TSTP Solution File: NUN077+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUN077+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n004.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 12:45:54 EDT 2023

% Result   : Theorem 14.01s 14.06s
% Output   : CNFRefutation 14.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   34
% Syntax   : Number of formulae    :  135 (  55 unt;  24 typ;   0 def)
%            Number of atoms       :  381 (  91 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  483 ( 213   ~; 186   |;  84   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   32 (   4 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   38 (  23   >;  15   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   20 (  20 usr;   1 con; 0-2 aty)
%            Number of variables   :  349 (  14 sgn;  66   !;  51   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    r1: $i > $o ).

tff(decl_23,type,
    r2: ( $i * $i ) > $o ).

tff(decl_24,type,
    r3: ( $i * $i * $i ) > $o ).

tff(decl_25,type,
    r4: ( $i * $i * $i ) > $o ).

tff(decl_26,type,
    esk1_0: $i ).

tff(decl_27,type,
    esk2_1: $i > $i ).

tff(decl_28,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_29,type,
    esk4_2: ( $i * $i ) > $i ).

tff(decl_30,type,
    esk5_2: ( $i * $i ) > $i ).

tff(decl_31,type,
    esk6_2: ( $i * $i ) > $i ).

tff(decl_32,type,
    esk7_2: ( $i * $i ) > $i ).

tff(decl_33,type,
    esk8_2: ( $i * $i ) > $i ).

tff(decl_34,type,
    esk9_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk10_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk11_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk12_2: ( $i * $i ) > $i ).

tff(decl_38,type,
    esk13_1: $i > $i ).

tff(decl_39,type,
    esk14_1: $i > $i ).

tff(decl_40,type,
    esk15_1: $i > $i ).

tff(decl_41,type,
    esk16_1: $i > $i ).

tff(decl_42,type,
    esk17_1: $i > $i ).

tff(decl_43,type,
    esk18_1: $i > $i ).

tff(decl_44,type,
    esk19_1: $i > $i ).

tff(decl_45,type,
    esk20_1: $i > $i ).

fof(twotimesthreeeqsix,conjecture,
    ? [X39] :
      ( ? [X22] :
          ( X39 = X22
          & ? [X23] :
              ( r2(X23,X22)
              & ? [X16] :
                  ( r2(X16,X23)
                  & ? [X17] :
                      ( r2(X17,X16)
                      & ? [X19] :
                          ( r2(X19,X17)
                          & ? [X42] :
                              ( r2(X42,X19)
                              & ? [X29] :
                                  ( r1(X29)
                                  & r2(X29,X42) ) ) ) ) ) ) )
      & ? [X25] :
          ( ? [X34] :
              ( r2(X34,X25)
              & ? [X40] :
                  ( r2(X40,X34)
                  & ? [X24] :
                      ( r1(X24)
                      & r2(X24,X40) ) ) )
          & ? [X31] :
              ( r4(X31,X25,X39)
              & ? [X28] :
                  ( r2(X28,X31)
                  & ? [X18] :
                      ( r1(X18)
                      & r2(X18,X28) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',twotimesthreeeqsix) ).

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

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/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_2a) ).

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

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

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

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

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/sandbox/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).

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

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

fof(c_0_10,negated_conjecture,
    ~ ? [X39] :
        ( ? [X22] :
            ( X39 = X22
            & ? [X23] :
                ( r2(X23,X22)
                & ? [X16] :
                    ( r2(X16,X23)
                    & ? [X17] :
                        ( r2(X17,X16)
                        & ? [X19] :
                            ( r2(X19,X17)
                            & ? [X42] :
                                ( r2(X42,X19)
                                & ? [X29] :
                                    ( r1(X29)
                                    & r2(X29,X42) ) ) ) ) ) ) )
        & ? [X25] :
            ( ? [X34] :
                ( r2(X34,X25)
                & ? [X40] :
                    ( r2(X40,X34)
                    & ? [X24] :
                        ( r1(X24)
                        & r2(X24,X40) ) ) )
            & ? [X31] :
                ( r4(X31,X25,X39)
                & ? [X28] :
                    ( r2(X28,X31)
                    & ? [X18] :
                        ( r1(X18)
                        & r2(X18,X28) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[twotimesthreeeqsix]) ).

fof(c_0_11,negated_conjecture,
    ! [X87,X88,X89,X90,X91,X92,X93,X94,X95,X96,X97,X98,X99,X100,X101] :
      ( X87 != X88
      | ~ r2(X89,X88)
      | ~ r2(X90,X89)
      | ~ r2(X91,X90)
      | ~ r2(X92,X91)
      | ~ r2(X93,X92)
      | ~ r1(X94)
      | ~ r2(X94,X93)
      | ~ r2(X96,X95)
      | ~ r2(X97,X96)
      | ~ r1(X98)
      | ~ r2(X98,X97)
      | ~ r4(X99,X95,X87)
      | ~ r2(X100,X99)
      | ~ r1(X101)
      | ~ r2(X101,X100) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_12,plain,
    ? [X1] :
    ! [X2] :
      ( ( ~ r1(X2)
        & X2 != X1 )
      | ( r1(X2)
        & X2 = X1 ) ),
    inference(fof_simplification,[status(thm)],[axiom_1]) ).

cnf(c_0_13,negated_conjecture,
    ( X1 != X2
    | ~ r2(X3,X2)
    | ~ r2(X4,X3)
    | ~ r2(X5,X4)
    | ~ r2(X6,X5)
    | ~ r2(X7,X6)
    | ~ r1(X8)
    | ~ r2(X8,X7)
    | ~ r2(X9,X10)
    | ~ r2(X11,X9)
    | ~ r1(X12)
    | ~ r2(X12,X11)
    | ~ r4(X13,X10,X1)
    | ~ r2(X14,X13)
    | ~ r1(X15)
    | ~ r2(X15,X14) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

fof(c_0_14,plain,
    ! [X63,X64] :
      ( r2(X64,esk11_2(X63,X64))
      & r4(X63,esk11_2(X63,X64),esk10_2(X63,X64))
      & esk10_2(X63,X64) = esk9_2(X63,X64)
      & r3(esk12_2(X63,X64),X63,esk9_2(X63,X64))
      & r4(X63,X64,esk12_2(X63,X64)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_2a])]) ).

fof(c_0_15,plain,
    ! [X45] :
      ( ( r1(X45)
        | ~ r1(X45) )
      & ( X45 = esk1_0
        | ~ r1(X45) )
      & ( r1(X45)
        | X45 != esk1_0 )
      & ( X45 = esk1_0
        | X45 != esk1_0 ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_12])])]) ).

cnf(c_0_16,negated_conjecture,
    ( ~ r4(X1,X2,X3)
    | ~ r2(X4,X5)
    | ~ r2(X5,X1)
    | ~ r2(X6,X7)
    | ~ r2(X7,X8)
    | ~ r2(X8,X2)
    | ~ r2(X9,X10)
    | ~ r2(X10,X11)
    | ~ r2(X11,X12)
    | ~ r2(X12,X13)
    | ~ r2(X13,X14)
    | ~ r2(X14,X3)
    | ~ r1(X4)
    | ~ r1(X6)
    | ~ r1(X9) ),
    inference(er,[status(thm)],[c_0_13]) ).

cnf(c_0_17,plain,
    r4(X1,X2,esk12_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,plain,
    ( r1(X1)
    | X1 != esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,negated_conjecture,
    ( ~ r2(X1,esk12_2(X2,X3))
    | ~ r2(X4,X5)
    | ~ r2(X5,X2)
    | ~ r2(X6,X7)
    | ~ r2(X7,X8)
    | ~ r2(X8,X3)
    | ~ r2(X9,X10)
    | ~ r2(X10,X11)
    | ~ r2(X11,X12)
    | ~ r2(X12,X13)
    | ~ r2(X13,X1)
    | ~ r1(X4)
    | ~ r1(X6)
    | ~ r1(X9) ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_20,plain,
    r1(esk1_0),
    inference(er,[status(thm)],[c_0_18]) ).

fof(c_0_21,plain,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( ~ r2(X3,X5)
        & X5 != X4 )
      | ( r2(X3,X5)
        & X5 = X4 ) ),
    inference(fof_simplification,[status(thm)],[axiom_2]) ).

fof(c_0_22,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(c_0_23,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(c_0_24,plain,
    ! [X76] :
      ( r1(esk16_1(X76))
      & r4(X76,esk16_1(X76),esk15_1(X76))
      & r1(esk17_1(X76))
      & esk15_1(X76) = esk17_1(X76) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).

cnf(c_0_25,negated_conjecture,
    ( ~ r2(X1,esk12_2(X2,X3))
    | ~ r2(esk1_0,X4)
    | ~ r2(X4,X2)
    | ~ r2(X5,X6)
    | ~ r2(X6,X7)
    | ~ r2(X7,X3)
    | ~ r2(X8,X9)
    | ~ r2(X9,X10)
    | ~ r2(X10,X11)
    | ~ r2(X11,X12)
    | ~ r2(X12,X1)
    | ~ r1(X5)
    | ~ r1(X8) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

fof(c_0_26,plain,
    ! [X46,X48] :
      ( ( r2(X46,X48)
        | ~ r2(X46,X48) )
      & ( X48 = esk2_1(X46)
        | ~ r2(X46,X48) )
      & ( r2(X46,X48)
        | X48 != esk2_1(X46) )
      & ( X48 = esk2_1(X46)
        | X48 != esk2_1(X46) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_21])])]) ).

fof(c_0_27,plain,
    ! [X49,X50,X52] :
      ( ( r3(X49,X50,X52)
        | ~ r3(X49,X50,X52) )
      & ( X52 = esk3_2(X49,X50)
        | ~ r3(X49,X50,X52) )
      & ( r3(X49,X50,X52)
        | X52 != esk3_2(X49,X50) )
      & ( X52 = esk3_2(X49,X50)
        | X52 != esk3_2(X49,X50) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_22])])]) ).

fof(c_0_28,plain,
    ! [X57,X58] :
      ( r2(X58,esk7_2(X57,X58))
      & r3(X57,esk7_2(X57,X58),esk6_2(X57,X58))
      & esk6_2(X57,X58) = esk5_2(X57,X58)
      & r2(esk8_2(X57,X58),esk5_2(X57,X58))
      & r3(X57,X58,esk8_2(X57,X58)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).

fof(c_0_29,plain,
    ! [X53,X54,X56] :
      ( ( r4(X53,X54,X56)
        | ~ r4(X53,X54,X56) )
      & ( X56 = esk4_2(X53,X54)
        | ~ r4(X53,X54,X56) )
      & ( r4(X53,X54,X56)
        | X56 != esk4_2(X53,X54) )
      & ( X56 = esk4_2(X53,X54)
        | X56 != esk4_2(X53,X54) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_23])])]) ).

cnf(c_0_30,plain,
    r1(esk17_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,plain,
    esk15_1(X1) = esk17_1(X1),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_32,negated_conjecture,
    ( ~ r2(X1,esk12_2(X2,X3))
    | ~ r2(esk1_0,X4)
    | ~ r2(esk1_0,X5)
    | ~ r2(X4,X2)
    | ~ r2(X5,X6)
    | ~ r2(X6,X3)
    | ~ r2(X7,X8)
    | ~ r2(X8,X9)
    | ~ r2(X9,X10)
    | ~ r2(X10,X11)
    | ~ r2(X11,X1)
    | ~ r1(X7) ),
    inference(spm,[status(thm)],[c_0_25,c_0_20]) ).

cnf(c_0_33,plain,
    ( r2(X1,X2)
    | X2 != esk2_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_34,plain,
    ( X1 = esk3_2(X2,X3)
    | ~ r3(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_35,plain,
    r3(X1,X2,esk8_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_36,plain,
    ( X1 = esk4_2(X2,X3)
    | ~ r4(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_37,plain,
    r4(X1,esk11_2(X1,X2),esk10_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_38,plain,
    esk10_2(X1,X2) = esk9_2(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_39,plain,
    ( X1 = esk2_1(X2)
    | ~ r2(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_40,plain,
    r2(X1,esk11_2(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_41,plain,
    ( X1 = esk1_0
    | ~ r1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_42,plain,
    r1(esk16_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_43,plain,
    r1(esk15_1(X1)),
    inference(rw,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_44,negated_conjecture,
    ( ~ r2(X1,esk12_2(X2,X3))
    | ~ r2(esk1_0,X4)
    | ~ r2(esk1_0,X5)
    | ~ r2(esk1_0,X6)
    | ~ r2(X4,X2)
    | ~ r2(X5,X7)
    | ~ r2(X7,X3)
    | ~ r2(X6,X8)
    | ~ r2(X8,X9)
    | ~ r2(X9,X10)
    | ~ r2(X10,X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_20]) ).

cnf(c_0_45,plain,
    r2(X1,esk2_1(X1)),
    inference(er,[status(thm)],[c_0_33]) ).

cnf(c_0_46,plain,
    esk3_2(X1,X2) = esk8_2(X1,X2),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_47,plain,
    esk4_2(X1,X2) = esk12_2(X1,X2),
    inference(spm,[status(thm)],[c_0_36,c_0_17]) ).

cnf(c_0_48,plain,
    r4(X1,esk11_2(X1,X2),esk9_2(X1,X2)),
    inference(rw,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_49,plain,
    esk11_2(X1,X2) = esk2_1(X2),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_50,plain,
    r4(X1,esk16_1(X1),esk15_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_51,plain,
    esk16_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_52,plain,
    esk15_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_41,c_0_43]) ).

cnf(c_0_53,negated_conjecture,
    ( ~ r2(X1,esk12_2(esk2_1(X2),X3))
    | ~ r2(esk1_0,X2)
    | ~ r2(esk1_0,X4)
    | ~ r2(esk1_0,X5)
    | ~ r2(X4,X6)
    | ~ r2(X6,X3)
    | ~ r2(X5,X7)
    | ~ r2(X7,X8)
    | ~ r2(X8,X9)
    | ~ r2(X9,X1) ),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

fof(c_0_54,plain,
    ! [X26,X27] :
      ( ! [X28] :
          ( ! [X29] :
              ( ~ r2(X26,X29)
              | X29 != X28 )
          | ~ r2(X27,X28) )
      | X26 = X27 ),
    inference(fof_simplification,[status(thm)],[axiom_3a]) ).

cnf(c_0_55,plain,
    ( X1 = esk8_2(X2,X3)
    | ~ r3(X2,X3,X1) ),
    inference(rw,[status(thm)],[c_0_34,c_0_46]) ).

cnf(c_0_56,plain,
    r3(esk12_2(X1,X2),X1,esk9_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_57,plain,
    ( X1 = esk12_2(X2,X3)
    | ~ r4(X2,X3,X1) ),
    inference(rw,[status(thm)],[c_0_36,c_0_47]) ).

cnf(c_0_58,plain,
    r4(X1,esk2_1(X2),esk9_2(X1,X2)),
    inference(rw,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_59,plain,
    r4(X1,esk1_0,esk1_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).

fof(c_0_60,plain,
    ! [X73] :
      ( r1(esk14_1(X73))
      & r3(X73,esk14_1(X73),esk13_1(X73))
      & esk13_1(X73) = X73 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).

cnf(c_0_61,negated_conjecture,
    ( ~ r2(X1,esk12_2(esk2_1(X2),X3))
    | ~ r2(esk2_1(X4),X3)
    | ~ r2(esk1_0,X2)
    | ~ r2(esk1_0,X4)
    | ~ r2(esk1_0,X5)
    | ~ r2(X5,X6)
    | ~ r2(X6,X7)
    | ~ r2(X7,X8)
    | ~ r2(X8,X1) ),
    inference(spm,[status(thm)],[c_0_53,c_0_45]) ).

fof(c_0_62,plain,
    ! [X69,X70,X71,X72] :
      ( ~ r2(X69,X72)
      | X72 != X71
      | ~ r2(X70,X71)
      | X69 = X70 ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_54])]) ).

cnf(c_0_63,plain,
    esk8_2(esk12_2(X1,X2),X1) = esk9_2(X1,X2),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_64,plain,
    esk12_2(X1,esk2_1(X2)) = esk9_2(X1,X2),
    inference(spm,[status(thm)],[c_0_57,c_0_58]) ).

cnf(c_0_65,plain,
    esk4_2(X1,esk1_0) = esk1_0,
    inference(spm,[status(thm)],[c_0_36,c_0_59]) ).

cnf(c_0_66,plain,
    r3(X1,esk7_2(X1,X2),esk6_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_67,plain,
    esk6_2(X1,X2) = esk5_2(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_68,plain,
    r2(X1,esk7_2(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_69,plain,
    r3(X1,esk14_1(X1),esk13_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

cnf(c_0_70,plain,
    esk13_1(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

cnf(c_0_71,plain,
    r1(esk14_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_60]) ).

cnf(c_0_72,negated_conjecture,
    ( ~ r2(X1,esk12_2(esk2_1(X2),X3))
    | ~ r2(esk2_1(X4),X3)
    | ~ r2(esk2_1(X5),X6)
    | ~ r2(esk1_0,X2)
    | ~ r2(esk1_0,X4)
    | ~ r2(esk1_0,X5)
    | ~ r2(X6,X7)
    | ~ r2(X7,X1) ),
    inference(spm,[status(thm)],[c_0_61,c_0_45]) ).

cnf(c_0_73,plain,
    ( X1 = X4
    | ~ r2(X1,X2)
    | X2 != X3
    | ~ r2(X4,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_74,plain,
    r2(esk8_2(X1,X2),esk5_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_75,plain,
    esk8_2(esk9_2(X1,X2),X1) = esk9_2(X1,esk2_1(X2)),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_76,plain,
    esk12_2(X1,esk1_0) = esk1_0,
    inference(rw,[status(thm)],[c_0_65,c_0_47]) ).

cnf(c_0_77,plain,
    r3(X1,esk7_2(X1,X2),esk5_2(X1,X2)),
    inference(rw,[status(thm)],[c_0_66,c_0_67]) ).

cnf(c_0_78,plain,
    esk7_2(X1,X2) = esk2_1(X2),
    inference(spm,[status(thm)],[c_0_39,c_0_68]) ).

cnf(c_0_79,plain,
    r3(X1,esk14_1(X1),X1),
    inference(rw,[status(thm)],[c_0_69,c_0_70]) ).

cnf(c_0_80,plain,
    esk14_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_41,c_0_71]) ).

cnf(c_0_81,negated_conjecture,
    ( ~ r2(X1,esk12_2(esk2_1(X2),X3))
    | ~ r2(esk2_1(X4),X3)
    | ~ r2(esk2_1(X5),X6)
    | ~ r2(esk2_1(X6),X1)
    | ~ r2(esk1_0,X2)
    | ~ r2(esk1_0,X4)
    | ~ r2(esk1_0,X5) ),
    inference(spm,[status(thm)],[c_0_72,c_0_45]) ).

cnf(c_0_82,plain,
    ( X1 = X2
    | ~ r2(X2,X3)
    | ~ r2(X1,X3) ),
    inference(er,[status(thm)],[c_0_73]) ).

cnf(c_0_83,plain,
    r2(esk9_2(X1,esk2_1(X2)),esk5_2(esk9_2(X1,X2),X1)),
    inference(spm,[status(thm)],[c_0_74,c_0_75]) ).

cnf(c_0_84,plain,
    r3(esk1_0,X1,esk9_2(X1,esk1_0)),
    inference(spm,[status(thm)],[c_0_56,c_0_76]) ).

cnf(c_0_85,plain,
    r3(X1,esk2_1(X2),esk5_2(X1,X2)),
    inference(rw,[status(thm)],[c_0_77,c_0_78]) ).

cnf(c_0_86,plain,
    r3(X1,esk1_0,X1),
    inference(rw,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_87,negated_conjecture,
    ( ~ r2(X1,esk12_2(esk2_1(esk2_1(esk1_0)),X2))
    | ~ r2(esk2_1(X3),X2)
    | ~ r2(esk2_1(X4),X5)
    | ~ r2(esk2_1(X5),X1)
    | ~ r2(esk1_0,X3)
    | ~ r2(esk1_0,X4) ),
    inference(spm,[status(thm)],[c_0_81,c_0_45]) ).

cnf(c_0_88,plain,
    ( X1 = esk9_2(X2,esk2_1(X3))
    | ~ r2(X1,esk5_2(esk9_2(X2,X3),X2)) ),
    inference(spm,[status(thm)],[c_0_82,c_0_83]) ).

cnf(c_0_89,plain,
    esk9_2(X1,esk1_0) = esk8_2(esk1_0,X1),
    inference(spm,[status(thm)],[c_0_55,c_0_84]) ).

cnf(c_0_90,plain,
    esk2_1(esk8_2(X1,X2)) = esk5_2(X1,X2),
    inference(spm,[status(thm)],[c_0_39,c_0_74]) ).

cnf(c_0_91,plain,
    esk8_2(X1,esk2_1(X2)) = esk5_2(X1,X2),
    inference(spm,[status(thm)],[c_0_55,c_0_85]) ).

cnf(c_0_92,plain,
    esk3_2(X1,esk1_0) = X1,
    inference(spm,[status(thm)],[c_0_34,c_0_86]) ).

cnf(c_0_93,negated_conjecture,
    ( ~ r2(X1,esk12_2(esk2_1(esk2_1(esk1_0)),X2))
    | ~ r2(esk2_1(esk2_1(esk1_0)),X2)
    | ~ r2(esk2_1(X3),X4)
    | ~ r2(esk2_1(X4),X1)
    | ~ r2(esk1_0,X3) ),
    inference(spm,[status(thm)],[c_0_87,c_0_45]) ).

cnf(c_0_94,plain,
    ( X1 = esk9_2(X2,esk2_1(esk1_0))
    | ~ r2(X1,esk5_2(esk8_2(esk1_0,X2),X2)) ),
    inference(spm,[status(thm)],[c_0_88,c_0_89]) ).

cnf(c_0_95,plain,
    esk5_2(X1,esk2_1(X2)) = esk2_1(esk5_2(X1,X2)),
    inference(spm,[status(thm)],[c_0_90,c_0_91]) ).

cnf(c_0_96,plain,
    esk8_2(X1,esk1_0) = X1,
    inference(rw,[status(thm)],[c_0_92,c_0_46]) ).

cnf(c_0_97,negated_conjecture,
    ( ~ r2(X1,esk12_2(esk2_1(esk2_1(esk1_0)),X2))
    | ~ r2(esk2_1(esk2_1(esk1_0)),X2)
    | ~ r2(esk2_1(esk2_1(esk1_0)),X3)
    | ~ r2(esk2_1(X3),X1) ),
    inference(spm,[status(thm)],[c_0_93,c_0_45]) ).

cnf(c_0_98,plain,
    ( X1 = esk9_2(esk2_1(X2),esk2_1(esk1_0))
    | ~ r2(X1,esk2_1(esk5_2(esk5_2(esk1_0,X2),X2))) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_91]),c_0_95]) ).

cnf(c_0_99,plain,
    r2(X1,esk5_2(X1,esk1_0)),
    inference(spm,[status(thm)],[c_0_74,c_0_96]) ).

cnf(c_0_100,negated_conjecture,
    ( ~ r2(esk2_1(esk2_1(X1)),esk12_2(esk2_1(esk2_1(esk1_0)),X2))
    | ~ r2(esk2_1(esk2_1(esk1_0)),X2)
    | ~ r2(esk2_1(esk2_1(esk1_0)),X1) ),
    inference(spm,[status(thm)],[c_0_97,c_0_45]) ).

cnf(c_0_101,plain,
    ( X1 = esk9_2(esk2_1(esk2_1(X2)),esk2_1(esk1_0))
    | ~ r2(X1,esk2_1(esk2_1(esk5_2(esk2_1(esk5_2(esk1_0,X2)),X2)))) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_95]),c_0_95]) ).

cnf(c_0_102,plain,
    esk5_2(X1,esk1_0) = esk2_1(X1),
    inference(spm,[status(thm)],[c_0_39,c_0_99]) ).

cnf(c_0_103,negated_conjecture,
    ( ~ r2(esk2_1(esk2_1(X1)),esk12_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk2_1(esk2_1(esk1_0)))))
    | ~ r2(esk2_1(esk2_1(esk1_0)),X1) ),
    inference(spm,[status(thm)],[c_0_100,c_0_45]) ).

cnf(c_0_104,plain,
    esk5_2(esk9_2(esk2_1(X1),X2),X1) = esk9_2(esk2_1(X1),esk2_1(X2)),
    inference(spm,[status(thm)],[c_0_91,c_0_75]) ).

cnf(c_0_105,plain,
    ( X1 = esk9_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk1_0))
    | ~ r2(X1,esk2_1(esk2_1(esk2_1(esk2_1(esk2_1(esk1_0)))))) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_102]) ).

cnf(c_0_106,negated_conjecture,
    ~ r2(esk2_1(esk2_1(esk2_1(esk2_1(esk2_1(esk1_0))))),esk12_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk2_1(esk2_1(esk1_0))))),
    inference(spm,[status(thm)],[c_0_103,c_0_45]) ).

cnf(c_0_107,plain,
    r2(esk8_2(esk9_2(esk2_1(X1),X2),X1),esk9_2(esk2_1(X1),esk2_1(X2))),
    inference(spm,[status(thm)],[c_0_74,c_0_104]) ).

cnf(c_0_108,plain,
    esk9_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk1_0)) = esk2_1(esk2_1(esk2_1(esk2_1(esk1_0)))),
    inference(spm,[status(thm)],[c_0_105,c_0_45]) ).

cnf(c_0_109,negated_conjecture,
    ~ r2(esk2_1(esk2_1(esk2_1(esk2_1(esk2_1(esk1_0))))),esk9_2(esk2_1(esk2_1(esk1_0)),esk2_1(esk2_1(esk1_0)))),
    inference(rw,[status(thm)],[c_0_106,c_0_64]) ).

cnf(c_0_110,plain,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_91]),c_0_102]),c_0_109]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUN077+2 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.35  % Computer : n004.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sun Aug 27 09:10:52 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.22/0.57  start to proof: theBenchmark
% 14.01/14.06  % Version  : CSE_E---1.5
% 14.01/14.06  % Problem  : theBenchmark.p
% 14.01/14.06  % Proof found
% 14.01/14.06  % SZS status Theorem for theBenchmark.p
% 14.01/14.06  % SZS output start Proof
% See solution above
% 14.01/14.07  % Total time : 13.480000 s
% 14.01/14.07  % SZS output end Proof
% 14.01/14.07  % Total time : 13.483000 s
%------------------------------------------------------------------------------