TSTP Solution File: SEU131+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU131+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n022.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 16:22:37 EDT 2023

% Result   : Theorem 1.63s 1.79s
% Output   : CNFRefutation 1.63s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   35
% Syntax   : Number of formulae    :  109 (  24 unt;  20 typ;   0 def)
%            Number of atoms       :  239 (  69 equ)
%            Maximal formula atoms :   20 (   2 avg)
%            Number of connectives :  247 (  97   ~;  97   |;  37   &)
%                                         (  12 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  15   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;   5 con; 0-3 aty)
%            Number of variables   :  222 (  30 sgn; 103   !;   4   ?;   0   :)

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

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

tff(decl_24,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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

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

tff(decl_29,type,
    empty: $i > $o ).

tff(decl_30,type,
    esk1_1: $i > $i ).

tff(decl_31,type,
    esk2_3: ( $i * $i * $i ) > $i ).

tff(decl_32,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_33,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_34,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_35,type,
    esk6_0: $i ).

tff(decl_36,type,
    esk7_0: $i ).

tff(decl_37,type,
    esk8_0: $i ).

tff(decl_38,type,
    esk9_0: $i ).

tff(decl_39,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_40,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_41,type,
    esk12_2: ( $i * $i ) > $i ).

fof(t4_xboole_0,lemma,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
      & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
          & disjoint(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).

fof(t3_xboole_0,lemma,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] :
              ~ ( in(X3,X1)
                & in(X3,X2) ) )
      & ~ ( ? [X3] :
              ( in(X3,X1)
              & in(X3,X2) )
          & disjoint(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).

fof(d1_xboole_0,axiom,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

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/sandbox/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/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(d7_xboole_0,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> set_intersection2(X1,X2) = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).

fof(commutativity_k3_xboole_0,axiom,
    ! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(t12_xboole_1,lemma,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_union2(X1,X2) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).

fof(t17_xboole_1,lemma,
    ! [X1,X2] : subset(set_intersection2(X1,X2),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).

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

fof(l32_xboole_1,conjecture,
    ! [X1,X2] :
      ( set_difference(X1,X2) = empty_set
    <=> subset(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).

fof(t1_xboole_1,lemma,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X2,X3) )
     => subset(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).

fof(t28_xboole_1,lemma,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_intersection2(X1,X2) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

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

fof(t7_xboole_1,lemma,
    ! [X1,X2] : subset(X1,set_union2(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).

fof(c_0_15,lemma,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
      & ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
          & disjoint(X1,X2) ) ),
    inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).

fof(c_0_16,lemma,
    ! [X1,X2] :
      ( ~ ( ~ disjoint(X1,X2)
          & ! [X3] :
              ~ ( in(X3,X1)
                & in(X3,X2) ) )
      & ~ ( ? [X3] :
              ( in(X3,X1)
              & in(X3,X2) )
          & disjoint(X1,X2) ) ),
    inference(fof_simplification,[status(thm)],[t3_xboole_0]) ).

fof(c_0_17,lemma,
    ! [X95,X96,X98,X99,X100] :
      ( ( disjoint(X95,X96)
        | in(esk12_2(X95,X96),set_intersection2(X95,X96)) )
      & ( ~ in(X100,set_intersection2(X98,X99))
        | ~ disjoint(X98,X99) ) ),
    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_15])])])])]) ).

fof(c_0_18,lemma,
    ! [X87,X88,X90,X91,X92] :
      ( ( in(esk11_2(X87,X88),X87)
        | disjoint(X87,X88) )
      & ( in(esk11_2(X87,X88),X88)
        | disjoint(X87,X88) )
      & ( ~ in(X92,X90)
        | ~ in(X92,X91)
        | ~ disjoint(X90,X91) ) ),
    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_16])])])])])]) ).

fof(c_0_19,plain,
    ! [X1] :
      ( X1 = empty_set
    <=> ! [X2] : ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).

fof(c_0_20,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_21,plain,
    ! [X17,X18,X19,X20,X21,X22,X23,X24] :
      ( ( ~ in(X20,X19)
        | in(X20,X17)
        | in(X20,X18)
        | X19 != set_union2(X17,X18) )
      & ( ~ in(X21,X17)
        | in(X21,X19)
        | X19 != set_union2(X17,X18) )
      & ( ~ in(X21,X18)
        | in(X21,X19)
        | X19 != set_union2(X17,X18) )
      & ( ~ in(esk2_3(X22,X23,X24),X22)
        | ~ in(esk2_3(X22,X23,X24),X24)
        | X24 = set_union2(X22,X23) )
      & ( ~ in(esk2_3(X22,X23,X24),X23)
        | ~ in(esk2_3(X22,X23,X24),X24)
        | X24 = set_union2(X22,X23) )
      & ( in(esk2_3(X22,X23,X24),X24)
        | in(esk2_3(X22,X23,X24),X22)
        | in(esk2_3(X22,X23,X24),X23)
        | X24 = set_union2(X22,X23) ) ),
    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_22,lemma,
    ( ~ in(X1,set_intersection2(X2,X3))
    | ~ disjoint(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,lemma,
    ( in(esk11_2(X1,X2),X2)
    | disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_24,plain,
    ! [X13,X14,X15] :
      ( ( X13 != empty_set
        | ~ in(X14,X13) )
      & ( in(esk1_1(X15),X15)
        | X15 = empty_set ) ),
    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_19])])])])]) ).

fof(c_0_25,plain,
    ! [X41,X42,X43,X44,X45,X46,X47,X48] :
      ( ( in(X44,X41)
        | ~ in(X44,X43)
        | X43 != set_difference(X41,X42) )
      & ( ~ in(X44,X42)
        | ~ in(X44,X43)
        | X43 != set_difference(X41,X42) )
      & ( ~ in(X45,X41)
        | in(X45,X42)
        | in(X45,X43)
        | X43 != set_difference(X41,X42) )
      & ( ~ in(esk5_3(X46,X47,X48),X48)
        | ~ in(esk5_3(X46,X47,X48),X46)
        | in(esk5_3(X46,X47,X48),X47)
        | X48 = set_difference(X46,X47) )
      & ( in(esk5_3(X46,X47,X48),X46)
        | in(esk5_3(X46,X47,X48),X48)
        | X48 = set_difference(X46,X47) )
      & ( ~ in(esk5_3(X46,X47,X48),X47)
        | in(esk5_3(X46,X47,X48),X48)
        | X48 = set_difference(X46,X47) ) ),
    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_20])])])])])]) ).

cnf(c_0_26,plain,
    ( in(X1,X3)
    | ~ in(X1,X2)
    | X3 != set_union2(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_27,lemma,
    ( in(esk11_2(X1,X2),X2)
    | ~ in(X3,set_intersection2(X1,X2)) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_28,plain,
    ( in(esk1_1(X1),X1)
    | X1 = empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_29,plain,
    ( ~ in(X1,X2)
    | ~ in(X1,X3)
    | X3 != set_difference(X4,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_30,plain,
    ( in(X1,set_union2(X2,X3))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[c_0_26]) ).

cnf(c_0_31,lemma,
    ( set_intersection2(X1,X2) = empty_set
    | in(esk11_2(X1,X2),X2) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

fof(c_0_32,plain,
    ! [X50,X51] :
      ( ( ~ disjoint(X50,X51)
        | set_intersection2(X50,X51) = empty_set )
      & ( set_intersection2(X50,X51) != empty_set
        | disjoint(X50,X51) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).

cnf(c_0_33,plain,
    ( ~ in(X1,set_difference(X2,X3))
    | ~ in(X1,X3) ),
    inference(er,[status(thm)],[c_0_29]) ).

cnf(c_0_34,lemma,
    ( set_intersection2(X1,X2) = empty_set
    | in(esk11_2(X1,X2),set_union2(X3,X2)) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,plain,
    ( set_intersection2(X1,X2) = empty_set
    | ~ disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_36,lemma,
    ( in(esk11_2(X1,X2),X1)
    | disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_37,plain,
    ! [X9,X10] : set_intersection2(X9,X10) = set_intersection2(X10,X9),
    inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).

cnf(c_0_38,lemma,
    ( set_intersection2(X1,X2) = empty_set
    | ~ in(esk11_2(X1,X2),set_difference(X3,set_union2(X4,X2))) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_39,lemma,
    ( set_intersection2(X1,X2) = empty_set
    | in(esk11_2(X1,X2),X1) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_40,plain,
    set_intersection2(X1,X2) = set_intersection2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

fof(c_0_41,lemma,
    ! [X65,X66] :
      ( ~ subset(X65,X66)
      | set_union2(X65,X66) = X66 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).

fof(c_0_42,lemma,
    ! [X67,X68] : subset(set_intersection2(X67,X68),X67),
    inference(variable_rename,[status(thm)],[t17_xboole_1]) ).

fof(c_0_43,plain,
    ! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
    inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).

cnf(c_0_44,plain,
    ( disjoint(X1,X2)
    | set_intersection2(X1,X2) != empty_set ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_45,lemma,
    set_intersection2(X1,set_difference(X2,set_union2(X3,X1))) = empty_set,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).

cnf(c_0_46,lemma,
    ( set_union2(X1,X2) = X2
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_47,lemma,
    subset(set_intersection2(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_48,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

fof(c_0_49,negated_conjecture,
    ~ ! [X1,X2] :
        ( set_difference(X1,X2) = empty_set
      <=> subset(X1,X2) ),
    inference(assume_negation,[status(cth)],[l32_xboole_1]) ).

cnf(c_0_50,lemma,
    disjoint(X1,set_difference(X2,set_union2(X3,X1))),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_51,lemma,
    set_union2(X1,set_intersection2(X1,X2)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).

fof(c_0_52,lemma,
    ! [X73,X74,X75] :
      ( ~ subset(X73,X74)
      | ~ subset(X74,X75)
      | subset(X73,X75) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).

fof(c_0_53,negated_conjecture,
    ( ( set_difference(esk6_0,esk7_0) != empty_set
      | ~ subset(esk6_0,esk7_0) )
    & ( set_difference(esk6_0,esk7_0) = empty_set
      | subset(esk6_0,esk7_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])]) ).

cnf(c_0_54,lemma,
    ( ~ in(X1,X2)
    | ~ in(X1,X3)
    | ~ disjoint(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_55,lemma,
    disjoint(set_intersection2(X1,X2),set_difference(X3,X1)),
    inference(spm,[status(thm)],[c_0_50,c_0_51]) ).

cnf(c_0_56,plain,
    ( in(X1,X2)
    | ~ in(X1,X3)
    | X3 != set_difference(X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_57,lemma,
    ( subset(X1,X3)
    | ~ subset(X1,X2)
    | ~ subset(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_58,negated_conjecture,
    ( set_difference(esk6_0,esk7_0) = empty_set
    | subset(esk6_0,esk7_0) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_59,lemma,
    ( ~ in(X1,set_difference(X2,X3))
    | ~ in(X1,set_intersection2(X3,X4)) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_60,plain,
    ( in(X1,X2)
    | ~ in(X1,set_difference(X2,X3)) ),
    inference(er,[status(thm)],[c_0_56]) ).

fof(c_0_61,lemma,
    ! [X79,X80] :
      ( ~ subset(X79,X80)
      | set_intersection2(X79,X80) = X79 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).

cnf(c_0_62,negated_conjecture,
    ( set_difference(esk6_0,esk7_0) = empty_set
    | subset(X1,esk7_0)
    | ~ subset(X1,esk6_0) ),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

fof(c_0_63,plain,
    ! [X26,X27,X28,X29,X30] :
      ( ( ~ subset(X26,X27)
        | ~ in(X28,X26)
        | in(X28,X27) )
      & ( in(esk3_2(X29,X30),X29)
        | subset(X29,X30) )
      & ( ~ in(esk3_2(X29,X30),X30)
        | subset(X29,X30) ) ),
    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_64,lemma,
    ( set_difference(X1,X2) = empty_set
    | ~ in(esk1_1(set_difference(X1,X2)),set_intersection2(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_59,c_0_28]) ).

cnf(c_0_65,plain,
    ( set_difference(X1,X2) = empty_set
    | in(esk1_1(set_difference(X1,X2)),X1) ),
    inference(spm,[status(thm)],[c_0_60,c_0_28]) ).

cnf(c_0_66,lemma,
    ( set_intersection2(X1,X2) = X1
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_67,lemma,
    ( set_difference(esk6_0,esk7_0) = empty_set
    | subset(set_intersection2(esk6_0,X1),esk7_0) ),
    inference(spm,[status(thm)],[c_0_62,c_0_47]) ).

fof(c_0_68,lemma,
    ! [X104,X105] : subset(X104,set_union2(X104,X105)),
    inference(variable_rename,[status(thm)],[t7_xboole_1]) ).

cnf(c_0_69,plain,
    ( in(X1,X3)
    | in(X1,X4)
    | ~ in(X1,X2)
    | X4 != set_difference(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_70,plain,
    ( in(esk3_2(X1,X2),X1)
    | subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_71,lemma,
    set_difference(set_intersection2(X1,X2),X1) = empty_set,
    inference(spm,[status(thm)],[c_0_64,c_0_65]) ).

cnf(c_0_72,lemma,
    ( set_intersection2(esk7_0,set_intersection2(esk6_0,X1)) = set_intersection2(esk6_0,X1)
    | set_difference(esk6_0,esk7_0) = empty_set ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_40]) ).

cnf(c_0_73,lemma,
    subset(X1,set_union2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_74,plain,
    ( in(X1,set_difference(X2,X3))
    | in(X1,X3)
    | ~ in(X1,X2) ),
    inference(er,[status(thm)],[c_0_69]) ).

cnf(c_0_75,lemma,
    ( set_intersection2(X1,X2) = X1
    | in(esk3_2(X1,X2),X1) ),
    inference(spm,[status(thm)],[c_0_66,c_0_70]) ).

cnf(c_0_76,lemma,
    ( set_difference(set_intersection2(esk6_0,X1),esk7_0) = empty_set
    | set_difference(esk6_0,esk7_0) = empty_set ),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_77,lemma,
    set_intersection2(X1,set_union2(X1,X2)) = X1,
    inference(spm,[status(thm)],[c_0_66,c_0_73]) ).

cnf(c_0_78,plain,
    ( X1 != empty_set
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_79,lemma,
    ( set_intersection2(X1,X2) = X1
    | in(esk3_2(X1,X2),set_difference(X1,X3))
    | in(esk3_2(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_74,c_0_75]) ).

cnf(c_0_80,lemma,
    set_difference(esk6_0,esk7_0) = empty_set,
    inference(spm,[status(thm)],[c_0_76,c_0_77]) ).

cnf(c_0_81,plain,
    ~ in(X1,empty_set),
    inference(er,[status(thm)],[c_0_78]) ).

cnf(c_0_82,negated_conjecture,
    ( set_difference(esk6_0,esk7_0) != empty_set
    | ~ subset(esk6_0,esk7_0) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_83,plain,
    ( subset(X1,X2)
    | ~ in(esk3_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_84,lemma,
    ( set_intersection2(esk6_0,X1) = esk6_0
    | in(esk3_2(esk6_0,X1),esk7_0) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).

cnf(c_0_85,negated_conjecture,
    ~ subset(esk6_0,esk7_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_80])]) ).

cnf(c_0_86,lemma,
    subset(set_intersection2(X1,X2),X2),
    inference(spm,[status(thm)],[c_0_47,c_0_40]) ).

cnf(c_0_87,lemma,
    set_intersection2(esk6_0,esk7_0) = esk6_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).

cnf(c_0_88,lemma,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_85]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU131+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Wed Aug 23 13:36:26 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 1.63/1.79  % Version  : CSE_E---1.5
% 1.63/1.79  % Problem  : theBenchmark.p
% 1.63/1.79  % Proof found
% 1.63/1.79  % SZS status Theorem for theBenchmark.p
% 1.63/1.79  % SZS output start Proof
% See solution above
% 1.63/1.80  % Total time : 1.217000 s
% 1.63/1.80  % SZS output end Proof
% 1.63/1.80  % Total time : 1.221000 s
%------------------------------------------------------------------------------