TSTP Solution File: SET812+4 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET812+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 : n029.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 14:35:39 EDT 2023

% Result   : Theorem 12.99s 13.16s
% Output   : CNFRefutation 12.99s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :  127
% Syntax   : Number of formulae    :  212 (  20 unt; 115 typ;   0 def)
%            Number of atoms       :  250 (   6 equ)
%            Maximal formula atoms :   15 (   2 avg)
%            Number of connectives :  262 ( 109   ~; 108   |;  29   &)
%                                         (  11 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   60 (  31   >;  29   *;   0   +;   0  <<)
%            Number of predicates  :   90 (  88 usr;  81 prp; 0-3 aty)
%            Number of functors    :   27 (  27 usr;   4 con; 0-3 aty)
%            Number of variables   :  218 (  30 sgn;  68   !;   1   ?;   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,
    on: $i ).

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

tff(decl_36,type,
    member_predicate: $i ).

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

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

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

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

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

tff(decl_42,type,
    suc: $i > $i ).

tff(decl_43,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_44,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_45,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_46,type,
    esk4_1: $i > $i ).

tff(decl_47,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_48,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_49,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_50,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_51,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_52,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_53,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_54,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_55,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_56,type,
    esk14_0: $i ).

tff(decl_57,type,
    epred1_0: $o ).

tff(decl_58,type,
    epred2_0: $o ).

tff(decl_59,type,
    epred3_0: $o ).

tff(decl_60,type,
    epred4_0: $o ).

tff(decl_61,type,
    epred5_0: $o ).

tff(decl_62,type,
    epred6_0: $o ).

tff(decl_63,type,
    epred7_0: $o ).

tff(decl_64,type,
    epred8_0: $o ).

tff(decl_65,type,
    epred9_0: $o ).

tff(decl_66,type,
    epred10_0: $o ).

tff(decl_67,type,
    epred11_0: $o ).

tff(decl_68,type,
    epred12_0: $o ).

tff(decl_69,type,
    epred13_0: $o ).

tff(decl_70,type,
    epred14_0: $o ).

tff(decl_71,type,
    epred15_0: $o ).

tff(decl_72,type,
    epred16_0: $o ).

tff(decl_73,type,
    epred17_0: $o ).

tff(decl_74,type,
    epred18_0: $o ).

tff(decl_75,type,
    epred19_0: $o ).

tff(decl_76,type,
    epred20_0: $o ).

tff(decl_77,type,
    epred21_0: $o ).

tff(decl_78,type,
    epred22_0: $o ).

tff(decl_79,type,
    epred23_0: $o ).

tff(decl_80,type,
    epred24_0: $o ).

tff(decl_81,type,
    epred25_0: $o ).

tff(decl_82,type,
    epred26_0: $o ).

tff(decl_83,type,
    epred27_0: $o ).

tff(decl_84,type,
    epred28_0: $o ).

tff(decl_85,type,
    epred29_0: $o ).

tff(decl_86,type,
    epred30_0: $o ).

tff(decl_87,type,
    epred31_0: $o ).

tff(decl_88,type,
    epred32_0: $o ).

tff(decl_89,type,
    epred33_0: $o ).

tff(decl_90,type,
    epred34_0: $o ).

tff(decl_91,type,
    epred35_0: $o ).

tff(decl_92,type,
    epred36_0: $o ).

tff(decl_93,type,
    epred37_0: $o ).

tff(decl_94,type,
    epred38_0: $o ).

tff(decl_95,type,
    epred39_0: $o ).

tff(decl_96,type,
    epred40_0: $o ).

tff(decl_97,type,
    epred41_0: $o ).

tff(decl_98,type,
    epred42_0: $o ).

tff(decl_99,type,
    epred43_0: $o ).

tff(decl_100,type,
    epred44_0: $o ).

tff(decl_101,type,
    epred45_0: $o ).

tff(decl_102,type,
    epred46_0: $o ).

tff(decl_103,type,
    epred47_0: $o ).

tff(decl_104,type,
    epred48_0: $o ).

tff(decl_105,type,
    epred49_0: $o ).

tff(decl_106,type,
    epred50_0: $o ).

tff(decl_107,type,
    epred51_0: $o ).

tff(decl_108,type,
    epred52_0: $o ).

tff(decl_109,type,
    epred53_0: $o ).

tff(decl_110,type,
    epred54_0: $o ).

tff(decl_111,type,
    epred55_0: $o ).

tff(decl_112,type,
    epred56_0: $o ).

tff(decl_113,type,
    epred57_0: $o ).

tff(decl_114,type,
    epred58_0: $o ).

tff(decl_115,type,
    epred59_0: $o ).

tff(decl_116,type,
    epred60_0: $o ).

tff(decl_117,type,
    epred61_0: $o ).

tff(decl_118,type,
    epred62_0: $o ).

tff(decl_119,type,
    epred63_0: $o ).

tff(decl_120,type,
    epred64_0: $o ).

tff(decl_121,type,
    epred65_0: $o ).

tff(decl_122,type,
    epred66_0: $o ).

tff(decl_123,type,
    epred67_0: $o ).

tff(decl_124,type,
    epred68_0: $o ).

tff(decl_125,type,
    epred69_0: $o ).

tff(decl_126,type,
    epred70_0: $o ).

tff(decl_127,type,
    epred71_0: $o ).

tff(decl_128,type,
    epred72_0: $o ).

tff(decl_129,type,
    epred73_0: $o ).

tff(decl_130,type,
    epred74_0: $o ).

tff(decl_131,type,
    epred75_0: $o ).

tff(decl_132,type,
    epred76_0: $o ).

tff(decl_133,type,
    epred77_0: $o ).

tff(decl_134,type,
    epred78_0: $o ).

tff(decl_135,type,
    epred79_0: $o ).

tff(decl_136,type,
    epred80_0: $o ).

fof(difference,axiom,
    ! [X2,X1,X4] :
      ( member(X2,difference(X4,X1))
    <=> ( member(X2,X4)
        & ~ member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).

fof(empty_set,axiom,
    ! [X3] : ~ member(X3,empty_set),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).

fof(initial_segment,axiom,
    ! [X3,X6,X1,X5] :
      ( member(X5,initial_segment(X3,X6,X1))
    <=> ( member(X5,X1)
        & apply(X6,X5,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',initial_segment) ).

fof(sum,axiom,
    ! [X3,X1] :
      ( member(X3,sum(X1))
    <=> ? [X5] :
          ( member(X5,X1)
          & member(X3,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',sum) ).

fof(product,axiom,
    ! [X3,X1] :
      ( member(X3,product(X1))
    <=> ! [X5] :
          ( member(X5,X1)
         => member(X3,X5) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',product) ).

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

fof(thV10,conjecture,
    ! [X1] :
      ( member(X1,on)
     => equal_set(X1,intersection(X1,power_set(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV10) ).

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

fof(ordinal_number,axiom,
    ! [X1] :
      ( member(X1,on)
    <=> ( set(X1)
        & strict_well_order(member_predicate,X1)
        & ! [X3] :
            ( member(X3,X1)
           => subset(X3,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',ordinal_number) ).

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

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

fof(equal_set,axiom,
    ! [X1,X2] :
      ( equal_set(X1,X2)
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).

fof(c_0_12,plain,
    ! [X2,X1,X4] :
      ( member(X2,difference(X4,X1))
    <=> ( member(X2,X4)
        & ~ member(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[difference]) ).

fof(c_0_13,plain,
    ! [X3] : ~ member(X3,empty_set),
    inference(fof_simplification,[status(thm)],[empty_set]) ).

fof(c_0_14,plain,
    ! [X86,X87,X88,X89] :
      ( ( member(X89,X88)
        | ~ member(X89,initial_segment(X86,X87,X88)) )
      & ( apply(X87,X89,X86)
        | ~ member(X89,initial_segment(X86,X87,X88)) )
      & ( ~ member(X89,X88)
        | ~ apply(X87,X89,X86)
        | member(X89,initial_segment(X86,X87,X88)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[initial_segment])])]) ).

fof(c_0_15,plain,
    ! [X34,X35,X37,X38,X39] :
      ( ( member(esk2_2(X34,X35),X35)
        | ~ member(X34,sum(X35)) )
      & ( member(X34,esk2_2(X34,X35))
        | ~ member(X34,sum(X35)) )
      & ( ~ member(X39,X38)
        | ~ member(X37,X39)
        | member(X37,sum(X38)) ) ),
    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)],[sum])])])])])]) ).

fof(c_0_16,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ( ~ member(X40,product(X41))
        | ~ member(X42,X41)
        | member(X40,X42) )
      & ( member(esk3_2(X43,X44),X44)
        | member(X43,product(X44)) )
      & ( ~ member(X43,esk3_2(X43,X44))
        | member(X43,product(X44)) ) ),
    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)],[product])])])])])]) ).

fof(c_0_17,plain,
    ! [X26,X27,X28] :
      ( ( member(X26,X28)
        | ~ member(X26,difference(X28,X27)) )
      & ( ~ member(X26,X27)
        | ~ member(X26,difference(X28,X27)) )
      & ( ~ member(X26,X28)
        | member(X26,X27)
        | member(X26,difference(X28,X27)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).

fof(c_0_18,plain,
    ! [X9,X10,X11,X12,X13] :
      ( ( ~ subset(X9,X10)
        | ~ member(X11,X9)
        | member(X11,X10) )
      & ( member(esk1_2(X12,X13),X12)
        | subset(X12,X13) )
      & ( ~ member(esk1_2(X12,X13),X13)
        | subset(X12,X13) ) ),
    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)],[subset])])])])])]) ).

fof(c_0_19,plain,
    ! [X25] : ~ member(X25,empty_set),
    inference(variable_rename,[status(thm)],[c_0_13]) ).

cnf(c_0_20,plain,
    ( member(X1,X2)
    | ~ member(X1,initial_segment(X3,X4,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21,plain,
    ( member(esk2_2(X1,X2),X2)
    | ~ member(X1,sum(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_22,negated_conjecture,
    ~ ! [X1] :
        ( member(X1,on)
       => equal_set(X1,intersection(X1,power_set(X1))) ),
    inference(assume_negation,[status(cth)],[thV10]) ).

cnf(c_0_23,plain,
    ( member(esk3_2(X1,X2),X2)
    | member(X1,product(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,plain,
    ( ~ member(X1,X2)
    | ~ member(X1,difference(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_26,plain,
    ( member(X1,X2)
    | ~ member(X1,difference(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_27,plain,
    ~ member(X1,empty_set),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_28,plain,
    ( member(esk2_2(X1,initial_segment(X2,X3,X4)),X4)
    | ~ member(X1,sum(initial_segment(X2,X3,X4))) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_29,plain,
    ( member(X3,sum(X2))
    | ~ member(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_30,negated_conjecture,
    ( member(esk14_0,on)
    & ~ equal_set(esk14_0,intersection(esk14_0,power_set(esk14_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).

cnf(c_0_31,plain,
    ( member(esk3_2(X1,initial_segment(X2,X3,X4)),X4)
    | member(X1,product(initial_segment(X2,X3,X4))) ),
    inference(spm,[status(thm)],[c_0_20,c_0_23]) ).

cnf(c_0_32,plain,
    ( subset(difference(X1,X2),X3)
    | ~ member(esk1_2(difference(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_33,plain,
    ( member(esk1_2(difference(X1,X2),X3),X1)
    | subset(difference(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_26,c_0_25]) ).

fof(c_0_34,plain,
    ! [X17,X18] :
      ( ( ~ member(X17,power_set(X18))
        | subset(X17,X18) )
      & ( ~ subset(X17,X18)
        | member(X17,power_set(X18)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).

cnf(c_0_35,plain,
    ~ member(X1,sum(initial_segment(X2,X3,empty_set))),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_36,plain,
    ( member(esk2_2(X1,X2),sum(X3))
    | ~ member(X1,sum(X2))
    | ~ member(X2,X3) ),
    inference(spm,[status(thm)],[c_0_29,c_0_21]) ).

cnf(c_0_37,negated_conjecture,
    member(esk14_0,on),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_38,plain,
    ( member(X1,X3)
    | ~ member(X1,product(X2))
    | ~ member(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_39,plain,
    member(X1,product(initial_segment(X2,X3,empty_set))),
    inference(spm,[status(thm)],[c_0_27,c_0_31]) ).

cnf(c_0_40,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_41,plain,
    subset(difference(X1,X1),X2),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_42,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_43,plain,
    ( member(X1,power_set(X2))
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

fof(c_0_44,plain,
    ! [X46,X47,X48] :
      ( ( set(X46)
        | ~ member(X46,on) )
      & ( strict_well_order(member_predicate,X46)
        | ~ member(X46,on) )
      & ( ~ member(X47,X46)
        | subset(X47,X46)
        | ~ member(X46,on) )
      & ( member(esk4_1(X48),X48)
        | ~ set(X48)
        | ~ strict_well_order(member_predicate,X48)
        | member(X48,on) )
      & ( ~ subset(esk4_1(X48),X48)
        | ~ set(X48)
        | ~ strict_well_order(member_predicate,X48)
        | member(X48,on) ) ),
    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)],[ordinal_number])])])])])]) ).

cnf(c_0_45,plain,
    ( ~ member(X1,initial_segment(X2,X3,empty_set))
    | ~ member(X4,sum(X1)) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_46,negated_conjecture,
    ( member(esk14_0,sum(X1))
    | ~ member(on,X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_37]) ).

cnf(c_0_47,plain,
    ( member(X1,X2)
    | ~ member(X2,initial_segment(X3,X4,empty_set)) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_48,plain,
    ( member(X1,X2)
    | ~ member(X1,difference(X3,X3)) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_49,plain,
    ( subset(X1,power_set(X2))
    | ~ subset(esk1_2(X1,power_set(X2)),X2) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_50,plain,
    ( subset(X1,X2)
    | ~ member(X1,X2)
    | ~ member(X2,on) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_51,negated_conjecture,
    ~ member(X1,initial_segment(X2,X3,empty_set)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).

cnf(c_0_52,plain,
    ( member(esk2_2(X1,difference(X2,X2)),X3)
    | ~ member(X1,sum(difference(X2,X2))) ),
    inference(spm,[status(thm)],[c_0_48,c_0_21]) ).

cnf(c_0_53,plain,
    ( member(X1,product(difference(X2,X3)))
    | ~ member(esk3_2(X1,difference(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_24,c_0_23]) ).

cnf(c_0_54,plain,
    ( member(esk3_2(X1,difference(X2,X3)),X2)
    | member(X1,product(difference(X2,X3))) ),
    inference(spm,[status(thm)],[c_0_26,c_0_23]) ).

cnf(c_0_55,plain,
    ( member(X1,X3)
    | member(X1,difference(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_56,plain,
    ( subset(X1,power_set(X2))
    | ~ member(esk1_2(X1,power_set(X2)),X2)
    | ~ member(X2,on) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_57,negated_conjecture,
    ~ member(X1,sum(difference(X2,X2))),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_58,plain,
    member(X1,product(difference(X2,X2))),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_59,plain,
    ( member(X1,difference(power_set(X2),X3))
    | member(X1,X3)
    | ~ subset(X1,X2) ),
    inference(spm,[status(thm)],[c_0_55,c_0_43]) ).

cnf(c_0_60,plain,
    ( subset(X1,power_set(X1))
    | ~ member(X1,on) ),
    inference(spm,[status(thm)],[c_0_56,c_0_25]) ).

cnf(c_0_61,negated_conjecture,
    ( ~ member(X1,difference(X2,X2))
    | ~ member(X3,sum(X1)) ),
    inference(spm,[status(thm)],[c_0_57,c_0_36]) ).

cnf(c_0_62,plain,
    ( member(X1,X2)
    | ~ member(X2,difference(X3,X3)) ),
    inference(spm,[status(thm)],[c_0_38,c_0_58]) ).

cnf(c_0_63,plain,
    ( member(X1,difference(power_set(power_set(X1)),X2))
    | member(X1,X2)
    | ~ member(X1,on) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_64,negated_conjecture,
    ~ member(X1,difference(X2,X2)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_46]),c_0_62]) ).

cnf(c_0_65,negated_conjecture,
    ( member(esk14_0,difference(power_set(power_set(esk14_0)),X1))
    | member(esk14_0,X1) ),
    inference(spm,[status(thm)],[c_0_63,c_0_37]) ).

fof(c_0_66,plain,
    ! [X29,X30] :
      ( ( ~ member(X29,singleton(X30))
        | X29 = X30 )
      & ( X29 != X30
        | member(X29,singleton(X30)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).

cnf(c_0_67,plain,
    ( subset(X1,X2)
    | ~ member(X1,power_set(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_68,negated_conjecture,
    member(esk14_0,power_set(power_set(esk14_0))),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_69,plain,
    ( X1 = X2
    | ~ member(X1,singleton(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

cnf(c_0_70,negated_conjecture,
    subset(esk14_0,power_set(esk14_0)),
    inference(spm,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_71,plain,
    ( member(X1,esk2_2(X1,X2))
    | ~ member(X1,sum(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_72,plain,
    ( esk2_2(X1,singleton(X2)) = X2
    | ~ member(X1,sum(singleton(X2))) ),
    inference(spm,[status(thm)],[c_0_69,c_0_21]) ).

cnf(c_0_73,negated_conjecture,
    ( member(X1,power_set(esk14_0))
    | ~ member(X1,esk14_0) ),
    inference(spm,[status(thm)],[c_0_40,c_0_70]) ).

cnf(c_0_74,plain,
    ( member(X1,X2)
    | ~ member(X1,sum(singleton(X2))) ),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

fof(c_0_75,plain,
    ! [X19,X20,X21] :
      ( ( member(X19,X20)
        | ~ member(X19,intersection(X20,X21)) )
      & ( member(X19,X21)
        | ~ member(X19,intersection(X20,X21)) )
      & ( ~ member(X19,X20)
        | ~ member(X19,X21)
        | member(X19,intersection(X20,X21)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).

cnf(c_0_76,negated_conjecture,
    ( subset(X1,power_set(esk14_0))
    | ~ member(esk1_2(X1,power_set(esk14_0)),esk14_0) ),
    inference(spm,[status(thm)],[c_0_42,c_0_73]) ).

cnf(c_0_77,plain,
    ( member(esk1_2(sum(singleton(X1)),X2),X1)
    | subset(sum(singleton(X1)),X2) ),
    inference(spm,[status(thm)],[c_0_74,c_0_25]) ).

cnf(c_0_78,plain,
    ( member(X1,singleton(X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_66]) ).

fof(c_0_79,plain,
    ! [X15,X16] :
      ( ( subset(X15,X16)
        | ~ equal_set(X15,X16) )
      & ( subset(X16,X15)
        | ~ equal_set(X15,X16) )
      & ( ~ subset(X15,X16)
        | ~ subset(X16,X15)
        | equal_set(X15,X16) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).

cnf(c_0_80,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_75]) ).

cnf(c_0_81,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_75]) ).

cnf(c_0_82,negated_conjecture,
    subset(sum(singleton(esk14_0)),power_set(esk14_0)),
    inference(spm,[status(thm)],[c_0_76,c_0_77]) ).

cnf(c_0_83,plain,
    ( member(esk1_2(X1,X2),sum(X3))
    | subset(X1,X2)
    | ~ member(X1,X3) ),
    inference(spm,[status(thm)],[c_0_29,c_0_25]) ).

cnf(c_0_84,plain,
    member(X1,singleton(X1)),
    inference(er,[status(thm)],[c_0_78]) ).

cnf(c_0_85,negated_conjecture,
    ~ equal_set(esk14_0,intersection(esk14_0,power_set(esk14_0))),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_86,plain,
    ( equal_set(X1,X2)
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_79]) ).

cnf(c_0_87,plain,
    ( member(esk1_2(intersection(X1,X2),X3),X1)
    | subset(intersection(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_80,c_0_25]) ).

cnf(c_0_88,plain,
    ( subset(X1,intersection(X2,X3))
    | ~ member(esk1_2(X1,intersection(X2,X3)),X3)
    | ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_42,c_0_81]) ).

cnf(c_0_89,negated_conjecture,
    ( member(X1,power_set(esk14_0))
    | ~ member(X1,sum(singleton(esk14_0))) ),
    inference(spm,[status(thm)],[c_0_40,c_0_82]) ).

cnf(c_0_90,plain,
    ( member(esk1_2(X1,X2),sum(singleton(X1)))
    | subset(X1,X2) ),
    inference(spm,[status(thm)],[c_0_83,c_0_84]) ).

cnf(c_0_91,negated_conjecture,
    ( ~ subset(intersection(esk14_0,power_set(esk14_0)),esk14_0)
    | ~ subset(esk14_0,intersection(esk14_0,power_set(esk14_0))) ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_92,plain,
    subset(intersection(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_42,c_0_87]) ).

cnf(c_0_93,plain,
    ( subset(X1,intersection(X1,X2))
    | ~ member(esk1_2(X1,intersection(X1,X2)),X2) ),
    inference(spm,[status(thm)],[c_0_88,c_0_25]) ).

cnf(c_0_94,negated_conjecture,
    ( member(esk1_2(esk14_0,X1),power_set(esk14_0))
    | subset(esk14_0,X1) ),
    inference(spm,[status(thm)],[c_0_89,c_0_90]) ).

cnf(c_0_95,negated_conjecture,
    ~ subset(esk14_0,intersection(esk14_0,power_set(esk14_0))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).

cnf(c_0_96,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET812+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n029.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 11:34:10 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.59  start to proof: theBenchmark
% 12.99/13.16  % Version  : CSE_E---1.5
% 12.99/13.16  % Problem  : theBenchmark.p
% 12.99/13.16  % Proof found
% 12.99/13.16  % SZS status Theorem for theBenchmark.p
% 12.99/13.16  % SZS output start Proof
% See solution above
% 12.99/13.18  % Total time : 12.568000 s
% 12.99/13.18  % SZS output end Proof
% 12.99/13.18  % Total time : 12.572000 s
%------------------------------------------------------------------------------