%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n005.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 08:23:48 AM UTC 2026
% Result : Theorem 0.13s 0.27s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 100 ( 15 unt; 0 typ; 8 def)
% Number of atoms : 654 ( 116 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 648 ( 139 ~; 138 |; 27 &; 323 @)
% ( 12 <=>; 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 : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 65 usr; 16 con; 0-4 aty)
% ( 0 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 92 ( 0 sgn 32 !; 21 ?; 92 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_44,type,
vAND: $o > $o > $o ).
thf(func_def_45,type,
vNOT: $o > $o ).
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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vIFF: $o > $o > $o ).
thf(func_def_52,type,
sK0: $i > $i > $o ).
thf(func_def_53,type,
sK1: $i > $i > $o ).
thf(f22,axiom,
( rel_composition
= ( ^ [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i,X3: $i] :
? [X4: $i] :
( ( X1 @ X4 @ X3 )
& ( X0 @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',rel_composition) ).
thf(f36,conjecture,
! [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( 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,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( rel_composition @ X0 @ X1 @ X2 @ X3 )
<=> ? [X4: $i] :
( ( X1 @ X4 @ X3 )
& ( X0 @ X2 @ X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f72,plain,
( rel_composition
= ( ^ [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i,X3: $i] :
? [X4: $i] :
( ( X1 @ X4 @ X3 )
& ( X0 @ X2 @ X4 ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f73,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,[],[f72]) ).
thf(f99,plain,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( rel_composition @ X0 @ X1 @ X2 @ X3 )
<=> ? [X4: $i] :
( ( X1 @ X4 @ X3 )
& ( X0 @ X2 @ X4 ) ) ),
inference(rectify,[],[f37]) ).
thf(f100,plain,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( ( rel_composition @ X0 @ X1 @ X2 @ X3 )
= $true )
<=> ? [X4: $i] :
( ( ( X1 @ X4 @ X3 )
= $true )
& ( ( X0 @ X2 @ X4 )
= $true ) ) ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( ( rel_composition @ X0 @ X1 @ X2 @ X3 )
= $true )
<~> ? [X4: $i] :
( ( ( X1 @ X4 @ X3 )
= $true )
& ( ( X0 @ X2 @ X4 )
= $true ) ) ),
inference(ennf_transformation,[],[f100]) ).
thf(f102,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( ! [X4: $i] :
( ( ( X1 @ X4 @ X3 )
!= $true )
| ( ( X0 @ X2 @ X4 )
!= $true ) )
| ( ( rel_composition @ X0 @ X1 @ X2 @ X3 )
!= $true ) )
& ( ? [X4: $i] :
( ( ( X1 @ X4 @ X3 )
= $true )
& ( ( X0 @ X2 @ X4 )
= $true ) )
| ( ( rel_composition @ X0 @ X1 @ X2 @ X3 )
= $true ) ) ),
inference(nnf_transformation,[],[f101]) ).
thf(f103,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o,X2: $i,X3: $i] :
( ( ! [X4: $i] :
( ( ( X1 @ X4 @ X3 )
!= $true )
| ( ( X0 @ X2 @ X4 )
!= $true ) )
| ( ( rel_composition @ X0 @ X1 @ X2 @ X3 )
!= $true ) )
& ( ? [X5: $i] :
( ( $true
= ( X1 @ X5 @ X3 ) )
& ( $true
= ( X0 @ X2 @ X5 ) ) )
| ( ( rel_composition @ X0 @ X1 @ X2 @ X3 )
= $true ) ) ),
inference(rectify,[],[f102]) ).
thf(f104,plain,
( ( ! [X4: $i] :
( ( $true
!= ( sK1 @ X4 @ sK3 ) )
| ( $true
!= ( sK0 @ sK2 @ X4 ) ) )
| ( $true
!= ( rel_composition @ sK0 @ sK1 @ sK2 @ sK3 ) ) )
& ( ( ( $true
= ( sK1 @ sK4 @ sK3 ) )
& ( $true
= ( sK0 @ sK2 @ sK4 ) ) )
| ( $true
= ( rel_composition @ sK0 @ sK1 @ sK2 @ 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)],[f103]) ).
thf(f126,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,[],[f73]) ).
thf(f140,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( rel_composition @ sK0 @ sK1 @ sK2 @ sK3 ) ) ),
inference(cnf_transformation,[],[f104]) ).
thf(f141,plain,
( ( $true
= ( sK1 @ sK4 @ sK3 ) )
| ( $true
= ( rel_composition @ sK0 @ sK1 @ sK2 @ sK3 ) ) ),
inference(cnf_transformation,[],[f104]) ).
thf(f142,plain,
! [X4: $i] :
( ( $true
!= ( sK1 @ X4 @ sK3 ) )
| ( $true
!= ( sK0 @ sK2 @ X4 ) )
| ( $true
!= ( rel_composition @ sK0 @ sK1 @ sK2 @ sK3 ) ) ),
inference(cnf_transformation,[],[f104]) ).
thf(f148,plain,
! [X4: $i] :
( ( $true
!= ( sK1 @ X4 @ sK3 ) )
| ( $true
!= ( sK0 @ sK2 @ X4 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) ) )
@ sK0
@ sK1
@ sK2
@ sK3 ) ) ),
inference(definition_unfolding,[],[f142,f126]) ).
thf(f149,plain,
( ( $true
= ( sK1 @ sK4 @ sK3 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) ) )
@ sK0
@ sK1
@ sK2
@ sK3 ) ) ),
inference(definition_unfolding,[],[f141,f126]) ).
thf(f150,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o,Y1: $i > $i > $o,Y2: $i,Y3: $i] :
( ?? @ $i
@ ^ [Y4: $i] :
( ( Y0 @ Y2 @ Y4 )
& ( Y1 @ Y4 @ Y3 ) ) )
@ sK0
@ sK1
@ sK2
@ sK3 ) ) ),
inference(definition_unfolding,[],[f140,f126]) ).
thf(f151,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 @ sK3 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( ( sK0 @ sK2 @ sK5 )
& ( sK1 @ sK5 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( sK1 @ sK5 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ( $true
= ( sK0 @ sK2 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f153]) ).
thf(f156,plain,
( ( $true
= ( sK1 @ sK4 @ sK3 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f157,plain,
( ( $true
= ( sK1 @ sK4 @ sK3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 @ sK3 ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( $true
= ( sK1 @ sK4 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK2 @ sK6 )
& ( sK1 @ sK6 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
( ( $true
= ( sK1 @ sK4 @ sK3 ) )
| ( $true
= ( sK1 @ sK6 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( $true
= ( sK1 @ sK4 @ sK3 ) )
| ( $true
= ( sK0 @ sK2 @ sK6 ) ) ),
inference(and_proxy_clausification,[],[f158]) ).
thf(f161,plain,
! [X4: $i] :
( ( $true
!= ( sK1 @ X4 @ sK3 ) )
| ( $true
!= ( sK0 @ sK2 @ X4 ) )
| ( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f162,plain,
! [X4: $i,X5: $i] :
( ( $true
!= ( sK1 @ X4 @ sK3 ) )
| ( $true
!= ( sK0 @ sK2 @ X4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK2 @ Y0 )
& ( sK1 @ Y0 @ sK3 ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X4: $i,X5: $i] :
( ( $true
!= ( sK1 @ X4 @ sK3 ) )
| ( $true
!= ( sK0 @ sK2 @ X4 ) )
| ( $false
= ( ( sK0 @ sK2 @ X5 )
& ( sK1 @ X5 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X4: $i,X5: $i] :
( ( $true
!= ( sK1 @ X4 @ sK3 ) )
| ( $true
!= ( sK0 @ sK2 @ X4 ) )
| ( $false
= ( sK1 @ X5 @ sK3 ) )
| ( $false
= ( sK0 @ sK2 @ X5 ) ) ),
inference(and_proxy_clausification,[],[f163]) ).
thf(f166,definition,
( spl7_1
<=> ( $true
= ( sK0 @ sK2 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f168,plain,
( ( $true
= ( sK0 @ sK2 @ sK5 ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f166]) ).
thf(f170,definition,
( spl7_2
<=> ( $true
= ( sK0 @ sK2 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f172,plain,
( ( $true
= ( sK0 @ sK2 @ sK4 ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f170]) ).
thf(f173,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f155,f170,f166]) ).
thf(f175,definition,
( spl7_3
<=> ( $true
= ( sK1 @ sK5 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f177,plain,
( ( $true
= ( sK1 @ sK5 @ sK3 ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f175]) ).
thf(f178,plain,
( spl7_3
| spl7_2 ),
inference(avatar_split_clause,[],[f154,f170,f175]) ).
thf(f180,definition,
( spl7_4
<=> ( $true
= ( sK0 @ sK2 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f182,plain,
( ( $true
= ( sK0 @ sK2 @ sK6 ) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f180]) ).
thf(f184,definition,
( spl7_5
<=> ( $true
= ( sK1 @ sK4 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f186,plain,
( ( $true
= ( sK1 @ sK4 @ sK3 ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f184]) ).
thf(f187,plain,
( spl7_4
| spl7_5 ),
inference(avatar_split_clause,[],[f160,f184,f180]) ).
thf(f189,definition,
( spl7_6
<=> ( $true
= ( sK1 @ sK6 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f191,plain,
( ( $true
= ( sK1 @ sK6 @ sK3 ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f189]) ).
thf(f192,plain,
( spl7_6
| spl7_5 ),
inference(avatar_split_clause,[],[f159,f184,f189]) ).
thf(f194,definition,
( spl7_7
<=> ! [X5: $i] :
( ( $false
= ( sK1 @ X5 @ sK3 ) )
| ( $false
= ( sK0 @ sK2 @ X5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f195,plain,
( ! [X5: $i] :
( ( $false
= ( sK1 @ X5 @ sK3 ) )
| ( $false
= ( sK0 @ sK2 @ X5 ) ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f194]) ).
thf(f197,definition,
( spl7_8
<=> ! [X4: $i] :
( ( $true
!= ( sK1 @ X4 @ sK3 ) )
| ( $true
!= ( sK0 @ sK2 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f198,plain,
( ! [X4: $i] :
( ( $true
!= ( sK1 @ X4 @ sK3 ) )
| ( $true
!= ( sK0 @ sK2 @ X4 ) ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f199,plain,
( spl7_7
| spl7_8 ),
inference(avatar_split_clause,[],[f164,f197,f194]) ).
thf(f201,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK2 @ sK4 ) )
| ~ spl7_5
| ~ spl7_7 ),
inference(constrained_superposition,[],[f195,f186]) ).
thf(f202,plain,
( ( $false
= ( sK0 @ sK2 @ sK4 ) )
| ~ spl7_5
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f201]) ).
thf(f204,plain,
( ( $false = $true )
| ~ spl7_2
| ~ spl7_5
| ~ spl7_7 ),
inference(constrained_superposition,[],[f202,f172]) ).
thf(f208,plain,
( $false
| ~ spl7_2
| ~ spl7_5
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f204]) ).
thf(f209,plain,
( ~ spl7_2
| ~ spl7_5
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[],[f208]) ).
thf(f223,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ~ spl7_6
| ~ spl7_7 ),
inference(constrained_superposition,[],[f195,f191]) ).
thf(f224,plain,
( ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ~ spl7_6
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f229,plain,
( ( $false = $true )
| ~ spl7_4
| ~ spl7_6
| ~ spl7_7 ),
inference(constrained_superposition,[],[f224,f182]) ).
thf(f235,plain,
( $false
| ~ spl7_4
| ~ spl7_6
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f229]) ).
thf(f236,plain,
( ~ spl7_4
| ~ spl7_6
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[],[f235]) ).
thf(f237,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK2 @ sK6 ) )
| ~ spl7_6
| ~ spl7_8 ),
inference(constrained_superposition,[],[f198,f191]) ).
thf(f240,plain,
( ( $true
!= ( sK0 @ sK2 @ sK6 ) )
| ~ spl7_6
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f237]) ).
thf(f241,plain,
( ~ spl7_4
| ~ spl7_6
| ~ spl7_8 ),
inference(avatar_split_clause,[],[f240,f197,f189,f180]) ).
thf(f244,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ~ spl7_5
| ~ spl7_8 ),
inference(constrained_superposition,[],[f198,f186]) ).
thf(f245,plain,
( ( $true
!= ( sK0 @ sK2 @ sK4 ) )
| ~ spl7_5
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f246,plain,
( $false
| ~ spl7_2
| ~ spl7_5
| ~ spl7_8 ),
inference(forward_subsumption_resolution,[],[f245,f172]) ).
thf(f247,plain,
( ~ spl7_2
| ~ spl7_5
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f246]) ).
thf(f250,plain,
( ( $true != $true )
| ( $true
!= ( sK0 @ sK2 @ sK5 ) )
| ~ spl7_3
| ~ spl7_8 ),
inference(constrained_superposition,[],[f198,f177]) ).
thf(f251,plain,
( ( $true
!= ( sK0 @ sK2 @ sK5 ) )
| ~ spl7_3
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f250]) ).
thf(f252,plain,
( $false
| ~ spl7_1
| ~ spl7_3
| ~ spl7_8 ),
inference(forward_subsumption_resolution,[],[f251,f168]) ).
thf(f253,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f252]) ).
thf(f260,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK2 @ sK5 ) )
| ~ spl7_3
| ~ spl7_7 ),
inference(constrained_superposition,[],[f177,f195]) ).
thf(f261,plain,
( ( $false
= ( sK0 @ sK2 @ sK5 ) )
| ~ spl7_3
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f260]) ).
thf(f272,plain,
( ( $false = $true )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_7 ),
inference(constrained_superposition,[],[f261,f168]) ).
thf(f278,plain,
( $false
| ~ spl7_1
| ~ spl7_3
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f272]) ).
thf(f279,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_7 ),
inference(avatar_contradiction_clause,[],[f278]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f173]) ).
cnf(s2,plain,
( spl7_2
| spl7_3 ),
inference(sat_conversion,[],[f178]) ).
cnf(s3,plain,
( spl7_4
| spl7_5 ),
inference(sat_conversion,[],[f187]) ).
cnf(s4,plain,
( spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f192]) ).
cnf(s5,plain,
( spl7_7
| spl7_8 ),
inference(sat_conversion,[],[f199]) ).
cnf(s7,plain,
( ~ spl7_2
| ~ spl7_5
| ~ spl7_7 ),
inference(sat_conversion,[],[f209]) ).
cnf(s9,plain,
( ~ spl7_4
| ~ spl7_6
| ~ spl7_7 ),
inference(sat_conversion,[],[f236]) ).
cnf(s10,plain,
( ~ spl7_4
| ~ spl7_6
| ~ spl7_8 ),
inference(sat_conversion,[],[f241]) ).
cnf(s11,plain,
( ~ spl7_2
| ~ spl7_5
| ~ spl7_8 ),
inference(sat_conversion,[],[f247]) ).
cnf(s12,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_8 ),
inference(sat_conversion,[],[f253]) ).
cnf(s14,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_7 ),
inference(sat_conversion,[],[f279]) ).
cnf(s15,plain,
( ~ spl7_5
| ~ spl7_2 ),
inference(rat,[],[s5,s7,s11]) ).
cnf(s16,plain,
( ~ spl7_4
| ~ spl7_6 ),
inference(rat,[],[s5,s9,s10]) ).
cnf(s17,plain,
spl7_5,
inference(rat,[],[s16,s3,s4]) ).
cnf(s18,plain,
~ spl7_2,
inference(rat,[],[s15,s17]) ).
cnf(s19,plain,
spl7_3,
inference(rat,[],[s2,s18]) ).
cnf(s20,plain,
spl7_1,
inference(rat,[],[s1,s18]) ).
cnf(s21,plain,
~ spl7_7,
inference(rat,[],[s14,s19,s20]) ).
cnf(s22,plain,
~ spl7_8,
inference(rat,[],[s12,s19,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s5,s22,s21]) ).
thf(f280,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.13/0.19 % Computer : n005.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Tue Sep 29 13:40:31 UTC 2026
% 0.13/0.19 % CPUTime :
% 0.13/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.22 Running first-order model finding
% 0.13/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.27 % (1680405)Will run a generic schedule for satisfiability detection.
% 0.13/0.27 % (1680414)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=996367366:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.27 % (1680414)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.13/0.27 % (1680411)% WARNING: option uhcvi not known.
% 0.13/0.27 % (1680414) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1680405-1680414"...
% 0.13/0.27 % (1680414)...printing done.
% 0.13/0.27 % (1680410)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2827246797_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.27 % (1680411)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3117734216:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.27 % (1680412)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=841790190:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.27 % (1680413)dis+10_1_sil=32000:sp=arity:random_seed=3833721599:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.13/0.27 % (1680416)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2533993299:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.27 % (1680415)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1377342131:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.27 % (1680411)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.13/0.27 % (1680414)Refutation found. Thanks to Tanya!
% 0.13/0.27 % SZS status Theorem for theBenchmark
% 0.13/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.28 % (1680414)------------------------------
% 0.13/0.28 % (1680414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.28 % (1680414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.28 % (1680414)CaDiCaL version: 2.1.3
% 0.13/0.28 % (1680414)Termination reason: Refutation
% 0.13/0.28 % (1680414)Time elapsed: 0.005 s
% 0.13/0.28 % (1680414)Peak memory usage: 13 MB
% 0.13/0.28 % (1680414)Instructions burned: 15 (million)
% 0.13/0.28 % (1680405)Success in time 0.044 s
% 0.13/0.28 % Vampire exiting
%------------------------------------------------------------------------------