TSTP Solution File: SEU176+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU176+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n031.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 16:23:05 EDT 2023

% Result   : Theorem 36.77s 37.00s
% Output   : CNFRefutation 36.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   72
% Syntax   : Number of formulae    :  124 (  20 unt;  58 typ;   0 def)
%            Number of atoms       :  130 (  56 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  119 (  55   ~;  44   |;   5   &)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  109 (  53   >;  56   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   51 (  51 usr;   5 con; 0-4 aty)
%            Number of variables   :   83 (   0 sgn;  50   !;   1   ?;   0   :)

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

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

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

tff(decl_25,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_26,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

tff(decl_29,type,
    set_meet: $i > $i ).

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

tff(decl_31,type,
    powerset: $i > $i ).

tff(decl_32,type,
    empty: $i > $o ).

tff(decl_33,type,
    element: ( $i * $i ) > $o ).

tff(decl_34,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

tff(decl_36,type,
    cast_to_subset: $i > $i ).

tff(decl_37,type,
    union: $i > $i ).

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

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

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

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

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

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

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

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

tff(decl_46,type,
    esk1_3: ( $i * $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_1: $i > $i ).

tff(decl_51,type,
    esk6_2: ( $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_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_55,type,
    esk10_4: ( $i * $i * $i * $i ) > $i ).

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

tff(decl_57,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_58,type,
    esk13_3: ( $i * $i * $i ) > $i ).

tff(decl_59,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_60,type,
    esk15_3: ( $i * $i * $i ) > $i ).

tff(decl_61,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_62,type,
    esk17_2: ( $i * $i ) > $i ).

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

tff(decl_64,type,
    esk19_3: ( $i * $i * $i ) > $i ).

tff(decl_65,type,
    esk20_3: ( $i * $i * $i ) > $i ).

tff(decl_66,type,
    esk21_1: $i > $i ).

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

tff(decl_68,type,
    esk23_1: $i > $i ).

tff(decl_69,type,
    esk24_0: $i ).

tff(decl_70,type,
    esk25_1: $i > $i ).

tff(decl_71,type,
    esk26_0: $i ).

tff(decl_72,type,
    esk27_1: $i > $i ).

tff(decl_73,type,
    esk28_2: ( $i * $i ) > $i ).

tff(decl_74,type,
    esk29_2: ( $i * $i ) > $i ).

tff(decl_75,type,
    esk30_0: $i ).

tff(decl_76,type,
    esk31_0: $i ).

tff(decl_77,type,
    esk32_2: ( $i * $i ) > $i ).

tff(decl_78,type,
    esk33_1: $i > $i ).

tff(decl_79,type,
    esk34_2: ( $i * $i ) > $i ).

fof(t47_setfam_1,lemma,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => ( X2 != empty_set
       => subset_difference(X1,cast_to_subset(X1),union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).

fof(d4_subset_1,axiom,
    ! [X1] : cast_to_subset(X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).

fof(t6_boole,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

fof(rc1_xboole_0,axiom,
    ? [X1] : empty(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(t48_setfam_1,conjecture,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => ( X2 != empty_set
       => union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).

fof(t46_setfam_1,lemma,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => ~ ( X2 != empty_set
          & complements_of_subsets(X1,X2) = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).

fof(dt_k7_setfam_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => element(complements_of_subsets(X1,X2),powerset(powerset(X1))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).

fof(dt_k2_subset_1,axiom,
    ! [X1] : element(cast_to_subset(X1),powerset(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).

fof(redefinition_k6_subset_1,axiom,
    ! [X1,X2,X3] :
      ( ( element(X2,powerset(X1))
        & element(X3,powerset(X1)) )
     => subset_difference(X1,X2,X3) = set_difference(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).

fof(involutiveness_k7_setfam_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => complements_of_subsets(X1,complements_of_subsets(X1,X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).

fof(dt_k6_subset_1,axiom,
    ! [X1,X2,X3] :
      ( ( element(X2,powerset(X1))
        & element(X3,powerset(X1)) )
     => element(subset_difference(X1,X2,X3),powerset(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).

fof(involutiveness_k3_subset_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => subset_complement(X1,subset_complement(X1,X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).

fof(d5_subset_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => subset_complement(X1,X2) = set_difference(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).

fof(dt_k5_setfam_1,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(powerset(X1)))
     => element(union_of_subsets(X1,X2),powerset(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).

fof(c_0_14,lemma,
    ! [X295,X296] :
      ( ~ element(X296,powerset(powerset(X295)))
      | X296 = empty_set
      | subset_difference(X295,cast_to_subset(X295),union_of_subsets(X295,X296)) = meet_of_subsets(X295,complements_of_subsets(X295,X296)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_setfam_1])]) ).

fof(c_0_15,plain,
    ! [X102] : cast_to_subset(X102) = X102,
    inference(variable_rename,[status(thm)],[d4_subset_1]) ).

fof(c_0_16,plain,
    ! [X328] :
      ( ~ empty(X328)
      | X328 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).

fof(c_0_17,plain,
    empty(esk24_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).

fof(c_0_18,negated_conjecture,
    ~ ! [X1,X2] :
        ( element(X2,powerset(powerset(X1)))
       => ( X2 != empty_set
         => union_of_subsets(X1,complements_of_subsets(X1,X2)) = subset_difference(X1,cast_to_subset(X1),meet_of_subsets(X1,X2)) ) ),
    inference(assume_negation,[status(cth)],[t48_setfam_1]) ).

cnf(c_0_19,lemma,
    ( X1 = empty_set
    | subset_difference(X2,cast_to_subset(X2),union_of_subsets(X2,X1)) = meet_of_subsets(X2,complements_of_subsets(X2,X1))
    | ~ element(X1,powerset(powerset(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,plain,
    cast_to_subset(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,plain,
    empty(esk24_0),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_23,lemma,
    ! [X291,X292] :
      ( ~ element(X292,powerset(powerset(X291)))
      | X292 = empty_set
      | complements_of_subsets(X291,X292) != empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t46_setfam_1])]) ).

fof(c_0_24,negated_conjecture,
    ( element(esk31_0,powerset(powerset(esk30_0)))
    & esk31_0 != empty_set
    & union_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0)) != subset_difference(esk30_0,cast_to_subset(esk30_0),meet_of_subsets(esk30_0,esk31_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).

cnf(c_0_25,lemma,
    ( X1 = empty_set
    | subset_difference(X2,X2,union_of_subsets(X2,X1)) = meet_of_subsets(X2,complements_of_subsets(X2,X1))
    | ~ element(X1,powerset(powerset(X2))) ),
    inference(rw,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_26,plain,
    empty_set = esk24_0,
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

fof(c_0_27,plain,
    ! [X146,X147] :
      ( ~ element(X147,powerset(powerset(X146)))
      | element(complements_of_subsets(X146,X147),powerset(powerset(X146))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_setfam_1])]) ).

cnf(c_0_28,lemma,
    ( X1 = empty_set
    | ~ element(X1,powerset(powerset(X2)))
    | complements_of_subsets(X2,X1) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,negated_conjecture,
    element(esk31_0,powerset(powerset(esk30_0))),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_30,negated_conjecture,
    esk31_0 != empty_set,
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,lemma,
    ( subset_difference(X1,X1,union_of_subsets(X1,X2)) = meet_of_subsets(X1,complements_of_subsets(X1,X2))
    | X2 = esk24_0
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_32,plain,
    ( element(complements_of_subsets(X2,X1),powerset(powerset(X2)))
    | ~ element(X1,powerset(powerset(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_33,negated_conjecture,
    complements_of_subsets(esk30_0,esk31_0) != empty_set,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).

fof(c_0_34,plain,
    ! [X136] : element(cast_to_subset(X136),powerset(X136)),
    inference(variable_rename,[status(thm)],[dt_k2_subset_1]) ).

fof(c_0_35,plain,
    ! [X202,X203,X204] :
      ( ~ element(X203,powerset(X202))
      | ~ element(X204,powerset(X202))
      | subset_difference(X202,X203,X204) = set_difference(X203,X204) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k6_subset_1])]) ).

cnf(c_0_36,lemma,
    ( subset_difference(X1,X1,union_of_subsets(X1,complements_of_subsets(X1,X2))) = meet_of_subsets(X1,complements_of_subsets(X1,complements_of_subsets(X1,X2)))
    | complements_of_subsets(X1,X2) = esk24_0
    | ~ element(X2,powerset(powerset(X1))) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_37,negated_conjecture,
    complements_of_subsets(esk30_0,esk31_0) != esk24_0,
    inference(rw,[status(thm)],[c_0_33,c_0_26]) ).

cnf(c_0_38,plain,
    element(cast_to_subset(X1),powerset(X1)),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_39,plain,
    ( subset_difference(X2,X1,X3) = set_difference(X1,X3)
    | ~ element(X1,powerset(X2))
    | ~ element(X3,powerset(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_40,negated_conjecture,
    subset_difference(esk30_0,esk30_0,union_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0))) = meet_of_subsets(esk30_0,complements_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0))),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_29]),c_0_37]) ).

cnf(c_0_41,plain,
    element(X1,powerset(X1)),
    inference(rw,[status(thm)],[c_0_38,c_0_20]) ).

fof(c_0_42,plain,
    ! [X161,X162] :
      ( ~ element(X162,powerset(powerset(X161)))
      | complements_of_subsets(X161,complements_of_subsets(X161,X162)) = X162 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k7_setfam_1])]) ).

fof(c_0_43,plain,
    ! [X143,X144,X145] :
      ( ~ element(X144,powerset(X143))
      | ~ element(X145,powerset(X143))
      | element(subset_difference(X143,X144,X145),powerset(X143)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_subset_1])]) ).

fof(c_0_44,plain,
    ! [X159,X160] :
      ( ~ element(X160,powerset(X159))
      | subset_complement(X159,subset_complement(X159,X160)) = X160 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).

fof(c_0_45,plain,
    ! [X123,X124] :
      ( ~ element(X124,powerset(X123))
      | subset_complement(X123,X124) = set_difference(X123,X124) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).

cnf(c_0_46,negated_conjecture,
    ( meet_of_subsets(esk30_0,complements_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0))) = set_difference(esk30_0,union_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0)))
    | ~ element(union_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0)),powerset(esk30_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).

cnf(c_0_47,plain,
    ( complements_of_subsets(X2,complements_of_subsets(X2,X1)) = X1
    | ~ element(X1,powerset(powerset(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

fof(c_0_48,plain,
    ! [X139,X140] :
      ( ~ element(X140,powerset(powerset(X139)))
      | element(union_of_subsets(X139,X140),powerset(X139)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_setfam_1])]) ).

cnf(c_0_49,plain,
    ( element(subset_difference(X2,X1,X3),powerset(X2))
    | ~ element(X1,powerset(X2))
    | ~ element(X3,powerset(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_50,negated_conjecture,
    union_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0)) != subset_difference(esk30_0,cast_to_subset(esk30_0),meet_of_subsets(esk30_0,esk31_0)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_51,plain,
    ( subset_complement(X2,subset_complement(X2,X1)) = X1
    | ~ element(X1,powerset(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_52,plain,
    ( subset_complement(X2,X1) = set_difference(X2,X1)
    | ~ element(X1,powerset(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_53,negated_conjecture,
    ( set_difference(esk30_0,union_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0))) = meet_of_subsets(esk30_0,esk31_0)
    | ~ element(union_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0)),powerset(esk30_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_29])]) ).

cnf(c_0_54,plain,
    ( element(union_of_subsets(X2,X1),powerset(X2))
    | ~ element(X1,powerset(powerset(X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_55,negated_conjecture,
    ( element(meet_of_subsets(esk30_0,complements_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0))),powerset(esk30_0))
    | ~ element(union_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0)),powerset(esk30_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_40]),c_0_41])]) ).

cnf(c_0_56,negated_conjecture,
    union_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0)) != subset_difference(esk30_0,esk30_0,meet_of_subsets(esk30_0,esk31_0)),
    inference(rw,[status(thm)],[c_0_50,c_0_20]) ).

cnf(c_0_57,plain,
    ( subset_complement(X1,set_difference(X1,X2)) = X2
    | ~ element(X2,powerset(X1)) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_58,negated_conjecture,
    ( set_difference(esk30_0,union_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0))) = meet_of_subsets(esk30_0,esk31_0)
    | ~ element(complements_of_subsets(esk30_0,esk31_0),powerset(powerset(esk30_0))) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_59,negated_conjecture,
    ( element(meet_of_subsets(esk30_0,esk31_0),powerset(esk30_0))
    | ~ element(union_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0)),powerset(esk30_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_47]),c_0_29])]) ).

cnf(c_0_60,negated_conjecture,
    ( union_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0)) != set_difference(esk30_0,meet_of_subsets(esk30_0,esk31_0))
    | ~ element(meet_of_subsets(esk30_0,esk31_0),powerset(esk30_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_39]),c_0_41])]) ).

cnf(c_0_61,negated_conjecture,
    ( union_of_subsets(esk30_0,complements_of_subsets(esk30_0,esk31_0)) = subset_complement(esk30_0,meet_of_subsets(esk30_0,esk31_0))
    | ~ element(complements_of_subsets(esk30_0,esk31_0),powerset(powerset(esk30_0))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_54]) ).

cnf(c_0_62,negated_conjecture,
    ( element(meet_of_subsets(esk30_0,esk31_0),powerset(esk30_0))
    | ~ element(complements_of_subsets(esk30_0,esk31_0),powerset(powerset(esk30_0))) ),
    inference(spm,[status(thm)],[c_0_59,c_0_54]) ).

cnf(c_0_63,negated_conjecture,
    ( subset_complement(esk30_0,meet_of_subsets(esk30_0,esk31_0)) != set_difference(esk30_0,meet_of_subsets(esk30_0,esk31_0))
    | ~ element(complements_of_subsets(esk30_0,esk31_0),powerset(powerset(esk30_0))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_62]) ).

cnf(c_0_64,negated_conjecture,
    ~ element(complements_of_subsets(esk30_0,esk31_0),powerset(powerset(esk30_0))),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_52]),c_0_62]) ).

cnf(c_0_65,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_32]),c_0_29])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.16/0.17  % Problem    : SEU176+2 : TPTP v8.1.2. Released v3.3.0.
% 0.16/0.18  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.19/0.40  % Computer : n031.cluster.edu
% 0.19/0.40  % Model    : x86_64 x86_64
% 0.19/0.40  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.40  % Memory   : 8042.1875MB
% 0.19/0.40  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.40  % CPULimit   : 300
% 0.19/0.40  % WCLimit    : 300
% 0.19/0.40  % DateTime   : Wed Aug 23 18:03:35 EDT 2023
% 0.19/0.40  % CPUTime  : 
% 0.26/0.68  start to proof: theBenchmark
% 36.77/37.00  % Version  : CSE_E---1.5
% 36.77/37.00  % Problem  : theBenchmark.p
% 36.77/37.00  % Proof found
% 36.77/37.00  % SZS status Theorem for theBenchmark.p
% 36.77/37.00  % SZS output start Proof
% See solution above
% 36.77/37.01  % Total time : 36.148000 s
% 36.77/37.01  % SZS output end Proof
% 36.77/37.01  % Total time : 36.155000 s
%------------------------------------------------------------------------------