TSTP Solution File: ITP020^2 by E---3.1.00

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%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP020^2 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n026.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 : Mon May 20 22:15:45 EDT 2024

% Result   : Theorem 1.63s 0.66s
% Output   : CNFRefutation 1.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   41 (  10 unt;  14 typ;   0 def)
%            Number of atoms       :   76 (   0 equ;   0 cnn)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :  722 (  39   ~;  35   |;   9   &; 634   @)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  12 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   22 (  22   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   14 (  13 usr;   4 con; 0-4 aty)
%            Number of variables   :   55 (   0   ^  50   !;   5   ?;  55   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    del: $tType ).

thf(decl_22,type,
    bool: del ).

thf(decl_24,type,
    arr: del > del > del ).

thf(decl_25,type,
    mem: $i > del > $o ).

thf(decl_26,type,
    ap: $i > $i > $i ).

thf(decl_28,type,
    p: $i > $o ).

thf(decl_38,type,
    c_2Epred__set_2EUNIV: del > $i ).

thf(decl_39,type,
    ty_2Epair_2Eprod: del > del > del ).

thf(decl_40,type,
    c_2Epred__set_2ECROSS: del > del > $i ).

thf(decl_41,type,
    c_2Epred__set_2EBIJ: del > del > $i ).

thf(decl_42,type,
    ty_2Enum_2Enum: del ).

thf(decl_75,type,
    esk24_0: $i ).

thf(decl_76,type,
    esk25_4: del > del > $i > $i > $i ).

thf(decl_77,type,
    esk26_4: del > del > $i > $i > $i ).

thf(conj_thm_2Eutil__prob_2ENUM__2D__BIJ__INV,conjecture,
    ? [X51: $i] :
      ( ( mem @ X51 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
      & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ X51 ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eutil__prob_2ENUM__2D__BIJ__INV) ).

thf(conj_thm_2Epred__set_2EBIJ__SYM,axiom,
    ! [X15: del,X19: del,X44: $i] :
      ( ( mem @ X44 @ ( arr @ X15 @ bool ) )
     => ! [X45: $i] :
          ( ( mem @ X45 @ ( arr @ X19 @ bool ) )
         => ( ? [X46: $i] :
                ( ( mem @ X46 @ ( arr @ X15 @ X19 ) )
                & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X15 @ X19 ) @ X46 ) @ X44 ) @ X45 ) ) )
          <=> ? [X47: $i] :
                ( ( mem @ X47 @ ( arr @ X19 @ X15 ) )
                & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X19 @ X15 ) @ X47 ) @ X45 ) @ X44 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EBIJ__SYM) ).

thf(conj_thm_2Eutil__prob_2ENUM__2D__BIJ,axiom,
    ? [X51: $i] :
      ( ( mem @ X51 @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) )
      & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) @ X51 ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eutil__prob_2ENUM__2D__BIJ) ).

thf(mem_c_2Epred__set_2EUNIV,axiom,
    ! [X15: del] : ( mem @ ( c_2Epred__set_2EUNIV @ X15 ) @ ( arr @ X15 @ bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2EUNIV) ).

thf(ap_tp,axiom,
    ! [X3: del,X4: del,X5: $i] :
      ( ( mem @ X5 @ ( arr @ X3 @ X4 ) )
     => ! [X6: $i] :
          ( ( mem @ X6 @ X3 )
         => ( mem @ ( ap @ X5 @ X6 ) @ X4 ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001^2.ax',ap_tp) ).

thf(mem_c_2Epred__set_2ECROSS,axiom,
    ! [X15: del,X19: del] : ( mem @ ( c_2Epred__set_2ECROSS @ X15 @ X19 ) @ ( arr @ ( arr @ X15 @ bool ) @ ( arr @ ( arr @ X19 @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ X15 @ X19 ) @ bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECROSS) ).

thf(c_0_6,negated_conjecture,
    ~ ? [X51: $i] :
        ( ( mem @ X51 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
        & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ X51 ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ),
    inference(assume_negation,[status(cth)],[conj_thm_2Eutil__prob_2ENUM__2D__BIJ__INV]) ).

thf(c_0_7,plain,
    ! [X285: del,X286: del,X287: $i,X288: $i,X289: $i,X291: $i] :
      ( ( ( mem @ ( esk25_4 @ X285 @ X286 @ X287 @ X288 ) @ ( arr @ X286 @ X285 ) )
        | ~ ( mem @ X289 @ ( arr @ X285 @ X286 ) )
        | ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X285 @ X286 ) @ X289 ) @ X287 ) @ X288 ) )
        | ~ ( mem @ X288 @ ( arr @ X286 @ bool ) )
        | ~ ( mem @ X287 @ ( arr @ X285 @ bool ) ) )
      & ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X286 @ X285 ) @ ( esk25_4 @ X285 @ X286 @ X287 @ X288 ) ) @ X288 ) @ X287 ) )
        | ~ ( mem @ X289 @ ( arr @ X285 @ X286 ) )
        | ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X285 @ X286 ) @ X289 ) @ X287 ) @ X288 ) )
        | ~ ( mem @ X288 @ ( arr @ X286 @ bool ) )
        | ~ ( mem @ X287 @ ( arr @ X285 @ bool ) ) )
      & ( ( mem @ ( esk26_4 @ X285 @ X286 @ X287 @ X288 ) @ ( arr @ X285 @ X286 ) )
        | ~ ( mem @ X291 @ ( arr @ X286 @ X285 ) )
        | ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X286 @ X285 ) @ X291 ) @ X288 ) @ X287 ) )
        | ~ ( mem @ X288 @ ( arr @ X286 @ bool ) )
        | ~ ( mem @ X287 @ ( arr @ X285 @ bool ) ) )
      & ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X285 @ X286 ) @ ( esk26_4 @ X285 @ X286 @ X287 @ X288 ) ) @ X287 ) @ X288 ) )
        | ~ ( mem @ X291 @ ( arr @ X286 @ X285 ) )
        | ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X286 @ X285 ) @ X291 ) @ X288 ) @ X287 ) )
        | ~ ( mem @ X288 @ ( arr @ X286 @ bool ) )
        | ~ ( mem @ X287 @ ( arr @ X285 @ bool ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_thm_2Epred__set_2EBIJ__SYM])])])])])]) ).

thf(c_0_8,plain,
    ( ( mem @ esk24_0 @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) )
    & ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) @ esk24_0 ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[conj_thm_2Eutil__prob_2ENUM__2D__BIJ])]) ).

thf(c_0_9,plain,
    ! [X275: del] : ( mem @ ( c_2Epred__set_2EUNIV @ X275 ) @ ( arr @ X275 @ bool ) ),
    inference(variable_rename,[status(thm)],[mem_c_2Epred__set_2EUNIV]) ).

thf(c_0_10,plain,
    ! [X266: del,X267: del,X268: $i,X269: $i] :
      ( ~ ( mem @ X268 @ ( arr @ X266 @ X267 ) )
      | ~ ( mem @ X269 @ X266 )
      | ( mem @ ( ap @ X268 @ X269 ) @ X267 ) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ap_tp])])])]) ).

thf(c_0_11,plain,
    ! [X281: del,X282: del] : ( mem @ ( c_2Epred__set_2ECROSS @ X281 @ X282 ) @ ( arr @ ( arr @ X281 @ bool ) @ ( arr @ ( arr @ X282 @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ X281 @ X282 ) @ bool ) ) ) ),
    inference(variable_rename,[status(thm)],[mem_c_2Epred__set_2ECROSS]) ).

thf(c_0_12,negated_conjecture,
    ! [X164: $i] :
      ( ~ ( mem @ X164 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
      | ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ X164 ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

thf(c_0_13,plain,
    ! [X2: $i,X3: del,X6: $i,X5: $i,X4: del] :
      ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X3 @ X4 ) @ ( esk25_4 @ X4 @ X3 @ X2 @ X5 ) ) @ X5 ) @ X2 ) )
      | ~ ( mem @ X6 @ ( arr @ X4 @ X3 ) )
      | ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X4 @ X3 ) @ X6 ) @ X2 ) @ X5 ) )
      | ~ ( mem @ X5 @ ( arr @ X3 @ bool ) )
      | ~ ( mem @ X2 @ ( arr @ X4 @ bool ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_14,plain,
    p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ) @ esk24_0 ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_15,plain,
    ! [X3: del] : ( mem @ ( c_2Epred__set_2EUNIV @ X3 ) @ ( arr @ X3 @ bool ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_16,plain,
    mem @ esk24_0 @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_17,plain,
    ! [X2: $i,X6: $i,X5: $i,X4: del,X3: del] :
      ( ( mem @ ( esk25_4 @ X3 @ X4 @ X2 @ X5 ) @ ( arr @ X4 @ X3 ) )
      | ~ ( mem @ X6 @ ( arr @ X3 @ X4 ) )
      | ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ X3 @ X4 ) @ X6 ) @ X2 ) @ X5 ) )
      | ~ ( mem @ X5 @ ( arr @ X4 @ bool ) )
      | ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

thf(c_0_18,plain,
    ! [X2: $i,X5: $i,X4: del,X3: del] :
      ( ( mem @ ( ap @ X2 @ X5 ) @ X4 )
      | ~ ( mem @ X2 @ ( arr @ X3 @ X4 ) )
      | ~ ( mem @ X5 @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_19,plain,
    ! [X3: del,X4: del] : ( mem @ ( c_2Epred__set_2ECROSS @ X3 @ X4 ) @ ( arr @ ( arr @ X3 @ bool ) @ ( arr @ ( arr @ X4 @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ X3 @ X4 ) @ bool ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_20,negated_conjecture,
    ! [X2: $i] :
      ( ~ ( mem @ X2 @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
      | ~ ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ X2 ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_21,plain,
    ( ( p @ ( ap @ ( ap @ ( ap @ ( c_2Epred__set_2EBIJ @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) @ ( esk25_4 @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) ) )
    | ~ ( mem @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ bool ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).

thf(c_0_22,plain,
    ( ( mem @ ( esk25_4 @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ty_2Enum_2Enum @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( arr @ ty_2Enum_2Enum @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ) )
    | ~ ( mem @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ bool ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15]),c_0_16])]) ).

thf(c_0_23,plain,
    ! [X2: $i,X4: del,X3: del] :
      ( ( mem @ ( ap @ ( c_2Epred__set_2ECROSS @ X3 @ X4 ) @ X2 ) @ ( arr @ ( arr @ X4 @ bool ) @ ( arr @ ( ty_2Epair_2Eprod @ X3 @ X4 ) @ bool ) ) )
      | ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

thf(c_0_24,negated_conjecture,
    ~ ( mem @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( c_2Epred__set_2EUNIV @ ty_2Enum_2Enum ) ) @ ( arr @ ( ty_2Epair_2Eprod @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) @ bool ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).

thf(c_0_25,plain,
    ! [X2: $i,X5: $i,X4: del,X3: del] :
      ( ( mem @ ( ap @ ( ap @ ( c_2Epred__set_2ECROSS @ X3 @ X4 ) @ X2 ) @ X5 ) @ ( arr @ ( ty_2Epair_2Eprod @ X3 @ X4 ) @ bool ) )
      | ~ ( mem @ X5 @ ( arr @ X4 @ bool ) )
      | ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
    inference(spm,[status(thm)],[c_0_18,c_0_23]) ).

thf(c_0_26,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : ITP020^2 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.12/0.13  % Command    : run_E %s %d THM
% 0.12/0.32  % Computer : n026.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sat May 18 18:11:23 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.17/0.45  Running higher-order theorem proving
% 0.17/0.45  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.63/0.66  # Version: 3.1.0-ho
% 1.63/0.66  # Preprocessing class: HSLSSMSMSSSNSFA.
% 1.63/0.66  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.63/0.66  # Starting new_ho_10 with 900s (3) cores
% 1.63/0.66  # Starting sh2lt with 300s (1) cores
% 1.63/0.66  # Starting new_ho_5 with 300s (1) cores
% 1.63/0.66  # Starting full_lambda_5 with 300s (1) cores
% 1.63/0.66  # Starting sh9 with 300s (1) cores
% 1.63/0.66  # Starting ehoh_best8_lambda with 300s (1) cores
% 1.63/0.66  # sh2lt with pid 27708 completed with status 0
% 1.63/0.66  # Result found by sh2lt
% 1.63/0.66  # Preprocessing class: HSLSSMSMSSSNSFA.
% 1.63/0.66  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.63/0.66  # Starting new_ho_10 with 900s (3) cores
% 1.63/0.66  # Starting sh2lt with 300s (1) cores
% 1.63/0.66  # SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 1.63/0.66  # Search class: HGHSM-FSLF32-MSFFFFNN
% 1.63/0.66  # partial match(1): HGHSM-FSLF32-MSFFFFBN
% 1.63/0.66  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.63/0.66  # Starting sh3 with 163s (1) cores
% 1.63/0.66  # sh3 with pid 27716 completed with status 0
% 1.63/0.66  # Result found by sh3
% 1.63/0.66  # Preprocessing class: HSLSSMSMSSSNSFA.
% 1.63/0.66  # Scheduled 6 strats onto 8 cores with 300 seconds (2400 total)
% 1.63/0.66  # Starting new_ho_10 with 900s (3) cores
% 1.63/0.66  # Starting sh2lt with 300s (1) cores
% 1.63/0.66  # SinE strategy is GSinE(CountFormulas,hypos,5,,4,20000,1.0,true)
% 1.63/0.66  # Search class: HGHSM-FSLF32-MSFFFFNN
% 1.63/0.66  # partial match(1): HGHSM-FSLF32-MSFFFFBN
% 1.63/0.66  # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 1.63/0.66  # Starting sh3 with 163s (1) cores
% 1.63/0.66  # Preprocessing time       : 0.002 s
% 1.63/0.66  # Presaturation interreduction done
% 1.63/0.66  
% 1.63/0.66  # Proof found!
% 1.63/0.66  # SZS status Theorem
% 1.63/0.66  # SZS output start CNFRefutation
% See solution above
% 1.63/0.66  # Parsed axioms                        : 95
% 1.63/0.66  # Removed by relevancy pruning/SinE    : 53
% 1.63/0.66  # Initial clauses                      : 356
% 1.63/0.66  # Removed in clause preprocessing      : 261
% 1.63/0.66  # Initial clauses in saturation        : 95
% 1.63/0.66  # Processed clauses                    : 483
% 1.63/0.66  # ...of these trivial                  : 0
% 1.63/0.66  # ...subsumed                          : 61
% 1.63/0.66  # ...remaining for further processing  : 422
% 1.63/0.66  # Other redundant clauses eliminated   : 0
% 1.63/0.66  # Clauses deleted for lack of memory   : 0
% 1.63/0.66  # Backward-subsumed                    : 4
% 1.63/0.66  # Backward-rewritten                   : 0
% 1.63/0.66  # Generated clauses                    : 6718
% 1.63/0.66  # ...of the previous two non-redundant : 6702
% 1.63/0.66  # ...aggressively subsumed             : 0
% 1.63/0.66  # Contextual simplify-reflections      : 1
% 1.63/0.66  # Paramodulations                      : 6717
% 1.63/0.66  # Factorizations                       : 0
% 1.63/0.66  # NegExts                              : 0
% 1.63/0.66  # Equation resolutions                 : 1
% 1.63/0.66  # Disequality decompositions           : 0
% 1.63/0.66  # Total rewrite steps                  : 117
% 1.63/0.66  # ...of those cached                   : 113
% 1.63/0.66  # Propositional unsat checks           : 0
% 1.63/0.66  #    Propositional check models        : 0
% 1.63/0.66  #    Propositional check unsatisfiable : 0
% 1.63/0.66  #    Propositional clauses             : 0
% 1.63/0.66  #    Propositional clauses after purity: 0
% 1.63/0.66  #    Propositional unsat core size     : 0
% 1.63/0.66  #    Propositional preprocessing time  : 0.000
% 1.63/0.66  #    Propositional encoding time       : 0.000
% 1.63/0.66  #    Propositional solver time         : 0.000
% 1.63/0.66  #    Success case prop preproc time    : 0.000
% 1.63/0.66  #    Success case prop encoding time   : 0.000
% 1.63/0.66  #    Success case prop solver time     : 0.000
% 1.63/0.66  # Current number of processed clauses  : 341
% 1.63/0.66  #    Positive orientable unit clauses  : 9
% 1.63/0.66  #    Positive unorientable unit clauses: 0
% 1.63/0.66  #    Negative unit clauses             : 1
% 1.63/0.66  #    Non-unit-clauses                  : 331
% 1.63/0.66  # Current number of unprocessed clauses: 6316
% 1.63/0.66  # ...number of literals in the above   : 34966
% 1.63/0.66  # Current number of archived formulas  : 0
% 1.63/0.66  # Current number of archived clauses   : 81
% 1.63/0.66  # Clause-clause subsumption calls (NU) : 13262
% 1.63/0.66  # Rec. Clause-clause subsumption calls : 3202
% 1.63/0.66  # Non-unit clause-clause subsumptions  : 61
% 1.63/0.66  # Unit Clause-clause subsumption calls : 7
% 1.63/0.66  # Rewrite failures with RHS unbound    : 0
% 1.63/0.66  # BW rewrite match attempts            : 0
% 1.63/0.66  # BW rewrite match successes           : 0
% 1.63/0.66  # Condensation attempts                : 0
% 1.63/0.66  # Condensation successes               : 0
% 1.63/0.66  # Termbank termtop insertions          : 284565
% 1.63/0.66  # Search garbage collected termcells   : 5576
% 1.63/0.66  
% 1.63/0.66  # -------------------------------------------------
% 1.63/0.66  # User time                : 0.193 s
% 1.63/0.66  # System time              : 0.006 s
% 1.63/0.66  # Total time               : 0.199 s
% 1.63/0.66  # Maximum resident set size: 2784 pages
% 1.63/0.66  
% 1.63/0.66  # -------------------------------------------------
% 1.63/0.66  # User time                : 0.198 s
% 1.63/0.66  # System time              : 0.007 s
% 1.63/0.66  # Total time               : 0.205 s
% 1.63/0.66  # Maximum resident set size: 1876 pages
% 1.63/0.66  % E---3.1 exiting
% 1.63/0.66  % E exiting
%------------------------------------------------------------------------------