TSTP Solution File: ITP069^1 by Lash---1.13

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%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP069^1 : 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 : n001.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 04:01:52 EDT 2023

% Result   : Theorem 0.20s 0.45s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

thf(ty_tree_a,type,
    tree_a: $tType ).

thf(ty_t_a,type,
    t_a: a > tree_a > tree_a > tree_a ).

thf(ty_l,type,
    l: tree_a ).

thf(ty_is_heap_a,type,
    is_heap_a: tree_a > $o ).

thf(ty_r,type,
    r: tree_a ).

thf(ty_heapIm970322378pify_a,type,
    heapIm970322378pify_a: tree_a > tree_a ).

thf(ty_v,type,
    v: a ).

thf(ty_heapIm1091024090Down_a,type,
    heapIm1091024090Down_a: tree_a > tree_a ).

thf(sP1,plain,
    ( sP1
  <=> ( is_heap_a @ ( heapIm970322378pify_a @ l ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) )
      = ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: tree_a,X2: tree_a] :
        ( ( heapIm970322378pify_a @ ( t_a @ v @ X1 @ X2 ) )
        = ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ X1 ) @ ( heapIm970322378pify_a @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: tree_a] :
        ( ( heapIm970322378pify_a @ ( t_a @ v @ l @ X1 ) )
        = ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( is_heap_a @ ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) )
      = ( heapIm970322378pify_a @ ( t_a @ v @ l @ r ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( is_heap_a @ ( heapIm1091024090Down_a @ ( t_a @ v @ ( heapIm970322378pify_a @ l ) @ ( heapIm970322378pify_a @ r ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( is_heap_a @ ( heapIm970322378pify_a @ r ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: a,X2: tree_a,X3: tree_a] :
        ( ( heapIm970322378pify_a @ ( t_a @ X1 @ X2 @ X3 ) )
        = ( heapIm1091024090Down_a @ ( t_a @ X1 @ ( heapIm970322378pify_a @ X2 ) @ ( heapIm970322378pify_a @ X3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(conj_0,conjecture,
    sP5 ).

thf(h0,negated_conjecture,
    ~ sP5,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ( sP8
   => sP7 ),
    introduced(assumption,[]) ).

thf(fact_1_T_Ohyps_I1_J,axiom,
    sP1 ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h1,h0])],[fact_1_T_Ohyps_I1_J,h1]) ).

thf(h3,assumption,
    ~ sP8,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(fact_0_T_Ohyps_I2_J,axiom,
    sP8 ).

thf(2,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h3,h2,h0])],[fact_0_T_Ohyps_I2_J,h3]) ).

thf(3,plain,
    ( ~ sP7
    | sP5
    | ~ sP6 ),
    inference(mating_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP2
    | sP6 ),
    inference(symeq,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP3
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP9
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_3_heapify_Osimps_I2_J,axiom,
    sP9 ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h2,h0])],[3,4,5,6,7,h0,fact_3_heapify_Osimps_I2_J,h4]) ).

thf(9,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h2,2,8,h3,h4]) ).

thf(fact_2__092_060open_062_092_060lbrakk_062is__heap_A_Iheapify_Al_J_059_Ais__heap_A_Iheapify_Ar_J_059_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_A_061_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ais__heap_A_IsiftDown_A_IT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_J_J_092_060close_062,axiom,
    ( sP1
   => ( sP8
     => sP7 ) ) ).

thf(10,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[fact_2__092_060open_062_092_060lbrakk_062is__heap_A_Iheapify_Al_J_059_Ais__heap_A_Iheapify_Ar_J_059_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_A_061_AT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Ais__heap_A_IsiftDown_A_IT_Av_A_Iheapify_Al_J_A_Iheapify_Ar_J_J_J_092_060close_062,1,9,h1,h2]) ).

thf(0,theorem,
    sP5,
    inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP069^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34  % Computer : n001.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Sun Aug 27 12:39:47 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.45  % SZS status Theorem
% 0.20/0.45  % Mode: cade22sinegrackle2x6978
% 0.20/0.45  % Steps: 1038
% 0.20/0.45  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------