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CSE_E---1.7.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : NUN080+2 : TPTP v9.2.1. Released v7.3.0.
% 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 : n025.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 05:00:52 PM UTC 2026

% Result   : Theorem 0.26s 1.61s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_25)

% Comments : 
%------------------------------------------------------------------------------
fof(xplustwoeqy,conjecture,
    ? [X39,X22,X23] :
      ( X23 = X22
      & ? [X16] :
          ( r3(X39,X16,X23)
          & ? [X17] :
              ( r2(X17,X16)
              & ? [X25] :
                  ( r1(X25)
                  & r2(X25,X17) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xplustwoeqy) ).

fof(axiom_2a,axiom,
    ! [X20,X21] :
    ? [X22] :
      ( ? [X23] :
          ( ? [X24] :
              ( r2(X21,X24)
              & r4(X20,X24,X23) )
          & X23 = X22 )
      & ? [X25] :
          ( r3(X25,X20,X22)
          & r4(X20,X21,X25) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2a) ).

fof(axiom_1a,axiom,
    ! [X14,X15] :
    ? [X16] :
      ( ? [X17] :
          ( ? [X18] :
              ( r2(X15,X18)
              & r3(X14,X18,X17) )
          & X17 = X16 )
      & ? [X19] :
          ( r2(X19,X16)
          & r3(X14,X15,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).

fof(axiom_4,axiom,
    ! [X10,X11] :
    ? [X12] :
    ! [X13] :
      ( ( ~ r4(X10,X11,X13)
        & X13 != X12 )
      | ( r4(X10,X11,X13)
        & X13 = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4) ).

fof(axiom_3,axiom,
    ! [X6,X7] :
    ? [X8] :
    ! [X9] :
      ( ( ~ r3(X6,X7,X9)
        & X9 != X8 )
      | ( r3(X6,X7,X9)
        & X9 = X8 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3) ).

fof(axiom_4a,axiom,
    ! [X30] :
    ? [X31] :
      ( ? [X32] :
          ( r1(X32)
          & r3(X30,X32,X31) )
      & X31 = X30 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).

fof(axiom_3a,axiom,
    ! [X26,X27] :
      ( ! [X28] :
          ( ! [X29] :
              ( ~ r2(X26,X29)
              | X29 != X28 )
          | ~ r2(X27,X28) )
      | X26 = X27 ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3a) ).

fof(axiom_7a,axiom,
    ! [X41,X42] :
      ( ! [X43] :
          ( ~ r1(X43)
          | X43 != X42 )
      | ~ r2(X41,X42) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).

fof(axiom_2,axiom,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( ~ r2(X3,X5)
        & X5 != X4 )
      | ( r2(X3,X5)
        & X5 = X4 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).

fof(axiom_5a,axiom,
    ! [X33] :
    ? [X34] :
      ( ? [X35] :
          ( r1(X35)
          & r4(X33,X35,X34) )
      & ? [X36] :
          ( r1(X36)
          & X34 = X36 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).

fof(axiom_1,axiom,
    ? [X1] :
    ! [X2] :
      ( ( ~ r1(X2)
        & X2 != X1 )
      | ( r1(X2)
        & X2 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).

fof(axiom_6a,axiom,
    ! [X37] :
      ( ? [X38] :
          ( r1(X38)
          & X37 = X38 )
      | ? [X39,X40] :
          ( r2(X39,X40)
          & X37 = X40 ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_6a) ).

fof(i_0_12,negated_conjecture,
    ~ ? [X39,X22,X23] :
        ( X23 = X22
        & ? [X16] :
            ( r3(X39,X16,X23)
            & ? [X17] :
                ( r2(X17,X16)
                & ? [X25] :
                    ( r1(X25)
                    & r2(X25,X17) ) ) ) ),
    inference(assume_negation,[status(cth)],[xplustwoeqy]) ).

fof(i_0_13,plain,
    ! [X112,X113] :
      ( r2(X113,esk11_2(X112,X113))
      & r4(X112,esk11_2(X112,X113),esk10_2(X112,X113))
      & esk10_2(X112,X113) = esk9_2(X112,X113)
      & r3(esk12_2(X112,X113),X112,esk9_2(X112,X113))
      & r4(X112,X113,esk12_2(X112,X113)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_2a])]) ).

fof(i_0_14,plain,
    ! [X106,X107] :
      ( r2(X107,esk7_2(X106,X107))
      & r3(X106,esk7_2(X106,X107),esk6_2(X106,X107))
      & esk6_2(X106,X107) = esk5_2(X106,X107)
      & r2(esk8_2(X106,X107),esk5_2(X106,X107))
      & r3(X106,X107,esk8_2(X106,X107)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).

fof(i_0_15,plain,
    ! [X10,X11] :
    ? [X12] :
    ! [X13] :
      ( ( ~ r4(X10,X11,X13)
        & X13 != X12 )
      | ( r4(X10,X11,X13)
        & X13 = X12 ) ),
    inference(fof_simplification,[status(thm)],[axiom_4]) ).

fof(i_0_16,plain,
    ! [X6,X7] :
    ? [X8] :
    ! [X9] :
      ( ( ~ r3(X6,X7,X9)
        & X9 != X8 )
      | ( r3(X6,X7,X9)
        & X9 = X8 ) ),
    inference(fof_simplification,[status(thm)],[axiom_3]) ).

fof(i_0_17,plain,
    ! [X122] :
      ( r1(esk14_1(X122))
      & r3(X122,esk14_1(X122),esk13_1(X122))
      & esk13_1(X122) = X122 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).

fof(i_0_18,plain,
    ! [X26,X27] :
      ( ! [X28] :
          ( ! [X29] :
              ( ~ r2(X26,X29)
              | X29 != X28 )
          | ~ r2(X27,X28) )
      | X26 = X27 ),
    inference(fof_simplification,[status(thm)],[axiom_3a]) ).

fof(i_0_19,plain,
    ! [X41,X42] :
      ( ! [X43] :
          ( ~ r1(X43)
          | X43 != X42 )
      | ~ r2(X41,X42) ),
    inference(fof_simplification,[status(thm)],[axiom_7a]) ).

fof(i_0_20,plain,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( ~ r2(X3,X5)
        & X5 != X4 )
      | ( r2(X3,X5)
        & X5 = X4 ) ),
    inference(fof_simplification,[status(thm)],[axiom_2]) ).

fof(i_0_21,plain,
    ! [X125] :
      ( r1(esk16_1(X125))
      & r4(X125,esk16_1(X125),esk15_1(X125))
      & r1(esk17_1(X125))
      & esk15_1(X125) = esk17_1(X125) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).

fof(i_0_22,plain,
    ? [X1] :
    ! [X2] :
      ( ( ~ r1(X2)
        & X2 != X1 )
      | ( r1(X2)
        & X2 = X1 ) ),
    inference(fof_simplification,[status(thm)],[axiom_1]) ).

fof(i_0_23,negated_conjecture,
    ! [X136,X137,X138,X139,X140,X141] :
      ( X138 != X137
      | ~ r3(X136,X139,X138)
      | ~ r2(X140,X139)
      | ~ r1(X141)
      | ~ r2(X141,X140) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_12])])]) ).

cnf(i_0_24,plain,
    r4(X1,esk11_2(X1,X2),esk10_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_13]) ).

cnf(i_0_25,plain,
    esk10_2(X1,X2) = esk9_2(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_13]) ).

cnf(i_0_26,plain,
    r3(X1,esk7_2(X1,X2),esk6_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_14]) ).

cnf(i_0_27,plain,
    esk6_2(X1,X2) = esk5_2(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_14]) ).

fof(i_0_28,plain,
    ! [X102,X103,X105] :
      ( ( r4(X102,X103,X105)
        | ~ r4(X102,X103,X105) )
      & ( X105 = esk4_2(X102,X103)
        | ~ r4(X102,X103,X105) )
      & ( r4(X102,X103,X105)
        | X105 != esk4_2(X102,X103) )
      & ( X105 = esk4_2(X102,X103)
        | X105 != esk4_2(X102,X103) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_15])])]) ).

fof(i_0_29,plain,
    ! [X98,X99,X101] :
      ( ( r3(X98,X99,X101)
        | ~ r3(X98,X99,X101) )
      & ( X101 = esk3_2(X98,X99)
        | ~ r3(X98,X99,X101) )
      & ( r3(X98,X99,X101)
        | X101 != esk3_2(X98,X99) )
      & ( X101 = esk3_2(X98,X99)
        | X101 != esk3_2(X98,X99) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_16])])]) ).

cnf(i_0_30,plain,
    r3(X1,esk14_1(X1),esk13_1(X1)),
    inference(split_conjunct,[status(thm)],[i_0_17]) ).

cnf(i_0_31,plain,
    esk13_1(X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_17]) ).

fof(i_0_32,plain,
    ! [X118,X119,X120,X121] :
      ( ~ r2(X118,X121)
      | X121 != X120
      | ~ r2(X119,X120)
      | X118 = X119 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[i_0_18])]) ).

fof(i_0_33,plain,
    ! [X129] :
      ( ( r2(esk19_1(X129),esk20_1(X129))
        | r1(esk18_1(X129)) )
      & ( X129 = esk20_1(X129)
        | r1(esk18_1(X129)) )
      & ( r2(esk19_1(X129),esk20_1(X129))
        | X129 = esk18_1(X129) )
      & ( X129 = esk20_1(X129)
        | X129 = esk18_1(X129) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_6a])])]) ).

fof(i_0_34,plain,
    ! [X133,X134,X135] :
      ( ~ r1(X135)
      | X135 != X134
      | ~ r2(X133,X134) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[i_0_19])]) ).

fof(i_0_35,plain,
    ! [X95,X97] :
      ( ( r2(X95,X97)
        | ~ r2(X95,X97) )
      & ( X97 = esk2_1(X95)
        | ~ r2(X95,X97) )
      & ( r2(X95,X97)
        | X97 != esk2_1(X95) )
      & ( X97 = esk2_1(X95)
        | X97 != esk2_1(X95) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_20])])]) ).

cnf(i_0_36,plain,
    r1(esk17_1(X1)),
    inference(split_conjunct,[status(thm)],[i_0_21]) ).

cnf(i_0_37,plain,
    esk15_1(X1) = esk17_1(X1),
    inference(split_conjunct,[status(thm)],[i_0_21]) ).

fof(i_0_38,plain,
    ! [X94] :
      ( ( r1(X94)
        | ~ r1(X94) )
      & ( X94 = esk1_0
        | ~ r1(X94) )
      & ( r1(X94)
        | X94 != esk1_0 )
      & ( X94 = esk1_0
        | X94 != esk1_0 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_22])])]) ).

cnf(i_0_39,negated_conjecture,
    ( X1 != X2
    | ~ r3(X3,X4,X1)
    | ~ r2(X5,X4)
    | ~ r1(X6)
    | ~ r2(X6,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_23]),
    [final] ).

cnf(i_0_40,plain,
    r3(esk12_2(X1,X2),X1,esk9_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_13]),
    [final] ).

cnf(i_0_41,plain,
    r4(X1,esk11_2(X1,X2),esk9_2(X1,X2)),
    inference(rw,[status(thm)],[i_0_24,c_0_25]),
    [final] ).

cnf(i_0_42,plain,
    r3(X1,esk7_2(X1,X2),esk5_2(X1,X2)),
    inference(rw,[status(thm)],[i_0_26,c_0_27]),
    [final] ).

cnf(i_0_43,plain,
    ( X1 = esk4_2(X2,X3)
    | ~ r4(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_28]),
    [final] ).

cnf(i_0_44,plain,
    ( X1 = esk3_2(X2,X3)
    | ~ r3(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_29]),
    [final] ).

cnf(i_0_45,plain,
    r4(X1,X2,esk12_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_13]),
    [final] ).

cnf(i_0_46,plain,
    r3(X1,X2,esk8_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_14]),
    [final] ).

cnf(i_0_47,plain,
    ( r4(X1,X2,X3)
    | X3 != esk4_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_28]),
    [final] ).

cnf(i_0_48,plain,
    ( r3(X1,X2,X3)
    | X3 != esk3_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_29]),
    [final] ).

cnf(i_0_49,plain,
    r4(X1,esk16_1(X1),esk15_1(X1)),
    inference(split_conjunct,[status(thm)],[i_0_21]),
    [final] ).

cnf(i_0_50,plain,
    r2(esk8_2(X1,X2),esk5_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_14]),
    [final] ).

cnf(i_0_51,plain,
    r3(X1,esk14_1(X1),X1),
    inference(rw,[status(thm)],[i_0_30,c_0_31]),
    [final] ).

cnf(i_0_52,plain,
    ( X1 = X4
    | ~ r2(X1,X2)
    | X2 != X3
    | ~ r2(X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_32]),
    [final] ).

cnf(i_0_53,plain,
    r2(X1,esk11_2(X2,X1)),
    inference(split_conjunct,[status(thm)],[i_0_13]),
    [final] ).

cnf(i_0_54,plain,
    r2(X1,esk7_2(X2,X1)),
    inference(split_conjunct,[status(thm)],[i_0_14]),
    [final] ).

cnf(i_0_55,plain,
    ( r2(esk19_1(X1),esk20_1(X1))
    | r1(esk18_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_33]),
    [final] ).

cnf(i_0_56,plain,
    ( ~ r1(X1)
    | X1 != X2
    | ~ r2(X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_34]),
    [final] ).

cnf(i_0_57,plain,
    ( r2(esk19_1(X1),esk20_1(X1))
    | X1 = esk18_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_33]),
    [final] ).

cnf(i_0_58,plain,
    ( X1 = esk2_1(X2)
    | ~ r2(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_35]),
    [final] ).

cnf(i_0_59,plain,
    ( r2(X1,X2)
    | X2 != esk2_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_35]),
    [final] ).

cnf(i_0_60,plain,
    ( X1 = esk20_1(X1)
    | r1(esk18_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_33]),
    [final] ).

cnf(i_0_61,plain,
    ( X1 = esk20_1(X1)
    | X1 = esk18_1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_33]),
    [final] ).

cnf(i_0_62,plain,
    r1(esk16_1(X1)),
    inference(split_conjunct,[status(thm)],[i_0_21]),
    [final] ).

cnf(i_0_63,plain,
    r1(esk15_1(X1)),
    inference(rw,[status(thm)],[i_0_36,c_0_37]),
    [final] ).

cnf(i_0_64,plain,
    r1(esk14_1(X1)),
    inference(split_conjunct,[status(thm)],[i_0_17]),
    [final] ).

cnf(i_0_65,plain,
    ( X1 = esk1_0
    | ~ r1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_38]),
    [final] ).

cnf(i_0_66,plain,
    ( r1(X1)
    | X1 != esk1_0 ),
    inference(split_conjunct,[status(thm)],[i_0_38]),
    [final] ).

cnf(i_0_67,axiom,
    X1 = X1 ).

cnf(i_0_68,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_69,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_70,axiom,
    ( X1 != X2
    | esk20_1(X1) = esk20_1(X2) ) ).

cnf(i_0_71,axiom,
    ( X1 != X2
    | esk18_1(X1) = esk18_1(X2) ) ).

cnf(i_0_72,axiom,
    ( X1 != X2
    | esk2_1(X1) = esk2_1(X2) ) ).

cnf(i_0_73,axiom,
    ( X1 != X2
    | esk4_2(X1,X3) = esk4_2(X2,X3) ) ).

cnf(i_0_74,axiom,
    ( X1 != X2
    | esk4_2(X3,X1) = esk4_2(X3,X2) ) ).

cnf(i_0_75,axiom,
    ( X1 != X2
    | esk3_2(X1,X3) = esk3_2(X2,X3) ) ).

cnf(i_0_76,axiom,
    ( X1 != X2
    | esk3_2(X3,X1) = esk3_2(X3,X2) ) ).

cnf(i_0_77,axiom,
    ( X1 != X2
    | ~ r3(X1,X3,X4)
    | r3(X2,X3,X4) ) ).

cnf(i_0_78,axiom,
    ( X1 != X2
    | ~ r3(X3,X1,X4)
    | r3(X3,X2,X4) ) ).

cnf(i_0_79,axiom,
    ( X1 != X2
    | ~ r3(X3,X4,X1)
    | r3(X3,X4,X2) ) ).

cnf(i_0_80,axiom,
    ( X1 != X2
    | ~ r2(X1,X3)
    | r2(X2,X3) ) ).

cnf(i_0_81,axiom,
    ( X1 != X2
    | ~ r2(X3,X1)
    | r2(X3,X2) ) ).

cnf(i_0_82,axiom,
    ( X1 != X2
    | ~ r1(X1)
    | r1(X2) ) ).

cnf(i_0_83,axiom,
    ( X1 != X2
    | ~ r4(X1,X3,X4)
    | r4(X2,X3,X4) ) ).

cnf(i_0_84,axiom,
    ( X1 != X2
    | ~ r4(X3,X1,X4)
    | r4(X3,X2,X4) ) ).

cnf(i_0_85,axiom,
    ( X1 != X2
    | ~ r4(X3,X4,X1)
    | r4(X3,X4,X2) ) ).

cnf(i_0_67_001,axiom,
    X1 = X1 ).

cnf(i_0_68_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_69_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_70_004,axiom,
    ( X1 != X2
    | esk20_1(X1) = esk20_1(X2) ) ).

cnf(i_0_71_005,axiom,
    ( X1 != X2
    | esk18_1(X1) = esk18_1(X2) ) ).

cnf(i_0_72_006,axiom,
    ( X1 != X2
    | esk2_1(X1) = esk2_1(X2) ) ).

cnf(i_0_73_007,axiom,
    ( X1 != X2
    | esk4_2(X1,X3) = esk4_2(X2,X3) ) ).

cnf(i_0_74_008,axiom,
    ( X1 != X2
    | esk4_2(X3,X1) = esk4_2(X3,X2) ) ).

cnf(i_0_75_009,axiom,
    ( X1 != X2
    | esk3_2(X1,X3) = esk3_2(X2,X3) ) ).

cnf(i_0_76_010,axiom,
    ( X1 != X2
    | esk3_2(X3,X1) = esk3_2(X3,X2) ) ).

cnf(i_0_77_011,axiom,
    ( X1 != X2
    | ~ r3(X1,X3,X4)
    | r3(X2,X3,X4) ) ).

cnf(i_0_78_012,axiom,
    ( X1 != X2
    | ~ r3(X3,X1,X4)
    | r3(X3,X2,X4) ) ).

cnf(i_0_79_013,axiom,
    ( X1 != X2
    | ~ r3(X3,X4,X1)
    | r3(X3,X4,X2) ) ).

cnf(i_0_80_014,axiom,
    ( X1 != X2
    | ~ r2(X1,X3)
    | r2(X2,X3) ) ).

cnf(i_0_81_015,axiom,
    ( X1 != X2
    | ~ r2(X3,X1)
    | r2(X3,X2) ) ).

cnf(i_0_82_016,axiom,
    ( X1 != X2
    | ~ r1(X1)
    | r1(X2) ) ).

cnf(i_0_83_017,axiom,
    ( X1 != X2
    | ~ r4(X1,X3,X4)
    | r4(X2,X3,X4) ) ).

cnf(i_0_84_018,axiom,
    ( X1 != X2
    | ~ r4(X3,X1,X4)
    | r4(X3,X2,X4) ) ).

cnf(i_0_85_019,axiom,
    ( X1 != X2
    | ~ r4(X3,X4,X1)
    | r4(X3,X4,X2) ) ).

cnf(i_0_86,plain,
    ( ~ r2(X1,X2)
    | ~ r3(X3,X4,X5)
    | ~ r2(X2,X4)
    | ~ r1(X1) ),
    inference(equality_inference,[],[39]) ).

cnf(i_0_87,plain,
    r4(X1,X2,esk4_2(X1,X2)),
    inference(equality_inference,[],[47]) ).

cnf(i_0_88,plain,
    r3(X1,X2,esk3_2(X1,X2)),
    inference(equality_inference,[],[48]) ).

cnf(i_0_89,plain,
    ( ~ r2(X1,X2)
    | X3 = X1
    | ~ r2(X3,X2) ),
    inference(equality_inference,[],[52]) ).

cnf(i_0_90,plain,
    ( ~ r1(X1)
    | ~ r2(X2,X1) ),
    inference(equality_inference,[],[56]) ).

cnf(i_0_91,plain,
    r2(X1,esk2_1(X1)),
    inference(equality_inference,[],[59]) ).

cnf(i_0_92,plain,
    r1(esk1_0),
    inference(equality_inference,[],[66]) ).

cnf(i_0_93,plain,
    $false,
    inference(scs_inference,[],[i_0_91,i_0_40,i_0_53,i_0_92,i_0_86]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUN080+2 : TPTP v9.2.1. Released v7.3.0.
% 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
% 0.14/0.33  % Computer : n025.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Tue May  5 01:23:13 EDT 2026
% 0.14/0.33  % CPUTime    : 
% 0.14/0.34  % start to proof: theBenchmark
% 0.26/1.61  % Version  : CSE_E---1.7
% 0.26/1.61  % Problem  : theBenchmark.p
% 0.26/1.61  % SZS status Theorem for theBenchmark.p
% 0.26/1.61  % SZS output start CNFRefutation
% See solution above
% 0.26/1.63  % Total time : 1.270s
%------------------------------------------------------------------------------