TSTP Solution File: SWV492+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV492+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% 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 : Thu Aug 31 21:41:32 EDT 2023

% Result   : Theorem 17.02s 17.16s
% Output   : CNFRefutation 17.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   36
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  220 (  23 unt;  16 typ;   0 def)
%            Number of atoms       :  654 ( 180 equ)
%            Maximal formula atoms :   32 (   3 avg)
%            Number of connectives :  718 ( 268   ~; 359   |;  62   &)
%                                         (   4 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (   7   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   9 con; 0-2 aty)
%            Number of variables   :  256 (   1 sgn;  81   !;   1   ?;   0   :)

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

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

tff(decl_24,type,
    int_zero: $i ).

tff(decl_25,type,
    int_one: $i ).

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

tff(decl_27,type,
    real_zero: $i ).

tff(decl_28,type,
    real_one: $i ).

tff(decl_29,type,
    n: $i ).

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

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

tff(decl_32,type,
    epred1_2: ( $i * $i ) > $o ).

tff(decl_33,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_34,type,
    esk2_0: $i ).

tff(decl_35,type,
    esk3_0: $i ).

tff(decl_36,type,
    esk4_0: $i ).

tff(decl_37,type,
    esk5_0: $i ).

fof(plus_and_inverse,axiom,
    ! [X1,X2] :
      ( int_less(X1,X2)
    <=> ? [X3] :
          ( plus(X1,X3) = X2
          & int_less(int_zero,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_inverse) ).

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

fof(int_less_transitive,axiom,
    ! [X1,X2,X3] :
      ( ( int_less(X1,X2)
        & int_less(X2,X3) )
     => int_less(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_transitive) ).

fof(int_leq,axiom,
    ! [X1,X2] :
      ( int_leq(X1,X2)
    <=> ( int_less(X1,X2)
        | X1 = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_leq) ).

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

fof(one_successor_of_zero,axiom,
    ! [X1] :
      ( int_less(int_zero,X1)
    <=> int_leq(int_one,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_successor_of_zero) ).

fof(int_less_total,axiom,
    ! [X1,X2] :
      ( int_less(X1,X2)
      | int_leq(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_total) ).

fof(plus_and_order1,axiom,
    ! [X4,X5,X6,X7] :
      ( ( int_less(X4,X5)
        & int_leq(X6,X7) )
     => int_leq(plus(X4,X6),plus(X5,X7)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_order1) ).

fof(plus_zero,axiom,
    ! [X1] : plus(X1,int_zero) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_zero) ).

fof(qih,hypothesis,
    ! [X1,X2] :
      ( ( int_leq(int_one,X1)
        & int_leq(X1,n)
        & int_leq(int_one,X2)
        & int_leq(X2,n) )
     => ( ! [X8] :
            ( ( int_less(int_zero,X8)
              & X1 = plus(X2,X8) )
           => ! [X3] :
                ( ( int_leq(int_one,X3)
                  & int_leq(X3,X2) )
               => a(plus(X3,X8),X3) = qr(plus(X3,X8),X3) ) )
        & ! [X3] :
            ( ( int_leq(int_one,X3)
              & int_leq(X3,X2) )
           => a(X3,X3) = real_one )
        & ! [X8] :
            ( ( int_less(int_zero,X8)
              & X2 = plus(X1,X8) )
           => ! [X3] :
                ( ( int_leq(int_one,X3)
                  & int_leq(X3,X1) )
               => a(X3,plus(X3,X8)) = real_zero ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qih) ).

fof(lti,conjecture,
    ( ! [X1,X2] :
        ( ( int_leq(int_one,X1)
          & int_less(X1,X2)
          & int_leq(X2,n) )
       => a(X1,X2) = real_zero )
    & ! [X1,X2] :
        ( ( int_leq(int_one,X1)
          & int_leq(X2,n)
          & X1 = X2 )
       => a(X1,X2) != real_zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lti) ).

fof(real_constants,axiom,
    real_zero != real_one,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',real_constants) ).

fof(int_zero_one,axiom,
    int_less(int_zero,int_one),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_zero_one) ).

fof(c_0_13,plain,
    ! [X25,X26,X28,X29,X30] :
      ( ( plus(X25,esk1_2(X25,X26)) = X26
        | ~ int_less(X25,X26) )
      & ( int_less(int_zero,esk1_2(X25,X26))
        | ~ int_less(X25,X26) )
      & ( plus(X28,X30) != X29
        | ~ int_less(int_zero,X30)
        | int_less(X28,X29) ) ),
    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)],[plus_and_inverse])])])])])]) ).

fof(c_0_14,plain,
    ! [X14,X15] :
      ( ~ int_less(X14,X15)
      | X14 != X15 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_less_irreflexive])]) ).

fof(c_0_15,plain,
    ! [X11,X12,X13] :
      ( ~ int_less(X11,X12)
      | ~ int_less(X12,X13)
      | int_less(X11,X13) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_less_transitive])]) ).

cnf(c_0_16,plain,
    ( int_less(X1,X3)
    | plus(X1,X2) != X3
    | ~ int_less(int_zero,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_17,plain,
    ( ~ int_less(X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,plain,
    ( int_less(X1,X3)
    | ~ int_less(X1,X2)
    | ~ int_less(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_19,plain,
    ( int_less(X1,plus(X1,X2))
    | ~ int_less(int_zero,X2) ),
    inference(er,[status(thm)],[c_0_16]) ).

cnf(c_0_20,plain,
    ~ int_less(X1,X1),
    inference(er,[status(thm)],[c_0_17]) ).

cnf(c_0_21,plain,
    ( int_less(X1,plus(X2,X3))
    | ~ int_less(int_zero,X3)
    | ~ int_less(X1,X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_22,plain,
    ( ~ int_less(plus(X1,X2),X1)
    | ~ int_less(int_zero,X2) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_23,plain,
    ( plus(X1,esk1_2(X1,X2)) = X2
    | ~ int_less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_24,plain,
    ( int_less(int_zero,esk1_2(X1,X2))
    | ~ int_less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_25,plain,
    ! [X9,X10] :
      ( ( ~ int_leq(X9,X10)
        | int_less(X9,X10)
        | X9 = X10 )
      & ( ~ int_less(X9,X10)
        | int_leq(X9,X10) )
      & ( X9 != X10
        | int_leq(X9,X10) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_leq])])]) ).

fof(c_0_26,plain,
    ! [X18,X19] : plus(X18,X19) = plus(X19,X18),
    inference(variable_rename,[status(thm)],[plus_commutative]) ).

cnf(c_0_27,plain,
    ( ~ int_less(X1,X2)
    | ~ int_less(X2,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).

cnf(c_0_28,plain,
    ( int_less(X1,X2)
    | X1 = X2
    | ~ int_leq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_29,plain,
    ! [X31] :
      ( ( ~ int_less(int_zero,X31)
        | int_leq(int_one,X31) )
      & ( ~ int_leq(int_one,X31)
        | int_less(int_zero,X31) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[one_successor_of_zero])]) ).

cnf(c_0_30,plain,
    plus(X1,X2) = plus(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_31,plain,
    ( X1 = X2
    | ~ int_less(X2,X1)
    | ~ int_leq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_32,plain,
    ( int_leq(int_one,X1)
    | ~ int_less(int_zero,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_33,plain,
    ( ~ int_less(plus(X1,X2),X2)
    | ~ int_less(int_zero,X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_30]) ).

fof(c_0_34,plain,
    ! [X16,X17] :
      ( int_less(X16,X17)
      | int_leq(X17,X16) ),
    inference(variable_rename,[status(thm)],[int_less_total]) ).

cnf(c_0_35,plain,
    ( X1 = X2
    | ~ int_leq(X1,X2)
    | ~ int_leq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_28]) ).

cnf(c_0_36,plain,
    ( int_leq(int_one,esk1_2(X1,X2))
    | ~ int_less(X1,X2) ),
    inference(spm,[status(thm)],[c_0_32,c_0_24]) ).

cnf(c_0_37,plain,
    ( ~ int_less(X1,esk1_2(X2,X1))
    | ~ int_less(int_zero,X2)
    | ~ int_less(X2,X1) ),
    inference(spm,[status(thm)],[c_0_33,c_0_23]) ).

cnf(c_0_38,plain,
    ( int_less(X1,X2)
    | int_leq(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_39,plain,
    ( int_less(X1,plus(X2,X1))
    | ~ int_less(int_zero,X2) ),
    inference(spm,[status(thm)],[c_0_19,c_0_30]) ).

cnf(c_0_40,plain,
    ( esk1_2(X1,X2) = int_one
    | ~ int_less(X1,X2)
    | ~ int_leq(esk1_2(X1,X2),int_one) ),
    inference(spm,[status(thm)],[c_0_35,c_0_36]) ).

cnf(c_0_41,plain,
    ( int_leq(esk1_2(X1,X2),X2)
    | ~ int_less(int_zero,X1)
    | ~ int_less(X1,X2) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

fof(c_0_42,plain,
    ! [X21,X22,X23,X24] :
      ( ~ int_less(X21,X22)
      | ~ int_leq(X23,X24)
      | int_leq(plus(X21,X23),plus(X22,X24)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[plus_and_order1])]) ).

fof(c_0_43,plain,
    ! [X20] : plus(X20,int_zero) = X20,
    inference(variable_rename,[status(thm)],[plus_zero]) ).

fof(c_0_44,plain,
    ! [X2,X1] :
      ( epred1_2(X1,X2)
    <=> ( ! [X8] :
            ( ( int_less(int_zero,X8)
              & X1 = plus(X2,X8) )
           => ! [X3] :
                ( ( int_leq(int_one,X3)
                  & int_leq(X3,X2) )
               => a(plus(X3,X8),X3) = qr(plus(X3,X8),X3) ) )
        & ! [X3] :
            ( ( int_leq(int_one,X3)
              & int_leq(X3,X2) )
           => a(X3,X3) = real_one )
        & ! [X8] :
            ( ( int_less(int_zero,X8)
              & X2 = plus(X1,X8) )
           => ! [X3] :
                ( ( int_leq(int_one,X3)
                  & int_leq(X3,X1) )
               => a(X3,plus(X3,X8)) = real_zero ) ) ) ),
    introduced(definition) ).

cnf(c_0_45,plain,
    ( int_less(esk1_2(X1,X2),X2)
    | ~ int_less(int_zero,X1)
    | ~ int_less(X1,X2) ),
    inference(spm,[status(thm)],[c_0_39,c_0_23]) ).

cnf(c_0_46,plain,
    ( esk1_2(X1,int_one) = int_one
    | ~ int_less(X1,int_one)
    | ~ int_less(int_zero,X1) ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_47,plain,
    ( int_leq(plus(X1,X3),plus(X2,X4))
    | ~ int_less(X1,X2)
    | ~ int_leq(X3,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_48,plain,
    plus(X1,int_zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

fof(c_0_49,plain,
    ! [X2,X1] :
      ( epred1_2(X1,X2)
     => ( ! [X8] :
            ( ( int_less(int_zero,X8)
              & X1 = plus(X2,X8) )
           => ! [X3] :
                ( ( int_leq(int_one,X3)
                  & int_leq(X3,X2) )
               => a(plus(X3,X8),X3) = qr(plus(X3,X8),X3) ) )
        & ! [X3] :
            ( ( int_leq(int_one,X3)
              & int_leq(X3,X2) )
           => a(X3,X3) = real_one )
        & ! [X8] :
            ( ( int_less(int_zero,X8)
              & X2 = plus(X1,X8) )
           => ! [X3] :
                ( ( int_leq(int_one,X3)
                  & int_leq(X3,X1) )
               => a(X3,plus(X3,X8)) = real_zero ) ) ) ),
    inference(split_equiv,[status(thm)],[c_0_44]) ).

cnf(c_0_50,plain,
    ( ~ int_less(int_zero,X1)
    | ~ int_less(X1,int_one) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_20]) ).

cnf(c_0_51,plain,
    ( int_leq(plus(X1,X2),plus(X3,X4))
    | ~ int_less(X1,X4)
    | ~ int_leq(X2,X3) ),
    inference(spm,[status(thm)],[c_0_47,c_0_30]) ).

cnf(c_0_52,plain,
    plus(int_zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_48,c_0_30]) ).

fof(c_0_53,plain,
    ! [X38,X39,X40,X41,X42,X43,X44] :
      ( ( ~ int_less(int_zero,X40)
        | X39 != plus(X38,X40)
        | ~ int_leq(int_one,X41)
        | ~ int_leq(X41,X38)
        | a(plus(X41,X40),X41) = qr(plus(X41,X40),X41)
        | ~ epred1_2(X39,X38) )
      & ( ~ int_leq(int_one,X42)
        | ~ int_leq(X42,X38)
        | a(X42,X42) = real_one
        | ~ epred1_2(X39,X38) )
      & ( ~ int_less(int_zero,X43)
        | X38 != plus(X39,X43)
        | ~ int_leq(int_one,X44)
        | ~ int_leq(X44,X39)
        | a(X44,plus(X44,X43)) = real_zero
        | ~ epred1_2(X39,X38) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).

fof(c_0_54,hypothesis,
    ! [X1,X2] :
      ( ( int_leq(int_one,X1)
        & int_leq(X1,n)
        & int_leq(int_one,X2)
        & int_leq(X2,n) )
     => epred1_2(X1,X2) ),
    inference(apply_def,[status(thm)],[qih,c_0_44]) ).

cnf(c_0_55,plain,
    ( ~ int_less(plus(X1,X2),int_one)
    | ~ int_less(int_zero,X2)
    | ~ int_less(int_zero,X1) ),
    inference(spm,[status(thm)],[c_0_50,c_0_21]) ).

cnf(c_0_56,plain,
    ( int_leq(X1,plus(X2,X3))
    | ~ int_less(int_zero,X3)
    | ~ int_leq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_52]) ).

fof(c_0_57,negated_conjecture,
    ~ ( ! [X1,X2] :
          ( ( int_leq(int_one,X1)
            & int_less(X1,X2)
            & int_leq(X2,n) )
         => a(X1,X2) = real_zero )
      & ! [X1,X2] :
          ( ( int_leq(int_one,X1)
            & int_leq(X2,n)
            & X1 = X2 )
         => a(X1,X2) != real_zero ) ),
    inference(assume_negation,[status(cth)],[lti]) ).

cnf(c_0_58,plain,
    ( a(X4,plus(X4,X1)) = real_zero
    | ~ int_less(int_zero,X1)
    | X2 != plus(X3,X1)
    | ~ int_leq(int_one,X4)
    | ~ int_leq(X4,X3)
    | ~ epred1_2(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

fof(c_0_59,hypothesis,
    ! [X32,X33] :
      ( ~ int_leq(int_one,X32)
      | ~ int_leq(X32,n)
      | ~ int_leq(int_one,X33)
      | ~ int_leq(X33,n)
      | epred1_2(X32,X33) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])]) ).

cnf(c_0_60,plain,
    ( ~ int_less(X1,int_one)
    | ~ int_less(int_zero,X2)
    | ~ int_less(X2,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_23]),c_0_24]) ).

cnf(c_0_61,plain,
    ( X1 = plus(X2,X3)
    | ~ int_less(int_zero,X3)
    | ~ int_leq(plus(X2,X3),X1)
    | ~ int_leq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_35,c_0_56]) ).

fof(c_0_62,negated_conjecture,
    ( ( int_leq(int_one,esk4_0)
      | int_leq(int_one,esk2_0) )
    & ( int_leq(esk5_0,n)
      | int_leq(int_one,esk2_0) )
    & ( esk4_0 = esk5_0
      | int_leq(int_one,esk2_0) )
    & ( a(esk4_0,esk5_0) = real_zero
      | int_leq(int_one,esk2_0) )
    & ( int_leq(int_one,esk4_0)
      | int_less(esk2_0,esk3_0) )
    & ( int_leq(esk5_0,n)
      | int_less(esk2_0,esk3_0) )
    & ( esk4_0 = esk5_0
      | int_less(esk2_0,esk3_0) )
    & ( a(esk4_0,esk5_0) = real_zero
      | int_less(esk2_0,esk3_0) )
    & ( int_leq(int_one,esk4_0)
      | int_leq(esk3_0,n) )
    & ( int_leq(esk5_0,n)
      | int_leq(esk3_0,n) )
    & ( esk4_0 = esk5_0
      | int_leq(esk3_0,n) )
    & ( a(esk4_0,esk5_0) = real_zero
      | int_leq(esk3_0,n) )
    & ( int_leq(int_one,esk4_0)
      | a(esk2_0,esk3_0) != real_zero )
    & ( int_leq(esk5_0,n)
      | a(esk2_0,esk3_0) != real_zero )
    & ( esk4_0 = esk5_0
      | a(esk2_0,esk3_0) != real_zero )
    & ( a(esk4_0,esk5_0) = real_zero
      | a(esk2_0,esk3_0) != real_zero ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).

cnf(c_0_63,plain,
    ( a(X1,plus(X1,X2)) = real_zero
    | ~ epred1_2(X3,plus(X3,X2))
    | ~ int_less(int_zero,X2)
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X1,X3) ),
    inference(er,[status(thm)],[c_0_58]) ).

cnf(c_0_64,hypothesis,
    ( epred1_2(X1,X2)
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X1,n)
    | ~ int_leq(int_one,X2)
    | ~ int_leq(X2,n) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_65,plain,
    ( int_leq(int_one,X1)
    | ~ int_less(int_zero,X2)
    | ~ int_less(X2,X1) ),
    inference(spm,[status(thm)],[c_0_60,c_0_38]) ).

cnf(c_0_66,plain,
    ( int_less(int_zero,X1)
    | ~ int_leq(int_one,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_29]) ).

cnf(c_0_67,plain,
    ( X1 = X2
    | ~ int_less(X3,X2)
    | ~ int_leq(X2,X1)
    | ~ int_leq(X1,X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_23]),c_0_24]) ).

cnf(c_0_68,negated_conjecture,
    ( esk4_0 = esk5_0
    | int_less(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_69,plain,
    ( int_leq(X1,X2)
    | ~ int_less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_70,hypothesis,
    ( a(X1,plus(X1,X2)) = real_zero
    | ~ int_less(int_zero,X2)
    | ~ int_leq(plus(X3,X2),n)
    | ~ int_leq(int_one,plus(X3,X2))
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X3,n)
    | ~ int_leq(int_one,X3)
    | ~ int_leq(X1,X3) ),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_71,plain,
    ( int_leq(int_one,X1)
    | ~ int_less(X2,X1)
    | ~ int_leq(int_one,X2) ),
    inference(spm,[status(thm)],[c_0_65,c_0_66]) ).

cnf(c_0_72,plain,
    ( int_leq(X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_73,negated_conjecture,
    ( esk4_0 = esk5_0
    | X1 = esk3_0
    | ~ int_leq(esk3_0,X1)
    | ~ int_leq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_74,plain,
    ( int_leq(X1,X2)
    | int_leq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_69,c_0_38]) ).

cnf(c_0_75,hypothesis,
    ( a(X1,plus(X1,esk1_2(X2,X3))) = real_zero
    | ~ int_less(X2,X3)
    | ~ int_leq(X3,n)
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X2,n)
    | ~ int_leq(int_one,X2)
    | ~ int_leq(X1,X2) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_23]),c_0_71]),c_0_24]) ).

cnf(c_0_76,plain,
    int_leq(X1,X1),
    inference(er,[status(thm)],[c_0_72]) ).

cnf(c_0_77,plain,
    ( X1 = X2
    | int_leq(X2,X3)
    | ~ int_leq(X2,X1)
    | ~ int_leq(X1,X3) ),
    inference(spm,[status(thm)],[c_0_67,c_0_38]) ).

cnf(c_0_78,negated_conjecture,
    ( esk4_0 = esk5_0
    | X1 = esk3_0
    | int_leq(X1,esk3_0)
    | ~ int_leq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_73,c_0_74]) ).

cnf(c_0_79,negated_conjecture,
    ( esk4_0 = esk5_0
    | a(esk2_0,esk3_0) != real_zero ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_80,hypothesis,
    ( a(X1,X2) = real_zero
    | ~ int_less(X1,X2)
    | ~ int_leq(X2,n)
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X1,n) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_23]),c_0_76])]) ).

cnf(c_0_81,negated_conjecture,
    ( esk4_0 = esk5_0
    | int_leq(int_one,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_82,negated_conjecture,
    ( esk4_0 = esk5_0
    | int_leq(esk3_0,n) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_83,negated_conjecture,
    ( esk4_0 = esk5_0
    | esk3_0 = X1
    | int_leq(X1,X2)
    | ~ int_leq(esk3_0,X2)
    | ~ int_leq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

cnf(c_0_84,plain,
    ( X1 = X2
    | int_less(X3,X2)
    | ~ int_less(X3,X1)
    | ~ int_leq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_18,c_0_28]) ).

cnf(c_0_85,negated_conjecture,
    ( int_leq(int_one,esk4_0)
    | int_leq(esk3_0,n) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_86,negated_conjecture,
    ( esk4_0 = esk5_0
    | ~ int_leq(esk2_0,n) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_82]),c_0_68]) ).

cnf(c_0_87,negated_conjecture,
    ( esk4_0 = esk5_0
    | esk3_0 = X1
    | int_leq(X1,n)
    | ~ int_leq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_83,c_0_82]) ).

cnf(c_0_88,plain,
    ( a(X1,X1) = real_one
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X1,X2)
    | ~ epred1_2(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_53]) ).

cnf(c_0_89,negated_conjecture,
    ( n = esk3_0
    | int_less(X1,n)
    | int_leq(int_one,esk4_0)
    | ~ int_less(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_84,c_0_85]) ).

cnf(c_0_90,negated_conjecture,
    ( int_leq(int_one,esk4_0)
    | int_less(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_91,negated_conjecture,
    ( int_leq(esk5_0,n)
    | int_less(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_92,negated_conjecture,
    ( esk3_0 = esk2_0
    | esk4_0 = esk5_0 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_76])]) ).

cnf(c_0_93,hypothesis,
    ( a(X1,X1) = real_one
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X2,n)
    | ~ int_leq(X3,n)
    | ~ int_leq(int_one,X2)
    | ~ int_leq(int_one,X3)
    | ~ int_leq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_88,c_0_64]) ).

cnf(c_0_94,negated_conjecture,
    ( n = esk3_0
    | int_leq(int_one,esk4_0)
    | ~ int_less(n,esk3_0) ),
    inference(spm,[status(thm)],[c_0_20,c_0_89]) ).

cnf(c_0_95,negated_conjecture,
    ( int_less(X1,esk3_0)
    | int_leq(int_one,esk4_0)
    | ~ int_less(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_18,c_0_90]) ).

cnf(c_0_96,negated_conjecture,
    ( int_leq(esk5_0,n)
    | int_leq(esk3_0,n) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_97,negated_conjecture,
    ( int_less(X1,esk3_0)
    | int_leq(esk5_0,n)
    | ~ int_less(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_18,c_0_91]) ).

cnf(c_0_98,negated_conjecture,
    ( a(esk4_0,esk5_0) = real_zero
    | int_less(esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_99,negated_conjecture,
    esk4_0 = esk5_0,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_92]),c_0_20]) ).

cnf(c_0_100,hypothesis,
    ( a(X1,X1) = real_one
    | ~ int_leq(int_one,n)
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X2,n)
    | ~ int_leq(int_one,X2)
    | ~ int_leq(X1,n) ),
    inference(spm,[status(thm)],[c_0_93,c_0_76]) ).

cnf(c_0_101,negated_conjecture,
    ( int_leq(int_one,esk4_0)
    | a(esk2_0,esk3_0) != real_zero ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_102,negated_conjecture,
    ( int_leq(int_one,esk4_0)
    | int_leq(int_one,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_103,negated_conjecture,
    ( n = esk3_0
    | int_leq(int_one,esk4_0)
    | ~ int_less(n,esk2_0) ),
    inference(spm,[status(thm)],[c_0_94,c_0_95]) ).

cnf(c_0_104,negated_conjecture,
    ( n = esk3_0
    | int_less(X1,n)
    | int_leq(esk5_0,n)
    | ~ int_less(X1,esk3_0) ),
    inference(spm,[status(thm)],[c_0_84,c_0_96]) ).

cnf(c_0_105,negated_conjecture,
    ( int_leq(esk5_0,n)
    | int_leq(int_one,esk3_0)
    | ~ int_less(int_zero,esk2_0) ),
    inference(spm,[status(thm)],[c_0_32,c_0_97]) ).

cnf(c_0_106,negated_conjecture,
    ( int_leq(esk5_0,n)
    | int_leq(int_one,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_107,negated_conjecture,
    ( a(esk5_0,esk5_0) = real_zero
    | int_less(esk2_0,esk3_0) ),
    inference(rw,[status(thm)],[c_0_98,c_0_99]) ).

cnf(c_0_108,hypothesis,
    ( a(X1,X1) = real_one
    | ~ int_leq(int_one,n)
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X1,n) ),
    inference(spm,[status(thm)],[c_0_100,c_0_76]) ).

cnf(c_0_109,plain,
    real_zero != real_one,
    inference(split_conjunct,[status(thm)],[real_constants]) ).

cnf(c_0_110,negated_conjecture,
    ( int_less(esk2_0,esk3_0)
    | int_leq(int_one,esk5_0) ),
    inference(rw,[status(thm)],[c_0_90,c_0_99]) ).

cnf(c_0_111,negated_conjecture,
    ( a(esk4_0,esk5_0) = real_zero
    | int_leq(esk3_0,n) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_112,negated_conjecture,
    ( a(esk4_0,esk5_0) = real_zero
    | a(esk2_0,esk3_0) != real_zero ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_113,negated_conjecture,
    ( a(esk4_0,esk5_0) = real_zero
    | int_leq(int_one,esk2_0) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_114,negated_conjecture,
    ( int_leq(int_one,esk5_0)
    | a(esk2_0,esk3_0) != real_zero ),
    inference(rw,[status(thm)],[c_0_101,c_0_99]) ).

cnf(c_0_115,negated_conjecture,
    ( int_leq(int_one,esk5_0)
    | int_leq(int_one,esk2_0) ),
    inference(rw,[status(thm)],[c_0_102,c_0_99]) ).

cnf(c_0_116,negated_conjecture,
    ( int_leq(esk3_0,n)
    | int_leq(int_one,esk5_0) ),
    inference(rw,[status(thm)],[c_0_85,c_0_99]) ).

cnf(c_0_117,negated_conjecture,
    ( n = esk3_0
    | int_leq(esk2_0,n)
    | int_leq(int_one,esk4_0) ),
    inference(spm,[status(thm)],[c_0_103,c_0_38]) ).

cnf(c_0_118,plain,
    ( int_leq(plus(X1,X2),X3)
    | ~ int_less(X1,X3)
    | ~ int_leq(X2,int_zero) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_119,plain,
    ( int_leq(X1,int_zero)
    | int_leq(int_one,X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_38]) ).

cnf(c_0_120,negated_conjecture,
    ( n = esk3_0
    | int_leq(esk5_0,n)
    | int_leq(int_one,n)
    | ~ int_less(int_zero,esk3_0) ),
    inference(spm,[status(thm)],[c_0_32,c_0_104]) ).

cnf(c_0_121,negated_conjecture,
    ( int_leq(int_one,esk3_0)
    | int_leq(esk5_0,n) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_66]),c_0_106]) ).

cnf(c_0_122,negated_conjecture,
    ( int_leq(int_one,esk4_0)
    | int_leq(int_one,esk3_0)
    | ~ int_less(int_zero,esk2_0) ),
    inference(spm,[status(thm)],[c_0_32,c_0_95]) ).

cnf(c_0_123,plain,
    ( plus(X1,X2) = X1
    | ~ int_less(int_zero,X2)
    | ~ int_leq(plus(X1,X2),X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_28]) ).

cnf(c_0_124,plain,
    ( int_leq(plus(X1,X2),X3)
    | ~ int_less(X1,int_zero)
    | ~ int_leq(X2,X3) ),
    inference(spm,[status(thm)],[c_0_47,c_0_52]) ).

cnf(c_0_125,negated_conjecture,
    ( int_less(esk2_0,esk3_0)
    | ~ int_leq(int_one,n) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]),c_0_91]),c_0_110]) ).

cnf(c_0_126,negated_conjecture,
    ( a(esk5_0,esk5_0) = real_zero
    | int_leq(esk3_0,n) ),
    inference(rw,[status(thm)],[c_0_111,c_0_99]) ).

cnf(c_0_127,negated_conjecture,
    ( a(esk5_0,esk5_0) = real_zero
    | a(esk2_0,esk3_0) != real_zero ),
    inference(rw,[status(thm)],[c_0_112,c_0_99]) ).

cnf(c_0_128,negated_conjecture,
    ( a(esk5_0,esk5_0) = real_zero
    | int_leq(int_one,esk2_0) ),
    inference(rw,[status(thm)],[c_0_113,c_0_99]) ).

cnf(c_0_129,negated_conjecture,
    ( int_leq(esk5_0,n)
    | a(esk2_0,esk3_0) != real_zero ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_130,hypothesis,
    ( int_leq(int_one,esk5_0)
    | ~ int_leq(esk2_0,n) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_80]),c_0_115]),c_0_116]),c_0_110]) ).

cnf(c_0_131,negated_conjecture,
    ( n = esk3_0
    | int_leq(int_one,esk5_0)
    | int_leq(esk2_0,n) ),
    inference(rw,[status(thm)],[c_0_117,c_0_99]) ).

cnf(c_0_132,plain,
    ( int_leq(X1,X2)
    | ~ int_less(int_zero,X2)
    | ~ int_leq(X1,int_zero) ),
    inference(spm,[status(thm)],[c_0_118,c_0_52]) ).

cnf(c_0_133,plain,
    int_less(int_zero,int_one),
    inference(split_conjunct,[status(thm)],[int_zero_one]) ).

cnf(c_0_134,plain,
    ( X1 = int_one
    | int_leq(X1,int_zero)
    | int_leq(int_one,X2)
    | ~ int_leq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_77,c_0_119]) ).

cnf(c_0_135,negated_conjecture,
    ( n = esk3_0
    | int_leq(int_one,n)
    | int_leq(esk5_0,n) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_66]),c_0_121]) ).

cnf(c_0_136,plain,
    ( plus(X1,X2) = X2
    | ~ int_less(int_zero,X1)
    | ~ int_leq(plus(X1,X2),X2) ),
    inference(spm,[status(thm)],[c_0_33,c_0_28]) ).

cnf(c_0_137,negated_conjecture,
    ( int_leq(int_one,esk3_0)
    | int_leq(int_one,esk4_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_66]),c_0_102]) ).

cnf(c_0_138,plain,
    ( plus(X1,X2) = X1
    | ~ int_less(int_zero,X2)
    | ~ int_less(X1,int_zero)
    | ~ int_leq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_123,c_0_124]) ).

cnf(c_0_139,negated_conjecture,
    ( n = esk3_0
    | int_leq(esk5_0,n)
    | ~ int_less(n,esk3_0) ),
    inference(spm,[status(thm)],[c_0_20,c_0_104]) ).

cnf(c_0_140,negated_conjecture,
    ( X1 = esk3_0
    | ~ int_leq(int_one,n)
    | ~ int_leq(esk3_0,X1)
    | ~ int_leq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_67,c_0_125]) ).

cnf(c_0_141,negated_conjecture,
    ( int_leq(esk3_0,n)
    | ~ int_leq(int_one,n) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_108]),c_0_109]),c_0_96]),c_0_116]) ).

cnf(c_0_142,hypothesis,
    ( a(esk5_0,esk5_0) = real_zero
    | ~ int_leq(esk2_0,n) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_80]),c_0_128]),c_0_126]),c_0_107]) ).

cnf(c_0_143,negated_conjecture,
    ( int_leq(esk5_0,n)
    | ~ int_leq(esk2_0,n) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_80]),c_0_106]),c_0_96]),c_0_91]) ).

cnf(c_0_144,negated_conjecture,
    ( n = esk3_0
    | int_leq(int_one,esk5_0) ),
    inference(spm,[status(thm)],[c_0_130,c_0_131]) ).

cnf(c_0_145,plain,
    ( int_leq(X1,int_one)
    | ~ int_leq(X1,int_zero) ),
    inference(spm,[status(thm)],[c_0_132,c_0_133]) ).

cnf(c_0_146,negated_conjecture,
    ( n = esk3_0
    | esk5_0 = int_one
    | int_leq(int_one,n)
    | int_leq(esk5_0,int_zero) ),
    inference(spm,[status(thm)],[c_0_134,c_0_135]) ).

cnf(c_0_147,plain,
    ( plus(X1,X2) = X2
    | ~ int_less(int_zero,X1)
    | ~ int_less(X1,X2)
    | ~ int_leq(X2,int_zero) ),
    inference(spm,[status(thm)],[c_0_136,c_0_118]) ).

cnf(c_0_148,negated_conjecture,
    ( a(X1,X1) = real_one
    | int_leq(int_one,esk3_0)
    | ~ int_leq(int_one,esk5_0)
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X2,n)
    | ~ int_leq(int_one,X2)
    | ~ int_leq(X1,esk5_0) ),
    inference(spm,[status(thm)],[c_0_93,c_0_121]) ).

cnf(c_0_149,negated_conjecture,
    ( int_leq(int_one,esk5_0)
    | int_leq(int_one,esk3_0) ),
    inference(rw,[status(thm)],[c_0_137,c_0_99]) ).

cnf(c_0_150,negated_conjecture,
    ( a(X1,X1) = real_one
    | int_leq(int_one,esk2_0)
    | ~ int_leq(int_one,esk5_0)
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X2,n)
    | ~ int_leq(int_one,X2)
    | ~ int_leq(X1,esk5_0) ),
    inference(spm,[status(thm)],[c_0_93,c_0_106]) ).

cnf(c_0_151,plain,
    ( ~ int_less(int_zero,X1)
    | ~ int_less(X2,int_zero)
    | ~ int_leq(X1,X2) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_138]),c_0_20]) ).

cnf(c_0_152,negated_conjecture,
    ( n = esk3_0
    | int_leq(esk5_0,n)
    | ~ int_less(n,esk2_0) ),
    inference(spm,[status(thm)],[c_0_139,c_0_97]) ).

cnf(c_0_153,negated_conjecture,
    ( n = esk3_0
    | ~ int_leq(int_one,n)
    | ~ int_leq(n,esk2_0) ),
    inference(spm,[status(thm)],[c_0_140,c_0_141]) ).

cnf(c_0_154,hypothesis,
    ( ~ int_leq(esk2_0,n)
    | ~ int_leq(int_one,n) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_108]),c_0_109]),c_0_143]),c_0_130]) ).

cnf(c_0_155,negated_conjecture,
    ( n = esk3_0
    | esk5_0 = int_one
    | ~ int_leq(esk5_0,int_one) ),
    inference(spm,[status(thm)],[c_0_35,c_0_144]) ).

cnf(c_0_156,negated_conjecture,
    ( esk5_0 = int_one
    | n = esk3_0
    | int_leq(int_one,n)
    | int_leq(esk5_0,int_one) ),
    inference(spm,[status(thm)],[c_0_145,c_0_146]) ).

cnf(c_0_157,plain,
    ( ~ int_less(int_zero,X1)
    | ~ int_less(X1,X2)
    | ~ int_leq(X2,int_zero) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_147]),c_0_20]) ).

cnf(c_0_158,negated_conjecture,
    ( a(X1,X1) = real_one
    | int_leq(int_one,esk3_0)
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X1,esk5_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_121]),c_0_149]) ).

cnf(c_0_159,negated_conjecture,
    ( a(X1,X1) = real_one
    | int_leq(int_one,esk2_0)
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X1,esk5_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_106]),c_0_115]) ).

cnf(c_0_160,negated_conjecture,
    ( int_leq(esk5_0,n)
    | ~ int_less(int_zero,esk2_0)
    | ~ int_less(X1,int_zero)
    | ~ int_leq(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_151,c_0_97]) ).

cnf(c_0_161,plain,
    ( X1 = X2
    | int_leq(int_one,X2)
    | ~ int_leq(int_one,X1)
    | ~ int_leq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_71,c_0_28]) ).

cnf(c_0_162,negated_conjecture,
    ( n = esk3_0
    | int_leq(esk2_0,n)
    | int_leq(esk5_0,n) ),
    inference(spm,[status(thm)],[c_0_152,c_0_38]) ).

cnf(c_0_163,negated_conjecture,
    ( n = esk3_0
    | ~ int_leq(int_one,n) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_74]),c_0_154]) ).

cnf(c_0_164,negated_conjecture,
    ( esk5_0 = int_one
    | n = esk3_0
    | int_leq(int_one,n) ),
    inference(spm,[status(thm)],[c_0_155,c_0_156]) ).

cnf(c_0_165,plain,
    ( ~ int_less(X1,X2)
    | ~ int_leq(X2,int_zero)
    | ~ int_leq(int_one,X1) ),
    inference(spm,[status(thm)],[c_0_157,c_0_66]) ).

cnf(c_0_166,negated_conjecture,
    ( int_less(esk2_0,esk3_0)
    | int_leq(int_one,esk3_0) ),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_158]),c_0_76])]),c_0_109]),c_0_149]) ).

cnf(c_0_167,negated_conjecture,
    int_leq(int_one,esk2_0),
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_159]),c_0_76])]),c_0_109]),c_0_115]) ).

cnf(c_0_168,plain,
    ( ~ int_less(X1,int_zero)
    | ~ int_leq(int_one,X2)
    | ~ int_leq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_151,c_0_66]) ).

cnf(c_0_169,negated_conjecture,
    ( int_leq(esk5_0,n)
    | ~ int_less(X1,int_zero)
    | ~ int_leq(esk3_0,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_66]),c_0_106]) ).

cnf(c_0_170,negated_conjecture,
    ( n = esk3_0
    | esk5_0 = X1
    | int_leq(int_one,X1)
    | ~ int_leq(esk5_0,X1) ),
    inference(spm,[status(thm)],[c_0_161,c_0_144]) ).

cnf(c_0_171,negated_conjecture,
    ( n = esk3_0
    | int_leq(esk5_0,n) ),
    inference(spm,[status(thm)],[c_0_143,c_0_162]) ).

cnf(c_0_172,negated_conjecture,
    ( esk5_0 = int_one
    | n = esk3_0 ),
    inference(spm,[status(thm)],[c_0_163,c_0_164]) ).

cnf(c_0_173,negated_conjecture,
    int_leq(int_one,esk3_0),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_167])]),c_0_119]) ).

cnf(c_0_174,plain,
    ( X1 = int_zero
    | int_less(X2,int_zero)
    | int_leq(int_one,X1)
    | ~ int_less(X2,X1) ),
    inference(spm,[status(thm)],[c_0_84,c_0_119]) ).

cnf(c_0_175,plain,
    ( int_leq(int_zero,X1)
    | ~ int_leq(int_one,X2)
    | ~ int_leq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_168,c_0_38]) ).

cnf(c_0_176,negated_conjecture,
    ( X1 = int_zero
    | int_leq(esk5_0,n)
    | ~ int_leq(esk3_0,X1)
    | ~ int_leq(X1,int_zero) ),
    inference(spm,[status(thm)],[c_0_169,c_0_28]) ).

cnf(c_0_177,negated_conjecture,
    ( n = esk5_0
    | n = esk3_0
    | int_leq(int_one,n) ),
    inference(spm,[status(thm)],[c_0_170,c_0_171]) ).

cnf(c_0_178,hypothesis,
    ( esk5_0 = int_one
    | ~ int_leq(esk2_0,esk3_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_172]),c_0_173])]) ).

cnf(c_0_179,negated_conjecture,
    ( int_leq(esk2_0,esk3_0)
    | ~ int_leq(int_one,n) ),
    inference(spm,[status(thm)],[c_0_69,c_0_125]) ).

cnf(c_0_180,plain,
    ( X1 = int_zero
    | X2 = X1
    | int_less(X2,int_zero)
    | int_leq(int_one,X1)
    | ~ int_leq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_174,c_0_28]) ).

cnf(c_0_181,negated_conjecture,
    ( n = esk3_0
    | int_leq(int_zero,X1)
    | ~ int_leq(esk5_0,X1) ),
    inference(spm,[status(thm)],[c_0_175,c_0_144]) ).

cnf(c_0_182,negated_conjecture,
    ( int_zero = n
    | int_leq(esk5_0,n)
    | ~ int_leq(n,int_zero) ),
    inference(spm,[status(thm)],[c_0_176,c_0_96]) ).

cnf(c_0_183,negated_conjecture,
    ( n = esk5_0
    | n = esk3_0 ),
    inference(spm,[status(thm)],[c_0_163,c_0_177]) ).

cnf(c_0_184,negated_conjecture,
    ( esk5_0 = int_one
    | ~ int_leq(int_one,n) ),
    inference(spm,[status(thm)],[c_0_178,c_0_179]) ).

cnf(c_0_185,negated_conjecture,
    ( n = esk3_0
    | X1 = int_zero
    | int_leq(int_one,X1)
    | ~ int_leq(esk5_0,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_20]) ).

cnf(c_0_186,negated_conjecture,
    ( int_zero = n
    | int_leq(int_one,n)
    | int_leq(esk5_0,n) ),
    inference(spm,[status(thm)],[c_0_182,c_0_119]) ).

cnf(c_0_187,hypothesis,
    ( n = esk5_0
    | ~ int_leq(esk2_0,esk3_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_183]),c_0_173])]) ).

cnf(c_0_188,negated_conjecture,
    esk5_0 = int_one,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_172]),c_0_173])]) ).

cnf(c_0_189,negated_conjecture,
    ( int_zero = n
    | n = esk3_0
    | int_leq(int_one,n) ),
    inference(spm,[status(thm)],[c_0_185,c_0_186]) ).

cnf(c_0_190,hypothesis,
    ( n = int_one
    | ~ int_leq(esk2_0,esk3_0) ),
    inference(rw,[status(thm)],[c_0_187,c_0_188]) ).

cnf(c_0_191,negated_conjecture,
    ( n = esk5_0
    | esk3_0 != esk5_0 ),
    inference(ef,[status(thm)],[c_0_183]) ).

cnf(c_0_192,negated_conjecture,
    ( int_zero = n
    | n = esk3_0 ),
    inference(spm,[status(thm)],[c_0_163,c_0_189]) ).

cnf(c_0_193,negated_conjecture,
    ( n = int_one
    | ~ int_leq(int_one,n) ),
    inference(spm,[status(thm)],[c_0_190,c_0_179]) ).

cnf(c_0_194,negated_conjecture,
    ( n = esk3_0
    | n = int_one ),
    inference(rw,[status(thm)],[c_0_183,c_0_188]) ).

cnf(c_0_195,negated_conjecture,
    ( n = int_one
    | esk3_0 != int_one ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_191,c_0_188]),c_0_188]) ).

cnf(c_0_196,negated_conjecture,
    ( n = esk3_0
    | int_less(n,int_one) ),
    inference(spm,[status(thm)],[c_0_133,c_0_192]) ).

cnf(c_0_197,negated_conjecture,
    n = int_one,
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_194]),c_0_173])]),c_0_195]) ).

cnf(c_0_198,negated_conjecture,
    ( ~ int_less(esk3_0,esk2_0)
    | ~ int_leq(int_one,n) ),
    inference(spm,[status(thm)],[c_0_27,c_0_125]) ).

cnf(c_0_199,negated_conjecture,
    esk3_0 = int_one,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_196,c_0_197]),c_0_197]),c_0_20]) ).

cnf(c_0_200,negated_conjecture,
    ~ int_less(int_one,esk2_0),
    inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_198,c_0_197]),c_0_76])]),c_0_199]) ).

cnf(c_0_201,hypothesis,
    ~ int_leq(esk2_0,int_one),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_154,c_0_197]),c_0_197]),c_0_76])]) ).

cnf(c_0_202,negated_conjecture,
    esk2_0 = int_one,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_28]),c_0_167])]) ).

cnf(c_0_203,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_201,c_0_202]),c_0_76])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV492+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 29 10:27:40 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.61  start to proof: theBenchmark
% 17.02/17.16  % Version  : CSE_E---1.5
% 17.02/17.16  % Problem  : theBenchmark.p
% 17.02/17.16  % Proof found
% 17.02/17.16  % SZS status Theorem for theBenchmark.p
% 17.02/17.16  % SZS output start Proof
% See solution above
% 17.02/17.17  % Total time : 16.539000 s
% 17.02/17.17  % SZS output end Proof
% 17.02/17.17  % Total time : 16.543000 s
%------------------------------------------------------------------------------