TSTP Solution File: SEU208+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SEU208+2 : 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 : n003.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 16:23:20 EDT 2023

% Result   : Theorem 31.11s 31.19s
% Output   : CNFRefutation 31.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :  113
% Syntax   : Number of formulae    :  166 (  16 unt; 107 typ;   0 def)
%            Number of atoms       :  185 (  22 equ)
%            Maximal formula atoms :   26 (   3 avg)
%            Number of connectives :  211 (  85   ~; 101   |;  16   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  211 (  98   >; 113   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   99 (  99 usr;   9 con; 0-5 aty)
%            Number of variables   :   98 (   1 sgn;  36   !;   3   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(decl_27,type,
    set_union2: ( $i * $i ) > $i ).

tff(decl_28,type,
    set_intersection2: ( $i * $i ) > $i ).

tff(decl_29,type,
    identity_relation: $i > $i ).

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

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

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

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

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

tff(decl_35,type,
    relation_inverse_image: ( $i * $i ) > $i ).

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

tff(decl_37,type,
    set_meet: $i > $i ).

tff(decl_38,type,
    singleton: $i > $i ).

tff(decl_39,type,
    powerset: $i > $i ).

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

tff(decl_41,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff(decl_42,type,
    relation_dom: $i > $i ).

tff(decl_43,type,
    cast_to_subset: $i > $i ).

tff(decl_44,type,
    union: $i > $i ).

tff(decl_45,type,
    set_difference: ( $i * $i ) > $i ).

tff(decl_46,type,
    relation_rng: $i > $i ).

tff(decl_47,type,
    subset_complement: ( $i * $i ) > $i ).

tff(decl_48,type,
    relation_field: $i > $i ).

tff(decl_49,type,
    relation_inverse: $i > $i ).

tff(decl_50,type,
    disjoint: ( $i * $i ) > $o ).

tff(decl_51,type,
    relation_composition: ( $i * $i ) > $i ).

tff(decl_52,type,
    complements_of_subsets: ( $i * $i ) > $i ).

tff(decl_53,type,
    union_of_subsets: ( $i * $i ) > $i ).

tff(decl_54,type,
    meet_of_subsets: ( $i * $i ) > $i ).

tff(decl_55,type,
    subset_difference: ( $i * $i * $i ) > $i ).

tff(decl_56,type,
    are_equipotent: ( $i * $i ) > $o ).

tff(decl_57,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_58,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_59,type,
    esk3_3: ( $i * $i * $i ) > $i ).

tff(decl_60,type,
    esk4_3: ( $i * $i * $i ) > $i ).

tff(decl_61,type,
    esk5_3: ( $i * $i * $i ) > $i ).

tff(decl_62,type,
    esk6_3: ( $i * $i * $i ) > $i ).

tff(decl_63,type,
    esk7_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_64,type,
    esk8_3: ( $i * $i * $i ) > $i ).

tff(decl_65,type,
    esk9_3: ( $i * $i * $i ) > $i ).

tff(decl_66,type,
    esk10_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_67,type,
    esk11_3: ( $i * $i * $i ) > $i ).

tff(decl_68,type,
    esk12_3: ( $i * $i * $i ) > $i ).

tff(decl_69,type,
    esk13_2: ( $i * $i ) > $i ).

tff(decl_70,type,
    esk14_2: ( $i * $i ) > $i ).

tff(decl_71,type,
    esk15_1: $i > $i ).

tff(decl_72,type,
    esk16_3: ( $i * $i * $i ) > $i ).

tff(decl_73,type,
    esk17_2: ( $i * $i ) > $i ).

tff(decl_74,type,
    esk18_2: ( $i * $i ) > $i ).

tff(decl_75,type,
    esk19_2: ( $i * $i ) > $i ).

tff(decl_76,type,
    esk20_1: $i > $i ).

tff(decl_77,type,
    esk21_2: ( $i * $i ) > $i ).

tff(decl_78,type,
    esk22_2: ( $i * $i ) > $i ).

tff(decl_79,type,
    esk23_2: ( $i * $i ) > $i ).

tff(decl_80,type,
    esk24_3: ( $i * $i * $i ) > $i ).

tff(decl_81,type,
    esk25_3: ( $i * $i * $i ) > $i ).

tff(decl_82,type,
    esk26_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_83,type,
    esk27_4: ( $i * $i * $i * $i ) > $i ).

tff(decl_84,type,
    esk28_3: ( $i * $i * $i ) > $i ).

tff(decl_85,type,
    esk29_3: ( $i * $i * $i ) > $i ).

tff(decl_86,type,
    esk30_3: ( $i * $i * $i ) > $i ).

tff(decl_87,type,
    esk31_2: ( $i * $i ) > $i ).

tff(decl_88,type,
    esk32_2: ( $i * $i ) > $i ).

tff(decl_89,type,
    esk33_2: ( $i * $i ) > $i ).

tff(decl_90,type,
    esk34_3: ( $i * $i * $i ) > $i ).

tff(decl_91,type,
    esk35_3: ( $i * $i * $i ) > $i ).

tff(decl_92,type,
    esk36_2: ( $i * $i ) > $i ).

tff(decl_93,type,
    esk37_2: ( $i * $i ) > $i ).

tff(decl_94,type,
    esk38_3: ( $i * $i * $i ) > $i ).

tff(decl_95,type,
    esk39_2: ( $i * $i ) > $i ).

tff(decl_96,type,
    esk40_2: ( $i * $i ) > $i ).

tff(decl_97,type,
    esk41_3: ( $i * $i * $i ) > $i ).

tff(decl_98,type,
    esk42_3: ( $i * $i * $i ) > $i ).

tff(decl_99,type,
    esk43_2: ( $i * $i ) > $i ).

tff(decl_100,type,
    esk44_2: ( $i * $i ) > $i ).

tff(decl_101,type,
    esk45_2: ( $i * $i ) > $i ).

tff(decl_102,type,
    esk46_2: ( $i * $i ) > $i ).

tff(decl_103,type,
    esk47_5: ( $i * $i * $i * $i * $i ) > $i ).

tff(decl_104,type,
    esk48_3: ( $i * $i * $i ) > $i ).

tff(decl_105,type,
    esk49_3: ( $i * $i * $i ) > $i ).

tff(decl_106,type,
    esk50_3: ( $i * $i * $i ) > $i ).

tff(decl_107,type,
    esk51_3: ( $i * $i * $i ) > $i ).

tff(decl_108,type,
    esk52_1: $i > $i ).

tff(decl_109,type,
    esk53_2: ( $i * $i ) > $i ).

tff(decl_110,type,
    esk54_0: $i ).

tff(decl_111,type,
    esk55_1: $i > $i ).

tff(decl_112,type,
    esk56_0: $i ).

tff(decl_113,type,
    esk57_0: $i ).

tff(decl_114,type,
    esk58_1: $i > $i ).

tff(decl_115,type,
    esk59_0: $i ).

tff(decl_116,type,
    esk60_1: $i > $i ).

tff(decl_117,type,
    esk61_3: ( $i * $i * $i ) > $i ).

tff(decl_118,type,
    esk62_0: $i ).

tff(decl_119,type,
    esk63_0: $i ).

tff(decl_120,type,
    esk64_0: $i ).

tff(decl_121,type,
    esk65_0: $i ).

tff(decl_122,type,
    esk66_2: ( $i * $i ) > $i ).

tff(decl_123,type,
    esk67_2: ( $i * $i ) > $i ).

tff(decl_124,type,
    esk68_2: ( $i * $i ) > $i ).

tff(decl_125,type,
    esk69_1: $i > $i ).

tff(decl_126,type,
    esk70_1: $i > $i ).

tff(decl_127,type,
    esk71_1: $i > $i ).

tff(decl_128,type,
    esk72_2: ( $i * $i ) > $i ).

fof(t166_relat_1,conjecture,
    ! [X1,X2,X3] :
      ( relation(X3)
     => ( in(X1,relation_inverse_image(X3,X2))
      <=> ? [X4] :
            ( in(X4,relation_rng(X3))
            & in(ordered_pair(X1,X4),X3)
            & in(X4,X2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t166_relat_1) ).

fof(d5_tarski,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).

fof(t69_enumset1,lemma,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).

fof(d14_relat_1,axiom,
    ! [X1] :
      ( relation(X1)
     => ! [X2,X3] :
          ( X3 = relation_inverse_image(X1,X2)
        <=> ! [X4] :
              ( in(X4,X3)
            <=> ? [X5] :
                  ( in(ordered_pair(X4,X5),X1)
                  & in(X5,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_1) ).

fof(commutativity_k2_tarski,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(t20_relat_1,lemma,
    ! [X1,X2,X3] :
      ( relation(X3)
     => ( in(ordered_pair(X1,X2),X3)
       => ( in(X1,relation_dom(X3))
          & in(X2,relation_rng(X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( relation(X3)
       => ( in(X1,relation_inverse_image(X3,X2))
        <=> ? [X4] :
              ( in(X4,relation_rng(X3))
              & in(ordered_pair(X1,X4),X3)
              & in(X4,X2) ) ) ),
    inference(assume_negation,[status(cth)],[t166_relat_1]) ).

fof(c_0_7,plain,
    ! [X218,X219] : ordered_pair(X218,X219) = unordered_pair(unordered_pair(X218,X219),singleton(X218)),
    inference(variable_rename,[status(thm)],[d5_tarski]) ).

fof(c_0_8,lemma,
    ! [X524] : unordered_pair(X524,X524) = singleton(X524),
    inference(variable_rename,[status(thm)],[t69_enumset1]) ).

fof(c_0_9,negated_conjecture,
    ! [X403] :
      ( relation(esk64_0)
      & ( ~ in(esk62_0,relation_inverse_image(esk64_0,esk63_0))
        | ~ in(X403,relation_rng(esk64_0))
        | ~ in(ordered_pair(esk62_0,X403),esk64_0)
        | ~ in(X403,esk63_0) )
      & ( in(esk65_0,relation_rng(esk64_0))
        | in(esk62_0,relation_inverse_image(esk64_0,esk63_0)) )
      & ( in(ordered_pair(esk62_0,esk65_0),esk64_0)
        | in(esk62_0,relation_inverse_image(esk64_0,esk63_0)) )
      & ( in(esk65_0,esk63_0)
        | in(esk62_0,relation_inverse_image(esk64_0,esk63_0)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).

cnf(c_0_10,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,lemma,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

fof(c_0_12,plain,
    ! [X58,X59,X60,X61,X63,X64,X65,X66,X68] :
      ( ( in(ordered_pair(X61,esk10_4(X58,X59,X60,X61)),X58)
        | ~ in(X61,X60)
        | X60 != relation_inverse_image(X58,X59)
        | ~ relation(X58) )
      & ( in(esk10_4(X58,X59,X60,X61),X59)
        | ~ in(X61,X60)
        | X60 != relation_inverse_image(X58,X59)
        | ~ relation(X58) )
      & ( ~ in(ordered_pair(X63,X64),X58)
        | ~ in(X64,X59)
        | in(X63,X60)
        | X60 != relation_inverse_image(X58,X59)
        | ~ relation(X58) )
      & ( ~ in(esk11_3(X58,X65,X66),X66)
        | ~ in(ordered_pair(esk11_3(X58,X65,X66),X68),X58)
        | ~ in(X68,X65)
        | X66 = relation_inverse_image(X58,X65)
        | ~ relation(X58) )
      & ( in(ordered_pair(esk11_3(X58,X65,X66),esk12_3(X58,X65,X66)),X58)
        | in(esk11_3(X58,X65,X66),X66)
        | X66 = relation_inverse_image(X58,X65)
        | ~ relation(X58) )
      & ( in(esk12_3(X58,X65,X66),X65)
        | in(esk11_3(X58,X65,X66),X66)
        | X66 = relation_inverse_image(X58,X65)
        | ~ relation(X58) ) ),
    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)],[d14_relat_1])])])])])]) ).

cnf(c_0_13,negated_conjecture,
    ( in(ordered_pair(esk62_0,esk65_0),esk64_0)
    | in(esk62_0,relation_inverse_image(esk64_0,esk63_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),
    inference(rw,[status(thm)],[c_0_10,c_0_11]) ).

fof(c_0_15,plain,
    ! [X12,X13] : unordered_pair(X12,X13) = unordered_pair(X13,X12),
    inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).

fof(c_0_16,lemma,
    ! [X416,X417,X418] :
      ( ( in(X416,relation_dom(X418))
        | ~ in(ordered_pair(X416,X417),X418)
        | ~ relation(X418) )
      & ( in(X417,relation_rng(X418))
        | ~ in(ordered_pair(X416,X417),X418)
        | ~ relation(X418) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_relat_1])])]) ).

cnf(c_0_17,plain,
    ( in(ordered_pair(X1,esk10_4(X2,X3,X4,X1)),X2)
    | ~ in(X1,X4)
    | X4 != relation_inverse_image(X2,X3)
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,negated_conjecture,
    ( ~ in(esk62_0,relation_inverse_image(esk64_0,esk63_0))
    | ~ in(X1,relation_rng(esk64_0))
    | ~ in(ordered_pair(esk62_0,X1),esk64_0)
    | ~ in(X1,esk63_0) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_19,negated_conjecture,
    ( in(esk62_0,relation_inverse_image(esk64_0,esk63_0))
    | in(unordered_pair(unordered_pair(esk62_0,esk65_0),unordered_pair(esk62_0,esk62_0)),esk64_0) ),
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_20,plain,
    unordered_pair(X1,X2) = unordered_pair(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,plain,
    ( in(esk10_4(X1,X2,X3,X4),X2)
    | ~ in(X4,X3)
    | X3 != relation_inverse_image(X1,X2)
    | ~ relation(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_22,lemma,
    ( in(X1,relation_rng(X2))
    | ~ in(ordered_pair(X3,X1),X2)
    | ~ relation(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_23,plain,
    ( in(unordered_pair(unordered_pair(X1,esk10_4(X2,X3,X4,X1)),unordered_pair(X1,X1)),X2)
    | X4 != relation_inverse_image(X2,X3)
    | ~ relation(X2)
    | ~ in(X1,X4) ),
    inference(rw,[status(thm)],[c_0_17,c_0_14]) ).

cnf(c_0_24,plain,
    ( in(X1,X5)
    | ~ in(ordered_pair(X1,X2),X3)
    | ~ in(X2,X4)
    | X5 != relation_inverse_image(X3,X4)
    | ~ relation(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_25,negated_conjecture,
    ( ~ in(X1,esk63_0)
    | ~ in(X1,relation_rng(esk64_0))
    | ~ in(esk62_0,relation_inverse_image(esk64_0,esk63_0))
    | ~ in(unordered_pair(unordered_pair(esk62_0,X1),unordered_pair(esk62_0,esk62_0)),esk64_0) ),
    inference(rw,[status(thm)],[c_0_18,c_0_14]) ).

cnf(c_0_26,negated_conjecture,
    ( in(unordered_pair(unordered_pair(esk62_0,esk62_0),unordered_pair(esk62_0,esk65_0)),esk64_0)
    | in(esk62_0,relation_inverse_image(esk64_0,esk63_0)) ),
    inference(rw,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_27,plain,
    ( in(esk10_4(X1,X2,relation_inverse_image(X1,X2),X3),X2)
    | ~ relation(X1)
    | ~ in(X3,relation_inverse_image(X1,X2)) ),
    inference(er,[status(thm)],[c_0_21]) ).

cnf(c_0_28,negated_conjecture,
    relation(esk64_0),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_29,lemma,
    ( in(X1,relation_rng(X2))
    | ~ relation(X2)
    | ~ in(unordered_pair(unordered_pair(X3,X1),unordered_pair(X3,X3)),X2) ),
    inference(rw,[status(thm)],[c_0_22,c_0_14]) ).

cnf(c_0_30,plain,
    ( in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,esk10_4(X2,X3,relation_inverse_image(X2,X3),X1))),X2)
    | ~ relation(X2)
    | ~ in(X1,relation_inverse_image(X2,X3)) ),
    inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_20])]) ).

cnf(c_0_31,plain,
    ( in(X1,X5)
    | X5 != relation_inverse_image(X3,X4)
    | ~ relation(X3)
    | ~ in(X2,X4)
    | ~ in(unordered_pair(unordered_pair(X1,X2),unordered_pair(X1,X1)),X3) ),
    inference(rw,[status(thm)],[c_0_24,c_0_14]) ).

cnf(c_0_32,negated_conjecture,
    ( in(unordered_pair(unordered_pair(esk62_0,esk62_0),unordered_pair(esk62_0,esk65_0)),esk64_0)
    | ~ in(unordered_pair(unordered_pair(esk62_0,X1),unordered_pair(esk62_0,esk62_0)),esk64_0)
    | ~ in(X1,relation_rng(esk64_0))
    | ~ in(X1,esk63_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_33,negated_conjecture,
    ( in(unordered_pair(unordered_pair(esk62_0,esk62_0),unordered_pair(esk62_0,esk65_0)),esk64_0)
    | in(esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0),esk63_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_26]),c_0_28])]) ).

cnf(c_0_34,lemma,
    ( in(X1,relation_rng(X2))
    | ~ relation(X2)
    | ~ in(unordered_pair(unordered_pair(X3,X3),unordered_pair(X3,X1)),X2) ),
    inference(spm,[status(thm)],[c_0_29,c_0_20]) ).

cnf(c_0_35,negated_conjecture,
    ( in(unordered_pair(unordered_pair(esk62_0,esk62_0),unordered_pair(esk62_0,esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0))),esk64_0)
    | in(unordered_pair(unordered_pair(esk62_0,esk62_0),unordered_pair(esk62_0,esk65_0)),esk64_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_26]),c_0_28])]) ).

cnf(c_0_36,negated_conjecture,
    ( in(esk65_0,esk63_0)
    | in(esk62_0,relation_inverse_image(esk64_0,esk63_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_37,plain,
    ( in(X1,relation_inverse_image(X2,X3))
    | ~ relation(X2)
    | ~ in(unordered_pair(unordered_pair(X1,X4),unordered_pair(X1,X1)),X2)
    | ~ in(X4,X3) ),
    inference(er,[status(thm)],[c_0_31]) ).

cnf(c_0_38,negated_conjecture,
    ( in(unordered_pair(unordered_pair(esk62_0,esk62_0),unordered_pair(esk62_0,esk65_0)),esk64_0)
    | ~ in(unordered_pair(unordered_pair(esk62_0,esk62_0),unordered_pair(esk62_0,esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0))),esk64_0)
    | ~ in(esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0),relation_rng(esk64_0)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_20]) ).

cnf(c_0_39,negated_conjecture,
    ( in(esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0),relation_rng(esk64_0))
    | in(unordered_pair(unordered_pair(esk62_0,esk62_0),unordered_pair(esk62_0,esk65_0)),esk64_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_28])]) ).

cnf(c_0_40,negated_conjecture,
    ( in(esk65_0,esk63_0)
    | ~ in(unordered_pair(unordered_pair(esk62_0,X1),unordered_pair(esk62_0,esk62_0)),esk64_0)
    | ~ in(X1,relation_rng(esk64_0))
    | ~ in(X1,esk63_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_36]) ).

cnf(c_0_41,negated_conjecture,
    ( in(esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0),esk63_0)
    | in(esk65_0,esk63_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_36]),c_0_28])]) ).

cnf(c_0_42,negated_conjecture,
    ( in(unordered_pair(unordered_pair(esk62_0,esk62_0),unordered_pair(esk62_0,esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0))),esk64_0)
    | in(esk65_0,esk63_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_36]),c_0_28])]) ).

cnf(c_0_43,plain,
    ( in(X1,relation_inverse_image(X2,X3))
    | ~ relation(X2)
    | ~ in(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,X4)),X2)
    | ~ in(X4,X3) ),
    inference(spm,[status(thm)],[c_0_37,c_0_20]) ).

cnf(c_0_44,negated_conjecture,
    in(unordered_pair(unordered_pair(esk62_0,esk62_0),unordered_pair(esk62_0,esk65_0)),esk64_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_35]) ).

cnf(c_0_45,negated_conjecture,
    ( in(esk65_0,esk63_0)
    | ~ in(unordered_pair(unordered_pair(esk62_0,esk62_0),unordered_pair(esk62_0,esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0))),esk64_0)
    | ~ in(esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0),relation_rng(esk64_0)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_20]) ).

cnf(c_0_46,negated_conjecture,
    ( in(esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0),relation_rng(esk64_0))
    | in(esk65_0,esk63_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_42]),c_0_28])]) ).

cnf(c_0_47,negated_conjecture,
    ( in(esk65_0,relation_rng(esk64_0))
    | in(esk62_0,relation_inverse_image(esk64_0,esk63_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_48,negated_conjecture,
    ( in(esk62_0,relation_inverse_image(esk64_0,X1))
    | ~ in(esk65_0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_28])]) ).

cnf(c_0_49,negated_conjecture,
    in(esk65_0,esk63_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_42]) ).

cnf(c_0_50,negated_conjecture,
    ( in(esk65_0,relation_rng(esk64_0))
    | ~ in(unordered_pair(unordered_pair(esk62_0,X1),unordered_pair(esk62_0,esk62_0)),esk64_0)
    | ~ in(X1,relation_rng(esk64_0))
    | ~ in(X1,esk63_0) ),
    inference(spm,[status(thm)],[c_0_25,c_0_47]) ).

cnf(c_0_51,negated_conjecture,
    ( in(esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0),esk63_0)
    | in(esk65_0,relation_rng(esk64_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_47]),c_0_28])]) ).

cnf(c_0_52,negated_conjecture,
    ( in(unordered_pair(unordered_pair(esk62_0,esk62_0),unordered_pair(esk62_0,esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0))),esk64_0)
    | in(esk65_0,relation_rng(esk64_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_47]),c_0_28])]) ).

cnf(c_0_53,negated_conjecture,
    in(esk62_0,relation_inverse_image(esk64_0,esk63_0)),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_54,negated_conjecture,
    ( in(esk65_0,relation_rng(esk64_0))
    | ~ in(unordered_pair(unordered_pair(esk62_0,esk62_0),unordered_pair(esk62_0,esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0))),esk64_0)
    | ~ in(esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0),relation_rng(esk64_0)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_20]) ).

cnf(c_0_55,negated_conjecture,
    ( in(esk10_4(esk64_0,esk63_0,relation_inverse_image(esk64_0,esk63_0),esk62_0),relation_rng(esk64_0))
    | in(esk65_0,relation_rng(esk64_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_52]),c_0_28])]) ).

cnf(c_0_56,negated_conjecture,
    ( ~ in(unordered_pair(unordered_pair(esk62_0,X1),unordered_pair(esk62_0,esk62_0)),esk64_0)
    | ~ in(X1,relation_rng(esk64_0))
    | ~ in(X1,esk63_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_53])]) ).

cnf(c_0_57,negated_conjecture,
    in(esk65_0,relation_rng(esk64_0)),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_52]) ).

cnf(c_0_58,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_49]),c_0_20]),c_0_44]),c_0_57])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU208+2 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36  % Computer : n003.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Wed Aug 23 14:35:37 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 31.11/31.19  % Version  : CSE_E---1.5
% 31.11/31.19  % Problem  : theBenchmark.p
% 31.11/31.19  % Proof found
% 31.11/31.19  % SZS status Theorem for theBenchmark.p
% 31.11/31.19  % SZS output start Proof
% See solution above
% 31.11/31.20  % Total time : 30.609000 s
% 31.11/31.20  % SZS output end Proof
% 31.11/31.20  % Total time : 30.614000 s
%------------------------------------------------------------------------------