%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET609^3 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:23:41 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 84 ( 29 unt; 0 typ; 5 def)
% Number of atoms : 648 ( 118 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 529 ( 84 ~; 101 |; 68 &; 271 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 43 ( 43 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 35 usr; 8 con; 0-4 aty)
% Number of variables : 68 ( 0 sgn 6 !; 3 ?; 68 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_17,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_20,type,
vOR: $o > $o > $o ).
thf(func_def_21,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_23,type,
vAND: $o > $o > $o ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SET008^0.ax',intersection) ).
thf(f9,axiom,
( setminus
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET008^0.ax',setminus) ).
thf(f15,conjecture,
! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( setminus @ X0 @ ( setminus @ X1 @ X2 ) )
= ( union @ ( setminus @ X0 @ X1 ) @ ( intersection @ X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f16,negated_conjecture,
~ ! [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( setminus @ X0 @ ( setminus @ X1 @ X2 ) )
= ( union @ ( setminus @ X0 @ X1 ) @ ( intersection @ X0 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f22,plain,
( union
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f23,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f26,plain,
( intersection
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f27,plain,
( intersection
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f28,plain,
( setminus
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ~ ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f9]) ).
thf(f29,plain,
( setminus
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f39,plain,
? [X0: $i > $o,X1: $i > $o,X2: $i > $o] :
( ( setminus @ X0 @ ( setminus @ X1 @ X2 ) )
!= ( union @ ( setminus @ X0 @ X1 ) @ ( intersection @ X0 @ X2 ) ) ),
inference(ennf_transformation,[],[f16]) ).
thf(f40,plain,
( ( setminus @ sK0 @ ( setminus @ sK1 @ sK2 ) )
!= ( union @ ( setminus @ sK0 @ sK1 ) @ ( intersection @ sK0 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f39]) ).
thf(f46,plain,
( union
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f48,plain,
( intersection
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f49,plain,
( setminus
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f55,plain,
( ( setminus @ sK0 @ ( setminus @ sK1 @ sK2 ) )
!= ( union @ ( setminus @ sK0 @ sK1 ) @ ( intersection @ sK0 @ sK2 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f59,plain,
( ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
@ sK0
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
@ sK1
@ sK2 ) )
!= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ~ ( Y1 @ Y2 ) )
@ sK0
@ sK1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ sK0
@ sK2 ) ) ),
inference(definition_unfolding,[],[f55,f49,f49,f46,f49,f48]) ).
thf(f60,plain,
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f59]) ).
thf(f68,plain,
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f60]) ).
thf(f69,plain,
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f68]) ).
thf(f70,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ~ ( ( sK1 @ Y0 )
& ~ ( sK2 @ Y0 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 )
& ~ ( sK1 @ Y0 ) )
| ( ( sK0 @ Y0 )
& ( sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f68]) ).
thf(f71,plain,
( ( $false
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f72,plain,
( ( $false
= ( ~ ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f71]) ).
thf(f73,plain,
( ( $true
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f72]) ).
thf(f74,plain,
( ( $true
= ( ~ ( sK2 @ sK3 ) ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f75,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f77,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f75]) ).
thf(f78,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( ~ ( sK1 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f78]) ).
thf(f80,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f79]) ).
thf(f83,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f74]) ).
thf(f84,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f83]) ).
thf(f89,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f84]) ).
thf(f90,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ( $false
= ( sK0 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f89]) ).
thf(f91,plain,
( ( $true
= ( ( sK0 @ sK3 )
& ~ ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f92,plain,
( ( $true
= ( ~ ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f91]) ).
thf(f93,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(and_proxy_clausification,[],[f91]) ).
thf(f94,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f93]) ).
thf(f96,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f94]) ).
thf(f98,plain,
( ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) )
| ( $true
= ( sK0 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f96]) ).
thf(f99,plain,
( $true
= ( sK0 @ sK3 ) ),
inference(duplicate_literal_removal,[],[f98]) ).
thf(f106,plain,
( ( $false
= ( ( sK1 @ sK3 )
& ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) ) ),
inference(not_proxy_clausification,[],[f92]) ).
thf(f107,plain,
( ( $false
= ( ~ ( sK2 @ sK3 ) ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f106]) ).
thf(f108,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) )
| ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f107]) ).
thf(f109,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ( sK2 @ sK3 ) ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f108]) ).
thf(f110,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK3 )
& ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f109]) ).
thf(f117,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $true
= ( ~ ( sK1 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f110]) ).
thf(f120,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f117]) ).
thf(f121,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK3 ) ) ),
inference(duplicate_literal_removal,[],[f120]) ).
thf(f123,definition,
( spl4_1
<=> ( $false
= ( sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f125,plain,
( ( $false
= ( sK0 @ sK3 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f123]) ).
thf(f127,definition,
( spl4_2
<=> ( $true
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f129,plain,
( ( $true
= ( sK1 @ sK3 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f127]) ).
thf(f130,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f80,f127,f123]) ).
thf(f132,definition,
( spl4_3
<=> ( $false
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f134,plain,
( ( $false
= ( sK2 @ sK3 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f132]) ).
thf(f137,plain,
( spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f90,f132,f123]) ).
thf(f139,definition,
( spl4_4
<=> ( $false
= ( sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f141,plain,
( ( $false
= ( sK1 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f139]) ).
thf(f143,definition,
( spl4_5
<=> ( $true
= ( sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f145,plain,
( ( $true
= ( sK2 @ sK3 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f146,plain,
( spl4_4
| spl4_5 ),
inference(avatar_split_clause,[],[f121,f143,f139]) ).
thf(f150,plain,
( ( $false = $true )
| ~ spl4_2
| ~ spl4_4 ),
inference(constrained_superposition,[],[f141,f129]) ).
thf(f154,plain,
( $false
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f150]) ).
thf(f155,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f154]) ).
thf(f159,plain,
( ( $false = $true )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f125,f99]) ).
thf(f163,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f159]) ).
thf(f164,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f163]) ).
thf(f168,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_5 ),
inference(forward_demodulation,[],[f145,f134]) ).
thf(f169,plain,
( $false
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f168]) ).
thf(f170,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f169]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f130]) ).
cnf(s4,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f137]) ).
cnf(s5,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f146]) ).
cnf(s7,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f155]) ).
cnf(s9,plain,
~ spl4_1,
inference(sat_conversion,[],[f164]) ).
cnf(s10,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f170]) ).
cnf(s11,plain,
spl4_3,
inference(rat,[],[s4,s9]) ).
cnf(s12,plain,
~ spl4_5,
inference(rat,[],[s10,s11]) ).
cnf(s13,plain,
spl4_4,
inference(rat,[],[s5,s12]) ).
cnf(s14,plain,
~ spl4_2,
inference(rat,[],[s7,s13]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s1,s14,s9]) ).
thf(f171,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET609^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n020.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 13:39:50 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.24 Running first-order model finding
% 0.10/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.28 % (1062642)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (1062651)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2601492687:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (1062651)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (1062648)% WARNING: option uhcvi not known.
% 0.20/0.28 % (1062651) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1062642-1062651"...
% 0.20/0.28 % (1062648)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3110152409:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (1062647)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1342140299_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (1062649)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2472044800:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (1062652)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2085184274:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (1062650)dis+10_1_sil=32000:sp=arity:random_seed=1179659102:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (1062653)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3370819142:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.28 % (1062648)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (1062651)...printing done.
% 0.20/0.28 % (1062648)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (1062651)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (1062651)------------------------------
% 0.20/0.29 % (1062651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1062651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1062651)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1062651)Termination reason: Refutation
% 0.20/0.29 % (1062651)Time elapsed: 0.006 s
% 0.20/0.29 % (1062651)Peak memory usage: 12 MB
% 0.20/0.29 % (1062651)Instructions burned: 8 (million)
% 0.20/0.29 % (1062642)Success in time 0.034 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------