%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV502^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:38:45 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 23 unt; 0 typ; 5 def)
% Number of atoms : 275 ( 71 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 603 ( 53 ~; 44 |; 15 &; 476 @)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 8 con; 0-5 aty)
% Number of variables : 77 ( 0 sgn 65 !; 12 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/nums/num': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/DELETE':
!>[X0: $tType] : ( ( X0 > $o ) > X0 > X0 > $o ) ).
thf(func_def_3,type,
'const/iterate/nsum':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > 'type/nums/num' ) > 'type/nums/num' ) ).
thf(func_def_4,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_5,type,
'const/iterate/iterate':
!>[X0: $tType,X1: $tType] : ( ( X1 > X1 > X1 ) > ( X0 > $o ) > ( X0 > X1 ) > X1 ) ).
thf(func_def_6,type,
'const/arith/+': 'type/nums/num' > 'type/nums/num' > 'type/nums/num' ).
thf(func_def_10,type,
sK1: sK0 ).
thf(func_def_11,type,
sK2: sK0 > $o ).
thf(func_def_12,type,
sK3: sK0 > 'type/nums/num' ).
thf(f1,axiom,
! [X0: $tType] :
( 'const/iterate/nsum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/nsum_') ).
thf(f2,axiom,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( 'const/sets/IN' @ X0 @ X5 @ X4 ) )
=> ( ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/ITERATE_DELETE_') ).
thf(f3,axiom,
'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/MONOIDAL_ADD_') ).
thf(f4,conjecture,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > 'type/nums/num'] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( ( 'const/arith/+' @ ( X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X3 ) @ X1 ) )
= ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/iterate/NSUM_DELETE_') ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > 'type/nums/num'] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
& ( 'const/sets/FINITE' @ X0 @ X2 ) )
=> ( ( 'const/arith/+' @ ( X1 @ X3 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X3 ) @ X1 ) )
= ( 'const/iterate/nsum' @ X0 @ X2 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0 > 'type/nums/num'] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
& ( 'const/sets/FINITE' @ X0 @ X1 ) )
=> ( ( 'const/iterate/nsum' @ X0 @ X1 @ X3 )
= ( 'const/arith/+' @ ( X3 @ X2 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X1 @ X2 ) @ X3 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
~ ! [X0: $tType,X1: X0 > $o,X3: X0 > 'type/nums/num',X2: X0] :
( ( ( $true
= ( 'const/sets/FINITE' @ X0 @ X1 ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ) )
=> ( ( 'const/iterate/nsum' @ X0 @ X1 @ X3 )
= ( 'const/arith/+' @ ( X3 @ X2 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X1 @ X2 ) @ X3 ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ( 'const/iterate/monoidal' @ X1 @ X2 )
=> ! [X3: X0 > X1,X4: X0 > $o,X5: X0] :
( ( ( 'const/sets/FINITE' @ X0 @ X4 )
& ( 'const/sets/IN' @ X0 @ X5 @ X4 ) )
=> ( ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f9,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1] :
( ( ( 'const/iterate/monoidal' @ X1 @ X2 )
= $true )
=> ! [X4: X0 > $o,X3: X0 > X1,X5: X0] :
( ( ( ( 'const/sets/FINITE' @ X0 @ X4 )
= $true )
& ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
= $true ) )
=> ( ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f10,plain,
'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+',
inference(rectify,[],[f3]) ).
thf(f11,plain,
( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
? [X0: $tType,X1: X0 > $o,X3: X0 > 'type/nums/num',X2: X0] :
( ( ( 'const/iterate/nsum' @ X0 @ X1 @ X3 )
!= ( 'const/arith/+' @ ( X3 @ X2 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X1 @ X2 ) @ X3 ) ) )
& ( $true
= ( 'const/sets/FINITE' @ X0 @ X1 ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ X1 ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f13,plain,
? [X0: $tType,X2: X0,X1: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( 'const/iterate/nsum' @ X0 @ X1 @ X3 )
!= ( 'const/arith/+' @ ( X3 @ X2 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X1 @ X2 ) @ X3 ) ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ X2 @ X1 ) )
& ( $true
= ( 'const/sets/FINITE' @ X0 @ X1 ) ) ),
inference(flattening,[],[f12]) ).
thf(f14,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1] :
( ! [X4: X0 > $o,X3: X0 > X1,X5: X0] :
( ( ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
!= $true ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f9]) ).
thf(f15,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ! [X4: X0 > $o,X3: X0 > X1,X5: X0] :
( ( ( 'const/sets/IN' @ X0 @ X5 @ X4 )
!= $true )
| ( ( 'const/sets/FINITE' @ X0 @ X4 )
!= $true )
| ( ( X2 @ ( X3 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X4 @ X5 ) @ X3 ) )
= ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X4 @ X3 ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(flattening,[],[f14]) ).
thf(f16,plain,
! [X0: $tType,X1: $tType,X2: X1 > X1 > X1] :
( ! [X3: X0 > $o,X4: X0 > X1,X5: X0] :
( ( ( 'const/sets/IN' @ X0 @ X5 @ X3 )
!= $true )
| ( $true
!= ( 'const/sets/FINITE' @ X0 @ X3 ) )
| ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X4 )
= ( X2 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X3 @ X5 ) @ X4 ) ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true ) ),
inference(rectify,[],[f15]) ).
thf(f17,plain,
? [X0: $tType,X1: X0,X2: X0 > $o,X3: X0 > 'type/nums/num'] :
( ( ( 'const/iterate/nsum' @ X0 @ X2 @ X3 )
!= ( 'const/arith/+' @ ( X3 @ X1 ) @ ( 'const/iterate/nsum' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X1 ) @ X3 ) ) )
& ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) )
& ( ( 'const/sets/FINITE' @ X0 @ X2 )
= $true ) ),
inference(rectify,[],[f13]) ).
thf(f18,plain,
( ( ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK3 )
!= ( 'const/arith/+' @ ( sK3 @ sK1 ) @ ( 'const/iterate/nsum' @ sK0 @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK1 ) @ sK3 ) ) )
& ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) )
& ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f17]) ).
thf(f19,plain,
( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f20,plain,
! [X1: $tType,X0: $tType,X2: X1 > X1 > X1,X3: X0 > $o,X4: X0 > X1,X5: X0] :
( ( ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ X3 @ X4 )
= ( X2 @ ( X4 @ X5 ) @ ( 'const/iterate/iterate' @ X0 @ X1 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X3 @ X5 ) @ X4 ) ) )
| ( ( 'const/iterate/monoidal' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ X0 @ X5 @ X3 )
!= $true )
| ( $true
!= ( 'const/sets/FINITE' @ X0 @ X3 ) ) ),
inference(cnf_transformation,[],[f16]) ).
thf(f21,plain,
( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f22,plain,
( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f23,plain,
( ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK3 )
!= ( 'const/arith/+' @ ( sK3 @ sK1 ) @ ( 'const/iterate/nsum' @ sK0 @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK1 ) @ sK3 ) ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f24,plain,
! [X0: $tType] :
( 'const/iterate/nsum'
@ ( X0
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' ) ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f27,definition,
( spl4_1
<=> ( ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK3 )
= ( 'const/arith/+' @ ( sK3 @ sK1 ) @ ( 'const/iterate/nsum' @ sK0 @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK1 ) @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f29,plain,
( ( ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK3 )
!= ( 'const/arith/+' @ ( sK3 @ sK1 ) @ ( 'const/iterate/nsum' @ sK0 @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK1 ) @ sK3 ) ) )
| spl4_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f30,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f23,f27]) ).
thf(f32,definition,
( spl4_2
<=> ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f34,plain,
( ( $true
= ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f35,plain,
spl4_2,
inference(avatar_split_clause,[],[f22,f32]) ).
thf(f37,definition,
( spl4_3
<=> ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f39,plain,
( ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
= $true )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
spl4_3,
inference(avatar_split_clause,[],[f19,f37]) ).
thf(f42,definition,
( spl4_4
<=> ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f44,plain,
( ( $true
= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f45,plain,
spl4_4,
inference(avatar_split_clause,[],[f21,f42]) ).
thf(f46,plain,
! [X0: $tType,X1: X0 > $o] :
( ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' @ X1 )
= ( 'const/iterate/nsum' @ X0 @ X1 ) ),
inference(argument_congruence,[],[f24]) ).
thf(f47,plain,
! [X0: $tType,X2: X0 > 'type/nums/num',X1: X0 > $o] :
( ( 'const/iterate/nsum' @ X0 @ X1 @ X2 )
= ( 'const/iterate/iterate' @ X0 @ 'type/nums/num' @ 'const/arith/+' @ X1 @ X2 ) ),
inference(argument_congruence,[],[f46]) ).
thf(f48,plain,
( ( ( 'const/iterate/nsum' @ sK0 @ sK2 @ sK3 )
!= ( 'const/arith/+' @ ( sK3 @ sK1 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK1 ) @ sK3 ) ) )
| spl4_1 ),
inference(superposition,[],[f29,f47]) ).
thf(f49,plain,
( ( ( 'const/arith/+' @ ( sK3 @ sK1 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK1 ) @ sK3 ) )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK2 @ sK3 ) )
| spl4_1 ),
inference(forward_demodulation,[],[f48,f47]) ).
thf(f51,definition,
( spl4_5
<=> ( ( 'const/arith/+' @ ( sK3 @ sK1 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK1 ) @ sK3 ) )
= ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f53,plain,
( ( ( 'const/arith/+' @ ( sK3 @ sK1 ) @ ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ ( 'const/sets/DELETE' @ sK0 @ sK2 @ sK1 ) @ sK3 ) )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK2 @ sK3 ) )
| spl4_5 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f54,plain,
( ~ spl4_5
| spl4_1 ),
inference(avatar_split_clause,[],[f49,f27,f51]) ).
thf(f98,plain,
( ( ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK2 @ sK3 )
!= ( 'const/iterate/iterate' @ sK0 @ 'type/nums/num' @ 'const/arith/+' @ sK2 @ sK3 ) )
| ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
!= $true )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) )
| ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| spl4_5 ),
inference(superposition,[],[f53,f20]) ).
thf(f99,plain,
( ( $true
!= ( 'const/sets/FINITE' @ sK0 @ sK2 ) )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) )
| ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
!= $true )
| spl4_5 ),
inference(trivial_inequality_removal,[],[f98]) ).
thf(f100,plain,
( ( ( 'const/iterate/monoidal' @ 'type/nums/num' @ 'const/arith/+' )
!= $true )
| ( $true
!= ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) )
| ~ spl4_4
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f99,f44]) ).
thf(f101,plain,
( ( $true
!= ( 'const/sets/IN' @ sK0 @ sK1 @ sK2 ) )
| ~ spl4_3
| ~ spl4_4
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f100,f39]) ).
thf(f102,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| spl4_5 ),
inference(forward_subsumption_resolution,[],[f101,f34]) ).
thf(f103,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| spl4_5 ),
inference(avatar_contradiction_clause,[],[f102]) ).
cnf(s1,plain,
~ spl4_1,
inference(sat_conversion,[],[f30]) ).
cnf(s2,plain,
spl4_2,
inference(sat_conversion,[],[f35]) ).
cnf(s3,plain,
spl4_3,
inference(sat_conversion,[],[f40]) ).
cnf(s4,plain,
spl4_4,
inference(sat_conversion,[],[f45]) ).
cnf(s5,plain,
( spl4_1
| ~ spl4_5 ),
inference(sat_conversion,[],[f54]) ).
cnf(s6,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f103]) ).
cnf(s7,plain,
spl4_5,
inference(rat,[],[s6,s3,s4,s2]) ).
cnf(s8,plain,
spl4_1,
inference(rat,[],[s5,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8]) ).
thf(f104,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV502^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 15:56:57 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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
% 0.21/0.28 % (777278)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (777286)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=1432240404: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 % (777283)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1351664326:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (777285)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3211796468:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (777286) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-777278-777286"...
% 0.21/0.28 % (777286)...printing done.
% 0.21/0.28 % (777286)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
% 0.21/0.28 % (777286)------------------------------
% 0.21/0.28 % (777286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (777286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (777286)CaDiCaL version: 2.1.3
% 0.21/0.28 % (777286)Termination reason: Refutation
% 0.21/0.28 % (777286)Time elapsed: 0.009 s
% 0.21/0.28 % (777286)Peak memory usage: 13 MB
% 0.21/0.28 % (777286)Instructions burned: 27 (million)
% 0.21/0.28 % (777278)Success in time 0.035 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------