TSTP Solution File: ITP023^1 by Lash---1.13
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- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP023^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 04:01:27 EDT 2023
% Result : Theorem 80.65s 80.90s
% Output : Proof 80.65s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mono_2Etyop_2Erealax_2Ereal,type,
mono_2Etyop_2Erealax_2Ereal: $tType ).
thf(ty_mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal,type,
mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal: mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Erealax_2Ereal > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).
thf(ty_mono_2Ec_2Ereal__topology_2Eball,type,
mono_2Ec_2Ereal__topology_2Eball: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(ty_mono_2Ec_2Ereal__topology_2Ecball,type,
mono_2Ec_2Ereal__topology_2Ecball: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Erealax_2Ereal > $o ).
thf(ty_mono_2Ec_2Ereal__topology_2Ebounded__def,type,
mono_2Ec_2Ereal__topology_2Ebounded__def: ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(ty_mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal,type,
mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal: ( mono_2Etyop_2Erealax_2Ereal > $o ) > ( mono_2Etyop_2Erealax_2Ereal > $o ) > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: mono_2Etyop_2Erealax_2Ereal > $o,X2: mono_2Etyop_2Erealax_2Ereal > $o] :
( ~ ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X2 )
=> ~ ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ~ ( ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Ecball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) )
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ X1 ) ) ) ) ) )
=> ~ ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) )
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ X1 ) ) ) ) )
@ ( mono_2Ec_2Ereal__topology_2Ecball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) )
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ X1 ) ) ) ) ) ) )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) )
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Ecball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) )
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: mono_2Etyop_2Erealax_2Ereal] :
( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ X1 ) )
@ ( mono_2Ec_2Ereal__topology_2Ecball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: mono_2Etyop_2Erealax_2Ereal > $o] :
( ~ ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ X1 )
=> ~ ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X3: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X4: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X3 @ X4 ) ) )
@ X2 ) ) ) ) )
@ X1 ) )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X3: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X4: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X3 @ X4 ) ) )
@ X2 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: mono_2Etyop_2Erealax_2Ereal] :
( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Ecball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: mono_2Etyop_2Erealax_2Ereal,X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: mono_2Etyop_2Erealax_2Ereal,X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( sP3
=> ~ ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) )
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ X1 ) ) ) ) )
@ ( mono_2Ec_2Ereal__topology_2Ecball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) )
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ X1 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( mono_2Ec_2Epred__set_2ESUBSET_2Emono_2Etyop_2Erealax_2Ereal
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) )
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ X1 ) ) ) ) )
@ ( mono_2Ec_2Ereal__topology_2Ecball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) )
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) )
@ @+[X1: mono_2Etyop_2Erealax_2Ereal] :
~ ( mono_2Ec_2Ereal__topology_2Ebounded__def
@ ( mono_2Ec_2Ereal__topology_2Eball
@ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal
@ @+[X2: mono_2Etyop_2Erealax_2Ereal] :
~ ! [X3: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X2 @ X3 ) ) )
@ X1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(thm_2Ereal__topology_2EBOUNDED__BALL,conjecture,
! [X1: mono_2Etyop_2Erealax_2Ereal,X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) ) ).
thf(h0,negated_conjecture,
~ ! [X1: mono_2Etyop_2Erealax_2Ereal,X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) ),
inference(assume_negation,[status(cth)],[thm_2Ereal__topology_2EBOUNDED__BALL]) ).
thf(1,plain,
( ~ sP9
| ~ sP3
| ~ sP10 ),
inference(prop_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP2
| sP9
| sP11 ),
inference(prop_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP6
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP4
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP7
| sP6 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP8
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(thm_2Ereal__topology_2EBOUNDED__CBALL,axiom,
sP7 ).
thf(thm_2Ereal__topology_2EBOUNDED__SUBSET,axiom,
sP1 ).
thf(thm_2Ereal__topology_2EBALL__SUBSET__CBALL,axiom,
sP8 ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0,h0])],[1,2,3,4,5,6,7,8,h0,thm_2Ereal__topology_2EBOUNDED__CBALL,thm_2Ereal__topology_2EBOUNDED__SUBSET,thm_2Ereal__topology_2EBALL__SUBSET__CBALL]) ).
thf(0,theorem,
! [X1: mono_2Etyop_2Erealax_2Ereal,X2: mono_2Etyop_2Erealax_2Ereal] : ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ X1 @ X2 ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ITP023^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.03/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Aug 27 14:49:20 EDT 2023
% 0.12/0.33 % CPUTime :
% 80.65/80.90 % SZS status Theorem
% 80.65/80.90 % Mode: cade22sinegrackle2x1406
% 80.65/80.90 % Steps: 165
% 80.65/80.90 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------