140,plain,
( ( $true
= ( rel_domain @ sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(cnf_transformation,[],[f105]) ).
thf(f141,plain,
( ( $true
= ( rel_domain @ sK2 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 ) ) ),
inference(cnf_transformation,[],[f105]) ).
thf(f142,plain,
! [X4: $i] :
( ( $true
!= ( rel_domain @ sK2 @ sK3 ) )
| ( $true
!= ( sK0 @ X4 ) )
| ( $true
!= ( sK2 @ sK3 @ X4 ) ) ),
inference(cnf_transformation,[],[f105]) ).
thf(f143,plain,
( ( is_rel_on @ sK2 @ sK1 @ sK0 )
= $true ),
inference(cnf_transformation,[],[f105]) ).
thf(f145,plain,
( is_rel_on
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 @ Y3 )
=> ( ( Y2 @ Y3 )
& ( Y1 @ Y4 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f151,plain,
( ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y4 @ Y3 )
=> ( ( Y2 @ Y3 )
& ( Y1 @ Y4 ) ) ) ) )
@ sK2
@ sK1
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f143,f145]) ).
thf(f152,plain,
! [X4: $i] :
( ( $true
!= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) )
@ sK2
@ sK3 ) )
| ( $true
!= ( sK0 @ X4 ) )
| ( $true
!= ( sK2 @ sK3 @ X4 ) ) ),
inference(definition_unfolding,[],[f142,f119]) ).
thf(f153,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) )
@ sK2
@ sK3 ) ) ),
inference(definition_unfolding,[],[f141,f119]) ).
thf(f154,plain,
( ( $true
= ( sK2 @ sK3 @ sK4 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o,Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) )
@ sK2
@ sK3 ) ) ),
inference(definition_unfolding,[],[f140,f119]) ).
thf(f155,plain,
! [X4: $i] :
( ( $true
!= ( sK2 @ sK3 @ X4 ) )
| ( $true
!= ( ?? @ $i @ ( sK2 @ sK3 ) ) )
| ( $true
!= ( sK0 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f156,plain,
! [X4: $i,X5: $i] :
( ( $true
!= ( sK0 @ X4 ) )
| ( ( sK2 @ sK3 @ X5 )
= $false )
| ( $true
!= ( sK2 @ sK3 @ X4 ) ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( sK0 @ Y0 )
& ( sK1 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f158,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK2 @ Y1 @ Y0 )
=> ( ( sK0 @ Y0 )
& ( sK1 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK2 @ Y0 @ X1 )
=> ( ( sK0 @ X1 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK2 @ Y0 @ X1 )
=> ( ( sK0 @ X1 )
& ( sK1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK2 @ X2 @ X1 )
=> ( ( sK0 @ X1 )
& ( sK1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK0 @ X1 )
& ( sK1 @ X2 ) )
= $true )
| ( ( sK2 @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f161]) ).
thf(f164,plain,
! [X2: $i,X1: $i] :
( ( ( sK2 @ X2 @ X1 )
= $false )
| ( $true
= ( sK0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( ?? @ $i @ ( sK2 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f166,plain,
( ( $true
= ( sK0 @ sK4 ) )
| ( $true
= ( sK2 @ sK3 @ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $true
= ( sK2 @ sK3 @ sK4 ) )
| ( $true
= ( ?? @ $i @ ( sK2 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f168,plain,
( ( $true
= ( sK2 @ sK3 @ sK6 ) )
| ( $true
= ( sK2 @ sK3 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f167]) ).
thf(f170,definition,
( spl7_1
<=> ! [X4: $i] :
( ( $true
!= ( sK0 @ X4 ) )
| ( $true
!= ( sK2 @ sK3 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f171,plain,
( ! [X4: $i] :
( ( $true
!= ( sK2 @ sK3 @ X4 ) )
| ( $true
!= ( sK0 @ X4 ) ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f170]) ).
thf(f173,definition,
( spl7_2
<=> ! [X5: $i] :
( ( sK2 @ sK3 @ X5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f174,plain,
( ! [X5: $i] :
( ( sK2 @ sK3 @ X5 )
= $false )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f173]) ).
thf(f175,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f156,f173,f170]) ).
thf(f177,definition,
( spl7_3
<=> ( $true
= ( sK2 @ sK3 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f179,plain,
( ( $true
= ( sK2 @ sK3 @ sK5 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f177]) ).
thf(f181,definition,
( spl7_4
<=> ( $true
= ( sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f184,plain,
( spl7_3
| spl7_4 ),
inference(avatar_split_clause,[],[f166,f181,f177]) ).
thf(f186,definition,
( spl7_5
<=> ( $true
= ( sK2 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f188,plain,
( ( $true
= ( sK2 @ sK3 @ sK4 ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f186]) ).
thf(f190,definition,
( spl7_6
<=> ( $true
= ( sK2 @ sK3 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f192,plain,
( ( $true
= ( sK2 @ sK3 @ sK6 ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f190]) ).
thf(f193,plain,
( spl7_5
| spl7_6 ),
inference(avatar_split_clause,[],[f168,f190,f186]) ).
thf(f200,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK5 ) )
| ~ spl7_1
| ~ spl7_3 ),
inference(constrained_superposition,[],[f171,f179]) ).
thf(f201,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK4 ) )
| ~ spl7_1
| ~ spl7_5 ),
inference(constrained_superposition,[],[f171,f188]) ).
thf(f202,plain,
( ( $true
!= ( sK0 @ sK5 ) )
| ~ spl7_1
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f200]) ).
thf(f203,plain,
( ( $true
!= ( sK0 @ sK4 ) )
| ~ spl7_1
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f201]) ).
thf(f204,plain,
( ~ spl7_4
| ~ spl7_1
| ~ spl7_5 ),
inference(avatar_split_clause,[],[f203,f186,f170,f181]) ).
thf(f216,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ( $true = $false )
| ~ spl7_3 ),
inference(constrained_superposition,[],[f179,f164]) ).
thf(f222,plain,
( ( $true
= ( sK0 @ sK5 ) )
| ~ spl7_3 ),
inference(trivial_inequality_removal,[],[f216]) ).
thf(f229,plain,
( $false
| ~ spl7_1
| ~ spl7_3 ),
inference(forward_subsumption_resolution,[],[f222,f202]) ).
thf(f230,plain,
( ~ spl7_1
| ~ spl7_3 ),
inference(avatar_contradiction_clause,[],[f229]) ).
thf(f233,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_5 ),
inference(constrained_superposition,[],[f188,f174]) ).
thf(f236,plain,
( $false
| ~ spl7_2
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f233]) ).
thf(f237,plain,
( ~ spl7_2
| ~ spl7_5 ),
inference(avatar_contradiction_clause,[],[f236]) ).
thf(f242,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK6 ) )
| ~ spl7_6 ),
inference(constrained_superposition,[],[f192,f164]) ).
thf(f247,plain,
( ( $true
= ( sK0 @ sK6 ) )
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f242]) ).
thf(f252,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK6 ) )
| ~ spl7_1
| ~ spl7_6 ),
inference(constrained_superposition,[],[f171,f192]) ).
thf(f253,plain,
( ( $true
!= ( sK0 @ sK6 ) )
| ~ spl7_1
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f252]) ).
thf(f254,plain,
( $false
| ~ spl7_1
| ~ spl7_6 ),
inference(forward_subsumption_resolution,[],[f253,f247]) ).
thf(f255,plain,
( ~ spl7_1
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f254]) ).
thf(f259,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_6 ),
inference(constrained_superposition,[],[f192,f174]) ).
thf(f262,plain,
( $false
| ~ spl7_2
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f259]) ).
thf(f263,plain,
( ~ spl7_2
| ~ spl7_6 ),
inference(avatar_contradiction_clause,[],[f262]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f175]) ).
cnf(s2,plain,
( spl7_3
| spl7_4 ),
inference(sat_conversion,[],[f184]) ).
cnf(s3,plain,
( spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f193]) ).
cnf(s6,plain,
( ~ spl7_1
| ~ spl7_4
| ~ spl7_5 ),
inference(sat_conversion,[],[f204]) ).
cnf(s10,plain,
( ~ spl7_1
| ~ spl7_3 ),
inference(sat_conversion,[],[f230]) ).
cnf(s14,plain,
( ~ spl7_2
| ~ spl7_5 ),
inference(sat_conversion,[],[f237]) ).
cnf(s15,plain,
( ~ spl7_1
| ~ spl7_6 ),
inference(sat_conversion,[],[f255]) ).
cnf(s17,plain,
( ~ spl7_2
| ~ spl7_6 ),
inference(sat_conversion,[],[f263]) ).
cnf(s18,plain,
~ spl7_2,
inference(rat,[],[s3,s14,s17]) ).
cnf(s19,plain,
spl7_1,
inference(rat,[],[s1,s18]) ).
cnf(s20,plain,
~ spl7_6,
inference(rat,[],[s15,s19]) ).
cnf(s21,plain,
~ spl7_3,
inference(rat,[],[s10,s19]) ).
cnf(s22,plain,
spl7_5,
inference(rat,[],[s3,s20]) ).
cnf(s23,plain,
spl7_4,
inference(rat,[],[s2,s21]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s6,s19,s22,s23]) ).
thf(f264,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET680^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n009.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:40:45 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.26 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
% 0.23/0.32 % (4005324)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.32 % (4005333)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1337680137:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.32 % (4005335)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.32 % (4005335)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
% 0.23/0.32 % (4005329)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2242813322:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.32 % (4005330)lrs+10_16_si=on:nwc=1.5:random_seed=1285502705:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.32 % (4005331)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2231105135:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.32 % (4005332)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=2769119861: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)
% 0.23/0.32 % (4005334)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2365702613:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.32 % (4005335)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=1685740916:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.32 % (4005333)Instruction limit reached!
% 0.23/0.32 % (4005333)------------------------------
% 0.23/0.32 % (4005333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (4005333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (4005333)CaDiCaL version: 2.1.3
% 0.23/0.32 % (4005333)Termination reason: Instruction limit
% 0.23/0.32 % (4005333)Termination phase: Saturation
% 0.23/0.32 % (4005333)Time elapsed: 0.008 s
% 0.23/0.32 % (4005333)Peak memory usage: 12 MB
% 0.23/0.32 % (4005333)Instructions burned: 27 (million)
% 0.23/0.32 % (4005331)Instruction limit reached!
% 0.23/0.32 % (4005331)------------------------------
% 0.23/0.32 % (4005331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (4005331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (4005331)CaDiCaL version: 2.1.3
% 0.23/0.32 % (4005331)Termination reason: Instruction limit
% 0.23/0.32 % (4005331)Termination phase: Preprocessing 2
% 0.23/0.32 % (4005331)Time elapsed: 0.002 s
% 0.23/0.32 % (4005331)Peak memory usage: 10 MB
% 0.23/0.32 % (4005331)Instructions burned: 4 (million)
% 0.23/0.32 % (4005329) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4005324-4005329"...
% 0.23/0.32 % (4005330) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4005324-4005330"...
% 0.23/0.32 % (4005334) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4005324-4005334"...
% 0.23/0.32 % (4005329)...printing done.
% 0.23/0.32 % (4005330)...printing done.
% 0.23/0.32 % (4005334)...printing done.
% 0.23/0.32 % (4005329)Refutation found. Thanks to Tanya!
% 0.23/0.32 % SZS status Theorem for theBenchmark
% 0.23/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.32 % (4005329)------------------------------
% 0.23/0.32 % (4005329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (4005329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (4005329)CaDiCaL version: 2.1.3
% 0.23/0.32 % (4005329)Termination reason: Refutation
% 0.23/0.32 % (4005329)Time elapsed: 0.009 s
% 0.23/0.32 % (4005329)Peak memory usage: 13 MB
% 0.23/0.32 % (4005329)Instructions burned: 15 (million)
% 0.23/0.32 % (4005324)Success in time 0.054 s
% 0.23/0.32 % Vampire exiting
%------------------------------------------------------------------------------