%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP107^1 : 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 : 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 04:02:07 EDT 2023

% Result   : Theorem 28.51s 28.53s
% Output   : Proof 28.51s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_s2,type,
    s2: a ).

thf(ty_locali1170246543t_unit,type,
    locali1170246543t_unit: partia1993116613t_unit > a > a > set_Product_prod_a_a ).

thf(ty_mult_a_ring_ext_a_b,type,
    mult_a_ring_ext_a_b: partia1833973666xt_a_b > a > a > a ).

thf(ty_s3,type,
    s3: a ).

thf(ty_r3,type,
    r3: a ).

thf(ty_r,type,
    r: partia1833973666xt_a_b ).

thf(ty_rel,type,
    rel: partia1993116613t_unit ).

thf(ty_r2,type,
    r2: a ).

thf(sP1,plain,
    ( sP1
  <=> ( ( mult_a_ring_ext_a_b @ r @ s2 @ s3 )
      = ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) )
      = ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) )
      = ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) )
      = ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( mult_a_ring_ext_a_b @ r @ r3 @ r2 )
      = ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) )
      = ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) )
      = ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r2 @ r3 ) @ ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) )
      = ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( mult_a_ring_ext_a_b @ r @ r2 @ r3 )
      = ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ( mult_a_ring_ext_a_b @ r @ s3 @ s2 )
      = ( mult_a_ring_ext_a_b @ r @ s2 @ s3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ( mult_s977248631t_unit @ ( locali1944243560ac_a_b @ r @ s ) @ ( locali1170246543t_unit @ rel @ r3 @ s3 ) @ ( locali1170246543t_unit @ rel @ r2 @ s2 ) )
      = ( locali1170246543t_unit @ rel @ ( mult_a_ring_ext_a_b @ r @ r3 @ r2 ) @ ( mult_a_ring_ext_a_b @ r @ s3 @ s2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(conj_0,conjecture,
    sP4 ).

thf(h0,negated_conjecture,
    ~ sP4,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( sP3
    | ~ sP11
    | ~ sP5
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | sP9 ),
    inference(symeq,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP7
    | sP6
    | ~ sP9
    | ~ sP2 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(4,plain,
    ~ sP8,
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP12
    | sP4
    | ~ sP6
    | sP8 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP7
    | sP2 ),
    inference(symeq,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP1
    | sP11 ),
    inference(symeq,[status(thm)],]) ).

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

thf(fact_4_f2,axiom,
    sP12 ).

thf(fact_3_f1,axiom,
    sP7 ).

thf(fact_1_f4,axiom,
    sP1 ).

thf(fact_0_f3,axiom,
    sP10 ).

thf(9,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,h0,fact_4_f2,fact_3_f1,fact_1_f4,fact_0_f3]) ).

thf(0,theorem,
    sP4,
    inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ITP107^1 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.12  % 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 11:33:50 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 28.51/28.53  % SZS status Theorem
% 28.51/28.53  % Mode: cade22sinegrackle2xfaf3
% 28.51/28.53  % Steps: 70344
% 28.51/28.53  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------