%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA069^1 : 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 : n014.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 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 3
% Syntax : Number of formulae : 55 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 594 ( 182 equ; 0 cnn)
% Maximal formula atoms : 9 ( 10 avg)
% Number of connectives : 696 ( 99 ~; 91 |; 41 &; 449 @)
% ( 1 <=>; 13 =>; 0 <=; 2 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 79 ( 0 ^; 60 !; 19 ?; 79 :)
% 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_le': 'type/realax/real' > 'type/realax/real' > $o ).
thf(func_def_8,type,
sK0: 'type/realax/real' > $o ).
thf(func_def_9,type,
sK1: 'type/realax/real' ).
thf(func_def_10,type,
sK2: 'type/realax/real' ).
thf(func_def_11,type,
sK3: 'type/realax/real' ).
thf(f1,axiom,
! [X2: 'type/realax/real',X1: 'type/realax/real',X0: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/realax/real_le' @ X0 @ X1 ) )
=> ( 'const/realax/real_le' @ X0 @ X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/realax/REAL_LE_TRANS_') ).
thf(f2,axiom,
! [X0: 'type/realax/real' > $o] :
( ( ( ( X0 != 'const/sets/EMPTY' ) @ 'type/realax/real' )
& ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ 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' ) )
=> ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) )
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/sets/REAL_LE_SUP_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' ) )
=> ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) )
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ 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_le' @ X1 @ X0 )
& ( 'const/realax/real_le' @ X2 @ X1 ) )
=> ( 'const/realax/real_le' @ X2 @ X0 ) ),
inference(rectify,[],[f1]) ).
thf(f6,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( ( $true
= ( 'const/realax/real_le' @ X2 @ X1 ) )
& ( $true
= ( 'const/realax/real_le' @ X1 @ X0 ) ) )
=> ( $true
= ( 'const/realax/real_le' @ X2 @ X0 ) ) ),
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 ) )
=> ( ! [X1: 'type/realax/real'] :
( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
=> ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) )
& ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ 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 ) ) )
=> ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true )
& ! [X1: 'type/realax/real'] :
( ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
= $true )
=> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ 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' ) )
=> ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
& ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 ) )
= ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) ) ) ),
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_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
<=> ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f11,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true )
& ! [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/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(ennf_transformation,[],[f8]) ).
thf(f12,plain,
! [X0: 'type/realax/real' > $o] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( ( ( 'const/sets/IN' @ 'type/realax/real' @ ( 'const/sets/sup' @ X0 ) @ X0 )
= $true )
& ! [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/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(flattening,[],[f11]) ).
thf(f13,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X2 @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X2 @ X1 ) )
| ( $true
!= ( 'const/realax/real_le' @ X1 @ X0 ) ) ),
inference(ennf_transformation,[],[f6]) ).
thf(f14,plain,
! [X2: 'type/realax/real',X0: 'type/realax/real',X1: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X1 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ X2 @ X0 ) )
| ( $true
!= ( 'const/realax/real_le' @ X2 @ X1 ) ) ),
inference(flattening,[],[f13]) ).
thf(f15,plain,
? [X1: 'type/realax/real',X0: 'type/realax/real' > $o] :
( ( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
<~> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f16,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) )
<~> ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(flattening,[],[f15]) ).
thf(f17,plain,
! [X0: 'type/realax/real',X1: 'type/realax/real',X2: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ X2 @ X1 ) )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true )
| ( ( 'const/realax/real_le' @ X0 @ X2 )
!= $true ) ),
inference(rectify,[],[f14]) ).
thf(f18,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true )
| ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) ) )
& ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(nnf_transformation,[],[f16]) ).
thf(f19,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true )
| ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) ) )
& ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ? [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
= $true )
& ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
= $true ) ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(flattening,[],[f18]) ).
thf(f20,plain,
? [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
!= $true )
| ! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ X2 )
!= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ X0 )
!= $true ) ) )
& ( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ? [X3: 'type/realax/real'] :
( ( $true
= ( 'const/realax/real_le' @ X1 @ X3 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ X3 @ X0 ) ) ) )
& ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
= $true )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != X0 ) ) ),
inference(rectify,[],[f19]) ).
thf(f21,plain,
( ( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| ! [X2: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ sK1 @ X2 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 ) ) ) )
& ( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ( ( $true
= ( 'const/realax/real_le' @ sK1 @ sK2 ) )
& ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) ) ) )
& ( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
& ( 'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ) ) ),
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'] :
( ( ( 'const/realax/real_le' @ X0 @ X2 )
!= $true )
| ( $true
!= ( 'const/realax/real_le' @ X2 @ X1 ) )
| ( ( 'const/realax/real_le' @ X0 @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f17]) ).
thf(f23,plain,
'const/sets/EMPTY' @ ( 'type/realax/real' != sK0 ),
inference(cnf_transformation,[],[f21]) ).
thf(f24,plain,
( $true
= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f25,plain,
( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f26,plain,
( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
= $true )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f27,plain,
! [X2: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X2 @ sK0 ) )
| ( $true
!= ( 'const/realax/real_le' @ sK1 @ X2 ) ) ),
inference(cnf_transformation,[],[f21]) ).
thf(f28,plain,
! [X0: 'type/realax/real' > $o,X1: 'type/realax/real'] :
( ( ( 'const/realax/real_le' @ X1 @ ( 'const/sets/sup' @ X0 ) )
= $true )
| ( ( 'const/sets/IN' @ 'type/realax/real' @ X1 @ X0 )
!= $true )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f29,plain,
! [X0: 'type/realax/real' > $o] :
( ( ( '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(cnf_transformation,[],[f12]) ).
thf(f40,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ sK1 @ X0 ) )
| ( $true != $true )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) ) ),
inference(superposition,[],[f27,f25]) ).
thf(f41,plain,
! [X0: 'type/realax/real'] :
( ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ sK1 @ X0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ sK2 ) ) ),
inference(superposition,[],[f27,f26]) ).
thf(f42,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
!= ( 'const/realax/real_le' @ sK1 @ X0 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f40]) ).
thf(f43,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
!= ( 'const/realax/real_le' @ sK1 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f41]) ).
thf(f48,plain,
( ( $true != $true )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) ) ),
inference(superposition,[],[f42,f29]) ).
thf(f49,plain,
( ( $true
= ( 'const/realax/real_le' @ sK1 @ sK2 ) )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| ( $true != $true )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(superposition,[],[f43,f29]) ).
thf(f50,plain,
( ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f48]) ).
thf(f51,plain,
( ( ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ sK0 ) )
!= $true )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ sK2 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f52,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f50,f25]) ).
thf(f53,plain,
( ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ sK2 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f51,f26]) ).
thf(f54,plain,
( ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f52,f23]) ).
thf(f55,plain,
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ sK2 ) ) ),
inference(forward_subsumption_resolution,[],[f53,f24]) ).
thf(f56,plain,
( $true
= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) ),
inference(forward_subsumption_resolution,[],[f54,f24]) ).
thf(f57,plain,
( $true
= ( 'const/realax/real_le' @ sK1 @ sK2 ) ),
inference(forward_subsumption_resolution,[],[f55,f23]) ).
thf(f58,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ sK2 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[],[f22,f57]) ).
thf(f59,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/realax/real_le' @ sK2 @ X0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f58]) ).
thf(f64,plain,
! [X0: 'type/realax/real' > $o] :
( ( $true != $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ X0 ) ) ) ),
inference(superposition,[],[f59,f28]) ).
thf(f67,plain,
! [X0: 'type/realax/real' > $o] :
( ( $true
= ( 'const/realax/real_le' @ sK1 @ ( 'const/sets/sup' @ X0 ) ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = X0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ X0 ) )
| ( ( 'const/sets/FINITE' @ 'type/realax/real' @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[],[f64]) ).
thf(f80,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ( $true
!= ( 'const/realax/real_le' @ sK1 @ X0 ) )
| ( $true != $true )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) ) ),
inference(superposition,[],[f27,f67]) ).
thf(f83,plain,
! [X0: 'type/realax/real'] :
( ( 'const/sets/EMPTY' @ ( 'type/realax/real' = sK0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) )
| ( $true
!= ( 'const/realax/real_le' @ sK1 @ X0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f84,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ sK2 @ sK0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) )
| ( $true
!= ( 'const/realax/real_le' @ sK1 @ X0 ) ) ),
inference(forward_subsumption_resolution,[],[f83,f23]) ).
thf(f85,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
!= ( 'const/realax/real_le' @ sK1 @ X0 ) )
| ( $true
!= ( 'const/sets/FINITE' @ 'type/realax/real' @ sK0 ) ) ),
inference(forward_subsumption_resolution,[],[f84,f42]) ).
thf(f86,plain,
! [X0: 'type/realax/real'] :
( ( $true
!= ( 'const/sets/IN' @ 'type/realax/real' @ X0 @ sK0 ) )
| ( $true
!= ( 'const/realax/real_le' @ sK1 @ X0 ) ) ),
inference(forward_subsumption_resolution,[],[f85,f24]) ).
thf(f87,plain,
( ( $true != $true )
| ( $true
!= ( 'const/realax/real_le' @ sK1 @ sK2 ) ) ),
inference(superposition,[],[f86,f56]) ).
thf(f90,plain,
( $true
!= ( 'const/realax/real_le' @ sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f87]) ).
thf(f92,plain,
$false,
inference(forward_subsumption_resolution,[],[f90,f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA069^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n014.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 17:39:00 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.19/0.27 % (2978798)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.27 % (2978807)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2014564611:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.27 % (2978807) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2978798-2978807"...
% 0.19/0.27 % (2978807)...printing done.
% 0.19/0.27 % (2978809)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.27 % (2978809)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
% 0.19/0.27 % (2978807)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (2978807)------------------------------
% 0.19/0.27 % (2978807)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (2978807)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (2978807)CaDiCaL version: 2.1.3
% 0.19/0.27 % (2978807)Termination reason: Refutation
% 0.19/0.27 % (2978807)Time elapsed: 0.003 s
% 0.19/0.27 % (2978807)Peak memory usage: 12 MB
% 0.19/0.27 % (2978807)Instructions burned: 10 (million)
% 0.19/0.27 % (2978798)Success in time 0.032 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------