TSTP Solution File: SET144+3 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SET144+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 : n007.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 14:33:18 EDT 2023

% Result   : Theorem 87.09s 87.08s
% Output   : CNFRefutation 87.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  110 (  42 unt;   9 typ;   0 def)
%            Number of atoms       :  209 (  47 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  169 (  61   ~;  85   |;  14   &)
%                                         (   6 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   3 avg)
%            Maximal term depth    :    5 (   1 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   :  249 (  30 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(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(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(prove_th44,conjecture,
    ! [X1,X2,X3] :
      ( subset(X1,X2)
     => union(X1,intersection(X3,X2)) = intersection(union(X1,X3),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th44) ).

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

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

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

fof(c_0_8,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_9,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_10,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_11,plain,
    ( member(esk2_2(X1,X2),X1)
    | member(esk2_2(X1,X2),X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_12,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_13,plain,
    ! [X10,X11,X12,X13,X14] :
      ( ( ~ subset(X10,X11)
        | ~ member(X12,X10)
        | member(X12,X11) )
      & ( member(esk1_2(X13,X14),X13)
        | subset(X13,X14) )
      & ( ~ member(esk1_2(X13,X14),X14)
        | subset(X13,X14) ) ),
    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])])])])])]) ).

cnf(c_0_14,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_10,c_0_11]) ).

cnf(c_0_15,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_16,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,plain,
    ( X1 = X2
    | ~ member(esk2_2(X1,X2),X1)
    | ~ member(esk2_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_18,plain,
    ( intersection(X1,X2) = X1
    | member(esk2_2(intersection(X1,X2),X1),X1) ),
    inference(ef,[status(thm)],[c_0_14]) ).

cnf(c_0_19,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

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_15,c_0_16]) ).

cnf(c_0_21,plain,
    ( member(X1,union(X3,X2))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_22,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( subset(X1,X2)
       => union(X1,intersection(X3,X2)) = intersection(union(X1,X3),X2) ),
    inference(assume_negation,[status(cth)],[prove_th44]) ).

cnf(c_0_23,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_24,plain,
    ( intersection(X1,X2) = X1
    | ~ member(esk2_2(intersection(X1,X2),X1),intersection(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_25,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_26,plain,
    ! [X20,X21] : intersection(X20,X21) = intersection(X21,X20),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

cnf(c_0_27,plain,
    ( subset(union(X1,X2),X2)
    | member(esk1_2(union(X1,X2),X2),X1) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

fof(c_0_28,plain,
    ! [X18,X19] : union(X18,X19) = union(X19,X18),
    inference(variable_rename,[status(thm)],[commutativity_of_union]) ).

cnf(c_0_29,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_21]) ).

fof(c_0_30,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    & union(esk3_0,intersection(esk5_0,esk4_0)) != intersection(union(esk3_0,esk5_0),esk4_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).

cnf(c_0_31,plain,
    ( subset(intersection(X1,X2),X3)
    | member(esk1_2(intersection(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_16]) ).

cnf(c_0_32,plain,
    ( intersection(X1,X2) = X1
    | ~ member(esk2_2(intersection(X1,X2),X1),X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_18]) ).

cnf(c_0_33,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

fof(c_0_34,plain,
    ! [X16,X17] :
      ( ( subset(X16,X17)
        | X16 != X17 )
      & ( subset(X17,X16)
        | X16 != X17 )
      & ( ~ subset(X16,X17)
        | ~ subset(X17,X16)
        | X16 = X17 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).

cnf(c_0_35,plain,
    ( subset(union(intersection(X1,X2),X3),X3)
    | member(esk1_2(union(intersection(X1,X2),X3),X3),X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_27]) ).

cnf(c_0_36,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_37,plain,
    subset(X1,union(X2,X1)),
    inference(spm,[status(thm)],[c_0_29,c_0_16]) ).

cnf(c_0_38,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_39,negated_conjecture,
    subset(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_40,plain,
    subset(intersection(X1,X2),union(X3,X2)),
    inference(spm,[status(thm)],[c_0_29,c_0_31]) ).

cnf(c_0_41,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_19,c_0_25]) ).

cnf(c_0_42,plain,
    ( intersection(X1,X2) = X2
    | ~ member(esk2_2(intersection(X1,X2),X2),X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

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

cnf(c_0_44,plain,
    subset(union(X1,intersection(X1,X2)),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_35]),c_0_36]) ).

cnf(c_0_45,plain,
    subset(X1,union(X1,X2)),
    inference(spm,[status(thm)],[c_0_37,c_0_36]) ).

cnf(c_0_46,negated_conjecture,
    ( member(X1,esk4_0)
    | ~ member(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_47,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,intersection(X4,X3)) ),
    inference(spm,[status(thm)],[c_0_38,c_0_40]) ).

cnf(c_0_48,plain,
    ( subset(X1,intersection(X2,X1))
    | ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
    inference(spm,[status(thm)],[c_0_41,c_0_16]) ).

cnf(c_0_49,plain,
    subset(intersection(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_19,c_0_31]) ).

cnf(c_0_50,plain,
    ( subset(X1,intersection(X2,union(X3,X4)))
    | ~ member(esk1_2(X1,intersection(X2,union(X3,X4))),X2)
    | ~ member(esk1_2(X1,intersection(X2,union(X3,X4))),X4) ),
    inference(spm,[status(thm)],[c_0_41,c_0_21]) ).

cnf(c_0_51,plain,
    ( subset(intersection(X1,X2),X3)
    | member(esk1_2(intersection(X1,X2),X3),X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_16]) ).

cnf(c_0_52,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_15,c_0_31]) ).

cnf(c_0_53,plain,
    ( intersection(union(X1,X2),X3) = X3
    | ~ member(esk2_2(intersection(union(X1,X2),X3),X3),X2) ),
    inference(spm,[status(thm)],[c_0_42,c_0_21]) ).

cnf(c_0_54,plain,
    union(X1,intersection(X1,X2)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45])]) ).

cnf(c_0_55,negated_conjecture,
    ( intersection(X1,esk4_0) = X1
    | ~ member(esk2_2(intersection(X1,esk4_0),X1),esk3_0) ),
    inference(spm,[status(thm)],[c_0_32,c_0_46]) ).

cnf(c_0_56,plain,
    ( intersection(union(X1,X2),X3) = union(X1,X2)
    | member(esk2_2(intersection(union(X1,X2),X3),union(X1,X2)),X1)
    | member(esk2_2(intersection(union(X1,X2),X3),union(X1,X2)),X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_18]) ).

cnf(c_0_57,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_58,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_47,c_0_18]) ).

cnf(c_0_59,plain,
    subset(X1,intersection(X1,X1)),
    inference(spm,[status(thm)],[c_0_48,c_0_16]) ).

cnf(c_0_60,plain,
    subset(intersection(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_49,c_0_33]) ).

cnf(c_0_61,plain,
    ( subset(intersection(X1,X2),intersection(X1,union(X3,X4)))
    | ~ member(esk1_2(intersection(X1,X2),intersection(X1,union(X3,X4))),X4) ),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_62,plain,
    ( subset(intersection(X1,union(X2,X3)),X3)
    | member(esk1_2(intersection(X1,union(X2,X3)),X3),X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_52]) ).

cnf(c_0_63,plain,
    ( intersection(X1,X2) = X2
    | ~ member(esk2_2(intersection(X1,X2),X2),intersection(X1,X3)) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_64,negated_conjecture,
    ( intersection(esk4_0,union(X1,esk3_0)) = union(X1,esk3_0)
    | member(esk2_2(intersection(esk4_0,union(X1,esk3_0)),union(X1,esk3_0)),X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_33]),c_0_33]) ).

cnf(c_0_65,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_57]) ).

cnf(c_0_66,plain,
    subset(intersection(X1,X2),intersection(X2,intersection(X1,X2))),
    inference(spm,[status(thm)],[c_0_48,c_0_31]) ).

cnf(c_0_67,plain,
    intersection(intersection(X1,X2),union(X3,X2)) = intersection(X1,X2),
    inference(spm,[status(thm)],[c_0_32,c_0_58]) ).

cnf(c_0_68,plain,
    intersection(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_59]),c_0_60])]) ).

cnf(c_0_69,plain,
    subset(intersection(X1,union(X2,intersection(X1,union(X3,X2)))),intersection(X1,union(X3,X2))),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

cnf(c_0_70,negated_conjecture,
    intersection(esk4_0,union(esk3_0,intersection(esk4_0,X1))) = union(esk3_0,intersection(esk4_0,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_36]),c_0_36]) ).

cnf(c_0_71,plain,
    ( subset(X1,union(union(X2,X3),X4))
    | ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3) ),
    inference(spm,[status(thm)],[c_0_65,c_0_21]) ).

cnf(c_0_72,plain,
    ( subset(union(X1,X2),union(X3,X2))
    | member(esk1_2(union(X1,X2),union(X3,X2)),X1) ),
    inference(spm,[status(thm)],[c_0_29,c_0_20]) ).

cnf(c_0_73,plain,
    intersection(X1,intersection(X2,X1)) = intersection(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_66]),c_0_49])]) ).

cnf(c_0_74,plain,
    intersection(X1,union(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_75,negated_conjecture,
    subset(union(esk3_0,intersection(esk4_0,union(X1,esk3_0))),intersection(esk4_0,union(X1,esk3_0))),
    inference(spm,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_76,plain,
    subset(union(X1,X2),union(union(X3,X1),X2)),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_77,plain,
    union(X1,intersection(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_54,c_0_73]) ).

cnf(c_0_78,plain,
    intersection(X1,union(X1,X2)) = X1,
    inference(spm,[status(thm)],[c_0_74,c_0_36]) ).

cnf(c_0_79,negated_conjecture,
    union(esk3_0,intersection(esk4_0,union(X1,esk3_0))) = intersection(esk4_0,union(X1,esk3_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_75]),c_0_37])]) ).

cnf(c_0_80,plain,
    ( subset(X1,intersection(intersection(X2,X3),X1))
    | ~ member(esk1_2(X1,intersection(intersection(X2,X3),X1)),X3)
    | ~ member(esk1_2(X1,intersection(intersection(X2,X3),X1)),X2) ),
    inference(spm,[status(thm)],[c_0_48,c_0_25]) ).

cnf(c_0_81,plain,
    ( subset(intersection(X1,X2),X3)
    | member(esk1_2(intersection(X1,X2),X3),union(X4,X2)) ),
    inference(spm,[status(thm)],[c_0_47,c_0_16]) ).

cnf(c_0_82,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_29,c_0_25]) ).

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

cnf(c_0_84,negated_conjecture,
    intersection(esk3_0,intersection(esk4_0,union(X1,esk3_0))) = esk3_0,
    inference(spm,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_85,plain,
    ( subset(intersection(X1,X2),intersection(intersection(X3,union(X4,X2)),intersection(X1,X2)))
    | ~ member(esk1_2(intersection(X1,X2),intersection(intersection(X3,union(X4,X2)),intersection(X1,X2))),X3) ),
    inference(spm,[status(thm)],[c_0_80,c_0_81]) ).

cnf(c_0_86,plain,
    ( subset(intersection(X1,X2),union(X3,intersection(X4,X1)))
    | ~ member(esk1_2(intersection(X1,X2),union(X3,intersection(X4,X1))),X4) ),
    inference(spm,[status(thm)],[c_0_82,c_0_51]) ).

cnf(c_0_87,plain,
    ( subset(intersection(X1,union(X2,X3)),union(X3,X4))
    | member(esk1_2(intersection(X1,union(X2,X3)),union(X3,X4)),X2) ),
    inference(spm,[status(thm)],[c_0_65,c_0_52]) ).

cnf(c_0_88,plain,
    subset(union(intersection(X1,X2),intersection(X3,X2)),X2),
    inference(spm,[status(thm)],[c_0_83,c_0_77]) ).

cnf(c_0_89,negated_conjecture,
    intersection(esk3_0,intersection(esk4_0,union(esk3_0,X1))) = esk3_0,
    inference(spm,[status(thm)],[c_0_84,c_0_36]) ).

cnf(c_0_90,plain,
    subset(intersection(X1,X2),intersection(intersection(X1,X2),intersection(X1,union(X3,X2)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_51]),c_0_33]) ).

cnf(c_0_91,plain,
    subset(intersection(X1,union(X2,X3)),union(X3,intersection(X2,X1))),
    inference(spm,[status(thm)],[c_0_86,c_0_87]) ).

cnf(c_0_92,negated_conjecture,
    subset(union(esk3_0,intersection(X1,intersection(esk4_0,union(esk3_0,X2)))),intersection(esk4_0,union(esk3_0,X2))),
    inference(spm,[status(thm)],[c_0_88,c_0_89]) ).

cnf(c_0_93,plain,
    intersection(intersection(X1,X2),intersection(X1,union(X3,X2))) = intersection(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_90]),c_0_60])]) ).

cnf(c_0_94,plain,
    subset(intersection(X1,union(X2,X3)),union(X3,intersection(X1,X2))),
    inference(spm,[status(thm)],[c_0_91,c_0_33]) ).

cnf(c_0_95,negated_conjecture,
    union(esk3_0,intersection(esk5_0,esk4_0)) != intersection(union(esk3_0,esk5_0),esk4_0),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_96,negated_conjecture,
    subset(union(esk3_0,intersection(esk4_0,X1)),intersection(esk4_0,union(esk3_0,X1))),
    inference(spm,[status(thm)],[c_0_92,c_0_93]) ).

cnf(c_0_97,plain,
    subset(intersection(X1,union(X2,X3)),union(X2,intersection(X1,X3))),
    inference(spm,[status(thm)],[c_0_94,c_0_36]) ).

cnf(c_0_98,negated_conjecture,
    intersection(esk4_0,union(esk3_0,esk5_0)) != union(esk3_0,intersection(esk4_0,esk5_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_33]),c_0_33]) ).

cnf(c_0_99,negated_conjecture,
    intersection(esk4_0,union(esk3_0,X1)) = union(esk3_0,intersection(esk4_0,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_96]),c_0_97])]) ).

cnf(c_0_100,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_99])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET144+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33  % Computer : n007.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Sat Aug 26 15:27:56 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.59  start to proof: theBenchmark
% 87.09/87.08  % Version  : CSE_E---1.5
% 87.09/87.08  % Problem  : theBenchmark.p
% 87.09/87.08  % Proof found
% 87.09/87.08  % SZS status Theorem for theBenchmark.p
% 87.09/87.08  % SZS output start Proof
% See solution above
% 87.09/87.09  % Total time : 86.487000 s
% 87.09/87.09  % SZS output end Proof
% 87.09/87.09  % Total time : 86.493000 s
%------------------------------------------------------------------------------