TSTP Solution File: ITP023^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP023^1 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n024.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 : 600s
% DateTime : Sun Jul 17 00:28:44 EDT 2022
% Result : Theorem 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_mono_2Etyop_2Erealax_2Ereal,type,
mono_2Etyop_2Erealax_2Ereal: $tType ).
thf(ty_mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29,type,
mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29: $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_eigen__1,type,
eigen__1: mono_2Etyop_2Erealax_2Ereal ).
thf(ty_eigen__0,type,
eigen__0: mono_2Etyop_2Erealax_2Ereal ).
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_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_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(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(sP1,plain,
( sP1
<=> ! [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,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( 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 @ eigen__0 @ eigen__1 ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ eigen__0 @ eigen__1 ) ) ) ),
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 @ eigen__0 @ eigen__1 ) ) )
=> ~ sP2 )
=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ eigen__0 @ eigen__1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Eball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ eigen__0 @ eigen__1 ) ) )
=> ~ sP2 ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [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,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [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 @ eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [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 @ eigen__0 @ eigen__1 ) ) @ X1 ) )
=> sP4 ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( mono_2Ec_2Ereal__topology_2Ebounded__def @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ eigen__0 @ eigen__1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [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 @ eigen__0 @ X1 ) ) @ ( mono_2Ec_2Ereal__topology_2Ecball @ ( mono_2Ec_2Epair_2E_2C_2Emono_2Etyop_2Erealax_2Ereal_20mono_2Etyop_2Erealax_2Ereal @ eigen__0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [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,[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(h1,assumption,
~ ! [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 @ eigen__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ sP4,
introduced(assumption,[]) ).
thf(1,plain,
( ~ sP7
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP8
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP3
| sP5
| sP4 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP5
| ~ sP9
| ~ sP2 ),
inference(prop_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP10
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP6
| sP10 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP11
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP1
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(thm_2Ereal__topology_2EBOUNDED__CBALL,axiom,
sP1 ).
thf(thm_2Ereal__topology_2EBOUNDED__SUBSET,axiom,
sP11 ).
thf(thm_2Ereal__topology_2EBALL__SUBSET__CBALL,axiom,
sP6 ).
thf(9,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,h2,thm_2Ereal__topology_2EBOUNDED__CBALL,thm_2Ereal__topology_2EBOUNDED__SUBSET,thm_2Ereal__topology_2EBALL__SUBSET__CBALL]) ).
thf(10,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,9,h2]) ).
thf(11,plain,
$false,
inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,10,h1]) ).
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])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP023^1 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jun 3 14:27:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 0.19/0.49 % Inferences: 20
% 0.19/0.49 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------