%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP019^1 : 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 : n022.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 04:01:19 EDT 2023

% Result   : Theorem 5.03s 5.21s
% Output   : Proof 5.03s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_mono_2Etyop_2Enum_2Enum,type,
    mono_2Etyop_2Enum_2Enum: $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_2Enum_2E0,type,
    mono_2Ec_2Enum_2E0: mono_2Etyop_2Enum_2Enum ).

thf(ty_eigen__0,type,
    eigen__0: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(ty_mono_2Ec_2Ecomplex_2Ecomplex__inv,type,
    mono_2Ec_2Ecomplex_2Ecomplex__inv: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(ty_mono_2Ec_2Ecomplex_2Ecomplex__of__num,type,
    mono_2Ec_2Ecomplex_2Ecomplex__of__num: mono_2Etyop_2Enum_2Enum > mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29 ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
        ( ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X1 )
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
        = ( X1
          = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( eigen__0
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ eigen__0 )
      = ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( sP3 = sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(thm_2Ecomplex_2ECOMPLEX__INV__NZ,conjecture,
    ! [X1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( X1
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X1 )
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
        ( ( X1
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
       => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X1 )
         != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(assume_negation,[status(cth)],[thm_2Ecomplex_2ECOMPLEX__INV__NZ]) ).

thf(h1,assumption,
    ~ ( ~ sP2
     => ~ sP3 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP4
    | ~ sP3
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(thm_2Ecomplex_2ECOMPLEX__INV__EQ__0,axiom,
    sP1 ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,h2,h3,thm_2Ecomplex_2ECOMPLEX__INV__EQ__0]) ).

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,3,h2,h3]) ).

thf(5,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,4,h1]) ).

thf(0,theorem,
    ! [X1: mono_2Etyop_2Epair_2Eprod_28tyop_2Erealax_2Ereal_2Ctyop_2Erealax_2Ereal_29] :
      ( ( X1
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) )
     => ( ( mono_2Ec_2Ecomplex_2Ecomplex__inv @ X1 )
       != ( mono_2Ec_2Ecomplex_2Ecomplex__of__num @ mono_2Ec_2Enum_2E0 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP019^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n022.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  : 300
% 0.13/0.34  % DateTime : Sun Aug 27 16:34:09 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 5.03/5.21  % SZS status Theorem
% 5.03/5.21  % Mode: cade22grackle2xfee4
% 5.03/5.21  % Steps: 193149
% 5.03/5.21  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------