TSTP Solution File: SET169+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n011.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 14:33:26 EDT 2023

% Result   : Theorem 140.89s 140.94s
% Output   : CNFRefutation 140.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  202 ( 133 unt;   9 typ;   0 def)
%            Number of atoms       :  301 (  77 equ)
%            Maximal formula atoms :   12 (   1 avg)
%            Number of connectives :  169 (  61   ~;  88   |;  13   &)
%                                         (   6 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :  572 (  81 sgn;  47   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_27,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_28,type,
    esk3_0: $i ).

tff(decl_29,type,
    esk4_0: $i ).

tff(decl_30,type,
    esk5_0: $i ).

fof(union_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).

fof(subset_defn,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

fof(intersection_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,intersection(X1,X2))
    <=> ( member(X3,X1)
        & member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).

fof(equal_member_defn,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ! [X3] :
          ( member(X3,X1)
        <=> member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

fof(commutativity_of_union,axiom,
    ! [X1,X2] : union(X1,X2) = union(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).

fof(commutativity_of_intersection,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(equal_defn,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).

fof(prove_intersection_distributes_over_union,conjecture,
    ! [X1,X2,X3] : intersection(X1,union(X2,X3)) = union(intersection(X1,X2),intersection(X1,X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_distributes_over_union) ).

fof(c_0_8,plain,
    ! [X4,X5,X6] :
      ( ( ~ member(X6,union(X4,X5))
        | member(X6,X4)
        | member(X6,X5) )
      & ( ~ member(X6,X4)
        | member(X6,union(X4,X5)) )
      & ( ~ member(X6,X5)
        | member(X6,union(X4,X5)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).

fof(c_0_9,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ( ~ subset(X16,X17)
        | ~ member(X18,X16)
        | member(X18,X17) )
      & ( member(esk1_2(X19,X20),X19)
        | subset(X19,X20) )
      & ( ~ member(esk1_2(X19,X20),X20)
        | subset(X19,X20) ) ),
    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_defn])])])])])]) ).

fof(c_0_10,plain,
    ! [X7,X8,X9] :
      ( ( member(X9,X7)
        | ~ member(X9,intersection(X7,X8)) )
      & ( member(X9,X8)
        | ~ member(X9,intersection(X7,X8)) )
      & ( ~ member(X9,X7)
        | ~ member(X9,X8)
        | member(X9,intersection(X7,X8)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).

fof(c_0_11,plain,
    ! [X23,X24,X25,X26,X27,X28] :
      ( ( ~ member(X25,X23)
        | member(X25,X24)
        | X23 != X24 )
      & ( ~ member(X26,X24)
        | member(X26,X23)
        | X23 != X24 )
      & ( ~ member(esk2_2(X27,X28),X27)
        | ~ member(esk2_2(X27,X28),X28)
        | X27 = X28 )
      & ( member(esk2_2(X27,X28),X27)
        | member(esk2_2(X27,X28),X28)
        | X27 = X28 ) ),
    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)],[equal_member_defn])])])])])]) ).

cnf(c_0_12,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_15,plain,
    ( member(esk2_2(X1,X2),X1)
    | member(esk2_2(X1,X2),X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_16,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_17,plain,
    ( member(X1,union(X3,X2))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_18,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_19,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_20,plain,
    ( subset(union(X1,X2),X3)
    | member(esk1_2(union(X1,X2),X3),X1)
    | member(esk1_2(union(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_21,plain,
    ( intersection(X1,X2) = X3
    | member(esk2_2(intersection(X1,X2),X3),X3)
    | member(esk2_2(intersection(X1,X2),X3),X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_22,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_23,plain,
    ( subset(intersection(X1,X2),X3)
    | member(esk1_2(intersection(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_13]) ).

cnf(c_0_24,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_16,c_0_19]) ).

cnf(c_0_25,plain,
    ( subset(intersection(X1,X2),X3)
    | member(esk1_2(intersection(X1,X2),X3),X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_13]) ).

cnf(c_0_26,plain,
    ( subset(union(X1,X2),X2)
    | member(esk1_2(union(X1,X2),X2),X1) ),
    inference(spm,[status(thm)],[c_0_16,c_0_20]) ).

fof(c_0_27,plain,
    ! [X12,X13] : union(X12,X13) = union(X13,X12),
    inference(variable_rename,[status(thm)],[commutativity_of_union]) ).

cnf(c_0_28,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_29,plain,
    ( X1 = X2
    | ~ member(esk2_2(X1,X2),X1)
    | ~ member(esk2_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_30,plain,
    ( intersection(X1,X2) = X1
    | member(esk2_2(intersection(X1,X2),X1),X1) ),
    inference(ef,[status(thm)],[c_0_21]) ).

cnf(c_0_31,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_32,plain,
    subset(intersection(X1,X2),union(X3,X2)),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

fof(c_0_33,plain,
    ! [X14,X15] : intersection(X14,X15) = intersection(X15,X14),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

cnf(c_0_34,plain,
    ( subset(intersection(X1,X2),intersection(X3,X1))
    | ~ member(esk1_2(intersection(X1,X2),intersection(X3,X1)),X3) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

fof(c_0_35,plain,
    ! [X10,X11] :
      ( ( subset(X10,X11)
        | X10 != X11 )
      & ( subset(X11,X10)
        | X10 != X11 )
      & ( ~ subset(X10,X11)
        | ~ subset(X11,X10)
        | X10 = X11 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).

cnf(c_0_36,plain,
    ( subset(union(intersection(X1,X2),X3),X3)
    | member(esk1_2(union(intersection(X1,X2),X3),X3),X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_26]) ).

cnf(c_0_37,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_38,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_28]) ).

cnf(c_0_39,plain,
    ( subset(X1,intersection(X2,X1))
    | ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_13]) ).

cnf(c_0_40,plain,
    ( intersection(X1,X2) = X1
    | ~ member(esk2_2(intersection(X1,X2),X1),intersection(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_41,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,intersection(X4,X3)) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_42,plain,
    subset(intersection(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_16,c_0_23]) ).

cnf(c_0_43,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_44,plain,
    subset(intersection(X1,X2),intersection(X2,X1)),
    inference(spm,[status(thm)],[c_0_34,c_0_23]) ).

cnf(c_0_45,plain,
    ( subset(intersection(X1,intersection(X2,X3)),X4)
    | member(esk1_2(intersection(X1,intersection(X2,X3)),X4),X3) ),
    inference(spm,[status(thm)],[c_0_18,c_0_23]) ).

cnf(c_0_46,plain,
    ( subset(intersection(X1,union(X2,X3)),X4)
    | member(esk1_2(intersection(X1,union(X2,X3)),X4),X2)
    | member(esk1_2(intersection(X1,union(X2,X3)),X4),X3) ),
    inference(spm,[status(thm)],[c_0_12,c_0_23]) ).

cnf(c_0_47,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_48,plain,
    subset(union(X1,intersection(X1,X2)),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_36]),c_0_37]) ).

cnf(c_0_49,plain,
    subset(X1,union(X1,X2)),
    inference(spm,[status(thm)],[c_0_38,c_0_13]) ).

cnf(c_0_50,plain,
    subset(intersection(X1,X2),intersection(X2,intersection(X1,X2))),
    inference(spm,[status(thm)],[c_0_39,c_0_23]) ).

cnf(c_0_51,plain,
    ( intersection(X1,X2) = X1
    | ~ member(esk2_2(intersection(X1,X2),X1),X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_19]),c_0_30]) ).

cnf(c_0_52,plain,
    ( intersection(intersection(X1,X2),X3) = intersection(X1,X2)
    | member(esk2_2(intersection(intersection(X1,X2),X3),intersection(X1,X2)),union(X4,X2)) ),
    inference(spm,[status(thm)],[c_0_41,c_0_30]) ).

cnf(c_0_53,plain,
    subset(X1,intersection(X1,X1)),
    inference(spm,[status(thm)],[c_0_39,c_0_13]) ).

cnf(c_0_54,plain,
    subset(intersection(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_55,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,intersection(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_31,c_0_44]) ).

cnf(c_0_56,plain,
    subset(intersection(X1,intersection(X2,X3)),intersection(X3,X1)),
    inference(spm,[status(thm)],[c_0_34,c_0_45]) ).

cnf(c_0_57,plain,
    ( subset(X1,union(intersection(X2,X3),X4))
    | ~ member(esk1_2(X1,union(intersection(X2,X3),X4)),X3)
    | ~ member(esk1_2(X1,union(intersection(X2,X3),X4)),X2) ),
    inference(spm,[status(thm)],[c_0_38,c_0_19]) ).

cnf(c_0_58,plain,
    ( subset(intersection(X1,X2),intersection(union(X3,X4),X1))
    | ~ member(esk1_2(intersection(X1,X2),intersection(union(X3,X4),X1)),X4) ),
    inference(spm,[status(thm)],[c_0_34,c_0_17]) ).

cnf(c_0_59,plain,
    ( subset(intersection(X1,union(X2,X3)),X3)
    | member(esk1_2(intersection(X1,union(X2,X3)),X3),X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_46]) ).

cnf(c_0_60,plain,
    union(X1,intersection(X1,X2)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).

cnf(c_0_61,plain,
    intersection(X1,intersection(X2,X1)) = intersection(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_50]),c_0_42])]) ).

cnf(c_0_62,plain,
    intersection(intersection(X1,X2),union(X3,X2)) = intersection(X1,X2),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_63,plain,
    intersection(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_53]),c_0_54])]) ).

cnf(c_0_64,plain,
    ( intersection(intersection(X1,X2),X3) = intersection(X1,X2)
    | member(esk2_2(intersection(intersection(X1,X2),X3),intersection(X1,X2)),intersection(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_55,c_0_30]) ).

cnf(c_0_65,plain,
    subset(intersection(X1,intersection(X2,X3)),intersection(X1,X3)),
    inference(spm,[status(thm)],[c_0_56,c_0_43]) ).

cnf(c_0_66,plain,
    ( subset(intersection(X1,X2),union(intersection(X3,X1),X4))
    | ~ member(esk1_2(intersection(X1,X2),union(intersection(X3,X1),X4)),X3) ),
    inference(spm,[status(thm)],[c_0_57,c_0_25]) ).

cnf(c_0_67,plain,
    ( subset(intersection(X1,union(X2,X3)),union(X4,X3))
    | member(esk1_2(intersection(X1,union(X2,X3)),union(X4,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_22,c_0_46]) ).

cnf(c_0_68,plain,
    subset(intersection(X1,union(X2,intersection(union(X3,X2),X1))),intersection(union(X3,X2),X1)),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_69,plain,
    union(X1,intersection(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_70,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X2,X3)),
    inference(spm,[status(thm)],[c_0_56,c_0_43]) ).

cnf(c_0_71,plain,
    intersection(X1,union(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_72,plain,
    intersection(intersection(X1,X2),intersection(X2,X1)) = intersection(X1,X2),
    inference(spm,[status(thm)],[c_0_51,c_0_64]) ).

cnf(c_0_73,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X3,X2)),
    inference(spm,[status(thm)],[c_0_65,c_0_43]) ).

cnf(c_0_74,plain,
    subset(intersection(X1,intersection(X2,X3)),intersection(X3,intersection(X1,intersection(X2,X3)))),
    inference(spm,[status(thm)],[c_0_39,c_0_45]) ).

cnf(c_0_75,plain,
    subset(intersection(X1,union(X2,X3)),union(intersection(X2,X1),X3)),
    inference(spm,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_76,plain,
    subset(intersection(X1,union(intersection(X2,X3),intersection(X3,X1))),intersection(X3,X1)),
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_77,plain,
    subset(intersection(X1,X2),intersection(X2,union(X3,intersection(X1,X2)))),
    inference(spm,[status(thm)],[c_0_70,c_0_71]) ).

cnf(c_0_78,plain,
    subset(intersection(X1,intersection(X2,X3)),intersection(intersection(X3,X2),X1)),
    inference(spm,[status(thm)],[c_0_56,c_0_72]) ).

cnf(c_0_79,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X3,intersection(X2,X1))),
    inference(spm,[status(thm)],[c_0_73,c_0_72]) ).

cnf(c_0_80,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X2,intersection(intersection(X1,X2),X3))),
    inference(spm,[status(thm)],[c_0_74,c_0_43]) ).

cnf(c_0_81,plain,
    ( subset(intersection(X1,intersection(X2,X3)),X4)
    | member(esk1_2(intersection(X1,intersection(X2,X3)),X4),X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_23]) ).

cnf(c_0_82,plain,
    subset(intersection(X1,union(X2,X3)),union(intersection(X1,X2),X3)),
    inference(spm,[status(thm)],[c_0_75,c_0_43]) ).

cnf(c_0_83,plain,
    intersection(X1,union(intersection(X2,X3),intersection(X3,X1))) = intersection(X3,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_76]),c_0_77])]) ).

cnf(c_0_84,plain,
    intersection(intersection(X1,X2),X3) = intersection(X3,intersection(X2,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_78]),c_0_79])]) ).

cnf(c_0_85,plain,
    intersection(X1,intersection(intersection(X2,X1),X3)) = intersection(intersection(X2,X1),X3),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_80]),c_0_42])]) ).

cnf(c_0_86,plain,
    subset(intersection(X1,intersection(X2,X3)),intersection(X2,X1)),
    inference(spm,[status(thm)],[c_0_34,c_0_81]) ).

cnf(c_0_87,plain,
    subset(intersection(X1,intersection(X2,X3)),intersection(X2,intersection(X1,intersection(X2,X3)))),
    inference(spm,[status(thm)],[c_0_39,c_0_81]) ).

cnf(c_0_88,plain,
    subset(intersection(X1,union(union(intersection(X2,X3),intersection(X3,X1)),X4)),union(intersection(X3,X1),X4)),
    inference(spm,[status(thm)],[c_0_82,c_0_83]) ).

cnf(c_0_89,plain,
    union(intersection(X1,X2),intersection(intersection(X2,X1),X3)) = intersection(X1,X2),
    inference(spm,[status(thm)],[c_0_69,c_0_84]) ).

cnf(c_0_90,plain,
    intersection(union(X1,X2),intersection(X2,X3)) = intersection(X2,X3),
    inference(spm,[status(thm)],[c_0_85,c_0_71]) ).

cnf(c_0_91,plain,
    subset(intersection(X1,intersection(X2,X3)),intersection(X1,X2)),
    inference(spm,[status(thm)],[c_0_86,c_0_43]) ).

cnf(c_0_92,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X1,intersection(intersection(X1,X2),X3))),
    inference(spm,[status(thm)],[c_0_87,c_0_43]) ).

cnf(c_0_93,plain,
    subset(intersection(X1,union(union(intersection(X2,X3),intersection(X3,X1)),intersection(intersection(X1,X3),X4))),intersection(X3,X1)),
    inference(spm,[status(thm)],[c_0_88,c_0_89]) ).

cnf(c_0_94,plain,
    intersection(X1,union(X2,intersection(union(X3,X2),X1))) = intersection(union(X3,X2),X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_68]),c_0_77])]) ).

cnf(c_0_95,plain,
    union(union(X1,X2),intersection(X2,X3)) = union(X1,X2),
    inference(spm,[status(thm)],[c_0_60,c_0_90]) ).

cnf(c_0_96,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X3,X1)),
    inference(spm,[status(thm)],[c_0_91,c_0_43]) ).

cnf(c_0_97,plain,
    intersection(X1,intersection(intersection(X1,X2),X3)) = intersection(intersection(X1,X2),X3),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_92]),c_0_42])]) ).

cnf(c_0_98,plain,
    ( subset(X1,union(X2,union(X3,X4)))
    | ~ member(esk1_2(X1,union(X2,union(X3,X4))),X4) ),
    inference(spm,[status(thm)],[c_0_22,c_0_17]) ).

cnf(c_0_99,plain,
    subset(intersection(union(X1,intersection(union(X2,X1),X3)),union(intersection(X4,X3),intersection(union(X2,X1),X3))),intersection(union(X2,X1),X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_43]),c_0_94]),c_0_95]) ).

cnf(c_0_100,plain,
    subset(intersection(intersection(intersection(X1,X2),X3),X4),intersection(X4,X1)),
    inference(spm,[status(thm)],[c_0_96,c_0_97]) ).

cnf(c_0_101,plain,
    intersection(intersection(X1,X2),union(X3,intersection(X2,X1))) = intersection(X1,X2),
    inference(spm,[status(thm)],[c_0_62,c_0_72]) ).

cnf(c_0_102,plain,
    ( subset(intersection(X1,union(X2,X3)),union(X4,union(X5,X3)))
    | member(esk1_2(intersection(X1,union(X2,X3)),union(X4,union(X5,X3))),X2) ),
    inference(spm,[status(thm)],[c_0_98,c_0_46]) ).

cnf(c_0_103,plain,
    subset(union(X1,union(X2,union(X3,X1))),union(X2,union(X3,X1))),
    inference(spm,[status(thm)],[c_0_98,c_0_26]) ).

cnf(c_0_104,plain,
    subset(union(intersection(X1,X2),intersection(X2,union(X3,intersection(X1,X2)))),intersection(X2,union(X3,intersection(X1,X2)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_63]),c_0_43]),c_0_43]) ).

cnf(c_0_105,plain,
    intersection(X1,intersection(X2,intersection(X1,X3))) = intersection(X2,intersection(X1,X3)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_87]),c_0_42])]) ).

cnf(c_0_106,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X1,union(X4,intersection(X3,intersection(X1,X2))))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_43]) ).

cnf(c_0_107,plain,
    union(X1,intersection(intersection(X1,X2),X3)) = X1,
    inference(spm,[status(thm)],[c_0_60,c_0_97]) ).

cnf(c_0_108,plain,
    subset(intersection(X1,union(X2,X3)),union(intersection(X2,X1),union(X4,X3))),
    inference(spm,[status(thm)],[c_0_66,c_0_102]) ).

cnf(c_0_109,plain,
    subset(union(X1,union(union(X2,X1),X3)),union(union(X2,X1),X3)),
    inference(spm,[status(thm)],[c_0_103,c_0_37]) ).

cnf(c_0_110,plain,
    subset(X1,union(X2,X1)),
    inference(spm,[status(thm)],[c_0_22,c_0_13]) ).

cnf(c_0_111,plain,
    subset(union(intersection(X1,X2),intersection(X1,union(X3,intersection(X1,X2)))),intersection(X1,union(X3,intersection(X1,X2)))),
    inference(spm,[status(thm)],[c_0_104,c_0_43]) ).

cnf(c_0_112,plain,
    union(X1,intersection(X2,intersection(X1,X3))) = X1,
    inference(spm,[status(thm)],[c_0_60,c_0_105]) ).

cnf(c_0_113,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X1,union(X4,intersection(intersection(X2,X1),X3)))),
    inference(spm,[status(thm)],[c_0_106,c_0_84]) ).

cnf(c_0_114,plain,
    subset(union(intersection(X1,X2),intersection(intersection(X2,X3),X1)),intersection(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_107]),c_0_37]) ).

cnf(c_0_115,plain,
    subset(intersection(X1,union(X2,X3)),union(intersection(X1,X2),union(X4,X3))),
    inference(spm,[status(thm)],[c_0_108,c_0_43]) ).

cnf(c_0_116,plain,
    union(X1,union(union(X2,X1),X3)) = union(union(X2,X1),X3),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_109]),c_0_110])]) ).

cnf(c_0_117,plain,
    subset(union(intersection(X1,X2),intersection(X1,intersection(X2,X3))),intersection(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_37]) ).

cnf(c_0_118,plain,
    subset(intersection(X1,intersection(X2,X3)),intersection(X2,union(X4,intersection(intersection(X3,X2),X1)))),
    inference(spm,[status(thm)],[c_0_113,c_0_43]) ).

cnf(c_0_119,plain,
    union(intersection(X1,X2),intersection(intersection(X2,X3),X1)) = intersection(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_114]),c_0_49])]) ).

cnf(c_0_120,plain,
    subset(intersection(X1,union(X2,X3)),union(union(X4,intersection(X1,X2)),X3)),
    inference(spm,[status(thm)],[c_0_115,c_0_116]) ).

cnf(c_0_121,plain,
    union(intersection(X1,X2),intersection(X1,intersection(X2,X3))) = intersection(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_117]),c_0_49])]) ).

cnf(c_0_122,plain,
    subset(intersection(X1,intersection(X2,X3)),intersection(X2,intersection(X1,X3))),
    inference(spm,[status(thm)],[c_0_118,c_0_119]) ).

cnf(c_0_123,plain,
    subset(intersection(X1,union(intersection(X2,X3),X4)),union(intersection(X1,X2),X4)),
    inference(spm,[status(thm)],[c_0_120,c_0_121]) ).

cnf(c_0_124,plain,
    intersection(X1,intersection(X2,X3)) = intersection(X2,intersection(X1,X3)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_122]),c_0_122])]) ).

cnf(c_0_125,plain,
    subset(union(intersection(X1,X2),X3),union(X3,intersection(X1,union(intersection(X1,X2),X3)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_63]),c_0_43]),c_0_37]) ).

cnf(c_0_126,plain,
    intersection(X1,intersection(X2,union(X3,X1))) = intersection(X2,X1),
    inference(spm,[status(thm)],[c_0_124,c_0_71]) ).

cnf(c_0_127,plain,
    ( subset(X1,union(union(X2,X3),X4))
    | ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3) ),
    inference(spm,[status(thm)],[c_0_38,c_0_17]) ).

cnf(c_0_128,plain,
    ( subset(union(X1,X2),union(X3,X2))
    | member(esk1_2(union(X1,X2),union(X3,X2)),X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_20]) ).

cnf(c_0_129,plain,
    intersection(union(X1,X2),intersection(X3,X2)) = intersection(X3,X2),
    inference(spm,[status(thm)],[c_0_43,c_0_62]) ).

cnf(c_0_130,plain,
    ( subset(X1,union(X2,union(X3,X4)))
    | ~ member(esk1_2(X1,union(X2,union(X3,X4))),X3) ),
    inference(spm,[status(thm)],[c_0_22,c_0_28]) ).

cnf(c_0_131,plain,
    ( subset(intersection(X1,X2),intersection(union(X3,X4),X1))
    | ~ member(esk1_2(intersection(X1,X2),intersection(union(X3,X4),X1)),X3) ),
    inference(spm,[status(thm)],[c_0_34,c_0_28]) ).

cnf(c_0_132,plain,
    subset(union(intersection(X1,X2),X3),union(X3,intersection(X2,union(intersection(X1,X2),X3)))),
    inference(spm,[status(thm)],[c_0_125,c_0_126]) ).

cnf(c_0_133,plain,
    intersection(X1,union(X1,X2)) = X1,
    inference(spm,[status(thm)],[c_0_71,c_0_37]) ).

cnf(c_0_134,plain,
    subset(union(X1,X2),union(union(X3,X1),X2)),
    inference(spm,[status(thm)],[c_0_127,c_0_128]) ).

cnf(c_0_135,plain,
    union(union(X1,X2),intersection(X3,X2)) = union(X1,X2),
    inference(spm,[status(thm)],[c_0_60,c_0_129]) ).

cnf(c_0_136,plain,
    ( subset(X1,union(union(X2,X3),X4))
    | ~ member(esk1_2(X1,union(union(X2,X3),X4)),X2) ),
    inference(spm,[status(thm)],[c_0_38,c_0_28]) ).

cnf(c_0_137,plain,
    subset(union(X1,union(X2,union(X1,X3))),union(X2,union(X1,X3))),
    inference(spm,[status(thm)],[c_0_130,c_0_26]) ).

cnf(c_0_138,plain,
    subset(intersection(X1,union(X2,intersection(union(X2,X3),X1))),intersection(union(X2,X3),X1)),
    inference(spm,[status(thm)],[c_0_131,c_0_59]) ).

cnf(c_0_139,plain,
    union(X1,union(X2,union(X3,X1))) = union(X2,union(X3,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_103]),c_0_110])]) ).

cnf(c_0_140,plain,
    subset(union(X1,X2),union(X2,intersection(union(X1,X3),union(X1,X2)))),
    inference(spm,[status(thm)],[c_0_132,c_0_133]) ).

cnf(c_0_141,plain,
    subset(union(X1,intersection(X2,union(X3,X1))),union(X3,X1)),
    inference(spm,[status(thm)],[c_0_134,c_0_69]) ).

cnf(c_0_142,plain,
    subset(union(X1,X2),union(X2,union(X3,X1))),
    inference(spm,[status(thm)],[c_0_134,c_0_37]) ).

cnf(c_0_143,plain,
    intersection(union(X1,X2),intersection(X1,X3)) = intersection(X1,X3),
    inference(spm,[status(thm)],[c_0_85,c_0_133]) ).

cnf(c_0_144,plain,
    subset(union(intersection(X1,X2),intersection(X1,union(X3,X2))),intersection(X1,union(X3,X2))),
    inference(spm,[status(thm)],[c_0_111,c_0_135]) ).

cnf(c_0_145,plain,
    subset(union(X1,X2),union(union(X1,X3),X2)),
    inference(spm,[status(thm)],[c_0_136,c_0_128]) ).

cnf(c_0_146,plain,
    union(X1,union(X2,union(X1,X3))) = union(X2,union(X1,X3)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_137]),c_0_110])]) ).

cnf(c_0_147,plain,
    subset(intersection(X1,union(X2,intersection(union(X3,union(X4,X2)),X1))),intersection(union(X3,union(X4,X2)),X1)),
    inference(spm,[status(thm)],[c_0_138,c_0_139]) ).

cnf(c_0_148,plain,
    union(X1,intersection(union(X2,X3),union(X2,X1))) = union(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_140]),c_0_141])]) ).

cnf(c_0_149,plain,
    subset(union(intersection(X1,X2),X3),union(X3,X2)),
    inference(spm,[status(thm)],[c_0_142,c_0_69]) ).

cnf(c_0_150,plain,
    intersection(X1,intersection(union(X1,X2),X3)) = intersection(X1,X3),
    inference(rw,[status(thm)],[c_0_143,c_0_124]) ).

cnf(c_0_151,plain,
    subset(union(intersection(X1,X2),intersection(union(X3,X2),X1)),intersection(union(X3,X2),X1)),
    inference(spm,[status(thm)],[c_0_144,c_0_43]) ).

cnf(c_0_152,plain,
    subset(union(X1,X2),union(union(X3,union(X1,X4)),X2)),
    inference(spm,[status(thm)],[c_0_145,c_0_146]) ).

cnf(c_0_153,plain,
    subset(union(X1,X2),intersection(union(X1,X2),union(X1,union(X3,X2)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_63]),c_0_43]) ).

cnf(c_0_154,plain,
    subset(union(intersection(X1,X2),X3),union(X3,intersection(union(X1,X4),X2))),
    inference(spm,[status(thm)],[c_0_149,c_0_150]) ).

cnf(c_0_155,plain,
    union(intersection(X1,X2),intersection(union(X3,X2),X1)) = intersection(union(X3,X2),X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_151]),c_0_110])]) ).

cnf(c_0_156,plain,
    intersection(X1,union(X2,union(X1,X3))) = X1,
    inference(spm,[status(thm)],[c_0_62,c_0_133]) ).

cnf(c_0_157,plain,
    subset(union(X1,intersection(X2,union(X3,union(X1,X4)))),union(X3,union(X1,X4))),
    inference(spm,[status(thm)],[c_0_152,c_0_69]) ).

cnf(c_0_158,plain,
    intersection(union(X1,X2),union(X1,union(X3,X2))) = union(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_153]),c_0_54])]) ).

cnf(c_0_159,plain,
    subset(intersection(X1,X2),intersection(X1,intersection(X1,X2))),
    inference(spm,[status(thm)],[c_0_39,c_0_25]) ).

cnf(c_0_160,plain,
    subset(union(intersection(X1,X2),intersection(X2,X3)),intersection(union(X1,X3),X2)),
    inference(spm,[status(thm)],[c_0_154,c_0_155]) ).

cnf(c_0_161,plain,
    intersection(X1,intersection(X2,union(X3,union(X1,X4)))) = intersection(X2,X1),
    inference(spm,[status(thm)],[c_0_124,c_0_156]) ).

cnf(c_0_162,plain,
    intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X3,X2)),
    inference(spm,[status(thm)],[c_0_43,c_0_124]) ).

cnf(c_0_163,plain,
    intersection(X1,union(X2,union(X3,X1))) = X1,
    inference(spm,[status(thm)],[c_0_62,c_0_71]) ).

cnf(c_0_164,plain,
    ( subset(X1,union(X2,intersection(X3,X4)))
    | ~ member(esk1_2(X1,union(X2,intersection(X3,X4))),X4)
    | ~ member(esk1_2(X1,union(X2,intersection(X3,X4))),X3) ),
    inference(spm,[status(thm)],[c_0_22,c_0_19]) ).

cnf(c_0_165,plain,
    subset(union(X1,union(X2,X3)),union(X2,union(X1,X3))),
    inference(spm,[status(thm)],[c_0_157,c_0_158]) ).

cnf(c_0_166,plain,
    intersection(X1,intersection(X1,X2)) = intersection(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_159]),c_0_42])]) ).

cnf(c_0_167,plain,
    subset(union(intersection(X1,X2),intersection(X1,X3)),intersection(X1,union(X2,X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_126]),c_0_161]),c_0_162]),c_0_163]) ).

cnf(c_0_168,plain,
    ( subset(intersection(X1,X2),union(X3,intersection(X4,X2)))
    | ~ member(esk1_2(intersection(X1,X2),union(X3,intersection(X4,X2))),X4) ),
    inference(spm,[status(thm)],[c_0_164,c_0_23]) ).

cnf(c_0_169,plain,
    ( subset(intersection(union(X1,X2),X3),X4)
    | member(esk1_2(intersection(union(X1,X2),X3),X4),X1)
    | member(esk1_2(intersection(union(X1,X2),X3),X4),X2) ),
    inference(spm,[status(thm)],[c_0_12,c_0_25]) ).

cnf(c_0_170,plain,
    subset(union(intersection(X1,X2),intersection(X3,X2)),intersection(X2,union(X1,intersection(X3,X2)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_61]),c_0_43]) ).

cnf(c_0_171,plain,
    union(X1,union(X2,X3)) = union(X2,union(X1,X3)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_165]),c_0_165])]) ).

fof(c_0_172,negated_conjecture,
    ~ ! [X1,X2,X3] : intersection(X1,union(X2,X3)) = union(intersection(X1,X2),intersection(X1,X3)),
    inference(assume_negation,[status(cth)],[prove_intersection_distributes_over_union]) ).

cnf(c_0_173,plain,
    subset(union(intersection(X1,X2),intersection(X2,X3)),intersection(X2,union(X1,intersection(X2,X3)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_166]),c_0_43]) ).

cnf(c_0_174,plain,
    subset(union(intersection(X1,X2),intersection(X3,X1)),intersection(X1,union(X2,intersection(X3,X1)))),
    inference(spm,[status(thm)],[c_0_167,c_0_61]) ).

cnf(c_0_175,plain,
    ( subset(X1,union(intersection(X2,X1),X3))
    | ~ member(esk1_2(X1,union(intersection(X2,X1),X3)),X2) ),
    inference(spm,[status(thm)],[c_0_57,c_0_13]) ).

cnf(c_0_176,plain,
    ( subset(intersection(union(X1,X2),X3),union(X4,intersection(X2,X3)))
    | member(esk1_2(intersection(union(X1,X2),X3),union(X4,intersection(X2,X3))),X1) ),
    inference(spm,[status(thm)],[c_0_168,c_0_169]) ).

cnf(c_0_177,plain,
    union(intersection(X1,X2),intersection(X3,X2)) = intersection(X2,union(X1,intersection(X3,X2))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_170]),c_0_75])]) ).

cnf(c_0_178,plain,
    subset(intersection(X1,X2),intersection(union(X3,X2),X1)),
    inference(spm,[status(thm)],[c_0_96,c_0_62]) ).

cnf(c_0_179,plain,
    union(X1,union(X2,intersection(X1,X3))) = union(X2,X1),
    inference(spm,[status(thm)],[c_0_171,c_0_60]) ).

fof(c_0_180,negated_conjecture,
    intersection(esk3_0,union(esk4_0,esk5_0)) != union(intersection(esk3_0,esk4_0),intersection(esk3_0,esk5_0)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_172])])]) ).

cnf(c_0_181,plain,
    subset(union(intersection(X1,X2),intersection(X1,X3)),intersection(X1,union(X2,intersection(X1,X3)))),
    inference(spm,[status(thm)],[c_0_167,c_0_166]) ).

cnf(c_0_182,plain,
    union(intersection(X1,X2),intersection(X2,X3)) = intersection(X2,union(X1,intersection(X2,X3))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_173]),c_0_75])]) ).

cnf(c_0_183,plain,
    union(intersection(X1,X2),intersection(X3,X1)) = intersection(X1,union(X2,intersection(X3,X1))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_174]),c_0_82])]) ).

cnf(c_0_184,plain,
    subset(intersection(union(X1,X2),X3),intersection(X3,union(X1,intersection(X2,X3)))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_150]),c_0_177]) ).

cnf(c_0_185,plain,
    subset(intersection(X1,union(X2,intersection(X3,X4))),intersection(union(X2,X3),X1)),
    inference(spm,[status(thm)],[c_0_178,c_0_179]) ).

cnf(c_0_186,negated_conjecture,
    intersection(esk3_0,union(esk4_0,esk5_0)) != union(intersection(esk3_0,esk4_0),intersection(esk3_0,esk5_0)),
    inference(split_conjunct,[status(thm)],[c_0_180]) ).

cnf(c_0_187,plain,
    union(intersection(X1,X2),intersection(X1,X3)) = intersection(X1,union(X2,intersection(X1,X3))),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_181]),c_0_82])]) ).

cnf(c_0_188,plain,
    intersection(X1,union(X2,intersection(X3,X1))) = intersection(X1,union(X3,intersection(X1,X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_182]),c_0_183]) ).

cnf(c_0_189,plain,
    intersection(X1,union(X2,intersection(X3,X1))) = intersection(union(X2,X3),X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_184]),c_0_185])]) ).

cnf(c_0_190,negated_conjecture,
    intersection(esk3_0,union(esk4_0,intersection(esk3_0,esk5_0))) != intersection(esk3_0,union(esk4_0,esk5_0)),
    inference(rw,[status(thm)],[c_0_186,c_0_187]) ).

cnf(c_0_191,plain,
    intersection(X1,union(X2,intersection(X1,X3))) = intersection(union(X3,X2),X1),
    inference(rw,[status(thm)],[c_0_188,c_0_189]) ).

cnf(c_0_192,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_190,c_0_191]),c_0_37]),c_0_43])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n011.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sat Aug 26 10:17:39 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.21/0.56  start to proof: theBenchmark
% 140.89/140.94  % Version  : CSE_E---1.5
% 140.89/140.94  % Problem  : theBenchmark.p
% 140.89/140.94  % Proof found
% 140.89/140.94  % SZS status Theorem for theBenchmark.p
% 140.89/140.94  % SZS output start Proof
% See solution above
% 140.89/140.95  % Total time : 140.298000 s
% 140.89/140.95  % SZS output end Proof
% 140.89/140.95  % Total time : 140.307000 s
%------------------------------------------------------------------------------