TSTP Solution File: NUN072+2 by E---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1
% Problem  : NUN072+2 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n021.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 : 2400s
% WCLimit  : 300s
% DateTime : Tue Oct 10 19:09:10 EDT 2023

% Result   : Theorem 0.22s 0.57s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   91 (  51 unt;   0 def)
%            Number of atoms       :  249 (  75 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  265 ( 107   ~;  86   |;  72   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;   1 con; 0-2 aty)
%            Number of variables   :  219 (  14 sgn;  48   !;  39   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(onetimestwoeqtwo,conjecture,
    ? [X39] :
      ( ? [X22] :
          ( ? [X16] :
              ( r2(X16,X22)
              & ? [X19] :
                  ( r1(X19)
                  & r2(X19,X16) ) )
          & ? [X17] :
              ( r4(X17,X22,X39)
              & ? [X34] :
                  ( r1(X34)
                  & r2(X34,X17) ) ) )
      & ? [X23] :
          ( X39 = X23
          & ? [X25] :
              ( r2(X25,X23)
              & ? [X31] :
                  ( r1(X31)
                  & r2(X31,X25) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.xKvZWaen6Q/E---3.1_31241.p',onetimestwoeqtwo) ).

fof(axiom_1,axiom,
    ? [X1] :
    ! [X2] :
      ( ( ~ r1(X2)
        & X2 != X1 )
      | ( r1(X2)
        & X2 = X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.xKvZWaen6Q/E---3.1_31241.p',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/tmp/tmp.xKvZWaen6Q/E---3.1_31241.p',axiom_2a) ).

fof(axiom_4a,axiom,
    ! [X30] :
    ? [X31] :
      ( ? [X32] :
          ( r1(X32)
          & r3(X30,X32,X31) )
      & X31 = X30 ),
    file('/export/starexec/sandbox/tmp/tmp.xKvZWaen6Q/E---3.1_31241.p',axiom_4a) ).

fof(axiom_2,axiom,
    ! [X3] :
    ? [X4] :
    ! [X5] :
      ( ( ~ r2(X3,X5)
        & X5 != X4 )
      | ( r2(X3,X5)
        & X5 = X4 ) ),
    file('/export/starexec/sandbox/tmp/tmp.xKvZWaen6Q/E---3.1_31241.p',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/tmp/tmp.xKvZWaen6Q/E---3.1_31241.p',axiom_3) ).

fof(axiom_5a,axiom,
    ! [X33] :
    ? [X34] :
      ( ? [X35] :
          ( r1(X35)
          & r4(X33,X35,X34) )
      & ? [X36] :
          ( r1(X36)
          & X34 = X36 ) ),
    file('/export/starexec/sandbox/tmp/tmp.xKvZWaen6Q/E---3.1_31241.p',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/tmp/tmp.xKvZWaen6Q/E---3.1_31241.p',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/sandbox/tmp/tmp.xKvZWaen6Q/E---3.1_31241.p',axiom_4) ).

fof(c_0_9,negated_conjecture,
    ~ ? [X39] :
        ( ? [X22] :
            ( ? [X16] :
                ( r2(X16,X22)
                & ? [X19] :
                    ( r1(X19)
                    & r2(X19,X16) ) )
            & ? [X17] :
                ( r4(X17,X22,X39)
                & ? [X34] :
                    ( r1(X34)
                    & r2(X34,X17) ) ) )
        & ? [X23] :
            ( X39 = X23
            & ? [X25] :
                ( r2(X25,X23)
                & ? [X31] :
                    ( r1(X31)
                    & r2(X31,X25) ) ) ) ),
    inference(assume_negation,[status(cth)],[onetimestwoeqtwo]) ).

fof(c_0_10,negated_conjecture,
    ! [X87,X88,X89,X90,X91,X92,X93,X94,X95] :
      ( ~ r2(X89,X88)
      | ~ r1(X90)
      | ~ r2(X90,X89)
      | ~ r4(X91,X88,X87)
      | ~ r1(X92)
      | ~ r2(X92,X91)
      | X87 != X93
      | ~ r2(X94,X93)
      | ~ r1(X95)
      | ~ r2(X95,X94) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

fof(c_0_11,plain,
    ? [X1] :
    ! [X2] :
      ( ( ~ r1(X2)
        & X2 != X1 )
      | ( r1(X2)
        & X2 = X1 ) ),
    inference(fof_simplification,[status(thm)],[axiom_1]) ).

cnf(c_0_12,negated_conjecture,
    ( ~ r2(X1,X2)
    | ~ r1(X3)
    | ~ r2(X3,X1)
    | ~ r4(X4,X2,X5)
    | ~ r1(X6)
    | ~ r2(X6,X4)
    | X5 != X7
    | ~ r2(X8,X7)
    | ~ r1(X9)
    | ~ r2(X9,X8) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_13,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_14,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_11])])]) ).

cnf(c_0_15,negated_conjecture,
    ( ~ r4(X1,X2,X3)
    | ~ r2(X4,X5)
    | ~ r2(X5,X3)
    | ~ r2(X6,X1)
    | ~ r2(X7,X8)
    | ~ r2(X8,X2)
    | ~ r1(X4)
    | ~ r1(X6)
    | ~ r1(X7) ),
    inference(er,[status(thm)],[c_0_12]) ).

cnf(c_0_16,plain,
    r4(X1,X2,esk12_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,plain,
    ( r1(X1)
    | X1 != esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

fof(c_0_18,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_19,negated_conjecture,
    ( ~ r2(X1,esk12_2(X2,X3))
    | ~ r2(X4,X1)
    | ~ r2(X5,X2)
    | ~ r2(X6,X7)
    | ~ r2(X7,X3)
    | ~ r1(X4)
    | ~ r1(X5)
    | ~ r1(X6) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_20,plain,
    r1(esk1_0),
    inference(er,[status(thm)],[c_0_17]) ).

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]) ).

cnf(c_0_23,plain,
    r3(X1,esk14_1(X1),esk13_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_24,plain,
    esk13_1(X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_25,plain,
    ( X1 = esk1_0
    | ~ r1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_26,plain,
    r1(esk14_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

fof(c_0_27,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_28,negated_conjecture,
    ( ~ r2(X1,esk12_2(X2,X3))
    | ~ r2(esk1_0,X1)
    | ~ r2(X4,X2)
    | ~ r2(X5,X6)
    | ~ r2(X6,X3)
    | ~ r1(X4)
    | ~ r1(X5) ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

fof(c_0_29,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_30,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])])]) ).

cnf(c_0_31,plain,
    r3(X1,esk14_1(X1),X1),
    inference(rw,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_32,plain,
    esk14_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

fof(c_0_33,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])]) ).

cnf(c_0_34,plain,
    r1(esk17_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_35,plain,
    esk15_1(X1) = esk17_1(X1),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_36,negated_conjecture,
    ( ~ r2(X1,esk12_2(X2,X3))
    | ~ r2(esk1_0,X1)
    | ~ r2(esk1_0,X2)
    | ~ r2(X4,X5)
    | ~ r2(X5,X3)
    | ~ r1(X4) ),
    inference(spm,[status(thm)],[c_0_28,c_0_20]) ).

cnf(c_0_37,plain,
    ( r2(X1,X2)
    | X2 != esk2_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

fof(c_0_38,plain,
    ! [X10,X11] :
    ? [X12] :
    ! [X13] :
      ( ( ~ r4(X10,X11,X13)
        & X13 != X12 )
      | ( r4(X10,X11,X13)
        & X13 = X12 ) ),
    inference(fof_simplification,[status(thm)],[axiom_4]) ).

cnf(c_0_39,plain,
    ( X1 = esk3_2(X2,X3)
    | ~ r3(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_40,plain,
    r3(X1,esk1_0,X1),
    inference(rw,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_41,plain,
    r3(X1,X2,esk8_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_42,plain,
    r3(X1,esk7_2(X1,X2),esk6_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_43,plain,
    esk6_2(X1,X2) = esk5_2(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_44,plain,
    ( X1 = esk2_1(X2)
    | ~ r2(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_45,plain,
    r2(X1,esk7_2(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_46,plain,
    r1(esk16_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_47,plain,
    r1(esk15_1(X1)),
    inference(rw,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_48,negated_conjecture,
    ( ~ r2(X1,esk12_2(X2,X3))
    | ~ r2(esk1_0,X1)
    | ~ r2(esk1_0,X2)
    | ~ r2(esk1_0,X4)
    | ~ r2(X4,X3) ),
    inference(spm,[status(thm)],[c_0_36,c_0_20]) ).

cnf(c_0_49,plain,
    r2(X1,esk2_1(X1)),
    inference(er,[status(thm)],[c_0_37]) ).

fof(c_0_50,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_38])])]) ).

cnf(c_0_51,plain,
    esk3_2(X1,esk1_0) = X1,
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_52,plain,
    esk3_2(X1,X2) = esk8_2(X1,X2),
    inference(spm,[status(thm)],[c_0_39,c_0_41]) ).

cnf(c_0_53,plain,
    r3(X1,esk7_2(X1,X2),esk5_2(X1,X2)),
    inference(rw,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_54,plain,
    esk7_2(X1,X2) = esk2_1(X2),
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_55,plain,
    r4(X1,esk16_1(X1),esk15_1(X1)),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_56,plain,
    esk16_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_25,c_0_46]) ).

cnf(c_0_57,plain,
    esk15_1(X1) = esk1_0,
    inference(spm,[status(thm)],[c_0_25,c_0_47]) ).

cnf(c_0_58,negated_conjecture,
    ( ~ r2(X1,esk12_2(X2,esk2_1(X3)))
    | ~ r2(esk1_0,X1)
    | ~ r2(esk1_0,X2)
    | ~ r2(esk1_0,X3) ),
    inference(spm,[status(thm)],[c_0_48,c_0_49]) ).

cnf(c_0_59,plain,
    ( X1 = esk4_2(X2,X3)
    | ~ r4(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_60,plain,
    r4(X1,esk11_2(X1,X2),esk10_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_61,plain,
    esk10_2(X1,X2) = esk9_2(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_62,plain,
    r2(X1,esk11_2(X2,X1)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_63,plain,
    r2(esk8_2(X1,X2),esk5_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_64,plain,
    esk8_2(X1,esk1_0) = X1,
    inference(rw,[status(thm)],[c_0_51,c_0_52]) ).

cnf(c_0_65,plain,
    ( X1 = esk8_2(X2,X3)
    | ~ r3(X2,X3,X1) ),
    inference(rw,[status(thm)],[c_0_39,c_0_52]) ).

cnf(c_0_66,plain,
    r3(X1,esk2_1(X2),esk5_2(X1,X2)),
    inference(rw,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_67,plain,
    r3(esk12_2(X1,X2),X1,esk9_2(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_68,plain,
    r4(X1,esk1_0,esk1_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).

cnf(c_0_69,negated_conjecture,
    ( ~ r2(esk2_1(esk1_0),esk12_2(X1,esk2_1(X2)))
    | ~ r2(esk1_0,X1)
    | ~ r2(esk1_0,X2) ),
    inference(spm,[status(thm)],[c_0_58,c_0_49]) ).

cnf(c_0_70,plain,
    esk4_2(X1,X2) = esk12_2(X1,X2),
    inference(spm,[status(thm)],[c_0_59,c_0_16]) ).

cnf(c_0_71,plain,
    r4(X1,esk11_2(X1,X2),esk9_2(X1,X2)),
    inference(rw,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_72,plain,
    esk11_2(X1,X2) = esk2_1(X2),
    inference(spm,[status(thm)],[c_0_44,c_0_62]) ).

cnf(c_0_73,plain,
    r2(X1,esk5_2(X1,esk1_0)),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_74,plain,
    esk8_2(X1,esk2_1(X2)) = esk5_2(X1,X2),
    inference(spm,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_75,plain,
    esk8_2(esk12_2(X1,X2),X1) = esk9_2(X1,X2),
    inference(spm,[status(thm)],[c_0_65,c_0_67]) ).

cnf(c_0_76,plain,
    esk4_2(X1,esk1_0) = esk1_0,
    inference(spm,[status(thm)],[c_0_59,c_0_68]) ).

cnf(c_0_77,negated_conjecture,
    ( ~ r2(esk2_1(esk1_0),esk12_2(esk2_1(esk1_0),esk2_1(X1)))
    | ~ r2(esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_69,c_0_49]) ).

cnf(c_0_78,plain,
    ( X1 = esk12_2(X2,X3)
    | ~ r4(X2,X3,X1) ),
    inference(rw,[status(thm)],[c_0_59,c_0_70]) ).

cnf(c_0_79,plain,
    r4(X1,esk2_1(X2),esk9_2(X1,X2)),
    inference(rw,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_80,plain,
    esk5_2(X1,esk1_0) = esk2_1(X1),
    inference(spm,[status(thm)],[c_0_44,c_0_73]) ).

cnf(c_0_81,plain,
    esk5_2(esk12_2(esk2_1(X1),X2),X1) = esk9_2(esk2_1(X1),X2),
    inference(spm,[status(thm)],[c_0_74,c_0_75]) ).

cnf(c_0_82,plain,
    esk12_2(X1,esk1_0) = esk1_0,
    inference(rw,[status(thm)],[c_0_76,c_0_70]) ).

cnf(c_0_83,negated_conjecture,
    ~ r2(esk2_1(esk1_0),esk12_2(esk2_1(esk1_0),esk2_1(esk2_1(esk1_0)))),
    inference(spm,[status(thm)],[c_0_77,c_0_49]) ).

cnf(c_0_84,plain,
    esk12_2(X1,esk2_1(X2)) = esk9_2(X1,X2),
    inference(spm,[status(thm)],[c_0_78,c_0_79]) ).

cnf(c_0_85,plain,
    esk2_1(esk12_2(esk2_1(esk1_0),X1)) = esk9_2(esk2_1(esk1_0),X1),
    inference(spm,[status(thm)],[c_0_80,c_0_81]) ).

cnf(c_0_86,plain,
    r3(esk1_0,X1,esk9_2(X1,esk1_0)),
    inference(spm,[status(thm)],[c_0_67,c_0_82]) ).

cnf(c_0_87,negated_conjecture,
    ~ r2(esk2_1(esk1_0),esk9_2(esk2_1(esk1_0),esk2_1(esk1_0))),
    inference(rw,[status(thm)],[c_0_83,c_0_84]) ).

cnf(c_0_88,plain,
    esk9_2(esk2_1(esk1_0),esk2_1(X1)) = esk2_1(esk9_2(esk2_1(esk1_0),X1)),
    inference(spm,[status(thm)],[c_0_85,c_0_84]) ).

cnf(c_0_89,plain,
    esk9_2(X1,esk1_0) = esk8_2(esk1_0,X1),
    inference(spm,[status(thm)],[c_0_65,c_0_86]) ).

cnf(c_0_90,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_74]),c_0_80]),c_0_49])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : NUN072+2 : TPTP v8.1.2. Released v7.3.0.
% 0.08/0.15  % Command    : run_E %s %d THM
% 0.15/0.36  % Computer : n021.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 2400
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Mon Oct  2 20:52:59 EDT 2023
% 0.15/0.36  % CPUTime    : 
% 0.22/0.50  Running first-order theorem proving
% 0.22/0.50  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.xKvZWaen6Q/E---3.1_31241.p
% 0.22/0.57  # Version: 3.1pre001
% 0.22/0.57  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.57  # Starting new_bool_3 with 300s (1) cores
% 0.22/0.57  # Starting new_bool_1 with 300s (1) cores
% 0.22/0.57  # Starting sh5l with 300s (1) cores
% 0.22/0.57  # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 31364 completed with status 0
% 0.22/0.57  # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.22/0.57  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.57  # No SInE strategy applied
% 0.22/0.57  # Search class: FGHSM-FFMF21-SFFFFFNN
% 0.22/0.57  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.57  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 811s (1) cores
% 0.22/0.57  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/0.57  # Starting new_bool_3 with 136s (1) cores
% 0.22/0.57  # Starting new_bool_1 with 136s (1) cores
% 0.22/0.57  # Starting G-E--_300_C18_F1_SE_CS_SP_PS_S0Y with 136s (1) cores
% 0.22/0.57  # G-E--_208_C18_F1_SE_CS_SP_PS_S4b with pid 31370 completed with status 0
% 0.22/0.57  # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S4b
% 0.22/0.57  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/0.57  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/0.57  # No SInE strategy applied
% 0.22/0.57  # Search class: FGHSM-FFMF21-SFFFFFNN
% 0.22/0.57  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.57  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S4b with 811s (1) cores
% 0.22/0.57  # Preprocessing time       : 0.002 s
% 0.22/0.57  # Presaturation interreduction done
% 0.22/0.57  
% 0.22/0.57  # Proof found!
% 0.22/0.57  # SZS status Theorem
% 0.22/0.57  # SZS output start CNFRefutation
% See solution above
% 0.22/0.57  # Parsed axioms                        : 12
% 0.22/0.57  # Removed by relevancy pruning/SinE    : 0
% 0.22/0.57  # Initial clauses                      : 40
% 0.22/0.57  # Removed in clause preprocessing      : 12
% 0.22/0.57  # Initial clauses in saturation        : 28
% 0.22/0.57  # Processed clauses                    : 546
% 0.22/0.57  # ...of these trivial                  : 4
% 0.22/0.57  # ...subsumed                          : 220
% 0.22/0.57  # ...remaining for further processing  : 322
% 0.22/0.57  # Other redundant clauses eliminated   : 7
% 0.22/0.57  # Clauses deleted for lack of memory   : 0
% 0.22/0.57  # Backward-subsumed                    : 3
% 0.22/0.57  # Backward-rewritten                   : 33
% 0.22/0.57  # Generated clauses                    : 1579
% 0.22/0.57  # ...of the previous two non-redundant : 1392
% 0.22/0.57  # ...aggressively subsumed             : 0
% 0.22/0.57  # Contextual simplify-reflections      : 2
% 0.22/0.57  # Paramodulations                      : 1572
% 0.22/0.57  # Factorizations                       : 0
% 0.22/0.57  # NegExts                              : 0
% 0.22/0.57  # Equation resolutions                 : 7
% 0.22/0.57  # Total rewrite steps                  : 662
% 0.22/0.57  # Propositional unsat checks           : 0
% 0.22/0.57  #    Propositional check models        : 0
% 0.22/0.57  #    Propositional check unsatisfiable : 0
% 0.22/0.57  #    Propositional clauses             : 0
% 0.22/0.57  #    Propositional clauses after purity: 0
% 0.22/0.57  #    Propositional unsat core size     : 0
% 0.22/0.57  #    Propositional preprocessing time  : 0.000
% 0.22/0.57  #    Propositional encoding time       : 0.000
% 0.22/0.57  #    Propositional solver time         : 0.000
% 0.22/0.57  #    Success case prop preproc time    : 0.000
% 0.22/0.57  #    Success case prop encoding time   : 0.000
% 0.22/0.57  #    Success case prop solver time     : 0.000
% 0.22/0.57  # Current number of processed clauses  : 251
% 0.22/0.57  #    Positive orientable unit clauses  : 49
% 0.22/0.57  #    Positive unorientable unit clauses: 0
% 0.22/0.57  #    Negative unit clauses             : 3
% 0.22/0.57  #    Non-unit-clauses                  : 199
% 0.22/0.57  # Current number of unprocessed clauses: 891
% 0.22/0.57  # ...number of literals in the above   : 2805
% 0.22/0.57  # Current number of archived formulas  : 0
% 0.22/0.57  # Current number of archived clauses   : 68
% 0.22/0.57  # Clause-clause subsumption calls (NU) : 18524
% 0.22/0.57  # Rec. Clause-clause subsumption calls : 6609
% 0.22/0.57  # Non-unit clause-clause subsumptions  : 184
% 0.22/0.57  # Unit Clause-clause subsumption calls : 175
% 0.22/0.57  # Rewrite failures with RHS unbound    : 0
% 0.22/0.57  # BW rewrite match attempts            : 44
% 0.22/0.57  # BW rewrite match successes           : 25
% 0.22/0.57  # Condensation attempts                : 0
% 0.22/0.57  # Condensation successes               : 0
% 0.22/0.57  # Termbank termtop insertions          : 25111
% 0.22/0.57  
% 0.22/0.57  # -------------------------------------------------
% 0.22/0.57  # User time                : 0.053 s
% 0.22/0.57  # System time              : 0.006 s
% 0.22/0.57  # Total time               : 0.059 s
% 0.22/0.57  # Maximum resident set size: 1828 pages
% 0.22/0.57  
% 0.22/0.57  # -------------------------------------------------
% 0.22/0.57  # User time                : 0.235 s
% 0.22/0.57  # System time              : 0.020 s
% 0.22/0.57  # Total time               : 0.255 s
% 0.22/0.57  # Maximum resident set size: 1744 pages
% 0.22/0.57  % E---3.1 exiting
% 0.22/0.57  % E---3.1 exiting
%------------------------------------------------------------------------------