TSTP Solution File: SEU135+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU135+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : 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 : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 16:22:39 EDT 2023

% Result   : Theorem 5.13s 5.49s
% Output   : CNFRefutation 5.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  134 (  64 unt;  13 typ;   0 def)
%            Number of atoms       :  247 (  63 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :  202 (  76   ~;  99   |;  18   &)
%                                         (   8 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (   8   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-3 aty)
%            Number of variables   :  329 (  40 sgn;  58   !;   0   ?;   0   :)

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

tff(decl_23,type,
    set_union2: ( $i * $i ) > $i ).

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

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

tff(decl_26,type,
    empty_set: $i ).

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

tff(decl_28,type,
    esk1_3: ( $i * $i * $i ) > $i ).

tff(decl_29,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_30,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_31,type,
    esk4_0: $i ).

tff(decl_32,type,
    esk5_0: $i ).

tff(decl_33,type,
    esk6_0: $i ).

tff(decl_34,type,
    esk7_0: $i ).

fof(d4_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).

fof(d2_xboole_0,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_union2(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            | in(X4,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(d3_tarski,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
    <=> ! [X3] :
          ( in(X3,X1)
         => in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(commutativity_k2_xboole_0,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(t4_boole,axiom,
    ! [X1] : set_difference(empty_set,X1) = empty_set,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).

fof(d10_xboole_0,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).

fof(t3_boole,axiom,
    ! [X1] : set_difference(X1,empty_set) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).

fof(t7_boole,axiom,
    ! [X1,X2] :
      ~ ( in(X1,X2)
        & empty(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).

fof(t1_boole,axiom,
    ! [X1] : set_union2(X1,empty_set) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).

fof(fc1_xboole_0,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).

fof(t39_xboole_1,conjecture,
    ! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).

fof(c_0_11,plain,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).

fof(c_0_12,plain,
    ! [X26,X27,X28,X29,X30,X31,X32,X33] :
      ( ( in(X29,X26)
        | ~ in(X29,X28)
        | X28 != set_difference(X26,X27) )
      & ( ~ in(X29,X27)
        | ~ in(X29,X28)
        | X28 != set_difference(X26,X27) )
      & ( ~ in(X30,X26)
        | in(X30,X27)
        | in(X30,X28)
        | X28 != set_difference(X26,X27) )
      & ( ~ in(esk3_3(X31,X32,X33),X33)
        | ~ in(esk3_3(X31,X32,X33),X31)
        | in(esk3_3(X31,X32,X33),X32)
        | X33 = set_difference(X31,X32) )
      & ( in(esk3_3(X31,X32,X33),X31)
        | in(esk3_3(X31,X32,X33),X33)
        | X33 = set_difference(X31,X32) )
      & ( ~ in(esk3_3(X31,X32,X33),X32)
        | in(esk3_3(X31,X32,X33),X33)
        | X33 = set_difference(X31,X32) ) ),
    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)],[c_0_11])])])])])]) ).

fof(c_0_13,plain,
    ! [X11,X12,X13,X14,X15,X16,X17,X18] :
      ( ( ~ in(X14,X13)
        | in(X14,X11)
        | in(X14,X12)
        | X13 != set_union2(X11,X12) )
      & ( ~ in(X15,X11)
        | in(X15,X13)
        | X13 != set_union2(X11,X12) )
      & ( ~ in(X15,X12)
        | in(X15,X13)
        | X13 != set_union2(X11,X12) )
      & ( ~ in(esk1_3(X16,X17,X18),X16)
        | ~ in(esk1_3(X16,X17,X18),X18)
        | X18 = set_union2(X16,X17) )
      & ( ~ in(esk1_3(X16,X17,X18),X17)
        | ~ in(esk1_3(X16,X17,X18),X18)
        | X18 = set_union2(X16,X17) )
      & ( in(esk1_3(X16,X17,X18),X18)
        | in(esk1_3(X16,X17,X18),X16)
        | in(esk1_3(X16,X17,X18),X17)
        | X18 = set_union2(X16,X17) ) ),
    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)],[d2_xboole_0])])])])])]) ).

cnf(c_0_14,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | X3 != set_difference(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_15,plain,
    ! [X20,X21,X22,X23,X24] :
      ( ( ~ subset(X20,X21)
        | ~ in(X22,X20)
        | in(X22,X21) )
      & ( in(esk2_2(X23,X24),X23)
        | subset(X23,X24) )
      & ( ~ in(esk2_2(X23,X24),X24)
        | subset(X23,X24) ) ),
    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)],[d3_tarski])])])])])]) ).

cnf(c_0_16,plain,
    ( ~ in(X1,X2)
    | ~ in(X1,X3)
    | X3 != set_difference(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_17,plain,
    ( in(X1,X3)
    | ~ in(X1,X2)
    | X3 != set_union2(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_18,plain,
    ! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
    inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).

cnf(c_0_19,plain,
    ( in(X1,X3)
    | in(X1,X4)
    | ~ in(X1,X2)
    | X4 != set_difference(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_20,plain,
    ! [X47] : set_difference(empty_set,X47) = empty_set,
    inference(variable_rename,[status(thm)],[t4_boole]) ).

cnf(c_0_21,plain,
    ( in(X1,X2)
    | ~ in(X1,set_difference(X2,X3)) ),
    inference(er,[status(thm)],[c_0_14]) ).

cnf(c_0_22,plain,
    ( in(esk2_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_23,plain,
    ( ~ in(X1,set_difference(X2,X3))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[c_0_16]) ).

cnf(c_0_24,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_25,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_26,plain,
    ( subset(X1,X2)
    | ~ in(esk2_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_27,plain,
    ( in(X1,set_difference(X2,X3))
    | in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[c_0_19]) ).

cnf(c_0_28,plain,
    set_difference(empty_set,X1) = empty_set,
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_29,plain,
    ( subset(set_difference(X1,X2),X3)
    | in(esk2_2(set_difference(X1,X2),X3),X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_30,plain,
    ( subset(set_difference(X1,X2),X3)
    | ~ in(esk2_2(set_difference(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_22]) ).

cnf(c_0_31,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_32,plain,
    ( subset(X1,set_difference(X2,X3))
    | in(esk2_2(X1,set_difference(X2,X3)),X3)
    | ~ in(esk2_2(X1,set_difference(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_33,plain,
    ( ~ in(X1,empty_set)
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_28]) ).

cnf(c_0_34,plain,
    ( subset(set_difference(set_difference(X1,X2),X3),X4)
    | ~ in(esk2_2(set_difference(set_difference(X1,X2),X3),X4),X2) ),
    inference(spm,[status(thm)],[c_0_23,c_0_29]) ).

cnf(c_0_35,plain,
    ( subset(set_difference(X1,set_difference(X2,X3)),X4)
    | in(esk2_2(set_difference(X1,set_difference(X2,X3)),X4),X3)
    | ~ in(esk2_2(set_difference(X1,set_difference(X2,X3)),X4),X2) ),
    inference(spm,[status(thm)],[c_0_30,c_0_27]) ).

cnf(c_0_36,plain,
    ( subset(set_difference(set_difference(X1,X2),X3),X4)
    | in(esk2_2(set_difference(set_difference(X1,X2),X3),X4),X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_29]) ).

fof(c_0_37,plain,
    ! [X9,X10] :
      ( ( subset(X9,X10)
        | X9 != X10 )
      & ( subset(X10,X9)
        | X9 != X10 )
      & ( ~ subset(X9,X10)
        | ~ subset(X10,X9)
        | X9 = X10 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).

cnf(c_0_38,plain,
    ( subset(set_difference(X1,set_union2(X2,X3)),X4)
    | ~ in(esk2_2(set_difference(X1,set_union2(X2,X3)),X4),X2) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_39,plain,
    ( subset(X1,set_difference(X1,X2))
    | in(esk2_2(X1,set_difference(X1,X2)),X2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_22]) ).

cnf(c_0_40,plain,
    ( subset(empty_set,X1)
    | ~ in(esk2_2(empty_set,X1),X2) ),
    inference(spm,[status(thm)],[c_0_33,c_0_22]) ).

cnf(c_0_41,plain,
    ( subset(set_difference(set_difference(X1,set_union2(X2,X3)),X4),X5)
    | ~ in(esk2_2(set_difference(set_difference(X1,set_union2(X2,X3)),X4),X5),X3) ),
    inference(spm,[status(thm)],[c_0_34,c_0_24]) ).

cnf(c_0_42,plain,
    ( subset(set_difference(set_difference(X1,X2),set_difference(X1,X3)),X4)
    | in(esk2_2(set_difference(set_difference(X1,X2),set_difference(X1,X3)),X4),X3) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_43,plain,
    ( X1 = X2
    | ~ subset(X1,X2)
    | ~ subset(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_44,plain,
    subset(set_difference(X1,set_union2(X2,X3)),set_difference(set_difference(X1,set_union2(X2,X3)),X2)),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_45,plain,
    subset(set_difference(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_26,c_0_29]) ).

cnf(c_0_46,plain,
    subset(empty_set,X1),
    inference(spm,[status(thm)],[c_0_40,c_0_22]) ).

cnf(c_0_47,plain,
    subset(set_difference(set_difference(X1,set_union2(X2,X3)),set_difference(X1,X3)),X4),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_48,plain,
    set_difference(set_difference(X1,set_union2(X2,X3)),X2) = set_difference(X1,set_union2(X2,X3)),
    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,
    ( X1 = empty_set
    | ~ subset(X1,empty_set) ),
    inference(spm,[status(thm)],[c_0_43,c_0_46]) ).

cnf(c_0_50,plain,
    subset(set_difference(X1,set_union2(X2,set_difference(X1,X2))),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_25]) ).

fof(c_0_51,plain,
    ! [X46] : set_difference(X46,empty_set) = X46,
    inference(variable_rename,[status(thm)],[t3_boole]) ).

cnf(c_0_52,plain,
    ( subset(set_difference(set_difference(set_difference(X1,X2),X3),X4),X5)
    | in(esk2_2(set_difference(set_difference(set_difference(X1,X2),X3),X4),X5),X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_36]) ).

cnf(c_0_53,plain,
    ( subset(set_difference(X1,set_difference(X1,X2)),X3)
    | in(esk2_2(set_difference(X1,set_difference(X1,X2)),X3),X2) ),
    inference(spm,[status(thm)],[c_0_35,c_0_29]) ).

cnf(c_0_54,plain,
    set_difference(X1,set_union2(X2,set_difference(X1,X2))) = empty_set,
    inference(spm,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_55,plain,
    set_difference(X1,empty_set) = X1,
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_56,plain,
    ( subset(set_difference(set_difference(set_difference(X1,X2),X3),set_difference(X1,X4)),X5)
    | in(esk2_2(set_difference(set_difference(set_difference(X1,X2),X3),set_difference(X1,X4)),X5),X4) ),
    inference(spm,[status(thm)],[c_0_35,c_0_52]) ).

cnf(c_0_57,plain,
    subset(set_difference(set_difference(X1,X2),X3),set_difference(set_difference(set_difference(X1,X2),X3),X2)),
    inference(spm,[status(thm)],[c_0_34,c_0_39]) ).

cnf(c_0_58,plain,
    ( in(X1,X3)
    | in(X1,X4)
    | ~ in(X1,X2)
    | X2 != set_union2(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_59,plain,
    ( subset(X1,set_difference(X1,set_difference(X2,X3)))
    | ~ in(esk2_2(X1,set_difference(X1,set_difference(X2,X3))),X3) ),
    inference(spm,[status(thm)],[c_0_23,c_0_39]) ).

cnf(c_0_60,plain,
    ( subset(X1,X2)
    | in(esk2_2(X1,X2),set_union2(X3,set_difference(X1,X3))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_55]) ).

cnf(c_0_61,plain,
    subset(set_difference(set_difference(set_difference(X1,X2),X3),set_difference(X1,X3)),X4),
    inference(spm,[status(thm)],[c_0_34,c_0_56]) ).

cnf(c_0_62,plain,
    set_difference(set_difference(set_difference(X1,X2),X3),X2) = set_difference(set_difference(X1,X2),X3),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_57]),c_0_45])]) ).

cnf(c_0_63,plain,
    ( in(X1,X2)
    | in(X1,X3)
    | ~ in(X1,set_union2(X3,X2)) ),
    inference(er,[status(thm)],[c_0_58]) ).

fof(c_0_64,plain,
    ! [X49,X50] :
      ( ~ in(X49,X50)
      | ~ empty(X50) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).

cnf(c_0_65,plain,
    subset(X1,set_difference(X1,set_difference(X2,set_union2(X3,set_difference(X1,X3))))),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_66,plain,
    subset(set_difference(set_difference(X1,set_difference(X1,X2)),X2),X3),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

fof(c_0_67,plain,
    ! [X43] : set_union2(X43,empty_set) = X43,
    inference(variable_rename,[status(thm)],[t1_boole]) ).

cnf(c_0_68,plain,
    ( subset(set_difference(set_difference(set_union2(X1,X2),X3),X4),X5)
    | in(esk2_2(set_difference(set_difference(set_union2(X1,X2),X3),X4),X5),X1)
    | in(esk2_2(set_difference(set_difference(set_union2(X1,X2),X3),X4),X5),X2) ),
    inference(spm,[status(thm)],[c_0_63,c_0_36]) ).

cnf(c_0_69,plain,
    ( ~ in(X1,X2)
    | ~ empty(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_64]) ).

cnf(c_0_70,plain,
    subset(X1,set_difference(X1,set_difference(X2,X1))),
    inference(spm,[status(thm)],[c_0_59,c_0_22]) ).

cnf(c_0_71,plain,
    set_difference(X1,set_difference(X2,set_union2(X3,set_difference(X1,X3)))) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_65]),c_0_45])]) ).

cnf(c_0_72,plain,
    set_difference(set_difference(X1,set_difference(X1,X2)),X2) = empty_set,
    inference(spm,[status(thm)],[c_0_49,c_0_66]) ).

cnf(c_0_73,plain,
    set_union2(X1,empty_set) = X1,
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_74,plain,
    ( subset(set_difference(set_difference(set_union2(X1,X2),X3),X2),X4)
    | in(esk2_2(set_difference(set_difference(set_union2(X1,X2),X3),X2),X4),X1) ),
    inference(spm,[status(thm)],[c_0_30,c_0_68]) ).

cnf(c_0_75,plain,
    ( subset(X1,set_union2(X2,X3))
    | ~ in(esk2_2(X1,set_union2(X2,X3)),X3) ),
    inference(spm,[status(thm)],[c_0_26,c_0_24]) ).

cnf(c_0_76,plain,
    ( subset(X1,set_union2(X2,X3))
    | ~ in(esk2_2(X1,set_union2(X2,X3)),X2) ),
    inference(spm,[status(thm)],[c_0_26,c_0_31]) ).

cnf(c_0_77,plain,
    ( subset(set_difference(set_union2(X1,X2),X3),X4)
    | in(esk2_2(set_difference(set_union2(X1,X2),X3),X4),X1)
    | in(esk2_2(set_difference(set_union2(X1,X2),X3),X4),X2) ),
    inference(spm,[status(thm)],[c_0_63,c_0_29]) ).

cnf(c_0_78,plain,
    ( subset(X1,set_difference(X1,X2))
    | ~ empty(X2) ),
    inference(spm,[status(thm)],[c_0_69,c_0_39]) ).

cnf(c_0_79,plain,
    set_difference(X1,set_difference(X2,X1)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_70]),c_0_45])]) ).

cnf(c_0_80,plain,
    set_difference(set_difference(X1,set_difference(X1,X2)),set_difference(X3,X2)) = set_difference(X1,set_difference(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]) ).

cnf(c_0_81,plain,
    subset(set_difference(set_difference(set_union2(X1,X2),X1),X2),X3),
    inference(spm,[status(thm)],[c_0_34,c_0_74]) ).

cnf(c_0_82,plain,
    ( subset(set_union2(X1,X2),X3)
    | in(esk2_2(set_union2(X1,X2),X3),X1)
    | in(esk2_2(set_union2(X1,X2),X3),X2) ),
    inference(spm,[status(thm)],[c_0_63,c_0_22]) ).

cnf(c_0_83,plain,
    ( subset(X1,set_union2(X2,set_union2(X3,X4)))
    | ~ in(esk2_2(X1,set_union2(X2,set_union2(X3,X4))),X4) ),
    inference(spm,[status(thm)],[c_0_75,c_0_24]) ).

cnf(c_0_84,plain,
    ( subset(set_difference(set_union2(X1,X2),X3),set_union2(X2,X4))
    | in(esk2_2(set_difference(set_union2(X1,X2),X3),set_union2(X2,X4)),X1) ),
    inference(spm,[status(thm)],[c_0_76,c_0_77]) ).

cnf(c_0_85,plain,
    subset(set_difference(X1,set_difference(X1,X2)),X2),
    inference(spm,[status(thm)],[c_0_26,c_0_53]) ).

cnf(c_0_86,plain,
    ( set_difference(X1,X2) = X1
    | ~ empty(X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_78]),c_0_45])]) ).

cnf(c_0_87,plain,
    set_difference(set_difference(X1,X2),set_difference(X3,set_difference(X3,X2))) = set_difference(X1,X2),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_88,plain,
    set_difference(set_difference(set_union2(X1,X2),X1),X2) = empty_set,
    inference(spm,[status(thm)],[c_0_49,c_0_81]) ).

cnf(c_0_89,plain,
    ( subset(set_union2(X1,X2),X2)
    | in(esk2_2(set_union2(X1,X2),X2),X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_82]) ).

cnf(c_0_90,plain,
    set_difference(X1,set_difference(set_difference(X2,X1),X3)) = X1,
    inference(spm,[status(thm)],[c_0_79,c_0_62]) ).

cnf(c_0_91,plain,
    subset(set_difference(set_union2(X1,X2),X3),set_union2(X2,set_union2(X4,X1))),
    inference(spm,[status(thm)],[c_0_83,c_0_84]) ).

cnf(c_0_92,plain,
    ( subset(X1,set_union2(X2,set_union2(X3,X4)))
    | ~ in(esk2_2(X1,set_union2(X2,set_union2(X3,X4))),X3) ),
    inference(spm,[status(thm)],[c_0_75,c_0_31]) ).

cnf(c_0_93,plain,
    ( subset(X1,X2)
    | ~ empty(set_difference(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_85,c_0_86]) ).

cnf(c_0_94,plain,
    set_difference(set_union2(X1,set_difference(X2,set_difference(X2,X1))),X1) = empty_set,
    inference(spm,[status(thm)],[c_0_87,c_0_88]) ).

cnf(c_0_95,plain,
    empty(empty_set),
    inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).

cnf(c_0_96,plain,
    subset(X1,set_union2(X2,X1)),
    inference(spm,[status(thm)],[c_0_75,c_0_22]) ).

cnf(c_0_97,plain,
    subset(set_union2(X1,set_union2(X2,set_union2(X3,X1))),set_union2(X2,set_union2(X3,X1))),
    inference(spm,[status(thm)],[c_0_83,c_0_89]) ).

cnf(c_0_98,plain,
    set_difference(set_difference(X1,X2),set_difference(X2,X3)) = set_difference(X1,X2),
    inference(spm,[status(thm)],[c_0_90,c_0_79]) ).

cnf(c_0_99,plain,
    subset(set_union2(X1,X2),set_union2(X2,set_union2(X3,X1))),
    inference(spm,[status(thm)],[c_0_91,c_0_55]) ).

cnf(c_0_100,plain,
    subset(set_union2(X1,set_union2(X2,set_union2(X1,X3))),set_union2(X2,set_union2(X1,X3))),
    inference(spm,[status(thm)],[c_0_92,c_0_89]) ).

cnf(c_0_101,plain,
    subset(set_union2(X1,set_difference(X2,set_difference(X2,X1))),X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95])]) ).

cnf(c_0_102,plain,
    subset(X1,set_union2(X1,X2)),
    inference(spm,[status(thm)],[c_0_96,c_0_25]) ).

cnf(c_0_103,plain,
    set_union2(X1,set_union2(X2,set_union2(X3,X1))) = set_union2(X2,set_union2(X3,X1)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_97]),c_0_96])]) ).

cnf(c_0_104,plain,
    set_difference(set_union2(X1,set_difference(X1,X2)),X1) = empty_set,
    inference(spm,[status(thm)],[c_0_98,c_0_88]) ).

cnf(c_0_105,plain,
    subset(set_union2(X1,X2),set_union2(X2,set_union2(X1,X3))),
    inference(spm,[status(thm)],[c_0_99,c_0_25]) ).

cnf(c_0_106,plain,
    set_union2(X1,set_union2(X2,set_union2(X1,X3))) = set_union2(X2,set_union2(X1,X3)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_100]),c_0_96])]) ).

cnf(c_0_107,plain,
    set_union2(X1,set_difference(X2,set_difference(X2,X1))) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_101]),c_0_102])]) ).

cnf(c_0_108,plain,
    set_union2(X1,set_union2(set_union2(X2,X1),X3)) = set_union2(set_union2(X2,X1),X3),
    inference(spm,[status(thm)],[c_0_103,c_0_25]) ).

cnf(c_0_109,plain,
    subset(set_union2(X1,set_difference(X1,X2)),X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_104]),c_0_95])]) ).

fof(c_0_110,negated_conjecture,
    ~ ! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
    inference(assume_negation,[status(cth)],[t39_xboole_1]) ).

cnf(c_0_111,plain,
    subset(set_union2(X1,X2),set_union2(X1,set_union2(X2,X3))),
    inference(spm,[status(thm)],[c_0_105,c_0_106]) ).

cnf(c_0_112,plain,
    set_union2(X1,set_union2(X2,set_difference(X1,X2))) = set_union2(X2,set_difference(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_54]),c_0_55]),c_0_25]) ).

cnf(c_0_113,plain,
    subset(set_union2(X1,X2),set_union2(set_union2(X3,X2),X1)),
    inference(spm,[status(thm)],[c_0_99,c_0_108]) ).

cnf(c_0_114,plain,
    set_union2(X1,set_difference(X1,X2)) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_109]),c_0_102])]) ).

fof(c_0_115,negated_conjecture,
    set_union2(esk6_0,set_difference(esk7_0,esk6_0)) != set_union2(esk6_0,esk7_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_110])])]) ).

cnf(c_0_116,plain,
    subset(set_union2(X1,X2),set_union2(X2,set_difference(X1,X2))),
    inference(spm,[status(thm)],[c_0_111,c_0_112]) ).

cnf(c_0_117,plain,
    subset(set_union2(X1,set_difference(X2,X3)),set_union2(X2,X1)),
    inference(spm,[status(thm)],[c_0_113,c_0_114]) ).

cnf(c_0_118,negated_conjecture,
    set_union2(esk6_0,set_difference(esk7_0,esk6_0)) != set_union2(esk6_0,esk7_0),
    inference(split_conjunct,[status(thm)],[c_0_115]) ).

cnf(c_0_119,plain,
    set_union2(X1,set_difference(X2,X1)) = set_union2(X2,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_116]),c_0_117])]) ).

cnf(c_0_120,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_118,c_0_119]),c_0_25])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.23  % Problem    : SEU135+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.23  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.44  % Computer : n027.cluster.edu
% 0.11/0.44  % Model    : x86_64 x86_64
% 0.11/0.44  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.44  % Memory   : 8042.1875MB
% 0.11/0.44  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.44  % CPULimit   : 300
% 0.11/0.44  % WCLimit    : 300
% 0.11/0.44  % DateTime   : Thu Aug 24 01:39:32 EDT 2023
% 0.11/0.44  % CPUTime  : 
% 0.16/0.72  start to proof: theBenchmark
% 5.13/5.49  % Version  : CSE_E---1.5
% 5.13/5.49  % Problem  : theBenchmark.p
% 5.13/5.49  % Proof found
% 5.13/5.49  % SZS status Theorem for theBenchmark.p
% 5.13/5.49  % SZS output start Proof
% See solution above
% 5.13/5.50  % Total time : 4.695000 s
% 5.13/5.50  % SZS output end Proof
% 5.13/5.50  % Total time : 4.697000 s
%------------------------------------------------------------------------------