%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : CSR142^2 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n006.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 : Wed Aug 30 21:33:27 EDT 2023

% Result   : Theorem 2.58s 2.93s
% Output   : Proof 2.58s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_lChris_THFTYPE_i,type,
    lChris_THFTYPE_i: $i ).

thf(ty_lCorina_THFTYPE_i,type,
    lCorina_THFTYPE_i: $i ).

thf(ty_inverse_THFTYPE_IIiioIIiioIoI,type,
    inverse_THFTYPE_IIiioIIiioIoI: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).

thf(ty_husband_THFTYPE_IiioI,type,
    husband_THFTYPE_IiioI: $i > $i > $o ).

thf(ty_wife_THFTYPE_IiioI,type,
    wife_THFTYPE_IiioI: $i > $i > $o ).

thf(sP1,plain,
    ( sP1
  <=> ( ( inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI )
     => ! [X1: $i,X2: $i] :
          ( ( husband_THFTYPE_IiioI @ X1 @ X2 )
          = ( wife_THFTYPE_IiioI @ X2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( inverse_THFTYPE_IIiioIIiioIoI @ husband_THFTYPE_IiioI @ wife_THFTYPE_IiioI ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i > $i > $o] :
        ( ( inverse_THFTYPE_IIiioIIiioIoI @ X1 @ wife_THFTYPE_IiioI )
       => ! [X2: $i,X3: $i] :
            ( ( X1 @ X2 @ X3 )
            = ( wife_THFTYPE_IiioI @ X3 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i] :
        ( ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ X1 )
        = ( wife_THFTYPE_IiioI @ X1 @ lChris_THFTYPE_i ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( husband_THFTYPE_IiioI @ lChris_THFTYPE_i @ lCorina_THFTYPE_i ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( sP5
      = ( wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: $i,X2: $i] :
        ( ( husband_THFTYPE_IiioI @ X1 @ X2 )
        = ( wife_THFTYPE_IiioI @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i > $i > $o,X2: $i > $i > $o] :
        ( ( inverse_THFTYPE_IIiioIIiioIoI @ X2 @ X1 )
       => ! [X3: $i,X4: $i] :
            ( ( X2 @ X3 @ X4 )
            = ( X1 @ X4 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( wife_THFTYPE_IiioI @ lCorina_THFTYPE_i @ lChris_THFTYPE_i ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: $i] :
        ~ ( husband_THFTYPE_IiioI @ X1 @ lCorina_THFTYPE_i ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP9 = sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(con,conjecture,
    ~ sP10 ).

thf(h0,negated_conjecture,
    sP10,
    inference(assume_negation,[status(cth)],[con]) ).

thf(1,plain,
    ( ~ sP4
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP7
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | ~ sP2
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP3
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP11
    | ~ sP9
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP6
    | sP11 ),
    inference(symeq,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP8
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP10
    | ~ sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(ax_051,axiom,
    sP9 ).

thf(ax_042,axiom,
    sP2 ).

thf(ax_006,axiom,
    sP8 ).

thf(9,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,h0,ax_051,ax_042,ax_006]) ).

thf(0,theorem,
    ~ sP10,
    inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : CSR142^2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Aug 28 10:44:21 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 2.58/2.93  % SZS status Theorem
% 2.58/2.93  % Mode: cade22sinegrackle2x6978
% 2.58/2.93  % Steps: 81734
% 2.58/2.93  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------