%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP118^1 : TPTP v8.1.2. Released v7.5.0.
% 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 : Thu Aug 31 04:02:12 EDT 2023

% Result   : Theorem 126.38s 126.68s
% Output   : Proof 126.38s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_n,type,
    n: $tType ).

thf(ty_finite1489363574real_n,type,
    finite1489363574real_n: $tType ).

thf(ty_int,type,
    int: $tType ).

thf(ty_abs_abs_int,type,
    abs_abs_int: int > int ).

thf(ty_minus_minus_real,type,
    minus_minus_real: real > real > real ).

thf(ty_i,type,
    i: n ).

thf(ty_minus_1037315151real_n,type,
    minus_1037315151real_n: finite1489363574real_n > finite1489363574real_n > finite1489363574real_n ).

thf(ty_ring_1_of_int_real,type,
    ring_1_of_int_real: int > real ).

thf(ty_finite772340589real_n,type,
    finite772340589real_n: finite1489363574real_n > n > real ).

thf(ty_abs_abs_real,type,
    abs_abs_real: real > real ).

thf(ty_m,type,
    m: int ).

thf(ty_x,type,
    x: finite1489363574real_n ).

thf(ty_y,type,
    y: finite1489363574real_n ).

thf(sP1,plain,
    ( sP1
  <=> ( ( ring_1_of_int_real @ m )
      = ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( abs_abs_real @ ( ring_1_of_int_real @ m ) )
      = ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: n] :
        ( ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ X1 )
        = ( minus_minus_real @ ( finite772340589real_n @ x @ X1 ) @ ( finite772340589real_n @ y @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
      = ( abs_abs_real @ ( ring_1_of_int_real @ m ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( ring_1_of_int_real @ m )
      = ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i )
      = ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( minus_minus_real @ ( finite772340589real_n @ x @ i ) @ ( finite772340589real_n @ y @ i ) )
      = ( ring_1_of_int_real @ m ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: int] :
        ( ( ring_1_of_int_real @ ( abs_abs_int @ X1 ) )
        = ( abs_abs_real @ ( ring_1_of_int_real @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( ring_1_of_int_real @ ( abs_abs_int @ m ) )
      = ( abs_abs_real @ ( finite772340589real_n @ ( minus_1037315151real_n @ x @ y ) @ i ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: finite1489363574real_n,X2: n] :
        ( ( finite772340589real_n @ ( minus_1037315151real_n @ x @ X1 ) @ X2 )
        = ( minus_minus_real @ ( finite772340589real_n @ x @ X2 ) @ ( finite772340589real_n @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: finite1489363574real_n,X2: finite1489363574real_n,X3: n] :
        ( ( finite772340589real_n @ ( minus_1037315151real_n @ X1 @ X2 ) @ X3 )
        = ( minus_minus_real @ ( finite772340589real_n @ X1 @ X3 ) @ ( finite772340589real_n @ X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(conj_0,conjecture,
    sP10 ).

thf(h0,negated_conjecture,
    ~ sP10,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP7
    | sP6
    | ~ sP8
    | sP3 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(2,plain,
    ~ sP3,
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP2
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP5
    | sP10
    | sP3
    | ~ sP2 ),
    inference(confrontation_rule,[status(thm)],]) ).

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

thf(6,plain,
    ( ~ sP4
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP11
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP12
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP1
    | sP8 ),
    inference(symeq,[status(thm)],]) ).

thf(fact_9_of__int__abs,axiom,
    sP9 ).

thf(fact_6_vector__minus__component,axiom,
    sP12 ).

thf(fact_2_m,axiom,
    sP1 ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,fact_9_of__int__abs,fact_6_vector__minus__component,fact_2_m,h0]) ).

thf(0,theorem,
    sP10,
    inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ITP118^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n006.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 11:53:36 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 126.38/126.68  % SZS status Theorem
% 126.38/126.68  % Mode: cade22sinegrackle2xec37
% 126.38/126.68  % Steps: 19848
% 126.38/126.68  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------