%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA072^1 : 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 : 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 07:45:51 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 80 ( 9 unt; 0 typ; 5 def)
% Number of atoms : 506 ( 121 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 614 ( 83 ~; 89 |; 21 &; 382 @)
% ( 5 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 11 con; 0-4 aty)
% ( 7 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 65 ( 0 sgn 52 !; 4 ?; 65 :)
% 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/sup': ( '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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_10,type,
vIMP: $o > $o > $o ).
thf(func_def_11,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_13,type,
sK0: 'type/realax/real' > $o ).
thf(func_def_14,type,
sK1: 'type/realax/real' ).
thf(func_def_15,type,
sK2: 'type/realax/real' ).
thf(func_def_17,type,
sK4: 'type/realax/real' ).
thf(f1,axiom,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X0 @ X1 )
& ( 'const/realax/real_lt' @ X1 @ X2 ) )
=> ( 'const/realax/real_lt' @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/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/sup' @ X0 ) @ X0 )
& ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/SUP_FINITE_') ).
thf(f3,conjecture,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' ) )
=> ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= ( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_lt' @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_SUP_LT_FINITE_') ).
thf(f4,negated_conjecture,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' ) )
=> ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= ( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_lt' @ X2 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f5,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/realax/real_lt' @ X2 @ X0 ) )
=> ( 'const/realax/real_lt' @ X1 @ X0 ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X1: 'type/realax/real',X2: 'type/realax/real',X0: 'type/realax/real'] :
( ( ( $true
= ( 'const/realax/real_lt' @ X2 @ X0 ) )
& ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true ) )
=> ( ( 'const/realax/real_lt' @ X1 @ X0 )
= $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/sup' @ X0 ) @ X0 )
& ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f8,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) )
=> ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f7]) ).
thf(f9,plain,
~ ! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
& ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' ) )
=> ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= ( ! [X2: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
=> ( 'const/realax/real_lt' @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f10,plain,
~ ! [X1: 'type/realax/real',X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true ) )
=> ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ X0 ) @ X1 )
= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
=> ( 'const/realax/real_lt' @ Y0 @ X1 ) ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
? [X1: 'type/realax/real',X0: 'type/realax/real' > $o] :
( ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ X0 ) @ X1 )
!= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
=> ( 'const/realax/real_lt' @ Y0 @ X1 ) ) ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ X0 ) @ X1 )
!= ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ X0 )
=> ( 'const/realax/real_lt' @ Y0 @ X1 ) ) ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f14,plain,
! [X0: 'type/realax/real' > $o] :
( ( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
! [X1: 'type/realax/real',X2: 'type/realax/real',X0: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X0 )
= $true )
| ( $true
!= ( 'const/realax/real_lt' @ X2 @ X0 ) )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f16,plain,
! [X0: 'type/realax/real',X2: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_lt' @ X2 @ X0 ) )
| ( ( 'const/realax/real_lt' @ X1 @ X0 )
= $true )
| ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_lt' @ X2 @ X0 ) )
| ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true ) ),
inference(rectify,[],[f16]) ).
thf(f18,plain,
( ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
=> ( 'const/realax/real_lt' @ Y0 @ sK1 ) ) )
!= ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f12]) ).
thf(f19,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X2 @ X1 )
!= $true )
| ( ( 'const/realax/real_lt' @ X1 @ X0 )
!= $true )
| ( $true
= ( 'const/realax/real_lt' @ X2 @ X0 ) ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f20,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ),
inference(cnf_transformation,[],[f18]) ).
thf(f21,plain,
( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
= $true ),
inference(cnf_transformation,[],[f18]) ).
thf(f22,plain,
( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
=> ( 'const/realax/real_lt' @ Y0 @ sK1 ) ) )
!= ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ),
inference(cnf_transformation,[],[f18]) ).
thf(f23,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true ) ),
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/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f27,plain,
( ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
=> ( 'const/realax/real_lt' @ Y0 @ sK1 ) ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f28,plain,
( ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 )
= $false )
| ( ( !! @ 'type/realax/real'
@ ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
=> ( 'const/realax/real_lt' @ Y0 @ sK1 ) ) )
= $false ) ),
inference(xor_proxy_clausification,[],[f22]) ).
thf(f29,plain,
( ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 )
= $false )
| ( ( ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
=> ( 'const/realax/real_lt' @ Y0 @ sK1 ) )
@ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( $false
= ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
=> ( 'const/realax/real_lt' @ sK2 @ sK1 ) ) )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 )
= $false ) ),
inference(beta-eta_normalization,[],[f29]) ).
thf(f31,plain,
( ( ( 'const/realax/real_lt' @ sK2 @ sK1 )
= $false )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 )
= $false )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true ) ),
inference(imp_proxy_clausification,[],[f30]) ).
thf(f33,plain,
! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( ( ^ [Y0: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ Y0 @ sK0 )
=> ( 'const/realax/real_lt' @ Y0 @ sK1 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f34,plain,
! [X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
=> ( 'const/realax/real_lt' @ X1 @ sK1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ sK1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
= $false )
| ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f37,definition,
( spl3_1
<=> ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f39,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 )
= $true )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f41,definition,
( spl3_2
<=> ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f43,plain,
( ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 )
= $false )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f44,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f32,f41,f37]) ).
thf(f46,definition,
( spl3_3
<=> ( ( 'const/realax/real_lt' @ sK2 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f48,plain,
( ( ( 'const/realax/real_lt' @ sK2 @ sK1 )
= $false )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f49,plain,
( spl3_2
| spl3_3 ),
inference(avatar_split_clause,[],[f31,f46,f41]) ).
thf(f51,definition,
( spl3_4
<=> ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f52,plain,
( ( $true
!= ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| spl3_4 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f53,plain,
( ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f51]) ).
thf(f55,definition,
( spl3_5
<=> ! [X1: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ X1 @ sK1 )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
thf(f56,plain,
( ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ sK0 )
= $false )
| ( ( 'const/realax/real_lt' @ X1 @ sK1 )
= $true ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f57,plain,
( spl3_4
| spl3_5 ),
inference(avatar_split_clause,[],[f35,f55,f51]) ).
thf(f86,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_4 ),
inference(constrained_superposition,[],[f43,f53]) ).
thf(f90,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f86]) ).
thf(f91,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f90]) ).
thf(f93,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sK0 ) @ sK0 )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f23,f21]) ).
thf(f94,plain,
( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sK0 ) @ sK0 )
= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f95,plain,
( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ sK0 ) @ sK0 )
= $true ),
inference(forward_subsumption_resolution,[],[f94,f20]) ).
thf(f96,plain,
( ( $true
= ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true != $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f24,f39]) ).
thf(f98,plain,
( ( $true
= ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/sup' @ sK0 ) ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f96]) ).
thf(f100,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/sup' @ sK0 ) ) )
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f98,f21]) ).
thf(f102,plain,
( ( $true
= ( 'const/realax/real_le' @ sK2 @ ( 'const/sets/sup' @ sK0 ) ) )
| ~ spl3_1 ),
inference(forward_subsumption_resolution,[],[f100,f20]) ).
thf(f104,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ sK2 @ X0 )
= $true )
| ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl3_1 ),
inference(constrained_superposition,[],[f19,f102]) ).
thf(f105,plain,
( ! [X0: 'type/realax/real'] :
( ( ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ X0 )
!= $true )
| ( ( 'const/realax/real_lt' @ sK2 @ X0 )
= $true ) )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f107,plain,
( ( $true != $true )
| ( ( 'const/realax/real_lt' @ sK2 @ sK1 )
= $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(constrained_superposition,[],[f105,f53]) ).
thf(f108,plain,
( ( ( 'const/realax/real_lt' @ sK2 @ sK1 )
= $true )
| ~ spl3_1
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f107]) ).
thf(f109,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(forward_demodulation,[],[f108,f48]) ).
thf(f110,plain,
( $false
| ~ spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f109]) ).
thf(f111,plain,
( ~ spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f110]) ).
thf(f113,plain,
( ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ( $true = $false )
| ~ spl3_5 ),
inference(constrained_superposition,[],[f56,f95]) ).
thf(f120,plain,
( ( $true
= ( 'const/realax/real_lt' @ ( 'const/sets/sup' @ sK0 ) @ sK1 ) )
| ~ spl3_5 ),
inference(trivial_inequality_removal,[],[f113]) ).
thf(f129,plain,
( $false
| spl3_4
| ~ spl3_5 ),
inference(forward_subsumption_resolution,[],[f120,f52]) ).
thf(f130,plain,
( spl3_4
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[],[f129]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f44]) ).
cnf(s2,plain,
( spl3_2
| spl3_3 ),
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
( spl3_4
| spl3_5 ),
inference(sat_conversion,[],[f57]) ).
cnf(s9,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f91]) ).
cnf(s10,plain,
( ~ spl3_1
| ~ spl3_3
| ~ spl3_4 ),
inference(sat_conversion,[],[f111]) ).
cnf(s14,plain,
( spl3_4
| ~ spl3_5 ),
inference(sat_conversion,[],[f130]) ).
cnf(s15,plain,
spl3_4,
inference(rat,[],[s3,s14]) ).
cnf(s16,plain,
~ spl3_2,
inference(rat,[],[s9,s15]) ).
cnf(s17,plain,
spl3_3,
inference(rat,[],[s2,s16]) ).
cnf(s18,plain,
spl3_1,
inference(rat,[],[s1,s16]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s10,s15,s18,s17]) ).
thf(f131,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA072^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n004.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 17:40:33 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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
% 0.20/0.26 % (1617713)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.26 % (1617723)lrs+10_16_si=on:nwc=1.5:random_seed=2594889046:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.26 % (1617723) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1617713-1617723"...
% 0.20/0.26 % (1617728)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.26 % (1617723)...printing done.
% 0.20/0.26 % (1617728)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
% 0.20/0.26 % (1617723)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (1617723)------------------------------
% 0.20/0.27 % (1617723)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1617723)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1617723)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1617723)Termination reason: Refutation
% 0.20/0.27 % (1617723)Time elapsed: 0.004 s
% 0.20/0.27 % (1617723)Peak memory usage: 13 MB
% 0.20/0.27 % (1617723)Instructions burned: 8 (million)
% 0.20/0.27 % (1617713)Success in time 0.019 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------