TSTP Solution File: SET169+3 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n027.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:22:21 EDT 2023

% Result   : Theorem 1401.94s 198.61s
% Output   : CNFRefutation 1401.94s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    7
% Syntax   : Number of formulae    :  104 (  55 unt;   0 def)
%            Number of atoms       :  187 (  31 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :  137 (  54   ~;  68   |;  10   &)
%                                         (   4 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  284 (  40 sgn;  38   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( member(X3,X1)
         => member(X3,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.QfAWT7Xx5q/E---3.1_15954.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/tmp/tmp.QfAWT7Xx5q/E---3.1_15954.p',intersection_defn) ).

fof(union_defn,axiom,
    ! [X1,X2,X3] :
      ( member(X3,union(X1,X2))
    <=> ( member(X3,X1)
        | member(X3,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.QfAWT7Xx5q/E---3.1_15954.p',union_defn) ).

fof(commutativity_of_intersection,axiom,
    ! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
    file('/export/starexec/sandbox2/tmp/tmp.QfAWT7Xx5q/E---3.1_15954.p',commutativity_of_intersection) ).

fof(equal_defn,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.QfAWT7Xx5q/E---3.1_15954.p',equal_defn) ).

fof(commutativity_of_union,axiom,
    ! [X1,X2] : union(X1,X2) = union(X2,X1),
    file('/export/starexec/sandbox2/tmp/tmp.QfAWT7Xx5q/E---3.1_15954.p',commutativity_of_union) ).

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/tmp/tmp.QfAWT7Xx5q/E---3.1_15954.p',prove_intersection_distributes_over_union) ).

fof(c_0_7,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_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])])]) ).

cnf(c_0_9,plain,
    ( subset(X1,X2)
    | ~ member(esk1_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_10,plain,
    ( member(X1,intersection(X2,X3))
    | ~ member(X1,X2)
    | ~ member(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_11,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_9,c_0_10]) ).

cnf(c_0_12,plain,
    ( member(esk1_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_13,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])])]) ).

cnf(c_0_14,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_15,plain,
    ( subset(X1,intersection(X2,X1))
    | ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_16,plain,
    ( member(X1,X2)
    | ~ member(X1,intersection(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_17,plain,
    ( member(X1,union(X3,X2))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_18,plain,
    ( subset(intersection(X1,X2),X3)
    | member(esk1_2(intersection(X1,X2),X3),X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_12]) ).

fof(c_0_19,plain,
    ! [X14,X15] : intersection(X14,X15) = intersection(X15,X14),
    inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).

cnf(c_0_20,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_15,c_0_10]) ).

cnf(c_0_21,plain,
    ( subset(intersection(X1,X2),X3)
    | member(esk1_2(intersection(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_12]) ).

fof(c_0_22,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_23,plain,
    ( subset(X1,intersection(union(X2,X3),X1))
    | ~ member(esk1_2(X1,intersection(union(X2,X3),X1)),X3) ),
    inference(spm,[status(thm)],[c_0_15,c_0_17]) ).

cnf(c_0_24,plain,
    subset(intersection(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_9,c_0_18]) ).

cnf(c_0_25,plain,
    intersection(X1,X2) = intersection(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_26,plain,
    ( subset(intersection(X1,X2),intersection(intersection(X3,X1),intersection(X1,X2)))
    | ~ member(esk1_2(intersection(X1,X2),intersection(intersection(X3,X1),intersection(X1,X2))),X3) ),
    inference(spm,[status(thm)],[c_0_20,c_0_18]) ).

cnf(c_0_27,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_21]) ).

cnf(c_0_28,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,plain,
    subset(intersection(X1,X2),intersection(union(X3,X2),intersection(X1,X2))),
    inference(spm,[status(thm)],[c_0_23,c_0_21]) ).

cnf(c_0_30,plain,
    subset(intersection(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_31,plain,
    ( subset(intersection(X1,X2),intersection(X3,X2))
    | ~ member(esk1_2(intersection(X1,X2),intersection(X3,X2)),X3) ),
    inference(spm,[status(thm)],[c_0_11,c_0_21]) ).

cnf(c_0_32,plain,
    ( subset(intersection(intersection(X1,X2),X3),X4)
    | member(esk1_2(intersection(intersection(X1,X2),X3),X4),X2) ),
    inference(spm,[status(thm)],[c_0_16,c_0_18]) ).

cnf(c_0_33,plain,
    subset(intersection(X1,intersection(X2,X3)),intersection(intersection(X2,X1),intersection(X1,intersection(X2,X3)))),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_34,plain,
    intersection(union(X1,X2),intersection(X3,X2)) = intersection(X3,X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).

cnf(c_0_35,plain,
    ( subset(intersection(intersection(X1,X2),X3),X4)
    | member(esk1_2(intersection(intersection(X1,X2),X3),X4),X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_18]) ).

cnf(c_0_36,plain,
    subset(X1,intersection(X1,union(X2,X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_12]),c_0_25]) ).

fof(c_0_37,plain,
    ! [X12,X13] : union(X12,X13) = union(X13,X12),
    inference(variable_rename,[status(thm)],[commutativity_of_union]) ).

cnf(c_0_38,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X2,X3)),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_39,plain,
    subset(intersection(X1,X2),intersection(intersection(X1,X2),intersection(X1,union(X3,X2)))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_25]) ).

cnf(c_0_40,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X1,X3)),
    inference(spm,[status(thm)],[c_0_31,c_0_35]) ).

cnf(c_0_41,plain,
    intersection(X1,union(X2,X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_36]),c_0_24])]) ).

cnf(c_0_42,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_43,plain,
    ( intersection(intersection(X1,X2),X3) = intersection(X2,X3)
    | ~ subset(intersection(X2,X3),intersection(intersection(X1,X2),X3)) ),
    inference(spm,[status(thm)],[c_0_28,c_0_38]) ).

cnf(c_0_44,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_28,c_0_39]),c_0_24])]) ).

cnf(c_0_45,plain,
    subset(intersection(X1,intersection(X2,X3)),intersection(X2,X1)),
    inference(spm,[status(thm)],[c_0_40,c_0_25]) ).

cnf(c_0_46,plain,
    intersection(X1,union(X1,X2)) = X1,
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_47,plain,
    ( subset(X1,intersection(X1,X2))
    | ~ member(esk1_2(X1,intersection(X1,X2)),X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_25]) ).

cnf(c_0_48,plain,
    intersection(X1,intersection(X2,union(X3,X1))) = intersection(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_49,plain,
    ( member(X3,X2)
    | ~ subset(X1,X2)
    | ~ member(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_50,plain,
    subset(intersection(X1,X2),intersection(X1,union(intersection(X1,X2),X3))),
    inference(spm,[status(thm)],[c_0_40,c_0_46]) ).

cnf(c_0_51,plain,
    ( member(X1,X2)
    | member(X1,X3)
    | ~ member(X1,union(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_52,plain,
    ( subset(X1,intersection(X2,X1))
    | ~ member(esk1_2(X1,intersection(X2,X1)),intersection(X2,union(X3,X1))) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_53,plain,
    ( member(X1,intersection(X2,union(intersection(X2,X3),X4)))
    | ~ member(X1,intersection(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_54,plain,
    ( member(X1,union(X2,X3))
    | ~ member(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_55,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_51,c_0_12]) ).

cnf(c_0_56,plain,
    ( subset(X1,intersection(X2,X1))
    | ~ member(esk1_2(X1,intersection(X2,X1)),intersection(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_57,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_9,c_0_17]) ).

cnf(c_0_58,plain,
    ( subset(X1,intersection(union(X2,X3),X1))
    | ~ member(esk1_2(X1,intersection(union(X2,X3),X1)),X2) ),
    inference(spm,[status(thm)],[c_0_15,c_0_54]) ).

cnf(c_0_59,plain,
    ( subset(union(X1,X2),intersection(union(X3,X1),union(X1,X2)))
    | member(esk1_2(union(X1,X2),intersection(union(X3,X1),union(X1,X2))),X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_55]) ).

cnf(c_0_60,plain,
    ( subset(union(X1,X2),X1)
    | ~ member(esk1_2(union(X1,X2),X1),intersection(X1,X3)) ),
    inference(spm,[status(thm)],[c_0_56,c_0_46]) ).

cnf(c_0_61,plain,
    ( subset(union(X1,X2),X1)
    | member(esk1_2(union(X1,X2),X1),X2) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_55]),c_0_46]),c_0_46]) ).

cnf(c_0_62,plain,
    subset(X1,union(X2,X1)),
    inference(spm,[status(thm)],[c_0_57,c_0_12]) ).

cnf(c_0_63,plain,
    subset(union(X1,X2),intersection(union(X2,X1),union(X1,X2))),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_64,plain,
    subset(intersection(X1,X2),intersection(intersection(X2,X1),intersection(X1,X2))),
    inference(spm,[status(thm)],[c_0_26,c_0_21]) ).

cnf(c_0_65,plain,
    ( subset(X1,union(X2,X3))
    | ~ member(esk1_2(X1,union(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_9,c_0_54]) ).

cnf(c_0_66,plain,
    subset(union(X1,intersection(X1,X2)),X1),
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_67,plain,
    subset(X1,union(X1,X2)),
    inference(spm,[status(thm)],[c_0_62,c_0_42]) ).

cnf(c_0_68,plain,
    intersection(union(X1,X2),union(X2,X1)) = union(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_63]),c_0_30])]) ).

cnf(c_0_69,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X3,X1)),
    inference(spm,[status(thm)],[c_0_40,c_0_25]) ).

cnf(c_0_70,plain,
    intersection(intersection(X1,X2),intersection(X2,X1)) = intersection(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_64]),c_0_30])]) ).

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_17]) ).

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_57,c_0_55]) ).

cnf(c_0_73,plain,
    union(X1,intersection(X1,X2)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_66]),c_0_67])]) ).

cnf(c_0_74,plain,
    subset(intersection(X1,union(X2,X3)),intersection(union(X3,X2),X1)),
    inference(spm,[status(thm)],[c_0_45,c_0_68]) ).

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

cnf(c_0_76,plain,
    subset(intersection(X1,intersection(X2,X3)),intersection(intersection(X3,X2),X1)),
    inference(spm,[status(thm)],[c_0_45,c_0_70]) ).

cnf(c_0_77,plain,
    subset(union(X1,X2),union(union(X3,X1),X2)),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_78,plain,
    union(X1,intersection(X2,X1)) = X1,
    inference(spm,[status(thm)],[c_0_73,c_0_48]) ).

cnf(c_0_79,plain,
    intersection(union(X1,X2),X3) = intersection(X3,union(X2,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_74]),c_0_75])]) ).

cnf(c_0_80,plain,
    subset(intersection(X1,X2),intersection(X2,intersection(union(X3,X2),X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_48]),c_0_25]) ).

cnf(c_0_81,plain,
    subset(intersection(intersection(X1,X2),X3),intersection(X3,X2)),
    inference(spm,[status(thm)],[c_0_38,c_0_25]) ).

cnf(c_0_82,plain,
    subset(union(X1,intersection(X2,union(X3,X1))),union(X3,X1)),
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

cnf(c_0_83,plain,
    intersection(X1,intersection(union(X1,X2),X3)) = intersection(X3,X1),
    inference(spm,[status(thm)],[c_0_48,c_0_79]) ).

cnf(c_0_84,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_57,c_0_10]) ).

cnf(c_0_85,plain,
    subset(intersection(X1,X2),intersection(X1,intersection(union(X3,X1),X2))),
    inference(spm,[status(thm)],[c_0_80,c_0_25]) ).

cnf(c_0_86,plain,
    subset(intersection(X1,intersection(X2,X3)),intersection(X1,X3)),
    inference(spm,[status(thm)],[c_0_81,c_0_25]) ).

fof(c_0_87,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_88,plain,
    subset(union(intersection(X1,X2),intersection(X3,X2)),X2),
    inference(spm,[status(thm)],[c_0_82,c_0_78]) ).

cnf(c_0_89,plain,
    intersection(X1,intersection(union(X1,X2),X3)) = intersection(X1,X3),
    inference(spm,[status(thm)],[c_0_25,c_0_83]) ).

cnf(c_0_90,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_65,c_0_10]) ).

cnf(c_0_91,plain,
    ( subset(X1,union(X2,intersection(X3,X1)))
    | ~ member(esk1_2(X1,union(X2,intersection(X3,X1))),X3) ),
    inference(spm,[status(thm)],[c_0_84,c_0_12]) ).

cnf(c_0_92,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_51,c_0_18]) ).

cnf(c_0_93,plain,
    intersection(X1,intersection(union(X2,X1),X3)) = intersection(X1,X3),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_85]),c_0_86])]) ).

fof(c_0_94,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_87])])]) ).

cnf(c_0_95,plain,
    subset(union(intersection(X1,X2),intersection(X3,intersection(union(X1,X4),X2))),intersection(union(X1,X4),X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_42]) ).

cnf(c_0_96,plain,
    ( subset(X1,union(intersection(X2,X1),X3))
    | ~ member(esk1_2(X1,union(intersection(X2,X1),X3)),X2) ),
    inference(spm,[status(thm)],[c_0_90,c_0_12]) ).

cnf(c_0_97,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_93]) ).

cnf(c_0_98,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_94]) ).

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

cnf(c_0_100,plain,
    subset(intersection(union(X1,X2),X3),union(intersection(X1,X3),intersection(X2,X3))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_89]) ).

cnf(c_0_101,negated_conjecture,
    union(intersection(esk4_0,esk3_0),intersection(esk5_0,esk3_0)) != intersection(esk3_0,union(esk4_0,esk5_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_25]),c_0_25]) ).

cnf(c_0_102,plain,
    union(intersection(X1,X2),intersection(X3,X2)) = intersection(union(X1,X3),X2),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_99]),c_0_100])]) ).

cnf(c_0_103,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_101,c_0_102]),c_0_25])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SET169+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.12  % Command    : run_E %s %d THM
% 0.10/0.32  % Computer : n027.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit   : 2400
% 0.10/0.32  % WCLimit    : 300
% 0.10/0.32  % DateTime   : Mon Oct  2 17:07:30 EDT 2023
% 0.10/0.32  % CPUTime    : 
% 0.16/0.44  Running first-order model finding
% 0.16/0.44  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.QfAWT7Xx5q/E---3.1_15954.p
% 1401.94/198.61  # Version: 3.1pre001
% 1401.94/198.61  # Preprocessing class: FSMSSMSSSSSNFFN.
% 1401.94/198.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1401.94/198.61  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1401.94/198.61  # Starting new_bool_3 with 300s (1) cores
% 1401.94/198.61  # Starting new_bool_1 with 300s (1) cores
% 1401.94/198.61  # Starting sh5l with 300s (1) cores
% 1401.94/198.61  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 16031 completed with status 0
% 1401.94/198.61  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1401.94/198.61  # Preprocessing class: FSMSSMSSSSSNFFN.
% 1401.94/198.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1401.94/198.61  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1401.94/198.61  # No SInE strategy applied
% 1401.94/198.61  # Search class: FGUSS-FFSF22-SFFFFFNN
% 1401.94/198.61  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1401.94/198.61  # Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 1401.94/198.61  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1401.94/198.61  # Starting new_bool_3 with 136s (1) cores
% 1401.94/198.61  # Starting new_bool_1 with 136s (1) cores
% 1401.94/198.61  # Starting sh5l with 136s (1) cores
% 1401.94/198.61  # new_bool_3 with pid 16039 completed with status 7
% 1401.94/198.61  # new_bool_1 with pid 16040 completed with status 7
% 1401.94/198.61  # Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 130s (1) cores
% 1401.94/198.61  # sh5l with pid 16041 completed with status 7
% 1401.94/198.61  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 16038 completed with status 7
% 1401.94/198.61  # U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 16100 completed with status 0
% 1401.94/198.61  # Result found by U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 1401.94/198.61  # Preprocessing class: FSMSSMSSSSSNFFN.
% 1401.94/198.61  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1401.94/198.61  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1401.94/198.61  # No SInE strategy applied
% 1401.94/198.61  # Search class: FGUSS-FFSF22-SFFFFFNN
% 1401.94/198.61  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1401.94/198.61  # Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 811s (1) cores
% 1401.94/198.61  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1401.94/198.61  # Starting new_bool_3 with 136s (1) cores
% 1401.94/198.61  # Starting new_bool_1 with 136s (1) cores
% 1401.94/198.61  # Starting sh5l with 136s (1) cores
% 1401.94/198.61  # new_bool_3 with pid 16039 completed with status 7
% 1401.94/198.61  # new_bool_1 with pid 16040 completed with status 7
% 1401.94/198.61  # Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 130s (1) cores
% 1401.94/198.61  # Preprocessing time       : 0.001 s
% 1401.94/198.61  # Presaturation interreduction done
% 1401.94/198.61  
% 1401.94/198.61  # Proof found!
% 1401.94/198.61  # SZS status Theorem
% 1401.94/198.61  # SZS output start CNFRefutation
% See solution above
% 1401.94/198.61  # Parsed axioms                        : 9
% 1401.94/198.61  # Removed by relevancy pruning/SinE    : 0
% 1401.94/198.61  # Initial clauses                      : 20
% 1401.94/198.61  # Removed in clause preprocessing      : 2
% 1401.94/198.61  # Initial clauses in saturation        : 18
% 1401.94/198.61  # Processed clauses                    : 129208
% 1401.94/198.61  # ...of these trivial                  : 23660
% 1401.94/198.61  # ...subsumed                          : 98058
% 1401.94/198.61  # ...remaining for further processing  : 7490
% 1401.94/198.61  # Other redundant clauses eliminated   : 2
% 1401.94/198.61  # Clauses deleted for lack of memory   : 696995
% 1401.94/198.61  # Backward-subsumed                    : 162
% 1401.94/198.61  # Backward-rewritten                   : 1514
% 1401.94/198.61  # Generated clauses                    : 3509373
% 1401.94/198.61  # ...of the previous two non-redundant : 2992682
% 1401.94/198.61  # ...aggressively subsumed             : 0
% 1401.94/198.61  # Contextual simplify-reflections      : 36
% 1401.94/198.61  # Paramodulations                      : 3501939
% 1401.94/198.61  # Factorizations                       : 7432
% 1401.94/198.61  # NegExts                              : 0
% 1401.94/198.61  # Equation resolutions                 : 2
% 1401.94/198.61  # Total rewrite steps                  : 4258805
% 1401.94/198.61  # Propositional unsat checks           : 0
% 1401.94/198.61  #    Propositional check models        : 0
% 1401.94/198.61  #    Propositional check unsatisfiable : 0
% 1401.94/198.61  #    Propositional clauses             : 0
% 1401.94/198.61  #    Propositional clauses after purity: 0
% 1401.94/198.61  #    Propositional unsat core size     : 0
% 1401.94/198.61  #    Propositional preprocessing time  : 0.000
% 1401.94/198.61  #    Propositional encoding time       : 0.000
% 1401.94/198.61  #    Propositional solver time         : 0.000
% 1401.94/198.61  #    Success case prop preproc time    : 0.000
% 1401.94/198.61  #    Success case prop encoding time   : 0.000
% 1401.94/198.61  #    Success case prop solver time     : 0.000
% 1401.94/198.61  # Current number of processed clauses  : 5796
% 1401.94/198.61  #    Positive orientable unit clauses  : 1593
% 1401.94/198.61  #    Positive unorientable unit clauses: 10
% 1401.94/198.61  #    Negative unit clauses             : 0
% 1401.94/198.61  #    Non-unit-clauses                  : 4193
% 1401.94/198.61  # Current number of unprocessed clauses: 1756905
% 1401.94/198.61  # ...number of literals in the above   : 4925649
% 1401.94/198.61  # Current number of archived formulas  : 0
% 1401.94/198.61  # Current number of archived clauses   : 1692
% 1401.94/198.61  # Clause-clause subsumption calls (NU) : 6039417
% 1401.94/198.61  # Rec. Clause-clause subsumption calls : 3550480
% 1401.94/198.61  # Non-unit clause-clause subsumptions  : 93813
% 1401.94/198.61  # Unit Clause-clause subsumption calls : 769925
% 1401.94/198.61  # Rewrite failures with RHS unbound    : 0
% 1401.94/198.61  # BW rewrite match attempts            : 109465
% 1401.94/198.61  # BW rewrite match successes           : 5658
% 1401.94/198.61  # Condensation attempts                : 0
% 1401.94/198.61  # Condensation successes               : 0
% 1401.94/198.61  # Termbank termtop insertions          : 82105332
% 1401.94/198.61  
% 1401.94/198.61  # -------------------------------------------------
% 1401.94/198.61  # User time                : 614.801 s
% 1401.94/198.61  # System time              : 3.521 s
% 1401.94/198.61  # Total time               : 618.321 s
% 1401.94/198.61  # Maximum resident set size: 1756 pages
% 1401.94/198.61  
% 1401.94/198.61  # -------------------------------------------------
% 1401.94/198.61  # User time                : 808.213 s
% 1401.94/198.61  # System time              : 5.775 s
% 1401.94/198.61  # Total time               : 813.988 s
% 1401.94/198.61  # Maximum resident set size: 1676 pages
% 1401.94/198.61  % E---3.1 exiting
%------------------------------------------------------------------------------