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E---3.5.1.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : E---3.5.1
% Problem  : SWV486+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 24 02:55:44 PM UTC 2026

% Result   : Theorem 0.22s 5.71s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   85 (  21 unt;   0 def)
%            Number of atoms       :  253 (  57 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  270 ( 102   ~; 106   |;  37   &)
%                                         (   4 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :  159 (   0 sgn  75   !;   1   ?)

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

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

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

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

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

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

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

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

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

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

fof(c_0_11,plain,
    ! [X1,X2] :
      ( int_less(X1,X2)
     => X1 != X2 ),
    inference(fof_simplification,[status(thm)],[int_less_irreflexive]) ).

fof(c_0_12,plain,
    ! [X25,X26,X28,X29,X30] :
      ( ( int_less(X28,X29)
        | ~ int_less(int_zero,X30)
        | plus(X28,X30) != X29 )
      & ( ~ int_less(X25,X26)
        | int_less(int_zero,esk1_2(X25,X26)) )
      & ( ~ int_less(X25,X26)
        | plus(X25,esk1_2(X25,X26)) = X26 ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[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_13,plain,
    ! [X14,X15] :
      ( X14 != X15
      | ~ int_less(X14,X15) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).

fof(c_0_14,plain,
    ! [X11,X12,X13] :
      ( int_less(X11,X13)
      | ~ int_less(X12,X13)
      | ~ int_less(X11,X12) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_less_transitive])])]) ).

cnf(c_0_15,plain,
    ( ~ int_less(int_zero,X2)
    | plus(X1,X2) != X3
    | int_less(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

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

cnf(c_0_17,plain,
    ( ~ int_less(X2,X3)
    | ~ int_less(X1,X2)
    | int_less(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,plain,
    ( ~ int_less(int_zero,X2)
    | int_less(X1,plus(X1,X2)) ),
    inference(er,[status(thm)],[c_0_15]) ).

fof(c_0_19,plain,
    ! [X2,X1] :
      ( epred1_2(X1,X2)
    <=> ( ! [X8] :
            ( ( X2 = plus(X1,X8)
              & int_less(int_zero,X8) )
           => ! [X3] :
                ( ( int_leq(X3,X1)
                  & int_leq(int_one,X3) )
               => a(X3,plus(X3,X8)) = real_zero ) )
        & ! [X8] :
            ( ( X1 = plus(X2,X8)
              & int_less(int_zero,X8) )
           => ! [X3] :
                ( ( int_leq(X3,X2)
                  & int_leq(int_one,X3) )
               => a(plus(X3,X8),X3) = qr(plus(X3,X8),X3) ) ) ) ),
    introduced(definition) ).

cnf(c_0_20,plain,
    ~ int_less(X1,X1),
    inference(er,[status(thm)],[c_0_16]) ).

cnf(c_0_21,plain,
    ( ~ int_less(X1,X2)
    | ~ int_less(int_zero,X3)
    | int_less(X1,plus(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

fof(c_0_22,plain,
    ! [X18,X19] : plus(X18,X19) = plus(X19,X18),
    inference(variable_rename,[status(thm)],[plus_commutative]) ).

fof(c_0_23,plain,
    ! [X9,X10] :
      ( ( int_leq(X9,X10)
        | X9 != X10 )
      & ( int_leq(X9,X10)
        | ~ int_less(X9,X10) )
      & ( X9 = X10
        | int_less(X9,X10)
        | ~ int_leq(X9,X10) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[int_leq])])])]) ).

fof(c_0_24,plain,
    ! [X31] :
      ( ( int_less(int_zero,X31)
        | ~ int_leq(int_one,X31) )
      & ( int_leq(int_one,X31)
        | ~ int_less(int_zero,X31) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[one_successor_of_zero])])]) ).

fof(c_0_25,plain,
    ! [X2,X1] :
      ( epred1_2(X1,X2)
     => ( ! [X8] :
            ( ( X2 = plus(X1,X8)
              & int_less(int_zero,X8) )
           => ! [X3] :
                ( ( int_leq(X3,X1)
                  & int_leq(int_one,X3) )
               => a(X3,plus(X3,X8)) = real_zero ) )
        & ! [X8] :
            ( ( X1 = plus(X2,X8)
              & int_less(int_zero,X8) )
           => ! [X3] :
                ( ( int_leq(X3,X2)
                  & int_leq(int_one,X3) )
               => a(plus(X3,X8),X3) = qr(plus(X3,X8),X3) ) ) ) ),
    inference(split_equiv,[status(thm)],[c_0_19]) ).

fof(c_0_26,plain,
    ! [X21,X22,X23,X24] :
      ( int_leq(plus(X21,X23),plus(X22,X24))
      | ~ int_leq(X23,X24)
      | ~ int_less(X21,X22) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[plus_and_order1])])]) ).

cnf(c_0_27,plain,
    ( ~ int_less(int_zero,X2)
    | ~ int_less(plus(X1,X2),X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_28,plain,
    plus(X1,X2) = plus(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_29,plain,
    ( ~ int_leq(X1,X2)
    | X1 = X2
    | int_less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_30,plain,
    ( ~ int_less(int_zero,X1)
    | int_leq(int_one,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

fof(c_0_31,plain,
    ! [X36,X37,X38,X39,X40,X41] :
      ( ( ~ epred1_2(X37,X36)
        | a(X41,plus(X41,X40)) = real_zero
        | ~ int_leq(X41,X37)
        | ~ int_leq(int_one,X41)
        | X36 != plus(X37,X40)
        | ~ int_less(int_zero,X40) )
      & ( ~ epred1_2(X37,X36)
        | a(plus(X39,X38),X39) = qr(plus(X39,X38),X39)
        | ~ int_leq(X39,X36)
        | ~ int_leq(int_one,X39)
        | X37 != plus(X36,X38)
        | ~ int_less(int_zero,X38) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])])]) ).

cnf(c_0_32,plain,
    ( ~ int_leq(X3,X4)
    | ~ int_less(X1,X2)
    | int_leq(plus(X1,X3),plus(X2,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_33,plain,
    ( ~ int_less(X1,X2)
    | plus(X1,esk1_2(X1,X2)) = X2 ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

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

fof(c_0_35,plain,
    ! [X20] : plus(X20,int_zero) = X20,
    inference(variable_rename,[status(thm)],[plus_zero]) ).

cnf(c_0_36,plain,
    ( ~ int_less(int_zero,X1)
    | ~ int_less(plus(X1,X2),X2) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_37,plain,
    ( ~ int_less(int_zero,X1)
    | int_less(int_one,X1)
    | int_one = X1 ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_38,plain,
    ( ~ int_less(X1,X2)
    | int_less(int_zero,esk1_2(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_39,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( int_leq(X2,n)
          & int_less(X1,X2)
          & int_leq(int_one,X1) )
       => a(X1,X2) = real_zero ),
    inference(assume_negation,[status(cth)],[lt]) ).

cnf(c_0_40,plain,
    ( ~ epred1_2(X3,X2)
    | ~ int_leq(X4,X3)
    | ~ int_leq(int_one,X4)
    | X2 != plus(X3,X1)
    | ~ int_less(int_zero,X1)
    | a(X4,plus(X4,X1)) = real_zero ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_41,plain,
    ( ~ int_leq(X2,esk1_2(X4,X3))
    | ~ int_less(X4,X3)
    | ~ int_less(X1,X4)
    | int_leq(plus(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_42,plain,
    ( ~ int_leq(int_one,X1)
    | int_less(int_zero,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_43,plain,
    ( int_leq(X2,X1)
    | int_less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_44,plain,
    plus(X1,int_zero) = X1,
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_45,plain,
    ( ~ int_less(int_zero,X2)
    | int_less(X1,plus(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_18,c_0_28]) ).

cnf(c_0_46,plain,
    ( ~ int_less(X2,X1)
    | ~ int_less(int_zero,X2)
    | ~ int_less(X1,esk1_2(X2,X1)) ),
    inference(spm,[status(thm)],[c_0_36,c_0_33]) ).

cnf(c_0_47,plain,
    ( ~ int_less(X1,X2)
    | int_less(int_one,esk1_2(X1,X2))
    | esk1_2(X1,X2) = int_one ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

fof(c_0_48,negated_conjecture,
    ( a(esk2_0,esk3_0) != real_zero
    & int_leq(esk3_0,n)
    & int_less(esk2_0,esk3_0)
    & int_leq(int_one,esk2_0) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])]) ).

cnf(c_0_49,plain,
    ( ~ int_leq(X1,X3)
    | ~ int_leq(int_one,X1)
    | ~ int_less(int_zero,X2)
    | ~ epred1_2(X3,plus(X3,X2))
    | a(X1,plus(X1,X2)) = real_zero ),
    inference(er,[status(thm)],[c_0_40]) ).

cnf(c_0_50,plain,
    ( X1 != X2
    | int_leq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_51,plain,
    ( ~ int_less(X3,X2)
    | ~ int_less(X1,X3)
    | int_leq(plus(X1,int_one),X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_30]),c_0_38]) ).

cnf(c_0_52,plain,
    ( int_less(int_zero,X1)
    | int_less(X1,int_one) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

cnf(c_0_53,plain,
    plus(int_zero,X1) = X1,
    inference(spm,[status(thm)],[c_0_44,c_0_28]) ).

cnf(c_0_54,plain,
    ( ~ int_less(X1,X2)
    | ~ int_less(int_zero,X1)
    | int_less(esk1_2(X1,X2),X2) ),
    inference(spm,[status(thm)],[c_0_45,c_0_33]) ).

cnf(c_0_55,plain,
    ( ~ int_less(X1,int_one)
    | ~ int_less(int_zero,X1)
    | esk1_2(X1,int_one) = int_one ),
    inference(spm,[status(thm)],[c_0_46,c_0_47]) ).

cnf(c_0_56,negated_conjecture,
    int_leq(int_one,esk2_0),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_57,negated_conjecture,
    int_leq(esk3_0,n),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_58,plain,
    ( ~ int_leq(X1,X2)
    | ~ int_leq(int_one,X1)
    | ~ int_less(X2,X3)
    | ~ epred1_2(X2,X3)
    | a(X1,plus(X1,esk1_2(X2,X3))) = real_zero ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_33]),c_0_38]) ).

cnf(c_0_59,plain,
    int_leq(X1,X1),
    inference(er,[status(thm)],[c_0_50]) ).

fof(c_0_60,hypothesis,
    ! [X1,X2] :
      ( ( int_leq(X2,n)
        & int_leq(int_one,X2)
        & int_leq(X1,n)
        & int_leq(int_one,X1) )
     => epred1_2(X1,X2) ),
    inference(apply_def,[status(thm)],[qih,c_0_19]) ).

cnf(c_0_61,plain,
    ( ~ int_less(X1,X2)
    | int_leq(int_one,X2)
    | int_less(X1,int_one) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).

cnf(c_0_62,negated_conjecture,
    int_less(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_63,plain,
    ( ~ int_less(X1,int_one)
    | ~ int_less(int_zero,X1) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_20]) ).

cnf(c_0_64,negated_conjecture,
    int_less(int_zero,esk2_0),
    inference(spm,[status(thm)],[c_0_42,c_0_56]) ).

cnf(c_0_65,negated_conjecture,
    ( int_less(esk3_0,n)
    | n = esk3_0 ),
    inference(spm,[status(thm)],[c_0_29,c_0_57]) ).

cnf(c_0_66,plain,
    ( int_less(X1,X2)
    | int_less(X2,X1)
    | X1 = X2 ),
    inference(spm,[status(thm)],[c_0_29,c_0_43]) ).

cnf(c_0_67,negated_conjecture,
    a(esk2_0,esk3_0) != real_zero,
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_68,plain,
    ( ~ int_leq(int_one,X1)
    | ~ int_less(X1,X2)
    | ~ epred1_2(X1,X2)
    | a(X1,X2) = real_zero ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_33]),c_0_59])]) ).

fof(c_0_69,hypothesis,
    ! [X32,X33] :
      ( epred1_2(X32,X33)
      | ~ int_leq(X33,n)
      | ~ int_leq(int_one,X33)
      | ~ int_leq(X32,n)
      | ~ int_leq(int_one,X32) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])]) ).

cnf(c_0_70,negated_conjecture,
    ( int_leq(int_one,esk3_0)
    | int_less(esk2_0,int_one) ),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

cnf(c_0_71,negated_conjecture,
    ~ int_less(esk2_0,int_one),
    inference(spm,[status(thm)],[c_0_63,c_0_64]) ).

cnf(c_0_72,negated_conjecture,
    ( ~ int_less(X1,esk3_0)
    | int_less(X1,n)
    | n = esk3_0 ),
    inference(spm,[status(thm)],[c_0_17,c_0_65]) ).

cnf(c_0_73,plain,
    ( ~ int_less(X3,X1)
    | int_less(X3,X2)
    | int_less(X2,X1)
    | X1 = X2 ),
    inference(spm,[status(thm)],[c_0_17,c_0_66]) ).

cnf(c_0_74,negated_conjecture,
    ~ epred1_2(esk2_0,esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_62]),c_0_56])]) ).

cnf(c_0_75,hypothesis,
    ( ~ int_leq(X2,n)
    | ~ int_leq(int_one,X2)
    | ~ int_leq(X1,n)
    | ~ int_leq(int_one,X1)
    | epred1_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_69]) ).

cnf(c_0_76,negated_conjecture,
    int_leq(int_one,esk3_0),
    inference(sr,[status(thm)],[c_0_70,c_0_71]) ).

cnf(c_0_77,negated_conjecture,
    ( ~ int_less(n,esk3_0)
    | n = esk3_0 ),
    inference(spm,[status(thm)],[c_0_20,c_0_72]) ).

cnf(c_0_78,negated_conjecture,
    ( int_less(X1,esk3_0)
    | int_less(esk2_0,X1)
    | esk3_0 = X1 ),
    inference(spm,[status(thm)],[c_0_73,c_0_62]) ).

cnf(c_0_79,hypothesis,
    ~ int_leq(esk2_0,n),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_57]),c_0_76]),c_0_56])]) ).

cnf(c_0_80,plain,
    ( ~ int_less(X1,X2)
    | int_leq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_81,negated_conjecture,
    ( int_less(esk2_0,n)
    | n = esk3_0 ),
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

cnf(c_0_82,hypothesis,
    ~ int_less(esk2_0,n),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_83,negated_conjecture,
    n = esk3_0,
    inference(sr,[status(thm)],[c_0_81,c_0_82]) ).

cnf(c_0_84,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_83]),c_0_62])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : SWV486+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07  % Command  : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/5.45  % Computer : n019.cluster.edu
% 0.18/5.45  % Model    : x86_64 x86_64
% 0.18/5.45  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.45  % Memory   : 8046.5625MB
% 0.18/5.45  % OS       : Linux 6.8.0-71-generic
% 0.18/5.45  % CPULimit : 300
% 0.18/5.45  % WCLimit  : 300
% 0.18/5.45  % DateTime : Mon Sep 21 08:54:11 UTC 2026
% 0.18/5.45  % CPUTime  : 
% 0.18/5.45  Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/5.52  Running first-order theorem proving
% 0.22/5.52  Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.22/5.71  % Version: 3.5.1
% 0.22/5.71  % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/5.71  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.71  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/5.71  % Starting new_bool_3 with 300s (1) cores
% 0.22/5.71  % Starting new_bool_1 with 300s (1) cores
% 0.22/5.71  % Starting sh5l with 300s (1) cores
% 0.22/5.71  % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2199506 completed with status 0
% 0.22/5.71  % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.22/5.71  % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/5.71  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.71  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/5.71  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/5.71  % No SInE strategy applied
% 0.22/5.71  % Search class: FGHSS-FFSS22-SFFFFFNN
% 0.22/5.71  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/5.71  % Starting SubtermCWHack with 136s (1) cores
% 0.22/5.71  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/5.71  % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.22/5.71  % Starting new_bool_3 with 136s (1) cores
% 0.22/5.71  % Starting new_bool_1 with 136s (1) cores
% 0.22/5.71  % G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with pid 2199513 completed with status 0
% 0.22/5.71  % Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y
% 0.22/5.71  % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.22/5.71  % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/5.71  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.22/5.71  % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.22/5.71  % No SInE strategy applied
% 0.22/5.71  % Search class: FGHSS-FFSS22-SFFFFFNN
% 0.22/5.71  % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/5.71  % Starting SubtermCWHack with 136s (1) cores
% 0.22/5.71  % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.22/5.71  % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.22/5.71  % Preprocessing time       : 0.001 s
% 0.22/5.71  % Presaturation interreduction done
% 0.22/5.71  
% 0.22/5.71  % Proof found!
% 0.22/5.71  % SZS status Theorem
% 0.22/5.71  % SZS output start CNFRefutation
% See solution above
% 0.22/5.72  % Parsed axioms                        : 13
% 0.22/5.72  % Removed by relevancy pruning/SinE    : 0
% 0.22/5.72  % Initial clauses                      : 23
% 0.22/5.72  % Removed in clause preprocessing      : 0
% 0.22/5.72  % Initial clauses in saturation        : 23
% 0.22/5.72  % Processed clauses                    : 2640
% 0.22/5.72  % ...of these trivial                  : 9
% 0.22/5.72  % ...subsumed                          : 2145
% 0.22/5.72  % ...remaining for further processing  : 486
% 0.22/5.72  % Other redundant clauses eliminated   : 5
% 0.22/5.72  % Clauses deleted for lack of memory   : 0
% 0.22/5.72  % Backward-subsumed                    : 74
% 0.22/5.72  % Backward-rewritten                   : 69
% 0.22/5.72  % Generated clauses                    : 7556
% 0.22/5.72  % ...of the previous two non-redundant : 7021
% 0.22/5.72  % ...aggressively subsumed             : 0
% 0.22/5.72  % Contextual simplify-reflections      : 9
% 0.22/5.72  % Paramodulations                      : 7545
% 0.22/5.72  % Factorizations                       : 2
% 0.22/5.72  % NegExts                              : 0
% 0.22/5.72  % Equation resolutions                 : 5
% 0.22/5.72  % Disequality decompositions           : 0
% 0.22/5.72  % Total rewrite steps                  : 817
% 0.22/5.72  % ...of those cached                   : 794
% 0.22/5.72  % Propositional unsat checks           : 0
% 0.22/5.72  %    Propositional check models        : 0
% 0.22/5.72  %    Propositional check unsatisfiable : 0
% 0.22/5.72  %    Propositional clauses             : 0
% 0.22/5.72  %    Propositional clauses after purity: 0
% 0.22/5.72  %    Propositional unsat core size     : 0
% 0.22/5.72  %    Propositional preprocessing time  : 0.000
% 0.22/5.72  %    Propositional encoding time       : 0.000
% 0.22/5.72  %    Propositional solver time         : 0.000
% 0.22/5.72  %    Success case prop preproc time    : 0.000
% 0.22/5.72  %    Success case prop encoding time   : 0.000
% 0.22/5.72  %    Success case prop solver time     : 0.000
% 0.22/5.72  % Current number of processed clauses  : 311
% 0.22/5.72  %    Positive orientable unit clauses  : 10
% 0.22/5.72  %    Positive unorientable unit clauses: 1
% 0.22/5.72  %    Negative unit clauses             : 10
% 0.22/5.72  %    Non-unit-clauses                  : 290
% 0.22/5.72  % Current number of unprocessed clauses: 4302
% 0.22/5.72  % ...number of literals in the above   : 20876
% 0.22/5.72  % Current number of archived formulas  : 0
% 0.22/5.72  % Current number of archived clauses   : 170
% 0.22/5.72  % Clause-clause subsumption calls (NU) : 29297
% 0.22/5.72  % Rec. Clause-clause subsumption calls : 13203
% 0.22/5.72  % Non-unit clause-clause subsumptions  : 1510
% 0.22/5.72  % Unit Clause-clause subsumption calls : 510
% 0.22/5.72  % Rewrite failures with RHS unbound    : 0
% 0.22/5.72  % BW rewrite match attempts            : 10
% 0.22/5.72  % BW rewrite match successes           : 7
% 0.22/5.72  % Condensation attempts                : 0
% 0.22/5.72  % Condensation successes               : 0
% 0.22/5.72  % Termbank termtop insertions          : 93735
% 0.22/5.72  % Search garbage collected termcells   : 356
% 0.22/5.72  
% 0.22/5.72  % -------------------------------------------------
% 0.22/5.72  % User time                : 0.161 s
% 0.22/5.72  % System time              : 0.008 s
% 0.22/5.72  % Total time               : 0.170 s
% 0.22/5.72  % Maximum resident set size: 3644 pages
% 0.22/5.72  
% 0.22/5.72  % -------------------------------------------------
% 0.22/5.72  % User time                : 0.801 s
% 0.22/5.72  % System time              : 0.041 s
% 0.22/5.72  % Total time               : 0.842 s
% 0.22/5.72  % Maximum resident set size: 4864 pages
% 0.22/5.72  % E exiting
%------------------------------------------------------------------------------