%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET609^3 : 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 : n004.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 08:23:21 AM UTC 2026
% Result : Theorem 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 93 ( 32 unt; 0 typ; 6 def)
% Number of atoms : 699 ( 130 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 579 ( 102 ~; 106 |; 69 &; 296 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 9 con; 0-4 aty)
% Number of variables : 74 ( 0 sgn 9 !; 6 ?; 74 :)
% 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,
vOR: $o > $o > $o ).
thf(func_def_16,type,
vAND: $o > $o > $o ).
thf(func_def_17,type,
vNOT: $o > $o ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vIMP: $o > $o > $o ).
thf(func_def_28,type,
sK0: $i > $o ).
thf(func_def_29,type,
sK1: $i > $o ).
thf(func_def_30,type,
sK2: $i > $o ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= union ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',union) ).
thf(f8,axiom,
( intersection
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',intersection) ).
thf(f9,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) )
= setminus ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^0.ax',setminus) ).
thf(f15,conjecture,
! [X1: $i > $o,X2: $i > $o,X0: $i > $o] :
( ( setminus @ X0 @ ( setminus @ X1 @ X2 ) )
= ( union @ ( setminus @ X0 @ X1 ) @ ( intersection @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X1: $i > $o,X2: $i > $o,X0: $i > $o] :
( ( setminus @ X0 @ ( setminus @ X1 @ X2 ) )
= ( union @ ( setminus @ X0 @ X1 ) @ ( intersection @ X0 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f19,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ~ ( X1 @ X2 ) ) )
= setminus ),
inference(rectify,[],[f9]) ).
thf(f20,plain,
( setminus
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f31,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= union ),
inference(rectify,[],[f6]) ).
thf(f32,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f36,plain,
( intersection
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f37,plain,
( intersection
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f39,plain,
~ ! [X0: $i > $o,X2: $i > $o,X1: $i > $o] :
( ( setminus @ X2 @ ( setminus @ X0 @ X1 ) )
= ( union @ ( setminus @ X2 @ X0 ) @ ( intersection @ X2 @ X1 ) ) ),
inference(rectify,[],[f16]) ).
thf(f40,plain,
? [X0: $i > $o,X2: $i > $o,X1: $i > $o] :
( ( setminus @ X2 @ ( setminus @ X0 @ X1 ) )
!= ( union @ ( setminus @ X2 @ X0 ) @ ( intersection @ X2 @ X1 ) ) ),
inference(ennf_transformation,[],[f39]) ).
thf(f41,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( union @ ( setminus @ X1 @ X0 ) @ ( intersection @ X1 @ X2 ) )
!= ( setminus @ X1 @ ( setminus @ X0 @ X2 ) ) ),
inference(rectify,[],[f40]) ).
thf(f42,plain,
( ( setminus @ sK1 @ ( setminus @ sK0 @ sK2 ) )
!= ( union @ ( setminus @ sK1 @ sK0 ) @ ( intersection @ sK1 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f41]) ).
thf(f43,plain,
( setminus
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f20]) ).
thf(f46,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f49,plain,
( ( setminus @ sK1 @ ( setminus @ sK0 @ sK2 ) )
!= ( union @ ( setminus @ sK1 @ sK0 ) @ ( intersection @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f55,plain,
( intersection
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f61,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ sK1
@ sK0 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ sK1
@ sK2 ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ sK1
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ~ ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ sK0
@ sK2 ) ) ),
inference(definition_unfolding,[],[f49,f43,f43,f46,f43,f55]) ).
thf(f62,plain,
( ( ^ [Y0: $i] :
( ~ ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) ) )
!= ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f61]) ).
thf(f63,plain,
( ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: $i] :
( ~ ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f62]) ).
thf(f64,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f63]) ).
thf(f65,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 )
& ( sK2 @ Y0 ) )
| ( ~ ( sK0 @ Y0 )
& ( sK1 @ Y0 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( ~ ( sK2 @ Y0 )
& ( sK0 @ Y0 ) )
& ( sK1 @ Y0 ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f63]) ).
thf(f66,plain,
( ( $false
= ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( ~ ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
& ( sK1 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f67,plain,
( ( $false
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( ~ ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f66]) ).
thf(f68,plain,
( ( $false
= ( ~ ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f66]) ).
thf(f69,plain,
( ( $false
= ( ~ ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f69]) ).
thf(f71,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f70]) ).
thf(f73,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f71]) ).
thf(f74,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f74]) ).
thf(f77,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ~ ( sK0 @ sK3 ) ) )
| ( $false
= ( ~ ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
& ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f67]) ).
thf(f78,plain,
( ( $false
= ( ~ ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( ~ ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f78]) ).
thf(f80,plain,
( ( $true
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f79]) ).
thf(f81,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f85,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f81]) ).
thf(f86,plain,
( ( $true
= ( ~ ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f87,plain,
( ( $true
= ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f86]) ).
thf(f88,plain,
( ( ( ~ ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
= $true )
| ( $true
= ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f86]) ).
thf(f89,plain,
( ( $false
= ( ~ ( sK2 @ sK3 )
& ( sK0 @ sK3 ) ) )
| ( $true
= ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f88]) ).
thf(f90,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
| ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f89]) ).
thf(f91,plain,
( ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f90]) ).
thf(f92,plain,
( ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f91]) ).
thf(f101,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( ( ~ ( sK0 @ sK3 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f92]) ).
thf(f102,plain,
( ( ( ~ ( sK0 @ sK3 ) )
= $true )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f101]) ).
thf(f103,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f102]) ).
thf(f104,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f103]) ).
thf(f107,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( ( sK1 @ sK3 )
& ( sK2 @ sK3 ) )
= $true )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f87]) ).
thf(f109,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( $true
= ( ~ ( sK0 @ sK3 )
& ( sK1 @ sK3 ) ) )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f107]) ).
thf(f110,plain,
( ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true )
| ( ( sK1 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f109]) ).
thf(f114,plain,
( ( sK1 @ sK3 )
= $true ),
inference(duplicate_literal_removal,[],[f110]) ).
thf(f120,definition,
( spl4_1
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f122,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f120]) ).
thf(f124,definition,
( spl4_2
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f126,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f124]) ).
thf(f127,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f75,f124,f120]) ).
thf(f129,definition,
( spl4_3
<=> ( $true
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f131,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f129]) ).
thf(f134,plain,
( spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f85,f129,f124]) ).
thf(f136,definition,
( spl4_4
<=> ( ( sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f138,plain,
( ( ( sK1 @ sK3 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f136]) ).
thf(f140,definition,
( spl4_5
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f142,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f140]) ).
thf(f144,definition,
( spl4_6
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f146,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f144]) ).
thf(f149,plain,
( spl4_6
| spl4_5 ),
inference(avatar_split_clause,[],[f104,f140,f144]) ).
thf(f152,plain,
spl4_4,
inference(avatar_split_clause,[],[f114,f136]) ).
thf(f155,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_4 ),
inference(forward_demodulation,[],[f138,f126]) ).
thf(f156,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f155]) ).
thf(f157,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f156]) ).
thf(f158,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_5 ),
inference(forward_demodulation,[],[f131,f142]) ).
thf(f159,plain,
( $false
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f158]) ).
thf(f160,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f159]) ).
thf(f161,plain,
( ( $false = $true )
| ~ spl4_1
| ~ spl4_6 ),
inference(forward_demodulation,[],[f146,f122]) ).
thf(f162,plain,
( $false
| ~ spl4_1
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f161]) ).
thf(f163,plain,
( ~ spl4_1
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f162]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f127]) ).
cnf(s4,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f134]) ).
cnf(s7,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f149]) ).
cnf(s10,plain,
spl4_4,
inference(sat_conversion,[],[f152]) ).
cnf(s13,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f157]) ).
cnf(s14,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f160]) ).
cnf(s15,plain,
( ~ spl4_1
| ~ spl4_6 ),
inference(sat_conversion,[],[f163]) ).
cnf(s16,plain,
~ spl4_2,
inference(rat,[],[s13,s10]) ).
cnf(s17,plain,
spl4_3,
inference(rat,[],[s4,s16]) ).
cnf(s18,plain,
~ spl4_5,
inference(rat,[],[s14,s17]) ).
cnf(s19,plain,
spl4_6,
inference(rat,[],[s7,s18]) ).
cnf(s20,plain,
~ spl4_1,
inference(rat,[],[s15,s19]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s16,s20]) ).
thf(f164,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET609^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:38:52 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.22 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
% 0.18/0.26 % (1293804)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.26 % (1293816)lrs+10_16_si=on:nwc=1.5:random_seed=1164044781:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.18/0.26 % (1293816) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1293804-1293816"...
% 0.18/0.26 % (1293816)...printing done.
% 0.18/0.26 % (1293816)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Theorem for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.26 % (1293816)------------------------------
% 0.18/0.26 % (1293816)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (1293816)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (1293816)CaDiCaL version: 2.1.3
% 0.18/0.26 % (1293816)Termination reason: Refutation
% 0.18/0.26 % (1293816)Time elapsed: 0.003 s
% 0.18/0.26 % (1293816)Peak memory usage: 12 MB
% 0.18/0.26 % (1293816)Instructions burned: 8 (million)
% 0.18/0.26 % (1293804)Success in time 0.029 s
% 0.18/0.26 % Vampire exiting
%------------------------------------------------------------------------------