TSTP Solution File: ITP004^2 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP004^2 : TPTP v8.2.0. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n019.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 22:15:11 EDT 2024

% Result   : Theorem 9.08s 1.65s
% Output   : CNFRefutation 9.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   52 (  13 unt;  14 typ;   0 def)
%            Number of atoms       :  123 (   7 equ;   0 cnn)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  813 (  57   ~;  59   |;   8   &; 671   @)
%                                         (   3 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (  10 avg)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   15 (  15   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   15 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :   72 (   0   ^  72   !;   0   ?;  72   :)

% 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_31,type,
    c_2Epred__set_2ESUBSET: del > $i ).

thf(decl_34,type,
    c_2Ebool_2EIN: del > $i ).

thf(decl_35,type,
    c_2Epred__set_2ECHOICE: del > $i ).

thf(decl_36,type,
    c_2Epred__set_2EDELETE: del > $i ).

thf(decl_37,type,
    c_2Epred__set_2EREST: del > $i ).

thf(decl_40,type,
    esk1_0: del ).

thf(decl_41,type,
    esk2_0: $i ).

thf(decl_43,type,
    esk4_3: del > $i > $i > $i ).

thf(conj_thm_2Epred__set_2EREST__SUBSET,conjecture,
    ! [X15: del,X19: $i] :
      ( ( mem @ X19 @ ( arr @ X15 @ bool ) )
     => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X15 ) @ ( ap @ ( c_2Epred__set_2EREST @ X15 ) @ X19 ) ) @ X19 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EREST__SUBSET) ).

thf(ax_thm_2Epred__set_2ESUBSET__DEF,axiom,
    ! [X15: del,X19: $i] :
      ( ( mem @ X19 @ ( arr @ X15 @ bool ) )
     => ! [X20: $i] :
          ( ( mem @ X20 @ ( arr @ X15 @ bool ) )
         => ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X15 ) @ X19 ) @ X20 ) )
          <=> ! [X21: $i] :
                ( ( mem @ X21 @ X15 )
               => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X15 ) @ X21 ) @ X19 ) )
                 => ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X15 ) @ X21 ) @ X20 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Epred__set_2ESUBSET__DEF) ).

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_2EREST,axiom,
    ! [X15: del] : ( mem @ ( c_2Epred__set_2EREST @ X15 ) @ ( arr @ ( arr @ X15 @ bool ) @ ( arr @ X15 @ bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2EREST) ).

thf(conj_thm_2Epred__set_2EIN__DELETE,axiom,
    ! [X15: del,X19: $i] :
      ( ( mem @ X19 @ ( arr @ X15 @ bool ) )
     => ! [X22: $i] :
          ( ( mem @ X22 @ X15 )
         => ! [X23: $i] :
              ( ( mem @ X23 @ X15 )
             => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X15 ) @ X22 ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X15 ) @ X19 ) @ X23 ) ) )
              <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X15 ) @ X22 ) @ X19 ) )
                  & ( X22 != X23 ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EIN__DELETE) ).

thf(mem_c_2Epred__set_2ECHOICE,axiom,
    ! [X15: del] : ( mem @ ( c_2Epred__set_2ECHOICE @ X15 ) @ ( arr @ ( arr @ X15 @ bool ) @ X15 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECHOICE) ).

thf(ax_thm_2Epred__set_2EREST__DEF,axiom,
    ! [X15: del,X19: $i] :
      ( ( mem @ X19 @ ( arr @ X15 @ bool ) )
     => ( ( ap @ ( c_2Epred__set_2EREST @ X15 ) @ X19 )
        = ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X15 ) @ X19 ) @ ( ap @ ( c_2Epred__set_2ECHOICE @ X15 ) @ X19 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Epred__set_2EREST__DEF) ).

thf(c_0_7,negated_conjecture,
    ~ ! [X15: del,X19: $i] :
        ( ( mem @ X19 @ ( arr @ X15 @ bool ) )
       => ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X15 ) @ ( ap @ ( c_2Epred__set_2EREST @ X15 ) @ X19 ) ) @ X19 ) ) ),
    inference(assume_negation,[status(cth)],[conj_thm_2Epred__set_2EREST__SUBSET]) ).

thf(c_0_8,plain,
    ! [X65: del,X66: $i,X67: $i,X68: $i] :
      ( ( ~ ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X65 ) @ X66 ) @ X67 ) )
        | ~ ( mem @ X68 @ X65 )
        | ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X65 ) @ X68 ) @ X66 ) )
        | ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X65 ) @ X68 ) @ X67 ) )
        | ~ ( mem @ X67 @ ( arr @ X65 @ bool ) )
        | ~ ( mem @ X66 @ ( arr @ X65 @ bool ) ) )
      & ( ( mem @ ( esk4_3 @ X65 @ X66 @ X67 ) @ X65 )
        | ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X65 ) @ X66 ) @ X67 ) )
        | ~ ( mem @ X67 @ ( arr @ X65 @ bool ) )
        | ~ ( mem @ X66 @ ( arr @ X65 @ bool ) ) )
      & ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X65 ) @ ( esk4_3 @ X65 @ X66 @ X67 ) ) @ X66 ) )
        | ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X65 ) @ X66 ) @ X67 ) )
        | ~ ( mem @ X67 @ ( arr @ X65 @ bool ) )
        | ~ ( mem @ X66 @ ( arr @ X65 @ bool ) ) )
      & ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X65 ) @ ( esk4_3 @ X65 @ X66 @ X67 ) ) @ X67 ) )
        | ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X65 ) @ X66 ) @ X67 ) )
        | ~ ( mem @ X67 @ ( arr @ X65 @ bool ) )
        | ~ ( mem @ X66 @ ( arr @ X65 @ 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)],[ax_thm_2Epred__set_2ESUBSET__DEF])])])])])]) ).

thf(c_0_9,negated_conjecture,
    ( ( mem @ esk2_0 @ ( arr @ esk1_0 @ bool ) )
    & ~ ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ esk1_0 ) @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ esk2_0 ) ) @ esk2_0 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).

thf(c_0_10,plain,
    ! [X52: del,X53: del,X54: $i,X55: $i] :
      ( ~ ( mem @ X54 @ ( arr @ X52 @ X53 ) )
      | ~ ( mem @ X55 @ X52 )
      | ( mem @ ( ap @ X54 @ X55 ) @ X53 ) ),
    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,
    ! [X61: del] : ( mem @ ( c_2Epred__set_2EREST @ X61 ) @ ( arr @ ( arr @ X61 @ bool ) @ ( arr @ X61 @ bool ) ) ),
    inference(variable_rename,[status(thm)],[mem_c_2Epred__set_2EREST]) ).

thf(c_0_12,plain,
    ! [X15: del,X19: $i] :
      ( ( mem @ X19 @ ( arr @ X15 @ bool ) )
     => ! [X22: $i] :
          ( ( mem @ X22 @ X15 )
         => ! [X23: $i] :
              ( ( mem @ X23 @ X15 )
             => ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X15 ) @ X22 ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X15 ) @ X19 ) @ X23 ) ) )
              <=> ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X15 ) @ X22 ) @ X19 ) )
                  & ( X22 != X23 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[conj_thm_2Epred__set_2EIN__DELETE]) ).

thf(c_0_13,plain,
    ! [X70: del] : ( mem @ ( c_2Epred__set_2ECHOICE @ X70 ) @ ( arr @ ( arr @ X70 @ bool ) @ X70 ) ),
    inference(variable_rename,[status(thm)],[mem_c_2Epred__set_2ECHOICE]) ).

thf(c_0_14,plain,
    ! [X2: $i,X5: $i,X3: del] :
      ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X3 ) @ ( esk4_3 @ X3 @ X2 @ X5 ) ) @ X2 ) )
      | ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X3 ) @ X2 ) @ X5 ) )
      | ~ ( mem @ X5 @ ( arr @ X3 @ bool ) )
      | ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_15,negated_conjecture,
    mem @ esk2_0 @ ( arr @ esk1_0 @ bool ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_16,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_17,plain,
    ! [X3: del] : ( mem @ ( c_2Epred__set_2EREST @ X3 ) @ ( arr @ ( arr @ X3 @ bool ) @ ( arr @ X3 @ bool ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_18,plain,
    ! [X2: $i,X5: $i,X3: del] :
      ( ( mem @ ( esk4_3 @ X3 @ X2 @ X5 ) @ X3 )
      | ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X3 ) @ X2 ) @ X5 ) )
      | ~ ( mem @ X5 @ ( arr @ X3 @ bool ) )
      | ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_19,plain,
    ! [X72: del,X73: $i,X74: $i,X75: $i] :
      ( ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X72 ) @ X74 ) @ X73 ) )
        | ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X72 ) @ X74 ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X72 ) @ X73 ) @ X75 ) ) )
        | ~ ( mem @ X75 @ X72 )
        | ~ ( mem @ X74 @ X72 )
        | ~ ( mem @ X73 @ ( arr @ X72 @ bool ) ) )
      & ( ( X74 != X75 )
        | ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X72 ) @ X74 ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X72 ) @ X73 ) @ X75 ) ) )
        | ~ ( mem @ X75 @ X72 )
        | ~ ( mem @ X74 @ X72 )
        | ~ ( mem @ X73 @ ( arr @ X72 @ bool ) ) )
      & ( ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X72 ) @ X74 ) @ X73 ) )
        | ( X74 = X75 )
        | ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X72 ) @ X74 ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X72 ) @ X73 ) @ X75 ) ) )
        | ~ ( mem @ X75 @ X72 )
        | ~ ( mem @ X74 @ X72 )
        | ~ ( mem @ X73 @ ( arr @ X72 @ bool ) ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])])])]) ).

thf(c_0_20,plain,
    ! [X62: del,X63: $i] :
      ( ~ ( mem @ X63 @ ( arr @ X62 @ bool ) )
      | ( ( ap @ ( c_2Epred__set_2EREST @ X62 ) @ X63 )
        = ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X62 ) @ X63 ) @ ( ap @ ( c_2Epred__set_2ECHOICE @ X62 ) @ X63 ) ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax_thm_2Epred__set_2EREST__DEF])])]) ).

thf(c_0_21,plain,
    ! [X3: del] : ( mem @ ( c_2Epred__set_2ECHOICE @ X3 ) @ ( arr @ ( arr @ X3 @ bool ) @ X3 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_22,negated_conjecture,
    ! [X2: $i] :
      ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ esk1_0 ) @ ( esk4_3 @ esk1_0 @ X2 @ esk2_0 ) ) @ X2 ) )
      | ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ esk1_0 ) @ X2 ) @ esk2_0 ) )
      | ~ ( mem @ X2 @ ( arr @ esk1_0 @ bool ) ) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

thf(c_0_23,plain,
    ! [X2: $i,X3: del] :
      ( ( mem @ ( ap @ ( c_2Epred__set_2EREST @ X3 ) @ X2 ) @ ( arr @ X3 @ bool ) )
      | ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

thf(c_0_24,negated_conjecture,
    ! [X2: $i] :
      ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ esk1_0 ) @ X2 ) @ esk2_0 ) )
      | ( mem @ ( esk4_3 @ esk1_0 @ X2 @ esk2_0 ) @ esk1_0 )
      | ~ ( mem @ X2 @ ( arr @ esk1_0 @ bool ) ) ),
    inference(spm,[status(thm)],[c_0_18,c_0_15]) ).

thf(c_0_25,plain,
    ! [X2: $i,X6: $i,X5: $i,X3: del] :
      ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X3 ) @ X2 ) @ X5 ) )
      | ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X3 ) @ X2 ) @ ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X3 ) @ X5 ) @ X6 ) ) )
      | ~ ( mem @ X6 @ X3 )
      | ~ ( mem @ X2 @ X3 )
      | ~ ( mem @ X5 @ ( arr @ X3 @ bool ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

thf(c_0_26,plain,
    ! [X2: $i,X3: del] :
      ( ( ( ap @ ( c_2Epred__set_2EREST @ X3 ) @ X2 )
        = ( ap @ ( ap @ ( c_2Epred__set_2EDELETE @ X3 ) @ X2 ) @ ( ap @ ( c_2Epred__set_2ECHOICE @ X3 ) @ X2 ) ) )
      | ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

thf(c_0_27,plain,
    ! [X2: $i,X3: del] :
      ( ( mem @ ( ap @ ( c_2Epred__set_2ECHOICE @ X3 ) @ X2 ) @ X3 )
      | ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
    inference(spm,[status(thm)],[c_0_16,c_0_21]) ).

thf(c_0_28,negated_conjecture,
    ! [X2: $i] :
      ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ esk1_0 ) @ ( esk4_3 @ esk1_0 @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ X2 ) @ esk2_0 ) ) @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ X2 ) ) )
      | ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ esk1_0 ) @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ X2 ) ) @ esk2_0 ) )
      | ~ ( mem @ X2 @ ( arr @ esk1_0 @ bool ) ) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

thf(c_0_29,negated_conjecture,
    ~ ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ esk1_0 ) @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ esk2_0 ) ) @ esk2_0 ) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

thf(c_0_30,negated_conjecture,
    ! [X2: $i] :
      ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ esk1_0 ) @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ X2 ) ) @ esk2_0 ) )
      | ( mem @ ( esk4_3 @ esk1_0 @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ X2 ) @ esk2_0 ) @ esk1_0 )
      | ~ ( mem @ X2 @ ( arr @ esk1_0 @ bool ) ) ),
    inference(spm,[status(thm)],[c_0_24,c_0_23]) ).

thf(c_0_31,plain,
    ! [X2: $i,X5: $i,X3: del] :
      ( ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X3 ) @ X2 ) @ X5 ) )
      | ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X3 ) @ X2 ) @ ( ap @ ( c_2Epred__set_2EREST @ X3 ) @ X5 ) ) )
      | ~ ( mem @ X5 @ ( arr @ X3 @ bool ) )
      | ~ ( mem @ X2 @ X3 ) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).

thf(c_0_32,negated_conjecture,
    p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ esk1_0 ) @ ( esk4_3 @ esk1_0 @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ esk2_0 ) @ esk2_0 ) ) @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ esk2_0 ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_15]),c_0_29]) ).

thf(c_0_33,negated_conjecture,
    mem @ ( esk4_3 @ esk1_0 @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ esk2_0 ) @ esk2_0 ) @ esk1_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_15]),c_0_29]) ).

thf(c_0_34,plain,
    ! [X2: $i,X5: $i,X3: del] :
      ( ( p @ ( ap @ ( ap @ ( c_2Epred__set_2ESUBSET @ X3 ) @ X2 ) @ X5 ) )
      | ~ ( p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ X3 ) @ ( esk4_3 @ X3 @ X2 @ X5 ) ) @ X5 ) )
      | ~ ( mem @ X5 @ ( arr @ X3 @ bool ) )
      | ~ ( mem @ X2 @ ( arr @ X3 @ bool ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_35,negated_conjecture,
    p @ ( ap @ ( ap @ ( c_2Ebool_2EIN @ esk1_0 ) @ ( esk4_3 @ esk1_0 @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ esk2_0 ) @ esk2_0 ) ) @ esk2_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_15]),c_0_33])]) ).

thf(c_0_36,negated_conjecture,
    ~ ( mem @ ( ap @ ( c_2Epred__set_2EREST @ esk1_0 ) @ esk2_0 ) @ ( arr @ esk1_0 @ bool ) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_15])]),c_0_29]) ).

thf(c_0_37,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_23]),c_0_15])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : ITP004^2 : TPTP v8.2.0. Bugfixed v7.5.0.
% 0.08/0.14  % Command    : run_E %s %d THM
% 0.15/0.36  % Computer : n019.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sat May 18 15:40:07 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.21/0.51  Running higher-order theorem proving
% 0.21/0.51  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
% 9.08/1.65  # Version: 3.1.0-ho
% 9.08/1.65  # Preprocessing class: HSMSSMSSSSSNSFA.
% 9.08/1.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.08/1.65  # Starting new_ho_14 with 1200s (4) cores
% 9.08/1.65  # Starting new_ho_13 with 600s (2) cores
% 9.08/1.65  # Starting new_ho_10_cnf2 with 300s (1) cores
% 9.08/1.65  # Starting new_bool_3 with 300s (1) cores
% 9.08/1.65  # new_bool_3 with pid 2434 completed with status 0
% 9.08/1.65  # Result found by new_bool_3
% 9.08/1.65  # Preprocessing class: HSMSSMSSSSSNSFA.
% 9.08/1.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.08/1.65  # Starting new_ho_14 with 1200s (4) cores
% 9.08/1.65  # Starting new_ho_13 with 600s (2) cores
% 9.08/1.65  # Starting new_ho_10_cnf2 with 300s (1) cores
% 9.08/1.65  # Starting new_bool_3 with 300s (1) cores
% 9.08/1.65  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.08/1.65  # Search class: HGHSM-FFMF31-MSFFFFNN
% 9.08/1.65  # partial match(2): FGHSM-FFMF31-MFFFFFNN
% 9.08/1.65  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 9.08/1.65  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN with 181s (1) cores
% 9.08/1.65  # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN with pid 2435 completed with status 0
% 9.08/1.65  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN
% 9.08/1.65  # Preprocessing class: HSMSSMSSSSSNSFA.
% 9.08/1.65  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 9.08/1.65  # Starting new_ho_14 with 1200s (4) cores
% 9.08/1.65  # Starting new_ho_13 with 600s (2) cores
% 9.08/1.65  # Starting new_ho_10_cnf2 with 300s (1) cores
% 9.08/1.65  # Starting new_bool_3 with 300s (1) cores
% 9.08/1.65  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 9.08/1.65  # Search class: HGHSM-FFMF31-MSFFFFNN
% 9.08/1.65  # partial match(2): FGHSM-FFMF31-MFFFFFNN
% 9.08/1.65  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 9.08/1.65  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN with 181s (1) cores
% 9.08/1.65  # Preprocessing time       : 0.002 s
% 9.08/1.65  # Presaturation interreduction done
% 9.08/1.65  
% 9.08/1.65  # Proof found!
% 9.08/1.65  # SZS status Theorem
% 9.08/1.65  # SZS output start CNFRefutation
% See solution above
% 9.08/1.65  # Parsed axioms                        : 45
% 9.08/1.65  # Removed by relevancy pruning/SinE    : 34
% 9.08/1.65  # Initial clauses                      : 18
% 9.08/1.65  # Removed in clause preprocessing      : 0
% 9.08/1.65  # Initial clauses in saturation        : 18
% 9.08/1.65  # Processed clauses                    : 395
% 9.08/1.65  # ...of these trivial                  : 0
% 9.08/1.65  # ...subsumed                          : 28
% 9.08/1.65  # ...remaining for further processing  : 367
% 9.08/1.65  # Other redundant clauses eliminated   : 1
% 9.08/1.65  # Clauses deleted for lack of memory   : 0
% 9.08/1.65  # Backward-subsumed                    : 20
% 9.08/1.65  # Backward-rewritten                   : 4
% 9.08/1.65  # Generated clauses                    : 2964
% 9.08/1.65  # ...of the previous two non-redundant : 2953
% 9.08/1.65  # ...aggressively subsumed             : 0
% 9.08/1.65  # Contextual simplify-reflections      : 12
% 9.08/1.65  # Paramodulations                      : 2962
% 9.08/1.65  # Factorizations                       : 0
% 9.08/1.65  # NegExts                              : 0
% 9.08/1.65  # Equation resolutions                 : 2
% 9.08/1.65  # Disequality decompositions           : 0
% 9.08/1.65  # Total rewrite steps                  : 87
% 9.08/1.65  # ...of those cached                   : 81
% 9.08/1.65  # Propositional unsat checks           : 0
% 9.08/1.65  #    Propositional check models        : 0
% 9.08/1.65  #    Propositional check unsatisfiable : 0
% 9.08/1.65  #    Propositional clauses             : 0
% 9.08/1.65  #    Propositional clauses after purity: 0
% 9.08/1.65  #    Propositional unsat core size     : 0
% 9.08/1.65  #    Propositional preprocessing time  : 0.000
% 9.08/1.65  #    Propositional encoding time       : 0.000
% 9.08/1.65  #    Propositional solver time         : 0.000
% 9.08/1.65  #    Success case prop preproc time    : 0.000
% 9.08/1.65  #    Success case prop encoding time   : 0.000
% 9.08/1.65  #    Success case prop solver time     : 0.000
% 9.08/1.65  # Current number of processed clauses  : 324
% 9.08/1.65  #    Positive orientable unit clauses  : 11
% 9.08/1.65  #    Positive unorientable unit clauses: 0
% 9.08/1.65  #    Negative unit clauses             : 2
% 9.08/1.65  #    Non-unit-clauses                  : 311
% 9.08/1.65  # Current number of unprocessed clauses: 2590
% 9.08/1.65  # ...number of literals in the above   : 15900
% 9.08/1.65  # Current number of archived formulas  : 0
% 9.08/1.65  # Current number of archived clauses   : 42
% 9.08/1.65  # Clause-clause subsumption calls (NU) : 21972
% 9.08/1.65  # Rec. Clause-clause subsumption calls : 4314
% 9.08/1.65  # Non-unit clause-clause subsumptions  : 53
% 9.08/1.65  # Unit Clause-clause subsumption calls : 108
% 9.08/1.65  # Rewrite failures with RHS unbound    : 0
% 9.08/1.65  # BW rewrite match attempts            : 83
% 9.08/1.65  # BW rewrite match successes           : 2
% 9.08/1.65  # Condensation attempts                : 0
% 9.08/1.65  # Condensation successes               : 0
% 9.08/1.65  # Termbank termtop insertions          : 265543
% 9.08/1.65  # Search garbage collected termcells   : 653
% 9.08/1.65  
% 9.08/1.65  # -------------------------------------------------
% 9.08/1.65  # User time                : 1.106 s
% 9.08/1.65  # System time              : 0.014 s
% 9.08/1.65  # Total time               : 1.121 s
% 9.08/1.65  # Maximum resident set size: 1848 pages
% 9.08/1.65  
% 9.08/1.65  # -------------------------------------------------
% 9.08/1.65  # User time                : 1.107 s
% 9.08/1.65  # System time              : 0.018 s
% 9.08/1.65  # Total time               : 1.125 s
% 9.08/1.65  # Maximum resident set size: 1784 pages
% 9.08/1.65  % E---3.1 exiting
% 9.08/1.65  % E exiting
%------------------------------------------------------------------------------