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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SEU217+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May  5 05:11:06 PM UTC 2026

% Result   : Theorem 0.27s 1.62s
% Output   : CNFRefutation 0.27s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named 51)

% Comments : 
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => ~ in(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

fof(fc5_relat_1,axiom,
    ! [X1] :
      ( ( ~ empty(X1)
        & relation(X1) )
     => ~ empty(relation_dom(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).

fof(t35_funct_1,conjecture,
    ! [X1,X2] :
      ( in(X2,X1)
     => apply(identity_relation(X1),X2) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).

fof(rc2_xboole_0,axiom,
    ? [X1] : ~ empty(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).

fof(rc2_relat_1,axiom,
    ? [X1] :
      ( ~ empty(X1)
      & relation(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).

fof(t34_funct_1,axiom,
    ! [X1,X2] :
      ( ( relation(X2)
        & function(X2) )
     => ( X2 = identity_relation(X1)
      <=> ( relation_dom(X2) = X1
          & ! [X3] :
              ( in(X3,X1)
             => apply(X2,X3) = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).

fof(t2_subset,axiom,
    ! [X1,X2] :
      ( element(X1,X2)
     => ( empty(X2)
        | in(X1,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(t1_subset,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => element(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

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

fof(existence_m1_subset_1,axiom,
    ! [X1] :
    ? [X2] : element(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(fc7_relat_1,axiom,
    ! [X1] :
      ( empty(X1)
     => ( empty(relation_dom(X1))
        & relation(relation_dom(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).

fof(t8_boole,axiom,
    ! [X1,X2] :
      ~ ( empty(X1)
        & X1 != X2
        & empty(X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).

fof(cc1_funct_1,axiom,
    ! [X1] :
      ( empty(X1)
     => function(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).

fof(cc1_relat_1,axiom,
    ! [X1] :
      ( empty(X1)
     => relation(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).

fof(fc2_funct_1,axiom,
    ! [X1] :
      ( relation(identity_relation(X1))
      & function(identity_relation(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).

fof(dt_k6_relat_1,axiom,
    ! [X1] : relation(identity_relation(X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).

fof(t6_boole,axiom,
    ! [X1] :
      ( empty(X1)
     => X1 = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

fof(rc1_funct_1,axiom,
    ? [X1] :
      ( relation(X1)
      & function(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).

fof(rc1_xboole_0,axiom,
    ? [X1] : empty(X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(rc1_relat_1,axiom,
    ? [X1] :
      ( empty(X1)
      & relation(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).

fof(rc3_relat_1,axiom,
    ? [X1] :
      ( relation(X1)
      & relation_empty_yielding(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).

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

fof(fc12_relat_1,axiom,
    ( empty(empty_set)
    & relation(empty_set)
    & relation_empty_yielding(empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).

fof(fc4_relat_1,axiom,
    ( empty(empty_set)
    & relation(empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).

fof(i_0_24,plain,
    ! [X1,X2] :
      ( in(X1,X2)
     => ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).

fof(i_0_25,plain,
    ! [X1] :
      ( ( ~ empty(X1)
        & relation(X1) )
     => ~ empty(relation_dom(X1)) ),
    inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).

fof(i_0_26,negated_conjecture,
    ~ ! [X1,X2] :
        ( in(X2,X1)
       => apply(identity_relation(X1),X2) = X2 ),
    inference(assume_negation,[status(cth)],[t35_funct_1]) ).

fof(i_0_27,plain,
    ? [X1] : ~ empty(X1),
    inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).

fof(i_0_28,plain,
    ? [X1] :
      ( ~ empty(X1)
      & relation(X1) ),
    inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).

fof(i_0_29,plain,
    ! [X61,X62,X63] :
      ( ( relation_dom(X62) = X61
        | X62 != identity_relation(X61)
        | ~ relation(X62)
        | ~ function(X62) )
      & ( ~ in(X63,X61)
        | apply(X62,X63) = X63
        | X62 != identity_relation(X61)
        | ~ relation(X62)
        | ~ function(X62) )
      & ( in(esk10_2(X61,X62),X61)
        | relation_dom(X62) != X61
        | X62 = identity_relation(X61)
        | ~ relation(X62)
        | ~ function(X62) )
      & ( apply(X62,esk10_2(X61,X62)) != esk10_2(X61,X62)
        | relation_dom(X62) != X61
        | X62 = identity_relation(X61)
        | ~ relation(X62)
        | ~ function(X62) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).

fof(i_0_30,plain,
    ! [X50,X51] :
      ( ~ in(X50,X51)
      | ~ in(X51,X50) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_24])]) ).

fof(i_0_31,plain,
    ! [X45,X46] :
      ( ~ element(X45,X46)
      | empty(X46)
      | in(X45,X46) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).

fof(i_0_32,plain,
    ! [X55,X56] :
      ( ~ in(X55,X56)
      | element(X55,X56) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).

fof(i_0_33,plain,
    ! [X57,X58] :
      ( ~ in(X57,X58)
      | ~ empty(X58) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).

fof(i_0_34,plain,
    ! [X41] :
      ( empty(X41)
      | ~ relation(X41)
      | ~ empty(relation_dom(X41)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_25])]) ).

fof(i_0_35,negated_conjecture,
    ( in(esk9_0,esk8_0)
    & apply(identity_relation(esk8_0),esk9_0) != esk9_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_26])])]) ).

fof(i_0_36,plain,
    ! [X35] : element(esk2_1(X35),X35),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).

fof(i_0_37,plain,
    ! [X42] :
      ( ( empty(relation_dom(X42))
        | ~ empty(X42) )
      & ( relation(relation_dom(X42))
        | ~ empty(X42) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).

fof(i_0_38,plain,
    ! [X48,X49] :
      ( ~ empty(X48)
      | X48 = X49
      | ~ empty(X49) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).

fof(i_0_39,plain,
    ! [X37] :
      ( ~ empty(X37)
      | function(X37) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).

fof(i_0_40,plain,
    ! [X39] :
      ( ~ empty(X39)
      | relation(X39) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).

fof(i_0_41,plain,
    ! [X54] :
      ( relation(identity_relation(X54))
      & function(identity_relation(X54)) ),
    inference(variable_rename,[status(thm)],[fc2_funct_1]) ).

fof(i_0_42,plain,
    ! [X52] : relation(identity_relation(X52)),
    inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).

fof(i_0_43,plain,
    ! [X47] :
      ( ~ empty(X47)
      | X47 = empty_set ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).

fof(i_0_44,plain,
    ~ empty(esk6_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_27])]) ).

fof(i_0_45,plain,
    ( ~ empty(esk4_0)
    & relation(esk4_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_28])]) ).

fof(i_0_46,plain,
    ( relation(esk7_0)
    & function(esk7_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).

fof(i_0_47,plain,
    empty(esk5_0),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).

fof(i_0_48,plain,
    ( empty(esk3_0)
    & relation(esk3_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).

fof(i_0_49,plain,
    ( relation(esk1_0)
    & relation_empty_yielding(esk1_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).

cnf(i_0_50,plain,
    ( X1 = identity_relation(X2)
    | apply(X1,esk10_2(X2,X1)) != esk10_2(X2,X1)
    | relation_dom(X1) != X2
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_29]),
    [final] ).

cnf(i_0_51,plain,
    ( in(esk10_2(X1,X2),X1)
    | X2 = identity_relation(X1)
    | relation_dom(X2) != X1
    | ~ relation(X2)
    | ~ function(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_29]),
    [final] ).

cnf(i_0_52,plain,
    ( apply(X3,X1) = X1
    | ~ in(X1,X2)
    | X3 != identity_relation(X2)
    | ~ relation(X3)
    | ~ function(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_29]),
    [final] ).

cnf(i_0_53,plain,
    ( ~ in(X1,X2)
    | ~ in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_30]),
    [final] ).

cnf(i_0_54,plain,
    ( empty(X2)
    | in(X1,X2)
    | ~ element(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_31]),
    [final] ).

cnf(i_0_55,plain,
    ( element(X1,X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_32]),
    [final] ).

cnf(i_0_56,plain,
    ( ~ in(X1,X2)
    | ~ empty(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_33]),
    [final] ).

cnf(i_0_57,plain,
    ( empty(X1)
    | ~ relation(X1)
    | ~ empty(relation_dom(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_34]),
    [final] ).

cnf(i_0_58,plain,
    ( relation_dom(X1) = X2
    | X1 != identity_relation(X2)
    | ~ relation(X1)
    | ~ function(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_29]),
    [final] ).

cnf(i_0_59,negated_conjecture,
    apply(identity_relation(esk8_0),esk9_0) != esk9_0,
    inference(split_conjunct,[status(thm)],[i_0_35]),
    [final] ).

cnf(i_0_60,plain,
    element(esk2_1(X1),X1),
    inference(split_conjunct,[status(thm)],[i_0_36]),
    [final] ).

cnf(i_0_61,plain,
    ( empty(relation_dom(X1))
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_37]),
    [final] ).

cnf(i_0_62,plain,
    ( relation(relation_dom(X1))
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_37]),
    [final] ).

cnf(i_0_63,plain,
    ( X1 = X2
    | ~ empty(X1)
    | ~ empty(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_38]),
    [final] ).

cnf(i_0_64,plain,
    ( function(X1)
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_39]),
    [final] ).

cnf(i_0_65,plain,
    ( relation(X1)
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_40]),
    [final] ).

cnf(i_0_66,negated_conjecture,
    in(esk9_0,esk8_0),
    inference(split_conjunct,[status(thm)],[i_0_35]),
    [final] ).

cnf(i_0_67,plain,
    function(identity_relation(X1)),
    inference(split_conjunct,[status(thm)],[i_0_41]),
    [final] ).

cnf(i_0_68,plain,
    relation(identity_relation(X1)),
    inference(split_conjunct,[status(thm)],[i_0_41]),
    [final] ).

cnf(i_0_69,plain,
    relation(identity_relation(X1)),
    inference(split_conjunct,[status(thm)],[i_0_42]),
    [final] ).

cnf(i_0_70,plain,
    ( X1 = empty_set
    | ~ empty(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_43]),
    [final] ).

cnf(i_0_71,plain,
    ~ empty(esk6_0),
    inference(split_conjunct,[status(thm)],[i_0_44]),
    [final] ).

cnf(i_0_72,plain,
    ~ empty(esk4_0),
    inference(split_conjunct,[status(thm)],[i_0_45]),
    [final] ).

cnf(i_0_73,plain,
    function(esk7_0),
    inference(split_conjunct,[status(thm)],[i_0_46]),
    [final] ).

cnf(i_0_74,plain,
    empty(esk5_0),
    inference(split_conjunct,[status(thm)],[i_0_47]),
    [final] ).

cnf(i_0_75,plain,
    empty(esk3_0),
    inference(split_conjunct,[status(thm)],[i_0_48]),
    [final] ).

cnf(i_0_76,plain,
    empty(empty_set),
    inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
    [final] ).

cnf(i_0_77,plain,
    empty(empty_set),
    inference(split_conjunct,[status(thm)],[fc12_relat_1]),
    [final] ).

cnf(i_0_78,plain,
    empty(empty_set),
    inference(split_conjunct,[status(thm)],[fc4_relat_1]),
    [final] ).

cnf(i_0_79,plain,
    relation_empty_yielding(esk1_0),
    inference(split_conjunct,[status(thm)],[i_0_49]),
    [final] ).

cnf(i_0_80,plain,
    relation_empty_yielding(empty_set),
    inference(split_conjunct,[status(thm)],[fc12_relat_1]),
    [final] ).

cnf(i_0_81,plain,
    relation(esk7_0),
    inference(split_conjunct,[status(thm)],[i_0_46]),
    [final] ).

cnf(i_0_82,plain,
    relation(esk4_0),
    inference(split_conjunct,[status(thm)],[i_0_45]),
    [final] ).

cnf(i_0_83,plain,
    relation(esk3_0),
    inference(split_conjunct,[status(thm)],[i_0_48]),
    [final] ).

cnf(i_0_84,plain,
    relation(esk1_0),
    inference(split_conjunct,[status(thm)],[i_0_49]),
    [final] ).

cnf(i_0_85,plain,
    relation(empty_set),
    inference(split_conjunct,[status(thm)],[fc12_relat_1]),
    [final] ).

cnf(i_0_86,plain,
    relation(empty_set),
    inference(split_conjunct,[status(thm)],[fc4_relat_1]),
    [final] ).

cnf(i_0_87,axiom,
    X1 = X1 ).

cnf(i_0_88,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_89,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_90,axiom,
    ( X1 != X2
    | identity_relation(X1) = identity_relation(X2) ) ).

cnf(i_0_91,axiom,
    ( X1 != X2
    | apply(X1,X3) = apply(X2,X3) ) ).

cnf(i_0_92,axiom,
    ( X1 != X2
    | apply(X3,X1) = apply(X3,X2) ) ).

cnf(i_0_93,axiom,
    ( X1 != X2
    | esk10_2(X1,X3) = esk10_2(X2,X3) ) ).

cnf(i_0_94,axiom,
    ( X1 != X2
    | esk10_2(X3,X1) = esk10_2(X3,X2) ) ).

cnf(i_0_95,axiom,
    ( X1 != X2
    | relation_dom(X1) = relation_dom(X2) ) ).

cnf(i_0_96,axiom,
    ( X1 != X2
    | ~ relation(X1)
    | relation(X2) ) ).

cnf(i_0_97,axiom,
    ( X1 != X2
    | ~ function(X1)
    | function(X2) ) ).

cnf(i_0_98,axiom,
    ( X1 != X2
    | ~ in(X1,X3)
    | in(X2,X3) ) ).

cnf(i_0_99,axiom,
    ( X1 != X2
    | ~ in(X3,X1)
    | in(X3,X2) ) ).

cnf(i_0_100,axiom,
    ( X1 != X2
    | ~ empty(X1)
    | empty(X2) ) ).

cnf(i_0_101,axiom,
    ( X1 != X2
    | ~ element(X1,X3)
    | element(X2,X3) ) ).

cnf(i_0_102,axiom,
    ( X1 != X2
    | ~ element(X3,X1)
    | element(X3,X2) ) ).

cnf(i_0_103,axiom,
    ( X1 != X2
    | ~ relation_empty_yielding(X1)
    | relation_empty_yielding(X2) ) ).

cnf(i_0_87_001,axiom,
    X1 = X1 ).

cnf(i_0_88_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_89_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_90_004,axiom,
    ( X1 != X2
    | identity_relation(X1) = identity_relation(X2) ) ).

cnf(i_0_91_005,axiom,
    ( X1 != X2
    | apply(X1,X3) = apply(X2,X3) ) ).

cnf(i_0_92_006,axiom,
    ( X1 != X2
    | apply(X3,X1) = apply(X3,X2) ) ).

cnf(i_0_93_007,axiom,
    ( X1 != X2
    | esk10_2(X1,X3) = esk10_2(X2,X3) ) ).

cnf(i_0_94_008,axiom,
    ( X1 != X2
    | esk10_2(X3,X1) = esk10_2(X3,X2) ) ).

cnf(i_0_95_009,axiom,
    ( X1 != X2
    | relation_dom(X1) = relation_dom(X2) ) ).

cnf(i_0_96_010,axiom,
    ( X1 != X2
    | ~ relation(X1)
    | relation(X2) ) ).

cnf(i_0_97_011,axiom,
    ( X1 != X2
    | ~ function(X1)
    | function(X2) ) ).

cnf(i_0_98_012,axiom,
    ( X1 != X2
    | ~ in(X1,X3)
    | in(X2,X3) ) ).

cnf(i_0_99_013,axiom,
    ( X1 != X2
    | ~ in(X3,X1)
    | in(X3,X2) ) ).

cnf(i_0_100_014,axiom,
    ( X1 != X2
    | ~ empty(X1)
    | empty(X2) ) ).

cnf(i_0_101_015,axiom,
    ( X1 != X2
    | ~ element(X1,X3)
    | element(X2,X3) ) ).

cnf(i_0_102_016,axiom,
    ( X1 != X2
    | ~ element(X3,X1)
    | element(X3,X2) ) ).

cnf(i_0_103_017,axiom,
    ( X1 != X2
    | ~ relation_empty_yielding(X1)
    | relation_empty_yielding(X2) ) ).

cnf(i_0_104,plain,
    ( ~ relation(X1)
    | ~ function(X1)
    | X1 = identity_relation(relation_dom(X1))
    | in(esk10_2(relation_dom(X1),X1),relation_dom(X1)) ),
    inference(equality_inference,[],[51]) ).

cnf(i_0_105,plain,
    ( ~ relation(identity_relation(X1))
    | ~ function(identity_relation(X1))
    | ~ in(X2,X1)
    | apply(identity_relation(X1),X2) = X2 ),
    inference(equality_inference,[],[52]) ).

cnf(i_0_106,plain,
    ( ~ relation(identity_relation(X1))
    | ~ function(identity_relation(X1))
    | relation_dom(identity_relation(X1)) = X1 ),
    inference(equality_inference,[],[58]) ).

cnf(i_0_107,plain,
    $false,
    inference(scs_inference,[],[i_0_69,i_0_67,i_0_66,i_0_59,i_0_105]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SEU217+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33  % Computer : n019.cluster.edu
% 0.16/0.33  % Model    : x86_64 x86_64
% 0.16/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33  % Memory   : 8042.1875MB
% 0.16/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33  % CPULimit   : 300
% 0.16/0.33  % WCLimit    : 300
% 0.16/0.33  % DateTime   : Tue May  5 02:49:59 EDT 2026
% 0.16/0.33  % CPUTime    : 
% 0.16/0.34  % start to proof: theBenchmark
% 0.27/1.62  % Version  : CSE_E---1.7
% 0.27/1.62  % Problem  : theBenchmark.p
% 0.27/1.62  % SZS status Theorem for theBenchmark.p
% 0.27/1.62  % SZS output start CNFRefutation
% See solution above
% 0.27/1.64  % Total time : 1.271s
%------------------------------------------------------------------------------