TSTP Solution File: SET634+3 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : SET634+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n009.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 : Tue May 21 02:55:05 EDT 2024

% Result   : Theorem 95.71s 12.47s
% Output   : CNFRefutation 95.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    7
% Syntax   : Number of formulae    :  112 (  53 unt;   0 def)
%            Number of atoms       :  213 (  48 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :  164 (  63   ~;  80   |;  13   &)
%                                         (   6 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            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   :  314 (  46 sgn  42   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(difference_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_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(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(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(member_equal,axiom,
    ! [X1,X2] :
      ( ! [X3] :
          ( member(X3,X1)
        <=> member(X3,X2) )
     => X1 = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).

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

fof(c_0_7,plain,
    ! [X1,X2,X3] :
      ( member(X3,difference(X1,X2))
    <=> ( member(X3,X1)
        & ~ member(X3,X2) ) ),
    inference(fof_simplification,[status(thm)],[difference_defn]) ).

fof(c_0_8,plain,
    ! [X10,X11,X12] :
      ( ( member(X12,X10)
        | ~ member(X12,intersection(X10,X11)) )
      & ( member(X12,X11)
        | ~ member(X12,intersection(X10,X11)) )
      & ( ~ member(X12,X10)
        | ~ member(X12,X11)
        | member(X12,intersection(X10,X11)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])])]) ).

fof(c_0_9,plain,
    ! [X25,X26,X27,X28,X29] :
      ( ( ~ subset(X25,X26)
        | ~ member(X27,X25)
        | member(X27,X26) )
      & ( member(esk6_2(X28,X29),X28)
        | subset(X28,X29) )
      & ( ~ member(esk6_2(X28,X29),X29)
        | subset(X28,X29) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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,difference(X7,X8)) )
      & ( ~ member(X9,X8)
        | ~ member(X9,difference(X7,X8)) )
      & ( ~ member(X9,X7)
        | member(X9,X8)
        | member(X9,difference(X7,X8)) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).

cnf(c_0_11,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    ( member(esk6_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_13,plain,
    ( member(X1,X2)
    | ~ member(X1,difference(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_14,plain,
    ( subset(X1,X2)
    | ~ member(esk6_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_15,plain,
    ( subset(intersection(X1,X2),X3)
    | member(esk6_2(intersection(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

fof(c_0_16,plain,
    ! [X13,X14] : intersection(X13,X14) = intersection(X14,X13),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

fof(c_0_17,plain,
    ! [X31,X32] :
      ( ( subset(X31,X32)
        | X31 != X32 )
      & ( subset(X32,X31)
        | X31 != X32 )
      & ( ~ subset(X31,X32)
        | ~ subset(X32,X31)
        | X31 = X32 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])])]) ).

cnf(c_0_18,plain,
    ( subset(difference(X1,X2),X3)
    | member(esk6_2(difference(X1,X2),X3),X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_12]) ).

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

cnf(c_0_20,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_21,plain,
    subset(intersection(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_22,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_24,plain,
    subset(difference(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_14,c_0_18]) ).

cnf(c_0_25,plain,
    ( subset(difference(X1,X2),X3)
    | ~ member(esk6_2(difference(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_12]) ).

cnf(c_0_26,plain,
    ( subset(intersection(X1,X2),X3)
    | member(esk6_2(intersection(X1,X2),X3),X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_12]) ).

cnf(c_0_27,plain,
    subset(intersection(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_28,plain,
    ( difference(X1,X2) = X1
    | ~ subset(X1,difference(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,plain,
    subset(difference(X1,X1),X2),
    inference(spm,[status(thm)],[c_0_25,c_0_18]) ).

cnf(c_0_30,plain,
    ( subset(intersection(difference(X1,X2),X3),X4)
    | ~ member(esk6_2(intersection(difference(X1,X2),X3),X4),X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_26]) ).

cnf(c_0_31,plain,
    ( subset(intersection(X1,difference(X2,X3)),X4)
    | member(esk6_2(intersection(X1,difference(X2,X3)),X4),X2) ),
    inference(spm,[status(thm)],[c_0_13,c_0_15]) ).

cnf(c_0_32,plain,
    ( intersection(X1,X2) = X1
    | ~ subset(X1,intersection(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_27]) ).

cnf(c_0_33,plain,
    difference(difference(X1,X1),X2) = difference(X1,X1),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_34,plain,
    ( member(X1,X3)
    | member(X1,difference(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_35,plain,
    ( X1 = difference(X2,X2)
    | ~ subset(X1,difference(X2,X2)) ),
    inference(spm,[status(thm)],[c_0_23,c_0_29]) ).

cnf(c_0_36,plain,
    subset(intersection(difference(X1,X2),difference(X2,X3)),X4),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_37,plain,
    intersection(difference(X1,X1),X2) = difference(X1,X1),
    inference(spm,[status(thm)],[c_0_32,c_0_29]) ).

cnf(c_0_38,plain,
    ( ~ member(X1,difference(X2,X2))
    | ~ member(X1,X3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_33]) ).

cnf(c_0_39,plain,
    ( subset(X1,difference(X2,X3))
    | member(esk6_2(X1,difference(X2,X3)),X3)
    | ~ member(esk6_2(X1,difference(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_34]) ).

cnf(c_0_40,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_41,plain,
    intersection(difference(X1,X2),difference(X2,X3)) = difference(X4,X4),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_42,plain,
    ~ member(X1,difference(X2,X2)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_37]),c_0_38]) ).

cnf(c_0_43,plain,
    ( subset(X1,difference(X1,X2))
    | member(esk6_2(X1,difference(X1,X2)),X2) ),
    inference(spm,[status(thm)],[c_0_39,c_0_12]) ).

cnf(c_0_44,plain,
    ( subset(difference(difference(X1,X2),X3),X4)
    | member(esk6_2(difference(difference(X1,X2),X3),X4),X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_18]) ).

cnf(c_0_45,plain,
    ( ~ member(X1,difference(X2,X3))
    | ~ member(X1,difference(X4,X2)) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).

cnf(c_0_46,plain,
    subset(X1,difference(X1,difference(X2,X2))),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_47,plain,
    subset(difference(difference(X1,X2),X1),X3),
    inference(spm,[status(thm)],[c_0_25,c_0_44]) ).

cnf(c_0_48,plain,
    ( subset(difference(X1,X2),X3)
    | ~ member(esk6_2(difference(X1,X2),X3),difference(X4,X1)) ),
    inference(spm,[status(thm)],[c_0_45,c_0_12]) ).

cnf(c_0_49,plain,
    difference(X1,difference(X2,X2)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_46]),c_0_24])]) ).

cnf(c_0_50,plain,
    difference(difference(difference(X1,X2),X1),X3) = difference(difference(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_28,c_0_47]) ).

cnf(c_0_51,plain,
    subset(difference(X1,X2),difference(difference(X1,X2),difference(X3,X1))),
    inference(spm,[status(thm)],[c_0_48,c_0_43]) ).

cnf(c_0_52,plain,
    difference(X1,difference(difference(X2,X3),X2)) = X1,
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_53,plain,
    ( subset(X1,intersection(X2,X3))
    | ~ member(esk6_2(X1,intersection(X2,X3)),X3)
    | ~ member(esk6_2(X1,intersection(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_14,c_0_40]) ).

cnf(c_0_54,plain,
    ( subset(difference(intersection(X1,X2),X3),X4)
    | member(esk6_2(difference(intersection(X1,X2),X3),X4),X2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_18]) ).

cnf(c_0_55,plain,
    ( subset(difference(X1,difference(X2,X3)),X4)
    | member(esk6_2(difference(X1,difference(X2,X3)),X4),X3)
    | ~ member(esk6_2(difference(X1,difference(X2,X3)),X4),X2) ),
    inference(spm,[status(thm)],[c_0_25,c_0_34]) ).

cnf(c_0_56,plain,
    ( subset(difference(intersection(X1,X2),X3),X4)
    | member(esk6_2(difference(intersection(X1,X2),X3),X4),X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_18]) ).

cnf(c_0_57,plain,
    ( subset(intersection(X1,X2),difference(X2,X3))
    | member(esk6_2(intersection(X1,X2),difference(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_39,c_0_15]) ).

cnf(c_0_58,plain,
    subset(X1,difference(X1,difference(X2,X1))),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_59,plain,
    ( subset(intersection(X1,difference(X2,X3)),X4)
    | ~ member(esk6_2(intersection(X1,difference(X2,X3)),X4),X3) ),
    inference(spm,[status(thm)],[c_0_19,c_0_15]) ).

cnf(c_0_60,plain,
    ( subset(difference(intersection(X1,X2),X3),intersection(X4,X2))
    | ~ member(esk6_2(difference(intersection(X1,X2),X3),intersection(X4,X2)),X4) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_61,plain,
    ( subset(difference(intersection(X1,X2),difference(X1,X3)),X4)
    | member(esk6_2(difference(intersection(X1,X2),difference(X1,X3)),X4),X3) ),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_62,plain,
    ( subset(difference(X1,X2),intersection(X3,X1))
    | ~ member(esk6_2(difference(X1,X2),intersection(X3,X1)),X3) ),
    inference(spm,[status(thm)],[c_0_53,c_0_18]) ).

cnf(c_0_63,plain,
    ( subset(difference(X1,difference(X1,X2)),X3)
    | member(esk6_2(difference(X1,difference(X1,X2)),X3),X2) ),
    inference(spm,[status(thm)],[c_0_55,c_0_18]) ).

cnf(c_0_64,plain,
    subset(intersection(difference(X1,X2),X3),difference(X3,X2)),
    inference(spm,[status(thm)],[c_0_30,c_0_57]) ).

cnf(c_0_65,plain,
    difference(X1,difference(X2,X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_58]),c_0_24])]) ).

cnf(c_0_66,plain,
    subset(intersection(X1,difference(X2,X1)),X3),
    inference(spm,[status(thm)],[c_0_59,c_0_26]) ).

cnf(c_0_67,plain,
    subset(difference(intersection(X1,X2),difference(X1,X3)),intersection(X3,X2)),
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_68,plain,
    ( subset(intersection(X1,X2),intersection(X3,X2))
    | ~ member(esk6_2(intersection(X1,X2),intersection(X3,X2)),X3) ),
    inference(spm,[status(thm)],[c_0_53,c_0_15]) ).

cnf(c_0_69,plain,
    ( subset(intersection(intersection(X1,X2),X3),X4)
    | member(esk6_2(intersection(intersection(X1,X2),X3),X4),X2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_26]) ).

cnf(c_0_70,plain,
    subset(difference(X1,difference(X1,X2)),intersection(X2,X1)),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_71,plain,
    subset(intersection(X1,X2),difference(X2,difference(X3,X1))),
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_72,plain,
    ( X1 = intersection(X2,difference(X3,X2))
    | ~ subset(X1,intersection(X2,difference(X3,X2))) ),
    inference(spm,[status(thm)],[c_0_23,c_0_66]) ).

cnf(c_0_73,plain,
    subset(difference(intersection(X1,X2),difference(X1,X3)),intersection(X2,X3)),
    inference(spm,[status(thm)],[c_0_67,c_0_22]) ).

cnf(c_0_74,plain,
    difference(intersection(X1,difference(X2,X1)),X3) = intersection(X1,difference(X2,X1)),
    inference(spm,[status(thm)],[c_0_28,c_0_66]) ).

cnf(c_0_75,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X2,X3)),
    inference(spm,[status(thm)],[c_0_68,c_0_69]) ).

cnf(c_0_76,plain,
    difference(X1,difference(X1,X2)) = intersection(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_70]),c_0_71])]) ).

cnf(c_0_77,plain,
    difference(intersection(X1,X2),difference(X1,difference(X3,X2))) = intersection(X2,difference(X3,X2)),
    inference(spm,[status(thm)],[c_0_72,c_0_73]) ).

cnf(c_0_78,plain,
    difference(X1,intersection(X2,difference(X3,X2))) = X1,
    inference(spm,[status(thm)],[c_0_49,c_0_74]) ).

fof(c_0_79,plain,
    ! [X15,X16] :
      ( ( ~ member(esk4_2(X15,X16),X15)
        | ~ member(esk4_2(X15,X16),X16)
        | X15 = X16 )
      & ( member(esk4_2(X15,X16),X15)
        | member(esk4_2(X15,X16),X16)
        | X15 = X16 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[member_equal])])])])]) ).

cnf(c_0_80,plain,
    ( subset(intersection(X1,intersection(X2,X3)),X4)
    | member(esk6_2(intersection(X1,intersection(X2,X3)),X4),X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_15]) ).

cnf(c_0_81,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X3,X2)),
    inference(spm,[status(thm)],[c_0_75,c_0_22]) ).

cnf(c_0_82,plain,
    intersection(intersection(X1,X2),difference(X1,difference(X3,X2))) = intersection(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_22]) ).

cnf(c_0_83,plain,
    ( subset(intersection(X1,X2),intersection(X3,X1))
    | ~ member(esk6_2(intersection(X1,X2),intersection(X3,X1)),X3) ),
    inference(spm,[status(thm)],[c_0_53,c_0_26]) ).

cnf(c_0_84,plain,
    ( member(esk4_2(X1,X2),X1)
    | member(esk4_2(X1,X2),X2)
    | X1 = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_79]) ).

cnf(c_0_85,plain,
    subset(intersection(X1,intersection(X2,X3)),X2),
    inference(spm,[status(thm)],[c_0_14,c_0_80]) ).

cnf(c_0_86,plain,
    subset(intersection(X1,X2),intersection(X2,difference(X1,difference(X3,X2)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_22]) ).

cnf(c_0_87,plain,
    subset(intersection(X1,difference(X2,X3)),intersection(X2,X1)),
    inference(spm,[status(thm)],[c_0_83,c_0_31]) ).

cnf(c_0_88,plain,
    ( X1 = X2
    | ~ member(esk4_2(X1,X2),X1)
    | ~ member(esk4_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_79]) ).

cnf(c_0_89,plain,
    ( X1 = intersection(X2,X3)
    | member(esk4_2(X1,intersection(X2,X3)),X1)
    | member(esk4_2(X1,intersection(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_11,c_0_84]) ).

cnf(c_0_90,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_91,plain,
    subset(intersection(intersection(X1,X2),X3),X1),
    inference(spm,[status(thm)],[c_0_85,c_0_22]) ).

cnf(c_0_92,plain,
    intersection(X1,difference(X2,difference(X3,X1))) = intersection(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_86]),c_0_87])]) ).

cnf(c_0_93,plain,
    ( X1 = intersection(X2,X3)
    | ~ member(esk4_2(X1,intersection(X2,X3)),X1)
    | ~ member(esk4_2(X1,intersection(X2,X3)),X3)
    | ~ member(esk4_2(X1,intersection(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_88,c_0_40]) ).

cnf(c_0_94,plain,
    ( intersection(X1,X2) = X2
    | member(esk4_2(X2,intersection(X1,X2)),X2) ),
    inference(ef,[status(thm)],[c_0_89]) ).

cnf(c_0_95,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(intersection(X2,X3),X4)) ),
    inference(spm,[status(thm)],[c_0_90,c_0_91]) ).

cnf(c_0_96,plain,
    intersection(difference(X1,X2),difference(X3,X2)) = intersection(X3,difference(X1,X2)),
    inference(spm,[status(thm)],[c_0_92,c_0_65]) ).

cnf(c_0_97,plain,
    ( intersection(X1,X2) = X2
    | ~ member(esk4_2(X2,intersection(X1,X2)),X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_94]) ).

cnf(c_0_98,plain,
    ( intersection(X1,intersection(intersection(X2,X3),X4)) = intersection(intersection(X2,X3),X4)
    | member(esk4_2(intersection(intersection(X2,X3),X4),intersection(X1,intersection(intersection(X2,X3),X4))),X2) ),
    inference(spm,[status(thm)],[c_0_95,c_0_94]) ).

cnf(c_0_99,plain,
    subset(difference(X1,X2),intersection(X1,difference(X1,X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_12]),c_0_22]) ).

fof(c_0_100,negated_conjecture,
    ~ ! [X1,X2,X3] : intersection(X1,difference(X2,X3)) = difference(intersection(X1,X2),X3),
    inference(assume_negation,[status(cth)],[prove_difference_and_intersection]) ).

cnf(c_0_101,plain,
    intersection(X1,difference(X2,X3)) = intersection(X2,difference(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_96]),c_0_96]) ).

cnf(c_0_102,plain,
    intersection(X1,intersection(intersection(X1,X2),X3)) = intersection(intersection(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_97,c_0_98]) ).

cnf(c_0_103,plain,
    intersection(X1,difference(X1,X2)) = difference(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_99]),c_0_21])]) ).

fof(c_0_104,negated_conjecture,
    intersection(esk1_0,difference(esk2_0,esk3_0)) != difference(intersection(esk1_0,esk2_0),esk3_0),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])])]) ).

cnf(c_0_105,plain,
    intersection(X1,difference(X2,difference(X1,X3))) = intersection(X2,intersection(X3,X1)),
    inference(spm,[status(thm)],[c_0_101,c_0_76]) ).

cnf(c_0_106,plain,
    difference(difference(X1,X2),difference(X3,X1)) = difference(X1,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_51]),c_0_24])]) ).

cnf(c_0_107,plain,
    intersection(difference(X1,X2),X3) = intersection(X1,difference(X3,X2)),
    inference(spm,[status(thm)],[c_0_22,c_0_101]) ).

cnf(c_0_108,plain,
    intersection(X1,difference(intersection(X1,X2),X3)) = difference(intersection(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_102,c_0_103]) ).

cnf(c_0_109,negated_conjecture,
    intersection(esk1_0,difference(esk2_0,esk3_0)) != difference(intersection(esk1_0,esk2_0),esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_104]) ).

cnf(c_0_110,plain,
    difference(intersection(X1,X2),X3) = intersection(X2,difference(X1,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107]),c_0_108]) ).

cnf(c_0_111,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110]),c_0_101])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem    : SET634+3 : TPTP v8.2.0. Released v2.2.0.
% 0.02/0.09  % Command    : run_E %s %d THM
% 0.09/0.29  % Computer : n009.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit   : 300
% 0.09/0.29  % WCLimit    : 300
% 0.09/0.29  % DateTime   : Mon May 20 12:59:22 EDT 2024
% 0.09/0.29  % CPUTime    : 
% 0.14/0.39  Running first-order theorem proving
% 0.14/0.39  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 95.71/12.47  # Version: 3.1.0
% 95.71/12.47  # Preprocessing class: FSMSSMSSSSSNFFN.
% 95.71/12.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 95.71/12.47  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 95.71/12.47  # Starting new_bool_3 with 300s (1) cores
% 95.71/12.47  # Starting new_bool_1 with 300s (1) cores
% 95.71/12.47  # Starting sh5l with 300s (1) cores
% 95.71/12.47  # sh5l with pid 770 completed with status 0
% 95.71/12.47  # Result found by sh5l
% 95.71/12.47  # Preprocessing class: FSMSSMSSSSSNFFN.
% 95.71/12.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 95.71/12.47  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 95.71/12.47  # Starting new_bool_3 with 300s (1) cores
% 95.71/12.47  # Starting new_bool_1 with 300s (1) cores
% 95.71/12.47  # Starting sh5l with 300s (1) cores
% 95.71/12.47  # SinE strategy is gf500_gu_R04_F100_L20000
% 95.71/12.47  # Search class: FGHSS-FFSF22-SFFFFFNN
% 95.71/12.47  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 95.71/12.47  # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 181s (1) cores
% 95.71/12.47  # G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with pid 777 completed with status 0
% 95.71/12.47  # Result found by G-E--_300_C18_F1_SE_CS_SP_PS_S0Y
% 95.71/12.47  # Preprocessing class: FSMSSMSSSSSNFFN.
% 95.71/12.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 95.71/12.47  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 95.71/12.47  # Starting new_bool_3 with 300s (1) cores
% 95.71/12.47  # Starting new_bool_1 with 300s (1) cores
% 95.71/12.47  # Starting sh5l with 300s (1) cores
% 95.71/12.47  # SinE strategy is gf500_gu_R04_F100_L20000
% 95.71/12.47  # Search class: FGHSS-FFSF22-SFFFFFNN
% 95.71/12.47  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 95.71/12.47  # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 181s (1) cores
% 95.71/12.47  # Preprocessing time       : 0.001 s
% 95.71/12.47  # Presaturation interreduction done
% 95.71/12.47  
% 95.71/12.47  # Proof found!
% 95.71/12.47  # SZS status Theorem
% 95.71/12.47  # SZS output start CNFRefutation
% See solution above
% 95.71/12.47  # Parsed axioms                        : 9
% 95.71/12.47  # Removed by relevancy pruning/SinE    : 0
% 95.71/12.47  # Initial clauses                      : 21
% 95.71/12.47  # Removed in clause preprocessing      : 2
% 95.71/12.47  # Initial clauses in saturation        : 19
% 95.71/12.47  # Processed clauses                    : 75059
% 95.71/12.47  # ...of these trivial                  : 3584
% 95.71/12.47  # ...subsumed                          : 68839
% 95.71/12.47  # ...remaining for further processing  : 2636
% 95.71/12.47  # Other redundant clauses eliminated   : 2
% 95.71/12.47  # Clauses deleted for lack of memory   : 0
% 95.71/12.47  # Backward-subsumed                    : 21
% 95.71/12.47  # Backward-rewritten                   : 1161
% 95.71/12.47  # Generated clauses                    : 1394835
% 95.71/12.47  # ...of the previous two non-redundant : 944235
% 95.71/12.47  # ...aggressively subsumed             : 0
% 95.71/12.47  # Contextual simplify-reflections      : 27
% 95.71/12.47  # Paramodulations                      : 1394293
% 95.71/12.47  # Factorizations                       : 540
% 95.71/12.47  # NegExts                              : 0
% 95.71/12.47  # Equation resolutions                 : 2
% 95.71/12.47  # Disequality decompositions           : 0
% 95.71/12.47  # Total rewrite steps                  : 2029509
% 95.71/12.47  # ...of those cached                   : 1961749
% 95.71/12.47  # Propositional unsat checks           : 0
% 95.71/12.47  #    Propositional check models        : 0
% 95.71/12.47  #    Propositional check unsatisfiable : 0
% 95.71/12.47  #    Propositional clauses             : 0
% 95.71/12.47  #    Propositional clauses after purity: 0
% 95.71/12.47  #    Propositional unsat core size     : 0
% 95.71/12.47  #    Propositional preprocessing time  : 0.000
% 95.71/12.47  #    Propositional encoding time       : 0.000
% 95.71/12.47  #    Propositional solver time         : 0.000
% 95.71/12.47  #    Success case prop preproc time    : 0.000
% 95.71/12.47  #    Success case prop encoding time   : 0.000
% 95.71/12.47  #    Success case prop solver time     : 0.000
% 95.71/12.47  # Current number of processed clauses  : 1435
% 95.71/12.47  #    Positive orientable unit clauses  : 367
% 95.71/12.47  #    Positive unorientable unit clauses: 13
% 95.71/12.47  #    Negative unit clauses             : 4
% 95.71/12.47  #    Non-unit-clauses                  : 1051
% 95.71/12.47  # Current number of unprocessed clauses: 867209
% 95.71/12.47  # ...number of literals in the above   : 1963586
% 95.71/12.47  # Current number of archived formulas  : 0
% 95.71/12.47  # Current number of archived clauses   : 1199
% 95.71/12.47  # Clause-clause subsumption calls (NU) : 654256
% 95.71/12.47  # Rec. Clause-clause subsumption calls : 358435
% 95.71/12.47  # Non-unit clause-clause subsumptions  : 11826
% 95.71/12.47  # Unit Clause-clause subsumption calls : 434672
% 95.71/12.47  # Rewrite failures with RHS unbound    : 9802
% 95.71/12.47  # BW rewrite match attempts            : 17682
% 95.71/12.47  # BW rewrite match successes           : 1201
% 95.71/12.47  # Condensation attempts                : 0
% 95.71/12.47  # Condensation successes               : 0
% 95.71/12.47  # Termbank termtop insertions          : 18141791
% 95.71/12.47  # Search garbage collected termcells   : 353
% 95.71/12.47  
% 95.71/12.47  # -------------------------------------------------
% 95.71/12.47  # User time                : 11.417 s
% 95.71/12.47  # System time              : 0.485 s
% 95.71/12.47  # Total time               : 11.902 s
% 95.71/12.47  # Maximum resident set size: 1752 pages
% 95.71/12.47  
% 95.71/12.47  # -------------------------------------------------
% 95.71/12.47  # User time                : 11.418 s
% 95.71/12.47  # System time              : 0.487 s
% 95.71/12.47  # Total time               : 11.905 s
% 95.71/12.47  # Maximum resident set size: 1692 pages
% 95.71/12.47  % E---3.1 exiting
% 95.71/12.47  % E exiting
%------------------------------------------------------------------------------