%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA084^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 07:45:53 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 68 ( 7 unt; 0 typ; 4 def)
% Number of atoms : 513 ( 139 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 613 ( 95 ~; 85 |; 41 &; 372 @)
% ( 5 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 70 ( 0 sgn 51 !; 19 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
'type/realax/real': $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
'const/sets/inf': ( 'type/realax/real' > $o ) > 'type/realax/real' ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/FINITE':
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
'const/sets/EMPTY':
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_4,type,
'const/realax/real_lt': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_5,type,
'const/realax/real_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_9,type,
sK0: 'type/realax/real' ).
thf(func_def_10,type,
sK1: 'type/realax/real' > $o ).
thf(func_def_11,type,
sK2: 'type/realax/real' ).
thf(func_def_13,type,
sK4: 'type/realax/real' ).
thf(f1,axiom,
! [X1: 'type/realax/real',X0: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X0 @ X1 ) )
=> ( 'const/realax/real_lt' @ X0 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/realarith/REAL_LET_TRANS_') ).
thf(f2,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
& ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/INF_FINITE_') ).
thf(f3,conjecture,
! [X1: 'type/realax/real',X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' ) )
=> ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ X2 @ X1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/REAL_INF_LT_FINITE_') ).
thf(f4,negated_conjecture,
~ ! [X1: 'type/realax/real',X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' ) )
=> ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ X2 @ X1 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X0 @ X2 )
& ( 'const/realax/real_le' @ X1 @ X0 ) )
=> ( 'const/realax/real_lt' @ X1 @ X2 ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X1: 'type/realax/real',X0: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( ( 'const/realax/real_lt' @ X0 @ X2 )
= $true )
& ( $true
= ( 'const/realax/real_le' @ X1 @ X0 ) ) )
=> ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f5]) ).
thf(f7,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
& ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true )
& ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) )
=> ( ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X1 ) @ X0 )
= ( ? [X2: 'type/realax/real'] :
( ( 'const/realax/real_lt' @ X2 @ X0 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ! [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) )
=> ( ? [X2: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 ) )
& ( $true
= ( 'const/realax/real_lt' @ X2 @ X0 ) ) )
<=> ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X1 ) @ X0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X1: 'type/realax/real',X0: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $true )
| ( ( 'const/realax/real_lt' @ X0 @ X2 )
!= $true )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ X0 ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f12,plain,
! [X2: 'type/realax/real',X1: 'type/realax/real',X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ X0 ) )
| ( ( 'const/realax/real_lt' @ X0 @ X2 )
!= $true )
| ( ( 'const/realax/real_lt' @ X1 @ X2 )
= $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X1 ) @ X0 ) )
<~> ? [X2: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 ) )
& ( $true
= ( 'const/realax/real_lt' @ X2 @ X0 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f16,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 ) )
& ( ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X1 ) @ X0 ) )
<~> ? [X2: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 ) )
& ( $true
= ( 'const/realax/real_lt' @ X2 @ X0 ) ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ X2 ) )
| ( $true
!= ( 'const/realax/real_lt' @ X2 @ X0 ) )
| ( ( 'const/realax/real_lt' @ X1 @ X0 )
= $true ) ),
inference(rectify,[],[f12]) ).
thf(f18,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 ) )
& ( ! [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 ) )
| ( $true
!= ( 'const/realax/real_lt' @ X2 @ X0 ) ) )
| ( $true
!= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X1 ) @ X0 ) ) )
& ( ? [X2: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 ) )
& ( $true
= ( 'const/realax/real_lt' @ X2 @ X0 ) ) )
| ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X1 ) @ X0 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(nnf_transformation,[],[f16]) ).
thf(f19,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 ) )
& ( ! [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 ) )
| ( $true
!= ( 'const/realax/real_lt' @ X2 @ X0 ) ) )
| ( $true
!= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X1 ) @ X0 ) ) )
& ( ? [X2: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 ) )
& ( $true
= ( 'const/realax/real_lt' @ X2 @ X0 ) ) )
| ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X1 ) @ X0 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
? [X0: 'type/realax/real',X1: 'type/realax/real' > $o] :
( ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ X1 ) )
& ( ! [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X1 ) )
| ( $true
!= ( 'const/realax/real_lt' @ X2 @ X0 ) ) )
| ( $true
!= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X1 ) @ X0 ) ) )
& ( ? [X3: 'type/realax/real'] :
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X1 ) )
& ( $true
= ( 'const/realax/real_lt' @ X3 @ X0 ) ) )
| ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ X1 ) @ X0 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X1 ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK1 ) )
& ( ! [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK1 ) )
| ( $true
!= ( 'const/realax/real_lt' @ X2 @ sK0 ) ) )
| ( $true
!= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ sK0 ) ) )
& ( ( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 )
= $true )
& ( ( 'const/realax/real_lt' @ sK2 @ sK0 )
= $true ) )
| ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ sK0 ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2)],[f20]) ).
thf(f22,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ X2 ) )
| ( ( 'const/realax/real_lt' @ X1 @ X0 )
= $true )
| ( $true
!= ( 'const/realax/real_lt' @ X2 @ X0 ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f23,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ X0 ) @ X0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f24,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ ( 'const/sets/inf' @ X0 ) @ X1 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f25,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK1 ),
inference(cnf_transformation,[],[f21]) ).
thf(f26,plain,
( ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ sK0 ) )
| ( ( 'const/realax/real_lt' @ sK2 @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f27,plain,
( ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ sK0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 )
= $true ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f28,plain,
! [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_lt' @ X2 @ sK0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK1 ) )
| ( $true
!= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ sK0 ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f29,plain,
( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK1 ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f33,definition,
( spl3_1
<=> ( ( 'const/realax/real_lt' @ sK2 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f35,plain,
( ( ( 'const/realax/real_lt' @ sK2 @ sK0 )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f37,definition,
( spl3_2
<=> ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f38,plain,
( ( $true
!= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ sK0 ) )
| spl3_2 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f39,plain,
( ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ sK0 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f40,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f26,f37,f33]) ).
thf(f42,definition,
( spl3_3
<=> ! [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_lt' @ X2 @ sK0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f43,plain,
( ! [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK1 ) )
| ( $true
!= ( 'const/realax/real_lt' @ X2 @ sK0 ) ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f42]) ).
thf(f44,plain,
( ~ spl3_2
| spl3_3 ),
inference(avatar_split_clause,[],[f28,f42,f37]) ).
thf(f46,definition,
( spl3_4
<=> ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f48,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK1 )
= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f49,plain,
( spl3_4
| spl3_2 ),
inference(avatar_split_clause,[],[f27,f37,f46]) ).
thf(f71,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK1 ) @ sK1 ) )
| ( $true != $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) ),
inference(constrained_superposition,[],[f23,f29]) ).
thf(f72,plain,
( ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK1 ) @ sK1 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) ) ),
inference(trivial_inequality_removal,[],[f71]) ).
thf(f73,plain,
( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/inf' @ sK1 ) @ sK1 ) ),
inference(forward_subsumption_resolution,[],[f72,f25]) ).
thf(f74,plain,
( ( $true != $true )
| ( $true
!= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ sK0 ) )
| ~ spl3_3 ),
inference(constrained_superposition,[],[f43,f73]) ).
thf(f75,plain,
( ( $true
!= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ sK0 ) )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f74]) ).
thf(f76,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_subsumption_resolution,[],[f75,f39]) ).
thf(f77,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f76]) ).
thf(f83,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true != $true )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK1 ) )
| ~ spl3_4 ),
inference(constrained_superposition,[],[f24,f48]) ).
thf(f84,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK1 ) )
| ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK1 ) )
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f83]) ).
thf(f86,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK1 ) )
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f84,f25]) ).
thf(f88,plain,
( ( $true
= ( 'const/realax/real_le' @ ( 'const/sets/inf' @ sK1 ) @ sK2 ) )
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f86,f29]) ).
thf(f90,plain,
( ! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ X0 ) )
| ( $true
!= ( 'const/realax/real_lt' @ sK2 @ X0 ) ) )
| ~ spl3_4 ),
inference(constrained_superposition,[],[f22,f88]) ).
thf(f91,plain,
( ! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_lt' @ sK2 @ X0 ) )
| ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ X0 ) ) )
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f90]) ).
thf(f93,plain,
( ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ sK0 ) )
| ( $true != $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(constrained_superposition,[],[f91,f35]) ).
thf(f94,plain,
( ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/inf' @ sK1 ) @ sK0 ) )
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f95,plain,
( $false
| ~ spl3_1
| spl3_2
| ~ spl3_4 ),
inference(forward_subsumption_resolution,[],[f94,f38]) ).
thf(f96,plain,
( ~ spl3_1
| spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f95]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f40]) ).
cnf(s2,plain,
( ~ spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f44]) ).
cnf(s3,plain,
( spl3_2
| spl3_4 ),
inference(sat_conversion,[],[f49]) ).
cnf(s6,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f77]) ).
cnf(s8,plain,
( ~ spl3_1
| spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f96]) ).
cnf(s9,plain,
~ spl3_2,
inference(rat,[],[s2,s6]) ).
cnf(s10,plain,
spl3_4,
inference(rat,[],[s3,s9]) ).
cnf(s11,plain,
spl3_1,
inference(rat,[],[s1,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s8,s9,s10,s11]) ).
thf(f97,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA084^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n015.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 17:44:18 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 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
% 0.21/0.28 % (3870966)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (3870976)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3936154455:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (3870976) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3870966-3870976"...
% 0.21/0.28 % (3870976)...printing done.
% 0.21/0.28 % (3870982)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (3870982)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
% 0.21/0.28 % (3870976)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
% 0.21/0.29 % (3870976)------------------------------
% 0.21/0.29 % (3870976)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3870976)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3870976)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3870976)Termination reason: Refutation
% 0.21/0.29 % (3870976)Time elapsed: 0.003 s
% 0.21/0.29 % (3870976)Peak memory usage: 13 MB
% 0.21/0.29 % (3870976)Instructions burned: 7 (million)
% 0.21/0.29 % (3870966)Success in time 0.034 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------