TSTP Solution File: NUM862+1 by E-SAT---3.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E-SAT---3.1
% Problem  : NUM862+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n006.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 19:08:45 EDT 2023

% Result   : Theorem 66.31s 8.92s
% Output   : CNFRefutation 66.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   73
%            Number of leaves      :   14
% Syntax   : Number of formulae    :  283 (  31 unt;   0 def)
%            Number of atoms       :  739 (  34 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  762 ( 306   ~; 423   |;  20   &)
%                                         (   9 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :  532 (  11 sgn;  88   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(max_is_ub_1,conjecture,
    ! [X1,X2,X3] :
      ( minsol_model_ub(X1,X2,X3)
    <=> minsol_model_max(X1,X2,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',max_is_ub_1) ).

fof(model_ub_5,axiom,
    ! [X1,X2,X4] :
      ( model_ub(X1,X2,X4)
    <=> ? [X3] :
          ( ub(X1,X2,X3)
          & lesseq(sum(c,summation(X3)),X4) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',model_ub_5) ).

fof(model_max_5,axiom,
    ! [X1,X2,X4] :
      ( model_max(X1,X2,X4)
    <=> lesseq(sum(c,summation(max(X1,X2))),X4) ),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',model_max_5) ).

fof(max_1,axiom,
    ! [X1,X2] :
      ( max(X1,X2) = X1
      | ~ lesseq(X2,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',max_1) ).

fof(minsol_model_ub,axiom,
    ! [X1,X2,X4] :
      ( minsol_model_ub(X1,X2,X4)
    <=> ( model_ub(X1,X2,X4)
        & ! [X3] :
            ( model_ub(X1,X2,X3)
           => lesseq(X4,X3) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',minsol_model_ub) ).

fof(minsol_model_max,axiom,
    ! [X1,X2,X4] :
      ( minsol_model_max(X1,X2,X4)
    <=> ( model_max(X1,X2,X4)
        & ! [X3] :
            ( model_max(X1,X2,X3)
           => lesseq(X4,X3) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',minsol_model_max) ).

fof(lesseq_total,axiom,
    ! [X1,X2] :
      ( lesseq(X1,X2)
      | lesseq(X2,X1) ),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',lesseq_total) ).

fof(ub,axiom,
    ! [X1,X2,X3] :
      ( ub(X1,X2,X3)
    <=> ( lesseq(X1,X3)
        & lesseq(X2,X3) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',ub) ).

fof(max_2,axiom,
    ! [X1,X2] :
      ( max(X1,X2) = X2
      | ~ lesseq(X1,X2) ),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',max_2) ).

fof(lesseq_ref,axiom,
    ! [X1] : lesseq(X1,X1),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',lesseq_ref) ).

fof(lesseq_trans,axiom,
    ! [X1,X2,X3] :
      ( ( lesseq(X1,X2)
        & lesseq(X2,X3) )
     => lesseq(X1,X3) ),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',lesseq_trans) ).

fof(lesseq_antisymmetric,axiom,
    ! [X1,X2] :
      ( ( lesseq(X1,X2)
        & lesseq(X2,X1) )
     => X1 = X2 ),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',lesseq_antisymmetric) ).

fof(sum_monotone_1,axiom,
    ! [X1,X2,X3] :
      ( lesseq(X1,X2)
    <=> lesseq(sum(X3,X1),sum(X3,X2)) ),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',sum_monotone_1) ).

fof(summation_monotone,axiom,
    ! [X1,X2] :
      ( lesseq(X1,X2)
    <=> lesseq(summation(X1),summation(X2)) ),
    file('/export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p',summation_monotone) ).

fof(c_0_14,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( minsol_model_ub(X1,X2,X3)
      <=> minsol_model_max(X1,X2,X3) ),
    inference(assume_negation,[status(cth)],[max_is_ub_1]) ).

fof(c_0_15,plain,
    ! [X44,X45,X46,X48,X49,X50,X51] :
      ( ( ub(X44,X45,esk6_3(X44,X45,X46))
        | ~ model_ub(X44,X45,X46) )
      & ( lesseq(sum(c,summation(esk6_3(X44,X45,X46))),X46)
        | ~ model_ub(X44,X45,X46) )
      & ( ~ ub(X48,X49,X51)
        | ~ lesseq(sum(c,summation(X51)),X50)
        | model_ub(X48,X49,X50) ) ),
    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)],[model_ub_5])])])])])]) ).

fof(c_0_16,plain,
    ! [X41,X42,X43] :
      ( ( ~ model_max(X41,X42,X43)
        | lesseq(sum(c,summation(max(X41,X42))),X43) )
      & ( ~ lesseq(sum(c,summation(max(X41,X42))),X43)
        | model_max(X41,X42,X43) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[model_max_5])]) ).

fof(c_0_17,plain,
    ! [X1,X2] :
      ( max(X1,X2) = X1
      | ~ lesseq(X2,X1) ),
    inference(fof_simplification,[status(thm)],[max_1]) ).

fof(c_0_18,plain,
    ! [X16,X17,X18,X19,X20,X21,X22] :
      ( ( model_ub(X16,X17,X18)
        | ~ minsol_model_ub(X16,X17,X18) )
      & ( ~ model_ub(X16,X17,X19)
        | lesseq(X18,X19)
        | ~ minsol_model_ub(X16,X17,X18) )
      & ( model_ub(X20,X21,esk5_3(X20,X21,X22))
        | ~ model_ub(X20,X21,X22)
        | minsol_model_ub(X20,X21,X22) )
      & ( ~ lesseq(X22,esk5_3(X20,X21,X22))
        | ~ model_ub(X20,X21,X22)
        | minsol_model_ub(X20,X21,X22) ) ),
    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)],[minsol_model_ub])])])])])]) ).

fof(c_0_19,negated_conjecture,
    ( ( ~ minsol_model_ub(esk1_0,esk2_0,esk3_0)
      | ~ minsol_model_max(esk1_0,esk2_0,esk3_0) )
    & ( minsol_model_ub(esk1_0,esk2_0,esk3_0)
      | minsol_model_max(esk1_0,esk2_0,esk3_0) ) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).

cnf(c_0_20,plain,
    ( model_ub(X1,X2,X4)
    | ~ ub(X1,X2,X3)
    | ~ lesseq(sum(c,summation(X3)),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,plain,
    ( lesseq(sum(c,summation(max(X1,X2))),X3)
    | ~ model_max(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_22,plain,
    ! [X37,X38] :
      ( max(X37,X38) = X37
      | ~ lesseq(X38,X37) ),
    inference(variable_rename,[status(thm)],[c_0_17]) ).

fof(c_0_23,plain,
    ! [X8,X9,X10,X11,X12,X13,X14] :
      ( ( model_max(X8,X9,X10)
        | ~ minsol_model_max(X8,X9,X10) )
      & ( ~ model_max(X8,X9,X11)
        | lesseq(X10,X11)
        | ~ minsol_model_max(X8,X9,X10) )
      & ( model_max(X12,X13,esk4_3(X12,X13,X14))
        | ~ model_max(X12,X13,X14)
        | minsol_model_max(X12,X13,X14) )
      & ( ~ lesseq(X14,esk4_3(X12,X13,X14))
        | ~ model_max(X12,X13,X14)
        | minsol_model_max(X12,X13,X14) ) ),
    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)],[minsol_model_max])])])])])]) ).

cnf(c_0_24,plain,
    ( model_ub(X1,X2,X3)
    | ~ minsol_model_ub(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_25,negated_conjecture,
    ( minsol_model_ub(esk1_0,esk2_0,esk3_0)
    | minsol_model_max(esk1_0,esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_26,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_max(X4,X5,X3)
    | ~ ub(X1,X2,max(X4,X5)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_27,plain,
    ( max(X1,X2) = X1
    | ~ lesseq(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_28,plain,
    ( model_max(X1,X2,X3)
    | ~ minsol_model_max(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_29,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | model_ub(esk1_0,esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_30,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_max(X4,X5,X3)
    | ~ ub(X1,X2,X4)
    | ~ lesseq(X5,X4) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_max(esk1_0,esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

fof(c_0_32,plain,
    ! [X30,X31] :
      ( lesseq(X30,X31)
      | lesseq(X31,X30) ),
    inference(variable_rename,[status(thm)],[lesseq_total]) ).

cnf(c_0_33,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(X1,X2,esk3_0)
    | ~ ub(X1,X2,esk1_0)
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_34,plain,
    ( lesseq(X1,X2)
    | lesseq(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_35,plain,
    ! [X52,X53,X54] :
      ( ( lesseq(X52,X54)
        | ~ ub(X52,X53,X54) )
      & ( lesseq(X53,X54)
        | ~ ub(X52,X53,X54) )
      & ( ~ lesseq(X52,X54)
        | ~ lesseq(X53,X54)
        | ub(X52,X53,X54) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ub])])]) ).

cnf(c_0_36,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(X1,X2,esk3_0)
    | lesseq(esk1_0,esk2_0)
    | ~ ub(X1,X2,esk1_0) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_37,plain,
    ( ub(X1,X3,X2)
    | ~ lesseq(X1,X2)
    | ~ lesseq(X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

fof(c_0_38,plain,
    ! [X1,X2] :
      ( max(X1,X2) = X2
      | ~ lesseq(X1,X2) ),
    inference(fof_simplification,[status(thm)],[max_2]) ).

cnf(c_0_39,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(X1,X2,esk3_0)
    | lesseq(esk1_0,esk2_0)
    | ~ lesseq(X2,esk1_0)
    | ~ lesseq(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

fof(c_0_40,plain,
    ! [X24] : lesseq(X24,X24),
    inference(variable_rename,[status(thm)],[lesseq_ref]) ).

fof(c_0_41,plain,
    ! [X39,X40] :
      ( max(X39,X40) = X40
      | ~ lesseq(X39,X40) ),
    inference(variable_rename,[status(thm)],[c_0_38]) ).

cnf(c_0_42,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(X1,X2,esk3_0)
    | lesseq(esk1_0,esk2_0)
    | lesseq(esk1_0,X2)
    | ~ lesseq(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_39,c_0_34]) ).

cnf(c_0_43,plain,
    lesseq(X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_44,plain,
    ( max(X1,X2) = X2
    | ~ lesseq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_45,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(esk1_0,X1,esk3_0)
    | lesseq(esk1_0,esk2_0)
    | lesseq(esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_42,c_0_43]) ).

fof(c_0_46,plain,
    ! [X25,X26,X27] :
      ( ~ lesseq(X25,X26)
      | ~ lesseq(X26,X27)
      | lesseq(X25,X27) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_trans])]) ).

cnf(c_0_47,plain,
    ( lesseq(X4,X3)
    | ~ model_max(X1,X2,X3)
    | ~ minsol_model_max(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_48,plain,
    ( model_max(X1,X2,X3)
    | ~ lesseq(sum(c,summation(max(X1,X2))),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_49,plain,
    ( lesseq(sum(c,summation(X1)),X2)
    | ~ model_max(X3,X1,X2)
    | ~ lesseq(X3,X1) ),
    inference(spm,[status(thm)],[c_0_21,c_0_44]) ).

cnf(c_0_50,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk1_0,esk2_0) ),
    inference(ef,[status(thm)],[c_0_45]) ).

cnf(c_0_51,plain,
    ( lesseq(X1,X3)
    | ~ lesseq(X1,X2)
    | ~ lesseq(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_52,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,X1)
    | ~ model_max(esk1_0,esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_47,c_0_29]) ).

cnf(c_0_53,plain,
    model_max(X1,X2,sum(c,summation(max(X1,X2)))),
    inference(spm,[status(thm)],[c_0_48,c_0_43]) ).

cnf(c_0_54,plain,
    ( model_max(X1,X2,X3)
    | ~ lesseq(sum(c,summation(X1)),X3)
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_48,c_0_27]) ).

cnf(c_0_55,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(sum(c,summation(esk2_0)),esk3_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_31]),c_0_50]) ).

cnf(c_0_56,plain,
    ( lesseq(X1,X2)
    | ~ model_max(X3,X4,X2)
    | ~ lesseq(X1,sum(c,summation(max(X3,X4)))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_21]) ).

cnf(c_0_57,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,sum(c,summation(max(esk1_0,esk2_0)))) ),
    inference(spm,[status(thm)],[c_0_52,c_0_53]) ).

cnf(c_0_58,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_max(esk2_0,X1,esk3_0)
    | ~ lesseq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_54,c_0_55]) ).

cnf(c_0_59,plain,
    ( lesseq(X1,X2)
    | ~ model_max(X3,X4,X2)
    | ~ lesseq(X1,sum(c,summation(X4)))
    | ~ lesseq(X3,X4) ),
    inference(spm,[status(thm)],[c_0_56,c_0_44]) ).

cnf(c_0_60,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,sum(c,summation(esk2_0))) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_44]),c_0_50]) ).

cnf(c_0_61,plain,
    ( model_max(X1,X2,esk4_3(X1,X2,X3))
    | minsol_model_max(X1,X2,X3)
    | ~ model_max(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_62,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_max(esk2_0,esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[c_0_58,c_0_43]) ).

cnf(c_0_63,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,X1)
    | ~ model_max(X2,esk2_0,X1)
    | ~ lesseq(X2,esk2_0) ),
    inference(spm,[status(thm)],[c_0_59,c_0_60]) ).

cnf(c_0_64,negated_conjecture,
    ( minsol_model_max(esk2_0,esk2_0,esk3_0)
    | model_ub(esk1_0,esk2_0,esk3_0)
    | model_max(esk2_0,esk2_0,esk4_3(esk2_0,esk2_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

fof(c_0_65,plain,
    ! [X28,X29] :
      ( ~ lesseq(X28,X29)
      | ~ lesseq(X29,X28)
      | X28 = X29 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[lesseq_antisymmetric])]) ).

cnf(c_0_66,plain,
    ( minsol_model_max(X2,X3,X1)
    | ~ lesseq(X1,esk4_3(X2,X3,X1))
    | ~ model_max(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_23]) ).

cnf(c_0_67,negated_conjecture,
    ( minsol_model_max(esk2_0,esk2_0,esk3_0)
    | model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,esk4_3(esk2_0,esk2_0,esk3_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_43])]) ).

fof(c_0_68,plain,
    ! [X32,X33,X34] :
      ( ( ~ lesseq(X32,X33)
        | lesseq(sum(X34,X32),sum(X34,X33)) )
      & ( ~ lesseq(sum(X34,X32),sum(X34,X33))
        | lesseq(X32,X33) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sum_monotone_1])]) ).

cnf(c_0_69,plain,
    ( X1 = X2
    | ~ lesseq(X1,X2)
    | ~ lesseq(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_65]) ).

cnf(c_0_70,negated_conjecture,
    ( minsol_model_max(esk2_0,esk2_0,esk3_0)
    | model_ub(esk1_0,esk2_0,esk3_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_62]) ).

cnf(c_0_71,plain,
    ( lesseq(X2,X3)
    | ~ lesseq(sum(X1,X2),sum(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_72,negated_conjecture,
    ( sum(c,summation(esk2_0)) = esk3_0
    | model_ub(esk1_0,esk2_0,esk3_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_60]),c_0_55]) ).

cnf(c_0_73,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,X1)
    | ~ model_max(esk2_0,esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_47,c_0_70]) ).

fof(c_0_74,plain,
    ! [X35,X36] :
      ( ( ~ lesseq(X35,X36)
        | lesseq(summation(X35),summation(X36)) )
      & ( ~ lesseq(summation(X35),summation(X36))
        | lesseq(X35,X36) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[summation_monotone])]) ).

cnf(c_0_75,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(summation(esk2_0),X1)
    | ~ lesseq(esk3_0,sum(c,X1)) ),
    inference(spm,[status(thm)],[c_0_71,c_0_72]) ).

cnf(c_0_76,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,sum(c,summation(max(esk2_0,esk2_0)))) ),
    inference(spm,[status(thm)],[c_0_73,c_0_53]) ).

cnf(c_0_77,plain,
    ( lesseq(X1,X2)
    | ~ lesseq(summation(X1),summation(X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

cnf(c_0_78,plain,
    ( lesseq(summation(max(X1,X2)),X3)
    | ~ model_max(X1,X2,sum(c,X3)) ),
    inference(spm,[status(thm)],[c_0_71,c_0_21]) ).

cnf(c_0_79,plain,
    ( model_max(X1,X2,X3)
    | ~ lesseq(sum(c,summation(X2)),X3)
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_48,c_0_44]) ).

cnf(c_0_80,plain,
    ( lesseq(sum(X3,X1),sum(X3,X2))
    | ~ lesseq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_81,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(summation(esk2_0),summation(max(esk2_0,esk2_0))) ),
    inference(spm,[status(thm)],[c_0_75,c_0_76]) ).

cnf(c_0_82,plain,
    ( lesseq(max(X1,X2),X3)
    | ~ model_max(X1,X2,sum(c,summation(X3))) ),
    inference(spm,[status(thm)],[c_0_77,c_0_78]) ).

cnf(c_0_83,plain,
    ( model_max(X1,X2,sum(c,X3))
    | ~ lesseq(summation(X2),X3)
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_79,c_0_80]) ).

cnf(c_0_84,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk2_0,max(esk2_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_77,c_0_81]) ).

cnf(c_0_85,plain,
    ( model_max(X1,X2,sum(c,summation(X2)))
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_79,c_0_43]) ).

cnf(c_0_86,plain,
    ( lesseq(max(X1,X2),X3)
    | ~ lesseq(summation(X2),summation(X3))
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_82,c_0_83]) ).

cnf(c_0_87,negated_conjecture,
    ( max(esk2_0,esk2_0) = esk2_0
    | model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(max(esk2_0,esk2_0),esk2_0) ),
    inference(spm,[status(thm)],[c_0_69,c_0_84]) ).

cnf(c_0_88,plain,
    ( lesseq(max(X1,X2),X2)
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_82,c_0_85]) ).

cnf(c_0_89,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(X1,X2,esk3_0)
    | ~ ub(X1,X2,esk2_0) ),
    inference(spm,[status(thm)],[c_0_20,c_0_55]) ).

cnf(c_0_90,plain,
    ( lesseq(X1,X2)
    | ~ lesseq(summation(X3),summation(X2))
    | ~ lesseq(X1,max(X4,X3))
    | ~ lesseq(X4,X3) ),
    inference(spm,[status(thm)],[c_0_51,c_0_86]) ).

cnf(c_0_91,plain,
    ( lesseq(summation(X1),summation(X2))
    | ~ lesseq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_74]) ).

cnf(c_0_92,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(summation(esk2_0),summation(max(esk1_0,esk2_0))) ),
    inference(spm,[status(thm)],[c_0_75,c_0_57]) ).

cnf(c_0_93,negated_conjecture,
    ( max(esk2_0,esk2_0) = esk2_0
    | model_ub(esk1_0,esk2_0,esk3_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_43])]) ).

cnf(c_0_94,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(X1,X2,esk3_0)
    | ~ lesseq(X2,esk2_0)
    | ~ lesseq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_89,c_0_37]) ).

cnf(c_0_95,plain,
    ( lesseq(X1,X2)
    | ~ lesseq(X1,max(X3,X4))
    | ~ lesseq(X3,X4)
    | ~ lesseq(X4,X2) ),
    inference(spm,[status(thm)],[c_0_90,c_0_91]) ).

cnf(c_0_96,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk2_0,max(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_77,c_0_92]) ).

cnf(c_0_97,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_max(esk2_0,esk2_0,sum(c,summation(esk2_0))) ),
    inference(spm,[status(thm)],[c_0_53,c_0_93]) ).

cnf(c_0_98,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(X1,esk2_0,esk3_0)
    | ~ lesseq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_94,c_0_43]) ).

cnf(c_0_99,plain,
    ( lesseq(max(X1,X2),X3)
    | ~ lesseq(X1,X2)
    | ~ lesseq(X2,X3) ),
    inference(spm,[status(thm)],[c_0_95,c_0_43]) ).

cnf(c_0_100,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(X1,max(esk1_0,esk2_0))
    | ~ lesseq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_51,c_0_96]) ).

cnf(c_0_101,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(max(esk2_0,esk2_0),esk2_0) ),
    inference(spm,[status(thm)],[c_0_82,c_0_97]) ).

cnf(c_0_102,plain,
    ( lesseq(X1,X2)
    | ~ ub(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_103,plain,
    ( ub(X1,X2,esk6_3(X1,X2,X3))
    | ~ model_ub(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_104,negated_conjecture,
    ( model_ub(max(X1,esk2_0),esk2_0,esk3_0)
    | model_ub(esk1_0,esk2_0,esk3_0)
    | ~ lesseq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_98,c_0_88]) ).

cnf(c_0_105,plain,
    ( X1 = max(X2,X3)
    | ~ lesseq(X1,max(X2,X3))
    | ~ lesseq(X2,X3)
    | ~ lesseq(X3,X1) ),
    inference(spm,[status(thm)],[c_0_69,c_0_99]) ).

cnf(c_0_106,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(max(esk2_0,esk2_0),max(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[c_0_100,c_0_101]) ).

cnf(c_0_107,plain,
    ( lesseq(sum(c,summation(esk6_3(X1,X2,X3))),X3)
    | ~ model_ub(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_108,plain,
    ( lesseq(X1,summation(X2))
    | ~ lesseq(X1,summation(X3))
    | ~ lesseq(X3,X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_91]) ).

cnf(c_0_109,plain,
    ( lesseq(X1,X2)
    | ~ ub(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_110,plain,
    ( lesseq(X1,esk6_3(X1,X2,X3))
    | ~ model_ub(X1,X2,X3) ),
    inference(spm,[status(thm)],[c_0_102,c_0_103]) ).

cnf(c_0_111,negated_conjecture,
    ( model_ub(max(esk2_0,esk2_0),esk2_0,esk3_0)
    | model_ub(esk1_0,esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[c_0_104,c_0_43]) ).

cnf(c_0_112,negated_conjecture,
    ( max(esk2_0,esk2_0) = max(esk1_0,esk2_0)
    | model_ub(esk1_0,esk2_0,esk3_0) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_50]),c_0_84]) ).

cnf(c_0_113,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(X1,esk2_0,esk3_0)
    | lesseq(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_98,c_0_34]) ).

cnf(c_0_114,plain,
    ( lesseq(X1,X2)
    | ~ model_ub(X3,X4,X2)
    | ~ lesseq(X1,sum(c,summation(esk6_3(X3,X4,X2)))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_107]) ).

cnf(c_0_115,plain,
    ( lesseq(summation(X1),summation(X2))
    | ~ lesseq(X3,X2)
    | ~ lesseq(X1,X3) ),
    inference(spm,[status(thm)],[c_0_108,c_0_91]) ).

cnf(c_0_116,plain,
    ( lesseq(X1,esk6_3(X2,X1,X3))
    | ~ model_ub(X2,X1,X3) ),
    inference(spm,[status(thm)],[c_0_109,c_0_103]) ).

cnf(c_0_117,plain,
    ( lesseq(X1,esk6_3(X2,X3,X4))
    | ~ model_ub(X2,X3,X4)
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_110]) ).

cnf(c_0_118,negated_conjecture,
    ( model_ub(max(esk1_0,esk2_0),esk2_0,esk3_0)
    | model_ub(esk1_0,esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[c_0_111,c_0_112]) ).

cnf(c_0_119,negated_conjecture,
    ( model_ub(esk1_0,esk2_0,esk3_0)
    | lesseq(esk2_0,esk1_0) ),
    inference(ef,[status(thm)],[c_0_113]) ).

cnf(c_0_120,plain,
    ( lesseq(sum(c,X1),X2)
    | ~ model_ub(X3,X4,X2)
    | ~ lesseq(X1,summation(esk6_3(X3,X4,X2))) ),
    inference(spm,[status(thm)],[c_0_114,c_0_80]) ).

cnf(c_0_121,plain,
    ( lesseq(summation(X1),summation(esk6_3(X2,X3,X4)))
    | ~ model_ub(X2,X3,X4)
    | ~ lesseq(X1,X3) ),
    inference(spm,[status(thm)],[c_0_115,c_0_116]) ).

cnf(c_0_122,plain,
    ( lesseq(X1,esk6_3(X2,X3,X4))
    | ~ model_ub(X2,X3,X4)
    | ~ lesseq(X1,X5)
    | ~ lesseq(X5,X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_117]) ).

cnf(c_0_123,negated_conjecture,
    model_ub(esk1_0,esk2_0,esk3_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_27]),c_0_119]) ).

cnf(c_0_124,plain,
    ( lesseq(sum(c,summation(X1)),X2)
    | ~ model_ub(X3,X4,X2)
    | ~ lesseq(X1,X4) ),
    inference(spm,[status(thm)],[c_0_120,c_0_121]) ).

cnf(c_0_125,plain,
    ( lesseq(X1,X2)
    | lesseq(X3,X1)
    | ~ lesseq(X3,X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_34]) ).

cnf(c_0_126,negated_conjecture,
    ( lesseq(X1,esk6_3(esk1_0,esk2_0,esk3_0))
    | ~ lesseq(X2,esk1_0)
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_122,c_0_123]) ).

cnf(c_0_127,negated_conjecture,
    ( lesseq(sum(c,summation(X1)),esk3_0)
    | ~ lesseq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_124,c_0_123]) ).

cnf(c_0_128,plain,
    ( lesseq(max(X1,X2),X3)
    | lesseq(X3,X2)
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_125,c_0_88]) ).

cnf(c_0_129,negated_conjecture,
    ( lesseq(X1,esk6_3(esk1_0,esk2_0,esk3_0))
    | ~ lesseq(X1,max(X2,esk1_0))
    | ~ lesseq(X2,esk1_0) ),
    inference(spm,[status(thm)],[c_0_126,c_0_88]) ).

cnf(c_0_130,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_max(X4,X5,X3)
    | ~ lesseq(X2,max(X4,X5))
    | ~ lesseq(X1,max(X4,X5)) ),
    inference(spm,[status(thm)],[c_0_26,c_0_37]) ).

cnf(c_0_131,negated_conjecture,
    ( model_max(X1,X2,esk3_0)
    | ~ lesseq(max(X1,X2),esk2_0) ),
    inference(spm,[status(thm)],[c_0_48,c_0_127]) ).

cnf(c_0_132,plain,
    ( lesseq(max(X1,X1),X2)
    | lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_128,c_0_43]) ).

cnf(c_0_133,negated_conjecture,
    ( lesseq(max(X1,esk1_0),esk6_3(esk1_0,esk2_0,esk3_0))
    | ~ lesseq(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_129,c_0_43]) ).

cnf(c_0_134,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_max(X4,X5,X3)
    | ~ lesseq(X2,X5)
    | ~ lesseq(X1,X5)
    | ~ lesseq(X4,X5) ),
    inference(spm,[status(thm)],[c_0_130,c_0_44]) ).

cnf(c_0_135,negated_conjecture,
    ( model_max(X1,X1,esk3_0)
    | lesseq(esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_131,c_0_132]) ).

cnf(c_0_136,negated_conjecture,
    ( lesseq(esk1_0,esk6_3(esk1_0,esk2_0,esk3_0))
    | ~ lesseq(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_133,c_0_44]) ).

cnf(c_0_137,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_ub(X4,X5,X3)
    | ~ ub(X1,X2,esk6_3(X4,X5,X3)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_107]) ).

cnf(c_0_138,negated_conjecture,
    ( model_ub(X1,X2,esk3_0)
    | lesseq(esk2_0,X3)
    | ~ lesseq(X2,X3)
    | ~ lesseq(X1,X3) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_43])]) ).

cnf(c_0_139,negated_conjecture,
    lesseq(esk1_0,esk6_3(esk1_0,esk2_0,esk3_0)),
    inference(spm,[status(thm)],[c_0_136,c_0_43]) ).

cnf(c_0_140,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_ub(X4,X5,X3)
    | ~ lesseq(X2,esk6_3(X4,X5,X3))
    | ~ lesseq(X1,esk6_3(X4,X5,X3)) ),
    inference(spm,[status(thm)],[c_0_137,c_0_37]) ).

cnf(c_0_141,negated_conjecture,
    ( model_ub(X1,esk1_0,esk3_0)
    | lesseq(esk2_0,esk6_3(esk1_0,esk2_0,esk3_0))
    | ~ lesseq(X1,esk6_3(esk1_0,esk2_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_138,c_0_139]) ).

cnf(c_0_142,negated_conjecture,
    ( model_ub(X1,esk1_0,esk3_0)
    | ~ lesseq(X1,esk6_3(esk1_0,esk2_0,esk3_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_139]),c_0_123])]) ).

cnf(c_0_143,negated_conjecture,
    ( model_ub(esk2_0,esk1_0,esk3_0)
    | lesseq(esk2_0,esk6_3(esk1_0,esk2_0,esk3_0)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_116]),c_0_123])]) ).

cnf(c_0_144,plain,
    ( summation(X1) = summation(X2)
    | ~ lesseq(summation(X1),summation(X2))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_69,c_0_91]) ).

cnf(c_0_145,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_ub(X2,X4,X3)
    | ~ lesseq(X1,esk6_3(X2,X4,X3)) ),
    inference(spm,[status(thm)],[c_0_140,c_0_110]) ).

cnf(c_0_146,plain,
    ( model_ub(X1,X2,esk5_3(X1,X2,X3))
    | minsol_model_ub(X1,X2,X3)
    | ~ model_ub(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_147,negated_conjecture,
    model_ub(esk2_0,esk1_0,esk3_0),
    inference(spm,[status(thm)],[c_0_142,c_0_143]) ).

cnf(c_0_148,plain,
    ( summation(X1) = summation(X2)
    | ~ lesseq(X2,X1)
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_144,c_0_91]) ).

cnf(c_0_149,plain,
    ( lesseq(X4,X3)
    | ~ model_ub(X1,X2,X3)
    | ~ minsol_model_ub(X1,X2,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_150,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_ub(X2,X1,X3) ),
    inference(spm,[status(thm)],[c_0_145,c_0_116]) ).

cnf(c_0_151,negated_conjecture,
    ( minsol_model_ub(esk2_0,esk1_0,esk3_0)
    | model_ub(esk2_0,esk1_0,esk5_3(esk2_0,esk1_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_146,c_0_147]) ).

cnf(c_0_152,negated_conjecture,
    ( lesseq(summation(X1),summation(esk6_3(esk1_0,esk2_0,esk3_0)))
    | ~ lesseq(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_115,c_0_139]) ).

cnf(c_0_153,negated_conjecture,
    ( summation(esk6_3(esk1_0,esk2_0,esk3_0)) = summation(esk1_0)
    | ~ lesseq(esk6_3(esk1_0,esk2_0,esk3_0),esk1_0) ),
    inference(spm,[status(thm)],[c_0_148,c_0_139]) ).

cnf(c_0_154,plain,
    ( lesseq(summation(X1),summation(X2))
    | lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_77,c_0_34]) ).

cnf(c_0_155,plain,
    ( model_max(X1,X2,sum(c,summation(X1)))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_54,c_0_43]) ).

cnf(c_0_156,plain,
    ( lesseq(summation(X1),X2)
    | ~ model_max(X3,X1,sum(c,X2))
    | ~ lesseq(X3,X1) ),
    inference(spm,[status(thm)],[c_0_78,c_0_44]) ).

cnf(c_0_157,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,X1)
    | ~ model_ub(esk1_0,esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_149,c_0_25]) ).

cnf(c_0_158,negated_conjecture,
    ( minsol_model_ub(esk2_0,esk1_0,esk3_0)
    | model_ub(esk1_0,esk2_0,esk5_3(esk2_0,esk1_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_150,c_0_151]) ).

cnf(c_0_159,negated_conjecture,
    model_ub(esk1_0,esk1_0,esk3_0),
    inference(spm,[status(thm)],[c_0_142,c_0_139]) ).

cnf(c_0_160,negated_conjecture,
    lesseq(summation(esk1_0),summation(esk6_3(esk1_0,esk2_0,esk3_0))),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_154]) ).

cnf(c_0_161,plain,
    ( X1 = X2
    | ~ lesseq(X1,X2)
    | ~ lesseq(X2,X3)
    | ~ lesseq(X3,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_27]),c_0_51]) ).

cnf(c_0_162,plain,
    ( lesseq(max(X1,X2),X1)
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_82,c_0_155]) ).

cnf(c_0_163,plain,
    ( lesseq(summation(X1),summation(max(X2,X1)))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_156,c_0_53]) ).

cnf(c_0_164,plain,
    ( minsol_model_ub(X2,X3,X1)
    | ~ lesseq(X1,esk5_3(X2,X3,X1))
    | ~ model_ub(X2,X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_165,negated_conjecture,
    ( minsol_model_ub(esk2_0,esk1_0,esk3_0)
    | minsol_model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,esk5_3(esk2_0,esk1_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_157,c_0_158]) ).

cnf(c_0_166,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_ub(X2,X4,X3)
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_145,c_0_117]) ).

cnf(c_0_167,negated_conjecture,
    ( minsol_model_ub(esk1_0,esk1_0,esk3_0)
    | model_ub(esk1_0,esk1_0,esk5_3(esk1_0,esk1_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_146,c_0_159]) ).

cnf(c_0_168,negated_conjecture,
    lesseq(sum(c,summation(esk1_0)),esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_160]),c_0_123])]) ).

cnf(c_0_169,plain,
    ( summation(X1) = summation(X2)
    | ~ lesseq(summation(X2),X3)
    | ~ lesseq(X3,summation(X1))
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_161,c_0_91]) ).

cnf(c_0_170,plain,
    ( lesseq(X1,X2)
    | lesseq(X2,X3)
    | lesseq(X3,X1) ),
    inference(spm,[status(thm)],[c_0_125,c_0_34]) ).

cnf(c_0_171,plain,
    ( lesseq(summation(X1),X2)
    | ~ model_max(X1,X3,sum(c,X2))
    | ~ lesseq(X3,X1) ),
    inference(spm,[status(thm)],[c_0_78,c_0_27]) ).

cnf(c_0_172,plain,
    ( summation(max(X1,X2)) = summation(X1)
    | ~ lesseq(X1,max(X1,X2))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_148,c_0_162]) ).

cnf(c_0_173,plain,
    ( lesseq(X1,max(X2,X1))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_77,c_0_163]) ).

cnf(c_0_174,negated_conjecture,
    ( minsol_model_ub(esk2_0,esk1_0,esk3_0)
    | minsol_model_max(esk1_0,esk2_0,esk3_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_147])]) ).

cnf(c_0_175,negated_conjecture,
    ( minsol_model_ub(esk1_0,esk1_0,esk3_0)
    | model_ub(X1,esk1_0,esk5_3(esk1_0,esk1_0,esk3_0))
    | ~ lesseq(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_166,c_0_167]) ).

cnf(c_0_176,negated_conjecture,
    ( model_max(esk1_0,X1,esk3_0)
    | ~ lesseq(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_54,c_0_168]) ).

cnf(c_0_177,plain,
    ( summation(X1) = summation(X2)
    | ~ lesseq(summation(X3),summation(X1))
    | ~ lesseq(X1,X2)
    | ~ lesseq(X2,X3) ),
    inference(spm,[status(thm)],[c_0_169,c_0_91]) ).

cnf(c_0_178,plain,
    ( lesseq(X1,X2)
    | ~ lesseq(X1,X3)
    | ~ lesseq(X3,X4)
    | ~ lesseq(X4,X2)
    | ~ lesseq(X4,X3) ),
    inference(spm,[status(thm)],[c_0_95,c_0_27]) ).

cnf(c_0_179,plain,
    ( lesseq(X1,X2)
    | lesseq(X3,X1)
    | lesseq(X4,X3)
    | ~ lesseq(X4,X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_170]) ).

cnf(c_0_180,plain,
    ( lesseq(summation(X1),summation(max(X1,X2)))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_171,c_0_53]) ).

cnf(c_0_181,plain,
    summation(max(X1,X1)) = summation(X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_172,c_0_173]),c_0_43])]) ).

cnf(c_0_182,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,X1)
    | ~ model_ub(esk2_0,esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_149,c_0_174]) ).

cnf(c_0_183,negated_conjecture,
    ( minsol_model_ub(esk1_0,esk1_0,esk3_0)
    | model_ub(X1,esk1_0,esk5_3(esk1_0,esk1_0,esk3_0))
    | lesseq(esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_175,c_0_34]) ).

cnf(c_0_184,plain,
    ( model_ub(X1,max(X2,X3),X4)
    | ~ model_max(X2,X3,X4)
    | ~ lesseq(X1,max(X2,X3)) ),
    inference(spm,[status(thm)],[c_0_130,c_0_43]) ).

cnf(c_0_185,negated_conjecture,
    ( minsol_model_max(esk1_0,X1,esk3_0)
    | model_max(esk1_0,X1,esk4_3(esk1_0,X1,esk3_0))
    | ~ lesseq(X1,esk1_0) ),
    inference(spm,[status(thm)],[c_0_61,c_0_176]) ).

cnf(c_0_186,negated_conjecture,
    ( lesseq(X1,esk3_0)
    | ~ lesseq(X1,sum(c,summation(esk1_0))) ),
    inference(spm,[status(thm)],[c_0_51,c_0_168]) ).

cnf(c_0_187,plain,
    ( summation(X1) = summation(X2)
    | ~ lesseq(X1,X2)
    | ~ lesseq(X2,X3)
    | ~ lesseq(X3,X1) ),
    inference(spm,[status(thm)],[c_0_177,c_0_91]) ).

cnf(c_0_188,plain,
    ( lesseq(X1,X2)
    | lesseq(X2,X3)
    | ~ lesseq(X1,X4)
    | ~ lesseq(X4,X3) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_34]),c_0_179]) ).

cnf(c_0_189,plain,
    ( lesseq(summation(esk6_3(X1,X2,sum(c,X3))),X3)
    | ~ model_ub(X1,X2,sum(c,X3)) ),
    inference(spm,[status(thm)],[c_0_71,c_0_107]) ).

cnf(c_0_190,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_max(X4,X2,X3)
    | ~ lesseq(X1,max(X4,X2))
    | ~ lesseq(X4,X2) ),
    inference(spm,[status(thm)],[c_0_130,c_0_173]) ).

cnf(c_0_191,plain,
    ( lesseq(X1,max(X1,X2))
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_77,c_0_180]) ).

cnf(c_0_192,plain,
    ( model_max(X1,X1,X2)
    | ~ lesseq(sum(c,summation(X1)),X2) ),
    inference(spm,[status(thm)],[c_0_48,c_0_181]) ).

cnf(c_0_193,negated_conjecture,
    ( model_max(X1,esk2_0,esk3_0)
    | ~ lesseq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_131,c_0_88]) ).

cnf(c_0_194,negated_conjecture,
    ( minsol_model_ub(esk1_0,esk1_0,esk3_0)
    | minsol_model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,esk5_3(esk1_0,esk1_0,esk3_0))
    | lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_182,c_0_183]) ).

cnf(c_0_195,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_max(X4,X2,X3)
    | ~ lesseq(X1,X2)
    | ~ lesseq(X4,X2) ),
    inference(spm,[status(thm)],[c_0_184,c_0_44]) ).

cnf(c_0_196,negated_conjecture,
    ( minsol_model_max(esk1_0,esk1_0,esk3_0)
    | model_max(esk1_0,esk1_0,esk4_3(esk1_0,esk1_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_185,c_0_43]) ).

cnf(c_0_197,negated_conjecture,
    ( lesseq(sum(c,X1),esk3_0)
    | ~ lesseq(X1,summation(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_186,c_0_80]) ).

cnf(c_0_198,plain,
    ( summation(max(X1,X2)) = summation(X2)
    | ~ lesseq(X3,max(X1,X2))
    | ~ lesseq(X2,X3)
    | ~ lesseq(X1,X2) ),
    inference(spm,[status(thm)],[c_0_187,c_0_88]) ).

cnf(c_0_199,plain,
    ( lesseq(X1,X2)
    | lesseq(X3,X1)
    | ~ model_ub(X3,X4,X5)
    | ~ lesseq(esk6_3(X3,X4,X5),X2) ),
    inference(spm,[status(thm)],[c_0_188,c_0_110]) ).

cnf(c_0_200,plain,
    ( lesseq(esk6_3(X1,X2,sum(c,summation(X3))),X3)
    | ~ model_ub(X1,X2,sum(c,summation(X3))) ),
    inference(spm,[status(thm)],[c_0_77,c_0_189]) ).

cnf(c_0_201,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_max(X1,X2,X3)
    | ~ lesseq(X1,X2)
    | ~ lesseq(X2,X1) ),
    inference(spm,[status(thm)],[c_0_190,c_0_191]) ).

cnf(c_0_202,plain,
    ( model_max(X1,X1,sum(c,X2))
    | ~ lesseq(summation(X1),X2) ),
    inference(spm,[status(thm)],[c_0_192,c_0_80]) ).

cnf(c_0_203,negated_conjecture,
    ( lesseq(sum(c,summation(esk2_0)),esk3_0)
    | ~ lesseq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_49,c_0_193]) ).

cnf(c_0_204,negated_conjecture,
    ( minsol_model_ub(esk1_0,esk1_0,esk3_0)
    | minsol_model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk1_0,esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_194]),c_0_159])]) ).

cnf(c_0_205,negated_conjecture,
    ( minsol_model_max(esk1_0,esk1_0,esk3_0)
    | model_ub(X1,esk1_0,esk4_3(esk1_0,esk1_0,esk3_0))
    | ~ lesseq(X1,esk1_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_43])]) ).

cnf(c_0_206,negated_conjecture,
    ( model_max(X1,X2,esk3_0)
    | ~ lesseq(summation(max(X1,X2)),summation(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_48,c_0_197]) ).

cnf(c_0_207,plain,
    ( summation(max(X1,X2)) = summation(X2)
    | ~ lesseq(X1,X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_173]),c_0_43])]) ).

cnf(c_0_208,plain,
    ( lesseq(X1,X2)
    | lesseq(X2,X3)
    | ~ model_ub(X1,X4,sum(c,summation(X3))) ),
    inference(spm,[status(thm)],[c_0_199,c_0_200]) ).

cnf(c_0_209,plain,
    ( model_ub(X1,X1,sum(c,X2))
    | ~ lesseq(summation(X1),X2) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_43])]) ).

cnf(c_0_210,negated_conjecture,
    lesseq(sum(c,summation(esk2_0)),esk3_0),
    inference(spm,[status(thm)],[c_0_203,c_0_43]) ).

cnf(c_0_211,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk1_0,esk2_0)
    | lesseq(esk3_0,X1)
    | ~ model_ub(esk1_0,esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_149,c_0_204]) ).

cnf(c_0_212,negated_conjecture,
    ( minsol_model_max(esk1_0,esk1_0,esk3_0)
    | model_ub(esk1_0,esk1_0,esk4_3(esk1_0,esk1_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_205,c_0_43]) ).

cnf(c_0_213,negated_conjecture,
    ( model_max(X1,X1,esk3_0)
    | ~ lesseq(summation(X1),summation(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_206,c_0_181]) ).

cnf(c_0_214,plain,
    ( lesseq(X1,X2)
    | ~ lesseq(X1,max(X2,X3))
    | ~ lesseq(X3,X2) ),
    inference(spm,[status(thm)],[c_0_51,c_0_162]) ).

cnf(c_0_215,plain,
    ( lesseq(X1,max(X2,X3))
    | ~ lesseq(summation(X1),summation(X3))
    | ~ lesseq(X2,X3) ),
    inference(spm,[status(thm)],[c_0_77,c_0_207]) ).

cnf(c_0_216,plain,
    ( lesseq(X1,X2)
    | lesseq(X3,X1)
    | ~ lesseq(summation(X3),summation(X2)) ),
    inference(spm,[status(thm)],[c_0_208,c_0_209]) ).

cnf(c_0_217,negated_conjecture,
    ( lesseq(summation(X1),summation(esk3_0))
    | ~ lesseq(X1,sum(c,summation(esk2_0))) ),
    inference(spm,[status(thm)],[c_0_115,c_0_210]) ).

cnf(c_0_218,plain,
    model_max(X1,X1,sum(c,summation(X1))),
    inference(spm,[status(thm)],[c_0_53,c_0_181]) ).

cnf(c_0_219,negated_conjecture,
    ( minsol_model_max(esk1_0,esk1_0,esk3_0)
    | minsol_model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,esk4_3(esk1_0,esk1_0,esk3_0))
    | lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_211,c_0_212]) ).

cnf(c_0_220,negated_conjecture,
    model_max(esk1_0,esk1_0,esk3_0),
    inference(spm,[status(thm)],[c_0_213,c_0_43]) ).

cnf(c_0_221,plain,
    ( lesseq(X1,X2)
    | ~ lesseq(summation(X1),summation(X3))
    | ~ lesseq(X3,X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_214,c_0_215]),c_0_216]) ).

cnf(c_0_222,negated_conjecture,
    lesseq(summation(sum(c,summation(esk2_0))),summation(esk3_0)),
    inference(spm,[status(thm)],[c_0_217,c_0_43]) ).

cnf(c_0_223,plain,
    lesseq(max(X1,X1),X1),
    inference(spm,[status(thm)],[c_0_82,c_0_218]) ).

cnf(c_0_224,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | minsol_model_max(esk1_0,esk1_0,esk3_0)
    | lesseq(esk1_0,esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_219]),c_0_220])]) ).

cnf(c_0_225,negated_conjecture,
    ( lesseq(sum(c,summation(esk2_0)),X1)
    | ~ lesseq(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_221,c_0_222]) ).

cnf(c_0_226,plain,
    ( max(X1,X1) = X1
    | ~ lesseq(X1,max(X1,X1)) ),
    inference(spm,[status(thm)],[c_0_69,c_0_223]) ).

cnf(c_0_227,negated_conjecture,
    ( minsol_model_max(esk1_0,esk1_0,esk3_0)
    | model_max(esk1_0,esk2_0,esk3_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_224]),c_0_193]) ).

cnf(c_0_228,negated_conjecture,
    ( model_max(esk2_0,esk2_0,X1)
    | ~ lesseq(esk3_0,X1) ),
    inference(spm,[status(thm)],[c_0_192,c_0_225]) ).

cnf(c_0_229,plain,
    max(X1,X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_173]),c_0_43])]) ).

cnf(c_0_230,negated_conjecture,
    ( model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,X1)
    | ~ model_max(esk1_0,esk1_0,X1) ),
    inference(spm,[status(thm)],[c_0_47,c_0_227]) ).

cnf(c_0_231,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_ub(X1,X3,X2) ),
    inference(spm,[status(thm)],[c_0_145,c_0_110]) ).

cnf(c_0_232,negated_conjecture,
    ( lesseq(esk2_0,X1)
    | ~ lesseq(esk3_0,sum(c,summation(X1))) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_228]),c_0_229]) ).

cnf(c_0_233,negated_conjecture,
    ( model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,sum(c,summation(esk1_0))) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_53]),c_0_181]) ).

cnf(c_0_234,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_max(X3,X4,X2)
    | ~ lesseq(X1,max(X3,X4)) ),
    inference(spm,[status(thm)],[c_0_231,c_0_184]) ).

cnf(c_0_235,negated_conjecture,
    model_max(esk1_0,esk2_0,esk3_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_232,c_0_233]),c_0_176]) ).

cnf(c_0_236,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_max(X1,X3,X2)
    | ~ lesseq(X3,X1) ),
    inference(spm,[status(thm)],[c_0_234,c_0_191]) ).

cnf(c_0_237,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | model_max(esk1_0,esk2_0,esk4_3(esk1_0,esk2_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_61,c_0_235]) ).

cnf(c_0_238,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | model_ub(esk1_0,esk1_0,esk4_3(esk1_0,esk2_0,esk3_0))
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_236,c_0_237]) ).

cnf(c_0_239,plain,
    ( model_ub(X1,X2,X3)
    | lesseq(max(X4,X5),X2)
    | ~ model_max(X4,X5,X3)
    | ~ lesseq(X1,max(X4,X5)) ),
    inference(spm,[status(thm)],[c_0_130,c_0_34]) ).

cnf(c_0_240,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | model_ub(esk1_0,esk1_0,esk4_3(esk1_0,esk2_0,esk3_0))
    | lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_238,c_0_34]) ).

cnf(c_0_241,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_max(X2,X4,X3)
    | ~ lesseq(X1,max(X2,X4))
    | ~ lesseq(X4,X2) ),
    inference(spm,[status(thm)],[c_0_130,c_0_191]) ).

cnf(c_0_242,plain,
    ( model_ub(X1,X2,X3)
    | lesseq(X4,X2)
    | ~ model_max(X5,X4,X3)
    | ~ lesseq(X1,X4)
    | ~ lesseq(X5,X4) ),
    inference(spm,[status(thm)],[c_0_239,c_0_44]) ).

cnf(c_0_243,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,esk4_3(esk1_0,esk2_0,esk3_0))
    | lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_211,c_0_240]) ).

cnf(c_0_244,plain,
    ( model_ub(X1,X2,X3)
    | ~ model_max(X2,X4,X3)
    | ~ lesseq(X1,X4)
    | ~ lesseq(X2,X4) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_44]),c_0_242]) ).

cnf(c_0_245,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk1_0,esk2_0) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_243]),c_0_235])]) ).

cnf(c_0_246,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | model_ub(X1,esk1_0,esk4_3(esk1_0,esk2_0,esk3_0))
    | ~ lesseq(X1,esk2_0) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_237]),c_0_245]) ).

cnf(c_0_247,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | model_ub(esk2_0,esk1_0,esk4_3(esk1_0,esk2_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_246,c_0_43]) ).

cnf(c_0_248,negated_conjecture,
    ( minsol_model_max(esk1_0,esk2_0,esk3_0)
    | lesseq(esk3_0,esk4_3(esk1_0,esk2_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_182,c_0_247]) ).

cnf(c_0_249,negated_conjecture,
    minsol_model_max(esk1_0,esk2_0,esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_248]),c_0_235])]) ).

cnf(c_0_250,negated_conjecture,
    ( ~ minsol_model_ub(esk1_0,esk2_0,esk3_0)
    | ~ minsol_model_max(esk1_0,esk2_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_251,negated_conjecture,
    ( lesseq(esk3_0,X1)
    | ~ model_max(esk1_0,esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_47,c_0_249]) ).

cnf(c_0_252,plain,
    ( lesseq(sum(c,summation(X1)),X2)
    | ~ model_ub(X3,X4,X2)
    | ~ lesseq(X1,esk6_3(X3,X4,X2)) ),
    inference(spm,[status(thm)],[c_0_120,c_0_91]) ).

cnf(c_0_253,negated_conjecture,
    ( minsol_model_ub(esk1_0,esk2_0,esk3_0)
    | model_ub(esk1_0,esk2_0,esk5_3(esk1_0,esk2_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_146,c_0_123]) ).

cnf(c_0_254,negated_conjecture,
    ~ minsol_model_ub(esk1_0,esk2_0,esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_250,c_0_249])]) ).

cnf(c_0_255,plain,
    ( X1 = sum(c,summation(max(X2,X3)))
    | ~ model_max(X2,X3,X1)
    | ~ lesseq(X1,sum(c,summation(max(X2,X3)))) ),
    inference(spm,[status(thm)],[c_0_69,c_0_21]) ).

cnf(c_0_256,negated_conjecture,
    lesseq(esk3_0,sum(c,summation(max(esk1_0,esk2_0)))),
    inference(spm,[status(thm)],[c_0_251,c_0_53]) ).

cnf(c_0_257,plain,
    ( lesseq(sum(c,summation(X1)),X2)
    | ~ model_ub(X1,X3,X2) ),
    inference(spm,[status(thm)],[c_0_252,c_0_110]) ).

cnf(c_0_258,negated_conjecture,
    model_ub(esk1_0,esk2_0,esk5_3(esk1_0,esk2_0,esk3_0)),
    inference(sr,[status(thm)],[c_0_253,c_0_254]) ).

cnf(c_0_259,negated_conjecture,
    sum(c,summation(max(esk1_0,esk2_0))) = esk3_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255,c_0_256]),c_0_235])]) ).

cnf(c_0_260,negated_conjecture,
    lesseq(sum(c,summation(esk1_0)),esk5_3(esk1_0,esk2_0,esk3_0)),
    inference(spm,[status(thm)],[c_0_257,c_0_258]) ).

cnf(c_0_261,negated_conjecture,
    ( sum(c,summation(esk1_0)) = esk3_0
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_259,c_0_27]) ).

cnf(c_0_262,negated_conjecture,
    model_ub(esk2_0,esk2_0,esk3_0),
    inference(spm,[status(thm)],[c_0_231,c_0_147]) ).

cnf(c_0_263,negated_conjecture,
    ( lesseq(esk3_0,esk5_3(esk1_0,esk2_0,esk3_0))
    | ~ lesseq(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[c_0_260,c_0_261]) ).

cnf(c_0_264,negated_conjecture,
    ( minsol_model_ub(esk2_0,esk2_0,esk3_0)
    | model_ub(esk2_0,esk2_0,esk5_3(esk2_0,esk2_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_146,c_0_262]) ).

cnf(c_0_265,negated_conjecture,
    ~ lesseq(esk2_0,esk1_0),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_263]),c_0_123])]),c_0_254]) ).

cnf(c_0_266,negated_conjecture,
    ( minsol_model_ub(esk2_0,esk2_0,esk3_0)
    | model_ub(X1,esk2_0,esk5_3(esk2_0,esk2_0,esk3_0))
    | ~ lesseq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_166,c_0_264]) ).

cnf(c_0_267,negated_conjecture,
    lesseq(esk1_0,esk2_0),
    inference(spm,[status(thm)],[c_0_265,c_0_34]) ).

cnf(c_0_268,negated_conjecture,
    ( sum(c,summation(esk2_0)) = esk3_0
    | ~ lesseq(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[c_0_259,c_0_44]) ).

cnf(c_0_269,plain,
    ( lesseq(sum(c,summation(X1)),X2)
    | ~ model_ub(X3,X1,X2) ),
    inference(spm,[status(thm)],[c_0_252,c_0_116]) ).

cnf(c_0_270,negated_conjecture,
    ( minsol_model_ub(esk2_0,esk2_0,esk3_0)
    | model_ub(esk1_0,esk2_0,esk5_3(esk2_0,esk2_0,esk3_0)) ),
    inference(spm,[status(thm)],[c_0_266,c_0_267]) ).

cnf(c_0_271,negated_conjecture,
    sum(c,summation(esk2_0)) = esk3_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_268,c_0_267])]) ).

cnf(c_0_272,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_max(X3,X3,X2)
    | ~ lesseq(X1,X3) ),
    inference(spm,[status(thm)],[c_0_234,c_0_229]) ).

cnf(c_0_273,plain,
    ( model_max(esk6_3(X1,X2,X3),X4,X3)
    | ~ model_ub(X1,X2,X3)
    | ~ lesseq(X4,esk6_3(X1,X2,X3)) ),
    inference(spm,[status(thm)],[c_0_54,c_0_107]) ).

cnf(c_0_274,negated_conjecture,
    ( minsol_model_ub(esk2_0,esk2_0,esk3_0)
    | lesseq(esk3_0,esk5_3(esk2_0,esk2_0,esk3_0)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_269,c_0_270]),c_0_271]) ).

cnf(c_0_275,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_ub(X3,X4,X2)
    | ~ lesseq(X1,esk6_3(X3,X4,X2)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_272,c_0_273]),c_0_43])]) ).

cnf(c_0_276,plain,
    ( lesseq(X1,esk6_3(X2,X3,X4))
    | ~ model_ub(X2,X3,X4)
    | ~ lesseq(X1,X3) ),
    inference(spm,[status(thm)],[c_0_51,c_0_116]) ).

cnf(c_0_277,negated_conjecture,
    minsol_model_ub(esk2_0,esk2_0,esk3_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_274]),c_0_262])]) ).

cnf(c_0_278,plain,
    ( model_ub(X1,X1,X2)
    | ~ model_ub(X3,X4,X2)
    | ~ lesseq(X1,X4) ),
    inference(spm,[status(thm)],[c_0_275,c_0_276]) ).

cnf(c_0_279,negated_conjecture,
    ( lesseq(esk3_0,X1)
    | ~ model_ub(esk2_0,esk2_0,X1) ),
    inference(spm,[status(thm)],[c_0_149,c_0_277]) ).

cnf(c_0_280,negated_conjecture,
    ( model_ub(X1,X1,esk5_3(esk1_0,esk2_0,esk3_0))
    | ~ lesseq(X1,esk2_0) ),
    inference(spm,[status(thm)],[c_0_278,c_0_258]) ).

cnf(c_0_281,negated_conjecture,
    lesseq(esk3_0,esk5_3(esk1_0,esk2_0,esk3_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_279,c_0_280]),c_0_43])]) ).

cnf(c_0_282,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_281]),c_0_123])]),c_0_254]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : NUM862+1 : TPTP v8.1.2. Released v4.1.0.
% 0.04/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n006.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 2400
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Oct  2 14:45:40 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.47  Running first-order model finding
% 0.20/0.47  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.bB8GnfDvbU/E---3.1_28618.p
% 66.31/8.92  # Version: 3.1pre001
% 66.31/8.92  # Preprocessing class: FSMSSMSSSSSNFFN.
% 66.31/8.92  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.31/8.92  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 66.31/8.92  # Starting new_bool_3 with 300s (1) cores
% 66.31/8.92  # Starting new_bool_1 with 300s (1) cores
% 66.31/8.92  # Starting sh5l with 300s (1) cores
% 66.31/8.92  # sh5l with pid 28700 completed with status 0
% 66.31/8.92  # Result found by sh5l
% 66.31/8.92  # Preprocessing class: FSMSSMSSSSSNFFN.
% 66.31/8.92  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.31/8.92  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 66.31/8.92  # Starting new_bool_3 with 300s (1) cores
% 66.31/8.92  # Starting new_bool_1 with 300s (1) cores
% 66.31/8.92  # Starting sh5l with 300s (1) cores
% 66.31/8.92  # SinE strategy is gf500_gu_R04_F100_L20000
% 66.31/8.92  # Search class: FGHSF-FFMF32-MFFFFFNN
% 66.31/8.92  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 66.31/8.92  # Starting G-E--_208_C18CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 66.31/8.92  # G-E--_208_C18CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 28706 completed with status 0
% 66.31/8.92  # Result found by G-E--_208_C18CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 66.31/8.92  # Preprocessing class: FSMSSMSSSSSNFFN.
% 66.31/8.92  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 66.31/8.92  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 66.31/8.92  # Starting new_bool_3 with 300s (1) cores
% 66.31/8.92  # Starting new_bool_1 with 300s (1) cores
% 66.31/8.92  # Starting sh5l with 300s (1) cores
% 66.31/8.92  # SinE strategy is gf500_gu_R04_F100_L20000
% 66.31/8.92  # Search class: FGHSF-FFMF32-MFFFFFNN
% 66.31/8.92  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 66.31/8.92  # Starting G-E--_208_C18CMA_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 181s (1) cores
% 66.31/8.92  # Preprocessing time       : 0.001 s
% 66.31/8.92  # Presaturation interreduction done
% 66.31/8.92  
% 66.31/8.92  # Proof found!
% 66.31/8.92  # SZS status Theorem
% 66.31/8.92  # SZS output start CNFRefutation
% See solution above
% 66.31/8.92  # Parsed axioms                        : 14
% 66.31/8.92  # Removed by relevancy pruning/SinE    : 0
% 66.31/8.92  # Initial clauses                      : 28
% 66.31/8.92  # Removed in clause preprocessing      : 0
% 66.31/8.92  # Initial clauses in saturation        : 28
% 66.31/8.92  # Processed clauses                    : 15621
% 66.31/8.92  # ...of these trivial                  : 17
% 66.31/8.92  # ...subsumed                          : 11497
% 66.31/8.92  # ...remaining for further processing  : 4107
% 66.31/8.92  # Other redundant clauses eliminated   : 0
% 66.31/8.92  # Clauses deleted for lack of memory   : 0
% 66.31/8.92  # Backward-subsumed                    : 259
% 66.31/8.92  # Backward-rewritten                   : 816
% 66.31/8.92  # Generated clauses                    : 805611
% 66.31/8.92  # ...of the previous two non-redundant : 783056
% 66.31/8.92  # ...aggressively subsumed             : 0
% 66.31/8.92  # Contextual simplify-reflections      : 40
% 66.31/8.92  # Paramodulations                      : 804781
% 66.31/8.92  # Factorizations                       : 778
% 66.31/8.92  # NegExts                              : 0
% 66.31/8.92  # Equation resolutions                 : 0
% 66.31/8.92  # Total rewrite steps                  : 43003
% 66.31/8.92  # Propositional unsat checks           : 0
% 66.31/8.92  #    Propositional check models        : 0
% 66.31/8.92  #    Propositional check unsatisfiable : 0
% 66.31/8.92  #    Propositional clauses             : 0
% 66.31/8.92  #    Propositional clauses after purity: 0
% 66.31/8.92  #    Propositional unsat core size     : 0
% 66.31/8.92  #    Propositional preprocessing time  : 0.000
% 66.31/8.92  #    Propositional encoding time       : 0.000
% 66.31/8.92  #    Propositional solver time         : 0.000
% 66.31/8.92  #    Success case prop preproc time    : 0.000
% 66.31/8.92  #    Success case prop encoding time   : 0.000
% 66.31/8.92  #    Success case prop solver time     : 0.000
% 66.31/8.92  # Current number of processed clauses  : 2952
% 66.31/8.92  #    Positive orientable unit clauses  : 54
% 66.31/8.92  #    Positive unorientable unit clauses: 0
% 66.31/8.92  #    Negative unit clauses             : 3
% 66.31/8.92  #    Non-unit-clauses                  : 2895
% 66.31/8.92  # Current number of unprocessed clauses: 764360
% 66.31/8.92  # ...number of literals in the above   : 3696407
% 66.31/8.92  # Current number of archived formulas  : 0
% 66.31/8.92  # Current number of archived clauses   : 1155
% 66.31/8.92  # Clause-clause subsumption calls (NU) : 1273484
% 66.31/8.92  # Rec. Clause-clause subsumption calls : 698143
% 66.31/8.92  # Non-unit clause-clause subsumptions  : 11714
% 66.31/8.92  # Unit Clause-clause subsumption calls : 14625
% 66.31/8.92  # Rewrite failures with RHS unbound    : 0
% 66.31/8.92  # BW rewrite match attempts            : 496
% 66.31/8.92  # BW rewrite match successes           : 31
% 66.31/8.92  # Condensation attempts                : 0
% 66.31/8.92  # Condensation successes               : 0
% 66.31/8.92  # Termbank termtop insertions          : 14937816
% 66.31/8.92  
% 66.31/8.92  # -------------------------------------------------
% 66.31/8.92  # User time                : 7.861 s
% 66.31/8.92  # System time              : 0.333 s
% 66.31/8.92  # Total time               : 8.194 s
% 66.31/8.92  # Maximum resident set size: 1848 pages
% 66.31/8.92  
% 66.31/8.92  # -------------------------------------------------
% 66.31/8.92  # User time                : 7.863 s
% 66.31/8.92  # System time              : 0.335 s
% 66.31/8.92  # Total time               : 8.198 s
% 66.31/8.92  # Maximum resident set size: 1732 pages
% 66.31/8.92  % E---3.1 exiting
%------------------------------------------------------------------------------