TSTP Solution File: ITP256^3 by Satallax---3.5

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%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : ITP256^3 : TPTP v8.1.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n024.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  : 600s
% DateTime : Sun Jul 17 00:30:09 EDT 2022

% Result   : Theorem 53.28s 52.89s
% Output   : Proof 53.28s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_vEBT_VEBT,type,
    vEBT_VEBT: $tType ).

thf(ty_list_VEBT_VEBT,type,
    list_VEBT_VEBT: $tType ).

thf(ty_nat,type,
    nat: $tType ).

thf(ty_set_VEBT_VEBT,type,
    set_VEBT_VEBT: $tType ).

thf(ty_nth_VEBT_VEBT,type,
    nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).

thf(ty_vEBT_VEBT_high,type,
    vEBT_VEBT_high: nat > nat > nat ).

thf(ty_treeList,type,
    treeList: list_VEBT_VEBT ).

thf(ty_vEBT_vebt_delete,type,
    vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).

thf(ty_member_VEBT_VEBT,type,
    member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).

thf(ty_na,type,
    na: nat ).

thf(ty_ord_less_nat,type,
    ord_less_nat: nat > nat > $o ).

thf(ty_set_VEBT_VEBT2,type,
    set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).

thf(ty_xa,type,
    xa: nat ).

thf(ty_vEBT_V8194947554948674370ptions,type,
    vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).

thf(ty_size_s6755466524823107622T_VEBT,type,
    size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).

thf(ty_vEBT_invar_vebt,type,
    vEBT_invar_vebt: vEBT_VEBT > nat > $o ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: list_VEBT_VEBT] :
        ( ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( size_s6755466524823107622T_VEBT @ X1 ) )
       => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ X1 @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( set_VEBT_VEBT2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: nat,X2: list_VEBT_VEBT] :
        ( ( ord_less_nat @ X1 @ ( size_s6755466524823107622T_VEBT @ X2 ) )
       => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ X2 @ X1 ) @ ( set_VEBT_VEBT2 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( set_VEBT_VEBT2 @ treeList ) )
     => ~ ( ( vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ na )
         => ~ ! [X1: nat,X2: nat] :
                ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X1 ) @ X2 )
                = ( ~ ( ( X1 != X2 )
                     => ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X2 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( size_s6755466524823107622T_VEBT @ treeList ) )
     => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( set_VEBT_VEBT2 @ treeList ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ na )
     => ~ ! [X1: nat,X2: nat] :
            ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X1 ) @ X2 )
            = ( ~ ( ( X1 != X2 )
                 => ~ ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( size_s6755466524823107622T_VEBT @ treeList ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( vEBT_invar_vebt @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ na ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: vEBT_VEBT] :
        ( ( member_VEBT_VEBT @ X1 @ ( set_VEBT_VEBT2 @ treeList ) )
       => ~ ( ( vEBT_invar_vebt @ X1 @ na )
           => ~ ! [X2: nat,X3: nat] :
                  ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ X1 @ X2 ) @ X3 )
                  = ( ~ ( ( X2 != X3 )
                       => ~ ( vEBT_V8194947554948674370ptions @ X1 @ X3 ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( set_VEBT_VEBT2 @ treeList ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(conj_0,conjecture,
    sP7 ).

thf(h0,negated_conjecture,
    ~ sP7,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( sP5
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | ~ sP6
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP3
    | ~ sP9
    | ~ sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP2
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP8
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_8__092_060open_062high_Ax_An_A_060_Alength_AtreeList_092_060close_062,axiom,
    sP6 ).

thf(fact_23__C4_OIH_C_I1_J,axiom,
    sP8 ).

thf(fact_137_nth__mem,axiom,
    sP2 ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,fact_8__092_060open_062high_Ax_An_A_060_Alength_AtreeList_092_060close_062,fact_23__C4_OIH_C_I1_J,fact_137_nth__mem,h0]) ).

thf(0,theorem,
    sP7,
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP256^3 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n024.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  : 600
% 0.13/0.34  % DateTime : Fri Jun  3 20:24:20 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 53.28/52.89  % SZS status Theorem
% 53.28/52.89  % Mode: mode9:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 53.28/52.89  % Inferences: 3813
% 53.28/52.89  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------