TSTP Solution File: SET795+4 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET795+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% 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 : Thu Aug 31 14:35:35 EDT 2023

% Result   : Theorem 10.32s 10.50s
% Output   : CNFRefutation 10.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   53
% Syntax   : Number of formulae    :   85 (   9 unt;  47 typ;   0 def)
%            Number of atoms       :  404 (  27 equ)
%            Maximal formula atoms :  256 (  10 avg)
%            Number of connectives :  478 ( 112   ~; 247   |;  99   &)
%                                         (   6 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   77 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  101 (  42   >;  59   *;   0   +;   0  <<)
%            Number of predicates  :   17 (  15 usr;   1 prp; 0-4 aty)
%            Number of functors    :   32 (  32 usr;   5 con; 0-4 aty)
%            Number of variables   :  122 (   3 sgn;  69   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    subset: ( $i * $i ) > $o ).

tff(decl_23,type,
    member: ( $i * $i ) > $o ).

tff(decl_24,type,
    equal_set: ( $i * $i ) > $o ).

tff(decl_25,type,
    power_set: $i > $i ).

tff(decl_26,type,
    intersection: ( $i * $i ) > $i ).

tff(decl_27,type,
    union: ( $i * $i ) > $i ).

tff(decl_28,type,
    empty_set: $i ).

tff(decl_29,type,
    difference: ( $i * $i ) > $i ).

tff(decl_30,type,
    singleton: $i > $i ).

tff(decl_31,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_32,type,
    sum: $i > $i ).

tff(decl_33,type,
    product: $i > $i ).

tff(decl_34,type,
    order: ( $i * $i ) > $o ).

tff(decl_35,type,
    apply: ( $i * $i * $i ) > $o ).

tff(decl_36,type,
    total_order: ( $i * $i ) > $o ).

tff(decl_37,type,
    upper_bound: ( $i * $i * $i ) > $o ).

tff(decl_38,type,
    lower_bound: ( $i * $i * $i ) > $o ).

tff(decl_39,type,
    greatest: ( $i * $i * $i ) > $o ).

tff(decl_40,type,
    least: ( $i * $i * $i ) > $o ).

tff(decl_41,type,
    max: ( $i * $i * $i ) > $o ).

tff(decl_42,type,
    min: ( $i * $i * $i ) > $o ).

tff(decl_43,type,
    least_upper_bound: ( $i * $i * $i * $i ) > $o ).

tff(decl_44,type,
    greatest_lower_bound: ( $i * $i * $i * $i ) > $o ).

tff(decl_45,type,
    epred1_2: ( $i * $i ) > $o ).

tff(decl_46,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_47,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_48,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_49,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_51,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_52,type,
    esk7_3: ( $i * $i * $i ) > $i ).

tff(decl_53,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_54,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_55,type,
    esk10_3: ( $i * $i * $i ) > $i ).

tff(decl_56,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_57,type,
    esk12_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_58,type,
    esk13_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_59,type,
    esk14_0: $i ).

tff(decl_60,type,
    esk15_0: $i ).

tff(decl_61,type,
    esk16_0: $i ).

tff(decl_62,type,
    esk17_0: $i ).

tff(decl_63,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_64,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_65,type,
    esk20_2: ( $i * $i ) > $i ).

tff(decl_66,type,
    esk21_2: ( $i * $i ) > $i ).

tff(decl_67,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_68,type,
    esk23_2: ( $i * $i ) > $i ).

fof(upper_bound,axiom,
    ! [X6,X4,X8] :
      ( upper_bound(X8,X6,X4)
    <=> ! [X3] :
          ( member(X3,X4)
         => apply(X6,X3,X8) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',upper_bound) ).

fof(least_upper_bound,axiom,
    ! [X1,X3,X6,X4] :
      ( least_upper_bound(X1,X3,X6,X4)
    <=> ( member(X1,X3)
        & upper_bound(X1,X6,X3)
        & ! [X8] :
            ( ( member(X8,X4)
              & upper_bound(X8,X6,X3) )
           => apply(X6,X1,X8) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',least_upper_bound) ).

fof(unordered_pair,axiom,
    ! [X3,X1,X2] :
      ( member(X3,unordered_pair(X1,X2))
    <=> ( X3 = X1
        | X3 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',unordered_pair) ).

fof(thIV7,conjecture,
    ! [X6,X4,X1,X2] :
      ( ( order(X6,X4)
        & member(X1,X4)
        & member(X2,X4)
        & apply(X6,X1,X2) )
     => least_upper_bound(X2,unordered_pair(X1,X2),X6,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV7) ).

fof(order,axiom,
    ! [X6,X4] :
      ( order(X6,X4)
    <=> ( ! [X3] :
            ( member(X3,X4)
           => apply(X6,X3,X3) )
        & ! [X3,X5] :
            ( ( member(X3,X4)
              & member(X5,X4) )
           => ( ( apply(X6,X3,X5)
                & apply(X6,X5,X3) )
             => X3 = X5 ) )
        & ! [X3,X5,X7] :
            ( ( member(X3,X4)
              & member(X5,X4)
              & member(X7,X4) )
           => ( ( apply(X6,X3,X5)
                & apply(X6,X5,X7) )
             => apply(X6,X3,X7) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',order) ).

fof(c_0_5,plain,
    ! [X56,X57,X58,X59,X60,X61,X62] :
      ( ( ~ upper_bound(X58,X56,X57)
        | ~ member(X59,X57)
        | apply(X56,X59,X58) )
      & ( member(esk6_3(X60,X61,X62),X61)
        | upper_bound(X62,X60,X61) )
      & ( ~ apply(X60,esk6_3(X60,X61,X62),X62)
        | upper_bound(X62,X60,X61) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[upper_bound])])])])])]) ).

fof(c_0_6,plain,
    ! [X104,X105,X106,X107,X108,X109,X110,X111,X112] :
      ( ( member(X104,X105)
        | ~ least_upper_bound(X104,X105,X106,X107) )
      & ( upper_bound(X104,X106,X105)
        | ~ least_upper_bound(X104,X105,X106,X107) )
      & ( ~ member(X108,X107)
        | ~ upper_bound(X108,X106,X105)
        | apply(X106,X104,X108)
        | ~ least_upper_bound(X104,X105,X106,X107) )
      & ( member(esk12_4(X109,X110,X111,X112),X112)
        | ~ member(X109,X110)
        | ~ upper_bound(X109,X111,X110)
        | least_upper_bound(X109,X110,X111,X112) )
      & ( upper_bound(esk12_4(X109,X110,X111,X112),X111,X110)
        | ~ member(X109,X110)
        | ~ upper_bound(X109,X111,X110)
        | least_upper_bound(X109,X110,X111,X112) )
      & ( ~ apply(X111,X109,esk12_4(X109,X110,X111,X112))
        | ~ member(X109,X110)
        | ~ upper_bound(X109,X111,X110)
        | least_upper_bound(X109,X110,X111,X112) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[least_upper_bound])])])])])]) ).

fof(c_0_7,plain,
    ! [X31,X32,X33] :
      ( ( ~ member(X31,unordered_pair(X32,X33))
        | X31 = X32
        | X31 = X33 )
      & ( X31 != X32
        | member(X31,unordered_pair(X32,X33)) )
      & ( X31 != X33
        | member(X31,unordered_pair(X32,X33)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair])])]) ).

fof(c_0_8,plain,
    ! [X4,X6] :
      ( epred1_2(X6,X4)
    <=> ( ! [X3] :
            ( member(X3,X4)
           => apply(X6,X3,X3) )
        & ! [X3,X5] :
            ( ( member(X3,X4)
              & member(X5,X4) )
           => ( ( apply(X6,X3,X5)
                & apply(X6,X5,X3) )
             => X3 = X5 ) )
        & ! [X3,X5,X7] :
            ( ( member(X3,X4)
              & member(X5,X4)
              & member(X7,X4) )
           => ( ( apply(X6,X3,X5)
                & apply(X6,X5,X7) )
             => apply(X6,X3,X7) ) ) ) ),
    introduced(definition) ).

fof(c_0_9,negated_conjecture,
    ~ ! [X6,X4,X1,X2] :
        ( ( order(X6,X4)
          & member(X1,X4)
          & member(X2,X4)
          & apply(X6,X1,X2) )
       => least_upper_bound(X2,unordered_pair(X1,X2),X6,X4) ),
    inference(assume_negation,[status(cth)],[thIV7]) ).

cnf(c_0_10,plain,
    ( apply(X2,X4,X1)
    | ~ upper_bound(X1,X2,X3)
    | ~ member(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_11,plain,
    ( upper_bound(esk12_4(X1,X2,X3,X4),X3,X2)
    | least_upper_bound(X1,X2,X3,X4)
    | ~ member(X1,X2)
    | ~ upper_bound(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_12,plain,
    ( X1 = X2
    | X1 = X3
    | ~ member(X1,unordered_pair(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_13,plain,
    ( member(esk6_3(X1,X2,X3),X2)
    | upper_bound(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

fof(c_0_14,axiom,
    ! [X6,X4] :
      ( order(X6,X4)
    <=> epred1_2(X6,X4) ),
    inference(apply_def,[status(thm)],[order,c_0_8]) ).

fof(c_0_15,negated_conjecture,
    ( order(esk14_0,esk15_0)
    & member(esk16_0,esk15_0)
    & member(esk17_0,esk15_0)
    & apply(esk14_0,esk16_0,esk17_0)
    & ~ least_upper_bound(esk17_0,unordered_pair(esk16_0,esk17_0),esk14_0,esk15_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

cnf(c_0_16,plain,
    ( least_upper_bound(X2,X3,X1,X4)
    | ~ apply(X1,X2,esk12_4(X2,X3,X1,X4))
    | ~ member(X2,X3)
    | ~ upper_bound(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_17,plain,
    ( least_upper_bound(X1,X2,X3,X4)
    | apply(X3,X5,esk12_4(X1,X2,X3,X4))
    | ~ upper_bound(X1,X3,X2)
    | ~ member(X5,X2)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_18,plain,
    ( member(X1,unordered_pair(X3,X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_19,plain,
    ( upper_bound(X3,X1,X2)
    | ~ apply(X1,esk6_3(X1,X2,X3),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_20,plain,
    ( esk6_3(X1,unordered_pair(X2,X3),X4) = X3
    | esk6_3(X1,unordered_pair(X2,X3),X4) = X2
    | upper_bound(X4,X1,unordered_pair(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

fof(c_0_21,plain,
    ! [X46,X47] :
      ( ( ~ order(X46,X47)
        | epred1_2(X46,X47) )
      & ( ~ epred1_2(X46,X47)
        | order(X46,X47) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])]) ).

cnf(c_0_22,negated_conjecture,
    ~ least_upper_bound(esk17_0,unordered_pair(esk16_0,esk17_0),esk14_0,esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_23,plain,
    ( least_upper_bound(X1,X2,X3,X4)
    | ~ upper_bound(X1,X3,X2)
    | ~ member(X1,X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_24,plain,
    member(X1,unordered_pair(X2,X1)),
    inference(er,[status(thm)],[c_0_18]) ).

cnf(c_0_25,plain,
    ( esk6_3(X1,unordered_pair(X2,X3),X4) = X3
    | upper_bound(X4,X1,unordered_pair(X2,X3))
    | ~ apply(X1,X2,X4) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

fof(c_0_26,plain,
    ! [X128,X129,X130,X131,X132,X133,X134,X135,X136,X137] :
      ( ( ~ member(X130,X128)
        | apply(X129,X130,X130)
        | ~ epred1_2(X129,X128) )
      & ( ~ member(X131,X128)
        | ~ member(X132,X128)
        | ~ apply(X129,X131,X132)
        | ~ apply(X129,X132,X131)
        | X131 = X132
        | ~ epred1_2(X129,X128) )
      & ( ~ member(X133,X128)
        | ~ member(X134,X128)
        | ~ member(X135,X128)
        | ~ apply(X129,X133,X134)
        | ~ apply(X129,X134,X135)
        | apply(X129,X133,X135)
        | ~ epred1_2(X129,X128) )
      & ( member(esk21_2(X136,X137),X136)
        | member(esk19_2(X136,X137),X136)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk22_2(X136,X137),X136)
        | member(esk19_2(X136,X137),X136)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk23_2(X136,X137),X136)
        | member(esk19_2(X136,X137),X136)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
        | member(esk19_2(X136,X137),X136)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
        | member(esk19_2(X136,X137),X136)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
        | member(esk19_2(X136,X137),X136)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk21_2(X136,X137),X136)
        | member(esk20_2(X136,X137),X136)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk22_2(X136,X137),X136)
        | member(esk20_2(X136,X137),X136)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk23_2(X136,X137),X136)
        | member(esk20_2(X136,X137),X136)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
        | member(esk20_2(X136,X137),X136)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
        | member(esk20_2(X136,X137),X136)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
        | member(esk20_2(X136,X137),X136)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk21_2(X136,X137),X136)
        | apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk22_2(X136,X137),X136)
        | apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk23_2(X136,X137),X136)
        | apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
        | apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
        | apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
        | apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk21_2(X136,X137),X136)
        | apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk22_2(X136,X137),X136)
        | apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk23_2(X136,X137),X136)
        | apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
        | apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
        | apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
        | apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk21_2(X136,X137),X136)
        | esk19_2(X136,X137) != esk20_2(X136,X137)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk22_2(X136,X137),X136)
        | esk19_2(X136,X137) != esk20_2(X136,X137)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk23_2(X136,X137),X136)
        | esk19_2(X136,X137) != esk20_2(X136,X137)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
        | esk19_2(X136,X137) != esk20_2(X136,X137)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
        | esk19_2(X136,X137) != esk20_2(X136,X137)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
        | esk19_2(X136,X137) != esk20_2(X136,X137)
        | member(esk18_2(X136,X137),X136)
        | epred1_2(X137,X136) )
      & ( member(esk21_2(X136,X137),X136)
        | member(esk19_2(X136,X137),X136)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk22_2(X136,X137),X136)
        | member(esk19_2(X136,X137),X136)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk23_2(X136,X137),X136)
        | member(esk19_2(X136,X137),X136)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
        | member(esk19_2(X136,X137),X136)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
        | member(esk19_2(X136,X137),X136)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
        | member(esk19_2(X136,X137),X136)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk21_2(X136,X137),X136)
        | member(esk20_2(X136,X137),X136)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk22_2(X136,X137),X136)
        | member(esk20_2(X136,X137),X136)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk23_2(X136,X137),X136)
        | member(esk20_2(X136,X137),X136)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
        | member(esk20_2(X136,X137),X136)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
        | member(esk20_2(X136,X137),X136)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
        | member(esk20_2(X136,X137),X136)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk21_2(X136,X137),X136)
        | apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk22_2(X136,X137),X136)
        | apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk23_2(X136,X137),X136)
        | apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
        | apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
        | apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
        | apply(X137,esk19_2(X136,X137),esk20_2(X136,X137))
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk21_2(X136,X137),X136)
        | apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk22_2(X136,X137),X136)
        | apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk23_2(X136,X137),X136)
        | apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
        | apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
        | apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
        | apply(X137,esk20_2(X136,X137),esk19_2(X136,X137))
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk21_2(X136,X137),X136)
        | esk19_2(X136,X137) != esk20_2(X136,X137)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk22_2(X136,X137),X136)
        | esk19_2(X136,X137) != esk20_2(X136,X137)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( member(esk23_2(X136,X137),X136)
        | esk19_2(X136,X137) != esk20_2(X136,X137)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( apply(X137,esk21_2(X136,X137),esk22_2(X136,X137))
        | esk19_2(X136,X137) != esk20_2(X136,X137)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( apply(X137,esk22_2(X136,X137),esk23_2(X136,X137))
        | esk19_2(X136,X137) != esk20_2(X136,X137)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) )
      & ( ~ apply(X137,esk21_2(X136,X137),esk23_2(X136,X137))
        | esk19_2(X136,X137) != esk20_2(X136,X137)
        | ~ apply(X137,esk18_2(X136,X137),esk18_2(X136,X137))
        | epred1_2(X137,X136) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])])])]) ).

cnf(c_0_27,plain,
    ( epred1_2(X1,X2)
    | ~ order(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,negated_conjecture,
    order(esk14_0,esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_29,negated_conjecture,
    ~ upper_bound(esk17_0,esk14_0,unordered_pair(esk16_0,esk17_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).

cnf(c_0_30,plain,
    ( upper_bound(X1,X2,unordered_pair(X3,X4))
    | ~ apply(X2,X4,X1)
    | ~ apply(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_25]) ).

cnf(c_0_31,negated_conjecture,
    apply(esk14_0,esk16_0,esk17_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_32,plain,
    ( apply(X3,X1,X1)
    | ~ member(X1,X2)
    | ~ epred1_2(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_33,negated_conjecture,
    epred1_2(esk14_0,esk15_0),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_34,negated_conjecture,
    ~ apply(esk14_0,esk17_0,esk17_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).

cnf(c_0_35,plain,
    ( apply(esk14_0,X1,X1)
    | ~ member(X1,esk15_0) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_36,negated_conjecture,
    member(esk17_0,esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_37,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET795+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n026.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sat Aug 26 11:12:03 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.59  start to proof: theBenchmark
% 10.32/10.50  % Version  : CSE_E---1.5
% 10.32/10.50  % Problem  : theBenchmark.p
% 10.32/10.50  % Proof found
% 10.32/10.50  % SZS status Theorem for theBenchmark.p
% 10.32/10.50  % SZS output start Proof
% See solution above
% 10.32/10.51  % Total time : 9.902000 s
% 10.32/10.51  % SZS output end Proof
% 10.32/10.51  % Total time : 9.907000 s
%------------------------------------------------------------------------------